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KINDERGARTEN MATHEMATICS
CURRICULUM GUIDE
Loudoun County Public Schools 2014-2015
Overview, Scope and Sequence, Unit Summaries, The First 20 Days Classroom Routines, Curriculum Framework, Learning Progressions
(additional attachments: Intervention Ideas, NCSM Great Tasks SOL alignment, Math Literature Connections)
INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE
This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun County Public Schools. The CURRICULUM GUIDE includes
excerpts from documents published by the Virginia Department of Education. Other statements, such as suggestions on the incorporation of technology and essential questions, represent the professional
consensus of Loudoun’s teachers concerning the implementation of these standards. This CURRICULUM GUIDE is the lead document for planning, assessment, and curriculum work.
NAVIGATING THE LCPS MATHEMATICS CURRICULUM GUIDE
The Curriculum Guide is created to link different components of the guide to related information from the Virginia Department of Education, resources created by Loudoun County Public Schools, as well as vetted outside resources.
To navigate the curriculum guide, click on the hyperlink (if in MSWord, hold the [ctrl] button and left click with the mouse on the hyperlink). It will direct you to either another resource within the curriculum guide, or to a website resource.
If you’re directed to a resource within the curriculum guide, to “go back,” hold the [alt] key and press the left arrow button. Mathematics Internet Safety Procedures 1. Teachers should review all Internet sites and links prior to using it in the classroom. During this review, teachers need to ensure the appropriateness of the content on the site, checking for broken links, and paying attention to any inappropriate pop-ups or solicitation of information. 2. Teachers should circulate throughout the classroom while students are on the internet checking to make sure the students are on the appropriate site and are not minimizing other inappropriate sites. 3. Teachers should periodically check and update any web addresses that they have on their LCPS web pages. 4. Teachers should assure that the use of websites correlate with the objectives of the lesson and provide students with the appropriate challenge.
LCPS Grade K Mathematics Curriculum Guide 2014-2015
Dates of LCPS Quarters
2014 – 2015 School Calendar
Starts Ends
First Quarter September 2 October 31
Second Quarter November 5 January 23
Third Quarter January 27 March 27
Fourth Quarter April 7 June 16
Quarter 1 Quarter 2 Quarter 3 Quarter 4
AUGUST
S M T W R F S
1 2
3 4 5 6 7 8 9
10 11 12 TI TI NH 16
17 NH NH SD SD P 23
24 CS CS CS P P 30
31
SEPTEMBER
S M T W R F S
H F 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30
OCTOBER
S M T W R F S
1 2 3 4
5 6 7 8 9 10 11
12 H 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30 31
NOVEMBER
S M T W R F S
1
2 P P 5 6 7 8
9 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 H H H 29
30
DECEMBER
S M T W R F S
1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
21 H H H H H 27
28 H H H
JANUARY
S M T W R F S
H H 3
4 5 6 7 8 9 10
11 12 13 14 15 16 17
18 H 20 21 22 23 24
25 MP 27 28 29 30 31
JANUARY
S M T W R F S
H H 3
4 5 6 7 8 9 10
11 12 13 14 15 16 17
18 H 20 21 22 23 24
25 MP 27 28 29 30 31
FEBRUARY
S M T W R F S
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 H 17 18 19 20 21
22 23 24 25 26 27 28
MARCH
S M T W R F S
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 H H
APRIL
S M T W R F S
H H H 4
5 P 7 8 9 10 11
APRIL
S M T W R F S
H H H 4
5 P 7 8 9 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30
MAY
S M T W R F S
1 2
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 H 26 27 28 29 30
31
JUNE
S M T W R F S
1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 L P P 19 20
21 22 23 24 25 26 27
28 29 30
P = Teacher Workday/Planning Day H = Holiday/ No School F = First Day of School TI = Teacher Institute for new professionals NH = New Hire Workday SD = In School Staff Development days CS = County Wide Staff Development Days
LCPS Grade K Mathematics Curriculum Guide 2014-2015
Grade K Nine Weeks Overview
1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
Unit 1-Classroom Routines: “The First 20 Days Classroom Routines” NUMBER TALKS K.3 Ordinal Position K.4 Count Forward & Backward K.8 Msmt Instruments K.9 Time K.13 Count/Tally Data K.14 Display Data K.15 Sort & Classify Unit 2-Counting K.4a Count to 100 K.2 Count Sets, Write & Identify Numerals K.13 Count/Tally Data K.4b One More/One Less K.16 Patterns Unit 3-Comparing Sets K.1 One-to-One Correspondence, More, Fewer, Same K.3 Ordinal Position K.13 Count/Tally Data K.14 Display Data
Unit 1-Classroom Routines: NUMBER TALKS K.3 Ordinal Position K.4 Count Forward & Backward K.8 Msmt Instruments K.9 Time K.13 Count/Tally Data K.14 Display Data K.15 Sort & Classify Unit 4-Geometry & Sorting K.15 Sort and Classify K.7 Recognize Coins & Value K.11 Identify & Compare Plane Geometric Figures Unit 5-Shapes in Space K.12 Location of Objects and Plane Geometric Figures K.16 Repeating Patterns
Unit 1-Classroom Routines: NUMBER TALKS K.3 Ordinal Position K.4 Count Forward & Backward K.7 Money K.8 Msmt Instruments K.9 Time K.13 Count/Tally Data K.14 Display Data K.15 Sort & Classify Unit 6-Geometry & Fractions K.11 Identify & Compare Plane Geometric Figures K.5 Fractions K.14 Display Data Unit 7-Measuring My World K.8 Measurement Instruments K.10 Non-standard Msmt K.9 Time Unit 8-Skip Counting & Money K.4c Count by 5’s and 10’s to 100 K.7 Recognize Coins & Value K.16 Repeating Patterns
Unit 1-Classroom Routines: NUMBER TALKS K.3 Ordinal Position K.4 Count Forward & Backward K.7 Money K.8 Msmt Instruments K.9 Time K.13 Count/Tally Data K.14 Display Data K.15 Sort & Classify Unit 8 (cont’d)-Skip Counting & Money K.4c Counting by 5’s and 10’s to 100 K.7 Recognize Coins and Value K.16 Repeating Patterns Unit 9-Combining & Separating K.4b One More/One Less K.6 Model Addition & Subtraction K.7 Recognize Coins & Value
43 days 44 days 43 days 50 days
LCPS Grade K Mathematics Curriculum Guide 2014-2015
Kindergarten Scope & Sequence Quarter 1: 43 days
Days Unit Standard Content Strand Topic
All
year
Unit 1: Classroom
Routines
“The First 20 Days Classroom Routines”
and NUMBER TALKS, Ordinal Numbers, Counting, Measurement, Time, Data, Sorting, Money
25
Unit 2: Counting
K.4a Number and
Number Sense
Counting to 100
K.2 Number and
Number Sense
Count Sets, Write, & Identify Numerals
K.13 Probability and
Statistics
Count/Tally Data
K.4b Number and
Number Sense
One more/ One Less
K.16 Patterns, Functions,
Algebra
Patterns
15
Unit 3: Comparing
Sets
K.1 Number and
Number Sense
One-to-one Correspondence, More, Fewer,
Same
K.3 Number and
Number Sense
Ordinal Position
K.13 Probability and
Statistics
Count/Tally Data
K.14 Probability and
Statistics
Display Data
3 Assessment, Review, and Intervention
LCPS Grade K Mathematics Curriculum Guide 2014-2015
Quarter 2: 44 days
Days Unit Standard Content Strand Topic All year Unit 1: Classroom Routines NUMBER TALKS, Ordinal Numbers, Counting, Measurement, Time, Data, Sorting, Money
21
Unit 4: Geometry & Sorting
K.15 Patterns, Functions, & Algebra
Sort and Classify
K.7 Measurement Recognize Coins & Value
K.11 Geometry Identify & Compare Plane Geometric Figures
17
Unit 5: Shapes in Space
K.12 Geometry Location of Objects and Plane Geometric Figures
K.16 Patterns, Functions, & Algebra
Repeating Patterns
6 Assessment, Review, and Intervention
LCPS Grade K Mathematics Curriculum Guide 2014-2015
Quarter 3: 43 days
Days Unit Standard Content Strand Topic All year Unit 1: Classroom Routines NUMBER TALKS, Ordinal Numbers, Counting, Measurement, Time, Data, Sorting, Money
15
Unit 6: Geometry & Fractions
K.11 Geometry Identify & Compare Plane Geometric Figures
K.5 Number and Number Sense Fractions
K.14 Probability and Statistics Display Data
15
Unit 7: Measuring My World
K.8 Measurement Measurement Instruments
K.10 Measurement Non-standard Measurement
K.9 Measurement Time
10
Unit 8: Skip Counting & Money
K.4c Number and Number Sense Counting by 5’s and 10’s to 100
K.7 Measurement Recognize Coins & Value
K.16 Patterns, Functions, & Algebra Repeating Patterns
3 Assessment, Review, and Intervention
LCPS Grade K Mathematics Curriculum Guide 2014-2015
Quarter 4: 50 days
Days Unit Standard Content Strand Topic All year Unit 1: Classroom Routines NUMBER TALKS, Ordinal Numbers, Counting, Measurement, Time, Data, Sorting, Money
10
Unit 8 (cont’d): Skip Counting & Money
K.4c Number and Number Sense
Counting by 5’s and 10’s to 100
K.7 Measurement Recognize Coins & Value
K.16 Patterns, Functions, & Algebra
Repeating Patterns
20
Unit 9: Combining & Separating
K.4b Number and Number Sense
One More/One Less
K.6 Computation & Estimation
Model Addition & Subtraction
K.7 Measurement Recognize Coins & Value
20 Assessment, Review, and Intervention
LCPS MATH Unit Summary Kindergarten 2014-15
Unit: 1 Quarters 1-4
Classroom Routines
VDOE Standards of Learning:
1st quarter: The First 20 Days Classroom Routines K.4 The student will
a) count forward to 100 and backward from 10; b) identify one more than a number and one less than a number; and c) count by fives and tens to 100.
K.3 The student, given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object.
K.7 The student will recognize a penny, nickel, dime, and quarter and will determine the value of a collection of pennies and/or nickels whose total value is 10 cents or less (beginning 3rd quarter).
K.8 The student will identify the instruments used to measure length (ruler), weight (scale), time (clock: digital and analog; calendar: day, month, and season), and temperature (thermometer).
K.9 The student will tell time to the hour, using analog and digital clocks.
K.13 The student will gather data by counting and tallying.
K.14 The student will display gathered data in object graphs, picture graphs, and tables, and will answer questions related to the data.
K.15 The student will sort and classify objects according to attributes.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can count forward to 100 by ones, fives, and tens and I can count backward from 10.
I can identify the ordinal positions for each object in a set of 10 objects that are in order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top).
Recognizes coins, and determines value of several coins.
I can identify one more than a number and one less than a number and show the relationship using objects.
I can identify the patterns of counting by ones, fives, and tens using different models (hundreds chart, number line, etc.).
I can identify instruments used to measure length, weight, time, and temperature.
I can tell time to the hour on an analog and digital clock and relate the time to daily routines.
I can collect answers to a question, keep track of the answers by using tally marks, and organize the answers in categories.
I can analyze data I have displayed in graphs and tables.
I can sort and classify a set of objects in at least two different ways and explain my reasoning.
LCPS MATH Unit Summary Kindergarten 2014-15
Big Ideas Essential Questions
Taking daily attendance and regular use of a counting jar gives students repeated practice of counting and helps make the connection of the number names and the quantities they represent.
Use temperature data for seasonal changes, patterns, and graphing.
Daily practice of counting aloud and working with
numbers on the hundreds chart and other forms of
representing numerals (number line, place value
straws, graphs, tallies).
Real world application of mathematics concepts.
What does a calendar measure?
How does calendar measure time?
Yesterday was Tuesday. What day is today? What day is tomorrow?
How many days are in this month?
What time will we be going to library? How will that look on an analog and digital clock?
Why do we collect data?
What are some strategies used to gather data?
Say the number name sequence to 100.
Show one more than a number and one less than a number.
How can we show an amount in tallies?
How can we show data in a graph? With pictures?
How can we sort objects in two different ways?
While we are in line for lunch, please count off using your ordinal numbers.
What patterns can we find on the hundreds chart? How do those patterns relate to skip counting?
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3
VDOE Vocabulary Word Wall Cards forward backward sort ones fives classify tens hundreds graph ordinal number pattern table more less tally hundreds chart number line data time temperature month clock thermometer day digital analog season calendar
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Sample Math Tasks are available in VISION: Search: LCPS-Math: K-12 Math Tasks
Enrollment key: mathisfun http://loudounvision.net/
NCSM Great Tasks (available in all LCPS Elementary Schools—click link)
Click here for a brief audio powerpoint slide
with more information about the Process Goals
LCPS MATH Unit Summary Kindergarten 2014-15
Classroom Routines
1st quarter: The First 20 Days Classroom Routines NUMBER TALKS: Example: http://www.mathsolutions.com/videopage/videos/Final/Guess_My_Number.swf Number Talks sample flipcharts available on the Elementary Math Resources VISION site INVESTIGATIONS: Mathematical Thinking in Kindergarten Investigation 1: Attendance Investigation 3: Calendar Investigation 2: Counting Jars Investigation 4: Today’s Question
Utilize hands-on objects and visual (promethean) activities.
Have students take turns manipulating different calendar components.
Utilize student groupings to involve all children in discussions and problem solving.
Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Kindergarten 2014-15
Unit: 2 Quarter 1
Counting
VDOE Standards of Learning:
K.4a The student will a) count forward to 100 and backward from 10;
K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; b) write the numeral to tell how many are in the set; and c) select the corresponding numeral from a given set of numerals.
Selecting on a number line
Selecting on a number chart
K.13 The student will gather data by counting and tallying.
K.4b The student will b) identify one more than a number and one less than a number;
K.16 The student will identify, describe, and extend repeating patterns.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can count forward to 100 by ones, fives, and tens and I can count backward from 10.
I can identify the number of objects in a set by counting the objects orally, selecting the numeral, and writing the numeral that matches the number of objects in the set. I can create a set of objects that matches a number from 0 through 15.
I can collect answers to a question, keep track of the answers by using tally marks, and organize the answers in categories.
I can identify one more than a number and one less than a number and show the relationship using objects.
I can compare the similarities and differences between patterns.
Big Ideas Essential Questions
Counting forward to 100 and backward from 10.
Counting aloud the number of objects in a set.
Matching a numeral to represent the amount in a set.
Writing a numeral to represent the amount in a set.
Show understanding of tallying and counting tallies.
Demonstrate one more and one less than a number
Recognize patterns in counting with number chart.
How can we count the quantity of items in a group? How can we count the quantity in another way?
How can you represent the quantity with a numeral?
How can you identify the quantity on a hundreds chart?
How can you identify the quantity on a number line?
Why do we collect data?
What are some strategies used to gather data?
Why do you think someone might use tally marks to record data as it is collected?”
Prove which of two sets has more, fewer, or the same objects as the other set.
Prove one more than a number and one less than a number.
What is a pattern?
LCPS MATH Unit Summary Kindergarten 2014-15
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3
Introduction to counting in Classroom Routines
Introduction to tallying in Classroom Routines
Introduction to one more and one less than a number
in Classroom Routines
VDOE Vocabulary Word Wall Cards number line number chart tally forward backward more less data pattern numeral set empty set number fewer same numerals 0-15 number words 0-15
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio powerpoint slide with more information about the Process Goals
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks
Enrollment key: mathisfun
http://loudounvision.net/
NCSM Great Tasks (available in all LCPS Elementary Schools—click link)
Differentiation Resources
Lead students in creating a picture chart of classroom items to count and record. The chart might include items such as desks, chairs, flags, computers, trash cans, and pencil sharpeners.
Use a highlighter to provide a guide for students to trace tally marks.
Use coffee stirrers or ice cream sticks to make physical models of tally marks.
ELL Model Performance Indicators
(click to link)
Investigations: Collecting, Counting, and Measuring Investigation 1: Counting Books Investigation 2: Taking Inventory Investigation 3: Comparing Towers Patterns, Trains, and Hopscotch Paths Investigation 2: What Comes Next? Counting Ourselves and Others Investigation 1: How Many Are We? ESS Lessons: K.2 - Counting Centers K.2 - Counting 15 Dots K.13 - Using Tally Marks BrainPOP Jr.: Tally Marks and Bar Graphs Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Kindergarten 2014-15
Unit: 3 Quarter 1
Comparing Sets
VDOE Standards of Learning:
K.1 The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.
K.3 The student, given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object. * In context of collecting data.
K.13 The student will gather data by counting and tallying.
K.14 The student will display gathered data in object graphs, picture graphs, and tables, and will answer questions related to the data.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can compare two sets of objects and describe a set as having more, fewer, or the same quantity of objects. I can create a set of objects which has more, fewer, or the same quantity as a given set.
I can identify the ordinal positions for each object in a set of 10 objects that are in order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top).
I can collect answers to a question, keep track of the answers by using tally marks, and organize the answers in categories.
I can analyze data I have displayed in graphs and tables.
Big Ideas Essential Questions
Compare sets as having more, fewer, or the same number of items.
Create a set of objects with more, fewer, or the same number of items as another set.
Identify the ordinal position (first through tenth) of objects in a set.
Identify the ordinal position (first through tenth) from most to least of a depicted set of data (ex. graph, groups of items)
Demonstrate understanding of the concept of tallies representing the amount in a set.
Create tables or graphs with objects or pictures to display data collected.
Answer questions or make observations aloud regarding data displayed in graphs or tables.
How can the quantity of two sets of objects be compared?
What strategies can be used to sort and sequence objects?
How can we display gathered data?
Why do we collect data?
What are some strategies used to gather data?
What is an ordinal position?
Give examples of how ordinal numbers are used in real life situations.
Compare and contrast the counting sequence and ordinal positions.
Prove which of two sets has more, fewer, or the same objects as the other set.
Have students make a train with 10 cubes. What color is the sixth cube? What is the position of the green cube?
What is the difference between five and fifth?
How do you know when both groups of counters are the same?
If the arrangement of the counters in two groups is different, can the number of counters be the same?
LCPS MATH Unit Summary Kindergarten 2014-15
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3
Introduction to counting in Classroom Routines
Introduction to tallying in Classroom Routines
Introduction to more, less, equal to in Classroom Routines
Introduction to data collection and graphs in Classroom Routines
VDOE Vocabulary Word Wall Cards set more fewer same ordinal position cardinal number first second third fourth fifth sixth seventh eighth ninth tenth tally mark data graph table less equal last compare picture graph
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio powerpoint slide with more information about the Process Goals
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks
Enrollment key: mathisfun
http://loudounvision.net/
NCSM Great Tasks (available in all LCPS Elementary Schools—click link)
Differentiation Resources
Divide students into groups, and ask each group to observe and graph such things as hair colors, types of shoes, colors of shirts, numbers of brothers and sisters, etc. This could also be done in cooperation with another class in the school, with the classes placing themselves into human graphs by class and transferring the information to a pictorial or object graph for comparison purposes.
Lead students in using the computer to type and print positional words to use for labeling items in the classroom.
As a large group, have students place positional words to label areas within the classroom. For example, have students place the word top to label the top of the door, the word middle to label the middle of the door, and the word bottom to label the bottom of the door.
ELL Model Performance Indicators
(click to link)
Investigations: Collecting, Counting, and Measuring Investigation 1: Counting Books Investigation 2: Taking Inventory Investigation 3: Comparing Towers Investigation 5: Least to Most Counting Ourselves and Others Investigation 2: What Did You Eat for Lunch? ESS Lessons: K.1 - More, Fewer, or the Same? K.3 - Counting on the Bus K.14 - My Favorite Things BrainPOP Jr.: Making Equal Groups Pictographs Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Kindergarten 2014-15
Unit: 4 Quarter 2
Geometry & Sorting
VDOE Standards of Learning:
K.15 The student will sort and classify objects according to attributes.
K.7 The student will recognize a penny, nickel, dime, and quarter and will determine the value of a collection of pennies and/or nickels whose total value is 10 cents or less.
K.11 The student will a) identify, describe, and trace plane geometric figures (circle, triangle,
square, and rectangle); and b) compare the size (larger, smaller) and shape of plane geometric
figures (circle, triangle, square, and rectangle).
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can sort and classify a set of objects in at least two different ways and explain my reasoning.
I can identify and describe a penny, nickel, dime, and quarter and determine the value of a collection of coins (10 cents or less) and equivalent amounts (a nickel is the same as 5 pennies).
I can name geometric shapes and tell how they are different.
I can tell (compare) which shape is larger and which is smaller.
Big Ideas Essential Questions
Sort and classify objects in multiple ways.
Sort coins by characteristics and label the groupings.
Sort shapes by characteristics and identify differences.
How can objects be sorted and classified according to attributes?
Use the coin names to label various groups of sorted coins.
Compare and contrast a variety of sorts for a set of objects.
Identify and describe plane geometric figures.
Compare and contrast the size and shape of plane geometric figures.
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3
VDOE Vocabulary Word Wall Cards sort classify coin penny nickel dime quarter larger smaller circle triangle square rectangle
LCPS MATH Unit Summary Kindergarten 2014-15
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio powerpoint slide with more information about the Process Goals
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: mathisfun
http://loudounvision.net/
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Have students use a Venn diagram to sort objects.
Have students use a drawing program on the computer to practice drawing geometric figures. Allow them to print their drawings.
Use larger objects for students who have trouble handling small ones.
Give students a way of sorting objects, then ask them to come up with another way.
Have students share different ways of sorting.
ELL Model Performance Indicators (click to link)
Investigations: Making Shapes and Building Blocks Investigation 1: 2-D Shapes Around Us Investigation 2: Exploring Shapes with the Computer ESS Lessons: K.11 - Geometric Figures in Our Classroom K.15 - The Button Box BrainPOP Jr.: Plane Shapes Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Kindergarten 2014-15
Unit: 5 Quarter 2
Shapes in Space
VDOE Standards of Learning:
K.12 The student will describe the location of one object relative to another (above, below, next to) and identify representations of plane geometric figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space.
(In contexts with Art, Social Science, Language Arts, and patterns)
K.16 The student will identify, describe, and extend repeating patterns.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can identify a triangle, circle, square, and rectangle and describe if one of them is above or below or next to another one.
I can compare the similarities and differences between patterns.
Big Ideas Essential Questions
Describe the location of one object relative to another.
Identify shapes regardless of position.
Utilize basic maps to encourage positional word use.
Compare patterns among shapes and positions.
Utilize Art, Social Science, and Language Arts lessons to develop vocabulary use of positional words and create a better understanding of real world use.
Identify and describe the location of one object relative to another.
Prove orientation does not change the identity of plane geometric figures.
What is a pattern?
Demonstrate and justify a pattern.
Compare and contrast student created pattern.
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3
Introduction to patterns in Classroom Routines
Shape identification and classification in Geometry and Shapes Unit
VDOE Vocabulary Word Wall Cards shape square rectangle circle triangle trace compare alike/same different smaller larger describe above below next to pattern core repeating predict describe
LCPS MATH Unit Summary Kindergarten 2014-15
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio powerpoint slide with more information about the Process Goals
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks
Enrollment key: mathisfun
http://loudounvision.net/
NCSM Great Tasks (available in all LCPS Elementary Schools—click link)
Differentiation Resources
As a large group, have students place positional words to label areas within the classroom. For example, have students place the word top to label the top of the door, the word middle to label the middle of the door, and the word bottom to label the bottom of the door.
Work with students to create an “Orientation Book,” as follows. Have students trace a rectangle on a left-hand page of their books. Then, have them rotate the rectangle a little and trace it on the opposing right-hand page. Direct them to turn the page and repeat the process, using another geometric figure. Continue until all figures have been traced.
Have students work in pairs to create shapes on a geoboard. Have student pairs explain how they created their shapes and how they know what each shape is.
Give students a wide variety of materials (e.g., buttons, toy cars, socks, seeds, noodles, crayons, wooden blocks), and ask them to use the materials to create different patterns. Encourage students to create patterns other than A-B-A-B.
ELL Model Performance Indicators (click to link)
Investigations: Making Shapes and Building Blocks Investigation 1: 2-D Shapes Around Us Investigation 2: Exploring Shapes with the Computer Investigation 3: Looking at 3D Shapes ESS Lessons: K.12 – Geometric Games K.16 – Repeating Patterns BrainPop Jr.: Congruent and Similar Shapes Patterns Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Kindergarten 2014-15
Unit: 6 Quarter 3
Geometry & Fractions
VDOE Standards of Learning:
K.11 The student will a) identify, describe, and trace plane geometric figures (circle, triangle,
square, and rectangle); and b) compare the size (larger, smaller) and shape of plane geometric
figures (circle, triangle, square, and rectangle).
K.5 The student will identify the parts of a set and/or region that represent fractions for halves and fourths.
K.14 The student will display gathered data in object graphs, picture graphs, and tables, and will answer questions related to the data.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can name geometric shapes and tell how they are different.
I can tell (compare) which shape is larger and which is smaller.
I can show (represent) halves and fourths as parts of sets and parts of regions.
I can analyze data I have displayed in graphs and tables.
Big Ideas Essential Questions
Utilize various shapes within other shapes (pattern blocks) to depict parts of a whole.
Discuss fractions in sets utilizing graphs and tables.
Area models (fraction circles, fraction squares), Set
models (two-color counters or any discrete objects), and Linear models (number lines, rope, etc.) should all be introduced as representations for fractions.
Identify and describe plane geometric figures.
Compare and contrast the size and shape of plane geometric figures.
What does a fraction represent?
How can we display gathered data?
Using an example of the region/area model and the set model for fractions, demonstrate an unfair sharing situation among four students. “Does each student have a fourth? How do you know?
What does it mean to be “fair” when working with fractions?
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3
Introduction to collecting data and graphs in Classroom Routines
Shape identification and classification in Geometry and Shapes Unit
VDOE Vocabulary Word Wall Cards
larger smaller circle rectangle triangle square set table region fraction halves fourths data graph
LCPS MATH Unit Summary Kindergarten 2014-15
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio powerpoint slide with more information about the Process Goals
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: mathisfun
http://loudounvision.net/
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Extend sharing problems to involve more than one whole. For example, three students sharing two cookies.
Give students opportunities to work with many different wholes and sharing situations. Always identify the whole, or show students a fraction and ask them to describe what the whole would be.
Incorporate fractions into everyday classroom tasks. For example, choose a group of students to represent halves or fourths based on clothing items. During graphing, use fraction vocabulary when possible to describe data. For example, “Half of the class has pets. Our whole class is made up of 24 children.” During snack time, discuss whether sharing is or is not “fair”—whether students get equal amounts.
ELL Model Performance Indicators (click to link)
Investigations: Making Shapes and Building Blocks Investigation 4: Making Shapes and Building Blocks
ESS Lessons: K.5 - Sharing Snacks BrainPOP Jr.: Basic Parts of a Whole Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Kindergarten 2014-15
Unit: 7 Quarter 3
Measuring My World
VDOE Standards of Learning:
K.8 The student will identify the instruments used to measure length (ruler), weight (scale), time (clock: digital and analog; calendar: day, month, and season), and temperature (thermometer).
K.10 The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block.
K.9 The student will tell time to the hour, using analog and digital clocks.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can identify instruments used to measure length, weight, time, and temperature.
I can compare and measure objects using foot length, hand span, new pencil, paper clip, and/or block.
I can tell time to the hour on an analog and digital clock and relate the time to daily routines.
Big Ideas Essential Questions
Identify different uses of measurement instruments.
Compare different instruments and how to distinguish between when to use the correct instrument.
Utilize nonstandard units and provide opportunities to choose the appropriate nonstandard unit depending on the item being measured.
Show a digital clock and an analog clock. “What is the same about these two clocks? What is different about these two clocks?”
What tool or tools would you use to measure the length of your foot? What tool or tools would you use to measure the length of the cafeteria?”
Display two different objects. “Which of these objects is heavier? How do you know?”
“When do you weigh things in your everyday life? What kinds of things do you weigh?”
What does a calendar measure?
How does calendar measure time?
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3
Introduction to calendar, clock, and thermometer in Classroom Routines
VDOE Vocabulary Word Wall Cards clock ruler thermometer scale weight digital analog calendar day season month temperature length shorter longer height taller heavier lighter hotter colder measure hour minute hands o’clock balance
LCPS MATH Unit Summary Kindergarten 2014-15
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio powerpoint slide with more information about the Process Goals
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks
Enrollment key: mathisfun
http://loudounvision.net/
NCSM Great Tasks (available in all LCPS Elementary Schools—click link)
Differentiation Resources
Guide students in creating a daily classroom schedule that pairs a symbol representing a daily classroom activity with a visual of a clock showing the time when the activity takes place.
Lead the class in singing songs that develop vocabulary for associations with different times of day and require physical modeling of the movement of the clock hands.
Use the body to model or represent “long” by spreading arms wide and “short” by using fingers. For example, ask, “Show me what ‘long’ looks like.” or “Show me how long an elephant’s trunk is.” “Show me what ‘short’ looks like.” or “Show me how short a worm is.”
Have students draw the classroom objects they measured and place their drawings on a class chart divided into columns by lengths: Longer and Shorter.
Lead students in creating minibooks with patterned sentences following instruction in the concepts. The patterned sentences could be placed one per page and might read as follows: “The pencil is longer than the eraser.” “The bookshelf is shorter than the door.” “The bike is shorter than the bus.” Guide students in illustrating their minibooks to show shorter and longer.
ELL Model Performance Indicators
(click to link)
ESS Lessons: K.9 - What Time Is It? K.10 - How Long Is It? K.10 – How Tall Are You? K.10 - How Heavy Is It? K.10 – Hot or Cold? BrianPOP Jr.: Time to the Hour Ounces Pounds and Tons Inches and Feet Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Kindergarten 2014-15
Unit: 8 Quarters 3-4
Skip Counting & Money
VDOE Standards of Learning:
K.4 The student will c) count by fives and tens to 100.
K.7 The student will recognize a penny, nickel, dime, and quarter and will determine the value of a collection of pennies and/or nickels whose total value is 10 cents or less.
K.16 The student will identify, describe, and extend repeating patterns.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can identify the patterns of counting by ones, fives, and tens using different models (hundreds chart, number line, etc.).
I can identify and describe a penny, nickel, dime, and quarter and determine the value of a collection of coins (10 cents or less) and equivalent amounts (a nickel is the same as 5 pennies).
I can compare the similarities and differences between patterns.
Big Ideas Essential Questions
Skip counting can be used to count different sets of object.
Skip counting numbers is creating number patterns.
Counting coins utilizes skip counting.
Describe patterns in skip counting and use those patterns to predict the next number or numbers in the skip counting sequence.
What is a pattern?
What patterns can we make when counting?
Demonstrate and justify a pattern.
Compare and contrast student created patterns.
Demonstrate strategies for counting the quantity of items in a group then represent it with a numeral.
Prove one more than a number and one less than a number.
How does skip counting help us count coins?
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3
Introduction to skip counting in Classroom Routines
Coin identification and sorting in Geometry and Sorting Unit
Patterns in Shapes in Space Unit
VDOE Vocabulary Word Wall Cards
count skip counting ones fives tens one more than one less than patterns penny nickel dime quarter cents value one cent five cents ten cents twenty-five cents
LCPS MATH Unit Summary Kindergarten 2014-15
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio powerpoint slide with more information about the Process Goals
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: mathisfun
http://loudounvision.net/
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Use manipulatives for counting experiences that include a variety of textures, e.g., foam shapes, plastic straws, ceramic tiles, plastic and metal bottle caps. Use grid paper to assist students in lining up objects into vertical columns.
Provide sorting charts (T-table or chart) to sort coins by coin name and by value.
Create a large T-table or chart to sort large images of coins by coin name and by value.
ELL Model Performance Indicators (click to link)
Investigations: Patterns, Trains, and Hopscotch Paths Investigation 2: What Comes Next? Investigation 3: Hopscotch Paths Investigation 4: Pattern Borders ESS Lessons: K.4 - Hundreds Board Math K.7 - Money Math BrainPOP Jr.: Counting Coins Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
LCPS MATH Unit Summary Kindergarten 2014-15
Unit: 9 Quarter 4
Combining & Separating
VDOE Standards of Learning:
K.4 The student will b) identify one more than a number and one less than a number; and
K.6 The student will model adding and subtracting whole numbers, using up to 10 concrete objects.
K.7 The student will recognize a penny, nickel, dime, and quarter and will determine the value of a collection of pennies and/or nickels whose total value is 10 cents or less.
VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations
Learning Targets:
I can identify one more than a number and one less than a number and show the relationship using objects.
I can use manipulatives to model and describe addition and subtraction.
I can identify and describe a penny, nickel, dime, and quarter and determine the value of a collection of coins (10 cents or less) and equivalent amounts (a nickel is the same as 5 pennies).
Big Ideas Essential Questions
Recognize the relationship of one more than and one less than a number using objects (i.e., five and one more is six; and one less than ten is nine).
Understand that addition means putting things together and that subtraction is the inverse of addition and means to separate things out.
Understand how different groups of coins can equal the same amount.
Demonstrate and justify strategies for a solution within story problem.
What strategies do you use to find the sum of two numbers?
What strategies do you use to find the difference between two numbers?
How can you show the same amount of money using different coins?
Prerequisite Skills Vocabulary
VDOE Vertical Alignment document K-3
Introduction to one more and one less in Classsroom Routines
Coin identification and sorting in Geometry and Sorting Unit
Coin values and counting in Skip Counting & Money Unit
VDOE Vocabulary Word Wall Cards penny nickel dime quarter cents value one cent five cents ten cents twenty-five cents add add on adding sum subtract difference equal plus minus total more fewer same
LCPS MATH Unit Summary Kindergarten 2014-15
Achievement Criteria How to Assess Achievement
“The content of the mathematics standards is intended to support the following five process goals for students:
• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and
interpret practical situations.” -2009 Mathematics Standards of Learning
Click here for a brief audio powerpoint slide with more information about the Process Goals
Sample Math Tasks are available in VISION:
Search: LCPS-Math: K-12 Math Tasks Enrollment key: mathisfun
http://loudounvision.net/
NCSM Great Tasks
(available in all LCPS Elementary Schools—click link)
Differentiation Resources
Draw pictures to ‘write’ your own number story. Use your pictures to show both the words and the numbers in your story.
Have students act out number stories provide by teacher or created by students.
ELL Model Performance Indicators (click to link)
Investigations: How Many In All? Investigation 2: Six Tiles Investigation 3: Story Problems Investigation 4: Blue and Red Crayons ESS Lessons: K.6 - Math Stories K.7 - Money Math BrainPOP Jr.: Basic Adding Basic Subtraction Equivalent Coins Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)
The First 20 Days Classroom Routines: Establishing a Mathematics Classroom Community
Overview: The mini lessons included in this guide are intended to be used in conjunction with your first unit of study. The daily 10-15 minute lessons will help
you set routines, develop references for students, establish protocols, and create norms for an engaging math classroom community. The lessons may be
modified or extended based on students’ need or grade level. The routines, protocols, and experiences should be revisited throughout the school year in order
to maintain a productive math community.
Goals:
Build a classroom community of learners
Support students’ understanding of math content by establishing guidelines related to the VA process goals (problem solving, communication,
reasoning, connections, and representation).
Develop routines that will help students become reflective problem solvers and engage in a rigorous study of mathematics.
Background: This guide is based on a document developed by Austin Independent School District. Their document was modeled after the First 20 Days of Independent Reading by Fountas & Pinnell. Many of the suggested routines will also connect to other effective protocols used in Being a Writer and Responsive Classroom. This guide was adapted from a resource created by Arlington Public Schools.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 1 Management: Classroom Procedures/ Community Guidelines
Establish routines, procedures, and student expectations for daily math lessons.
Students develop criteria for a “Being a Mathematician” chart that will be posted in the classroom. Students understand that the information posted in the classroom will be a valuable reference for them.
Develop a “Being a Mathematician” anchor chart to which students can refer. The chart should have less than 6 criteria to be effective and manageable. Example behaviors:
• Remain on task • Participate/stay engaged • Listen actively • Discuss math ideas • Treat materials with respect • Always try your best
*Brainstorm the list with the students
Chart paper, Markers Have a discussion about routines and procedures with the students. This is a good time to have students talk about expectations for engaging in classroom discussions and completing their work.
Day 2 Management: Mathematical Tools VA Process Goals: Problem Solving & Representation
Mathematicians can utilize math tools to help them solve problems.
Tools are a valuable resource for mathematicians. Students are aware of the tools that are available in the classroom.
Brainstorm a list of mathematical tools and discuss how they can be used and stored. Add additional information to the “Being a Mathematician” chart about placing materials in their proper storage containers and location after use. Examples: Base ten blocks Cubes Number cubes Hundreds chart Two-colored counters
Emphasize how and why materials are to be used during math instruction.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 3 Math Talk/ Classroom Discourse VA Process Goal: Communication
Mathematicians communicate orally about their work. Norms for classroom discussions need to be established in order to engage in respectful discourse and have equitable participation.
In order to communicate and learn from each other, mathematicians must listen to, as well as speak, with their classmates. We will function as a respectful classroom community in order to learn.
Create an anchor chart for “Norms for a Math Discussion” or “Rights and Obligations During Discussions” Example norms include: Speak respectfully Take turns (equitable participation) Give others time to think Eyes on the speaker
Norms may be similar to those you establish in other content areas. These established routines should be revisited all year long.
Day 4 Math Talk/ Classroom Discourse VA Process Goal: Communication
Mathematicians communicate orally about their work. Different talk moves can be used while facilitating classroom discussions. Students learn content through the process goal of communication.
Math can be more rigorous when you communicate with others. There are sentence starters that can be used to help one engage in discussions.
Post and discuss Talk Moves to encourage students to share their thinking. Identify 1 or 2 moves to begin the year with (based on your first units of study).
- Talk bubbles or Talk move sticks
Introduce talk moves
- Turn and Talk (also called partner talk, or think-pair-share)
- Say More: You ask an individual student to expand on what he or she said
- Revoicing (also called verify and clarify)
- Repeat - Agree/Disagree and why?
Encourage students to speak in complete thoughts when communicating orally. The utilization and introduction of talk moves is a continuous process. This day is one way to introduce moves, but it should be ongoing.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 5 Collaboration (Game) VA Process Goal: Communication
Mathematicians can work collaboratively while playing a game in order to learn important math concepts.
Students understand that they can work with others to explore math content. Cooperation is a key component of working with a partner.
Establish rules for working with a partner while playing a math game. Try the “Say it to Play it” guideline: When playing a game in partners, the students must state their move and/or provide an explanation for why they are playing that move (Ex: In the game Compare, a student may say “9 is greater than 5, so I win the cards”).
Post rules and directions for engaging in a game with a partner. Consider utilizing a fact fluency game for this mini lesson.
Rules and clear directions will help make group work successful. After the mini lesson, have students practice a game during the math lesson for the day.
Day 6 Collaborative/ Independent Work (Rotations) VA Process Goal: Communication
Mathematicians can explore/ engage in a variety of experiences within a math period. Work may be collaborative or independent.
In order to have a variety of activities during a math block, it is important to be mindful of procedures, noise level, expectations, etc.
Review procedures for moving around the classroom to different centers Consider utilizing visual time reminders Use cues for sound control/reminders
Post clear directions at independent centers. Provide a materials checklist.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 7 Real Life Connections to Math VA Process Goal: Connections
Mathematicians make connections between math ideas and the world around them.
Math connects to other content areas/disciplines (i.e. Science). Students relate math to the world around them.
Brainstorm a list of math concepts that relate to the real world. Consider using the following discussion prompts: Where in the world do you see numbers? When do you use math in your everyday life?
Chart paper Calendar / Daily Schedule
Consider connecting this discussion to everyday events in their life.
Day 8 Representing Thinking VA Process Goals: Representation, Communication
Mathematicians can represent ideas in multiple ways. Mathematicians use words to explain their thinking. Mathematicians can explain their thinking verbally or in writing in order to process information.
Students will become more familiar with ways they can represent math ideas. Students can show their math thinking in written words.
In order to fully communicate their understanding, mathematicians may provide written explanations of their reasoning.
Brainstorm ways that students can represent their thinking. Ex: Pictures/drawing Words Numbers Symbols Manipulative models
Utilize sentence frames: “This is a ______________. It is a ______ because it ______________. “ This example shows a picture, numbers, and a written explanation.
Encourage students to show math concepts in a variety of ways. Encourage students to write about their understanding or show their thinking using words, pictures, numbers, etc.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 9 Recording & Reflecting in Math
VA Process Goal: Communication
Mathematicians keep a record of their daily experiences (i.e. math game).
Students will understand how to utilize a recording sheet or guide as they play a game or solve a problem. Students will record and reflect upon their work to communicate their understanding in writing.
Example of Game Recording Sheet:
Introduce a Recording Sheet as a student tool.
Day 10 Academic Language of Math VA Process Goal: Communication
Specialized language is used in math. Mathematical language can be modeled and explicitly taught.
Students will develop an understanding of specific math terminology. Conceptual understanding is developed as students use math terminology.
Post examples of key vocabulary terms with visual examples.
Math Word Wall, Word Banks, VDOE Vocabulary Cards http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/index.shtml The vocabulary terms introduced are then posted for class reference.
New vocabulary should be explicitly introduced and utilized within daily lessons. This is a continuous routine/ element for all units of study.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 11 Vocabulary Development VA Process Goals: Representation, Communication, Connections
Mathematicians use a variety of strategies to build vocabulary.
Students will utilize a tool to reinforce their math vocabulary.
Select model to implement with students (i.e. Frayer).
Student math journal VDOE Math Vocabulary Cards Frayer Model
Students can utilize math journals to keep a record of math vocabulary. Their journals can also serve as a valuable resource in addition to the Word Wall or class references (see Day 10).
Day 12 Math Strategies
VA Process Goals: Problem Solving, Representation, Connections
A variety of strategies can be used to solve problems and explore mathematical concepts.
Students develop a repertoire of strategies. Students see connections between different strategies used to solve problems.
Build or add to a strategy wall showing models of strategies for various skills or concepts.
Anchor charts can be developed for a wide variety of strategies depending on the grade level. Examples are shown to the left.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 13 Connections VA Process Goals: Connections, Communication
Mathematicians make and recognize connections among mathematical ideas.
Students understand that they can make connections among math ideas. Math can be related to the world outside the classroom.
Discussion questions: How is that answer like the one you modeled yesterday? Where have you seen that before?
Consider having students glue question/ comment starters in the back of their math journal. They can refer to it during class discussions.
Day 14 Justification VA Process Goals: Reasoning, Representation
Mathematicians verify their thinking by showing it multiple ways.
Students will develop a deeper understanding of content when asked to justify their thinking.
Create an anchor chart that depicts ways that students can justify their thinking.
Justify means: explain, defend,
describe, prove, give reasons, show
you understand, validate…
Using verbal explanation first can help facilitate written justification.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 15 Problem Solving Strategies VA Process Goals: Problem Solving, Communication
Mathematicians choose from a variety of strategies to solve problems.
Students have a resource of strategies to help them solve problems . Sample strategies: -find a pattern - estimate and check -make an organized list -draw a diagram -write an equation -work backward -solve a simpler problem -read a table/chart
Introduce problem solving strategies (a variety of strategies can be used). Explain that the different strategies can be used to help students with problem solving. Choose 1 strategy to explain/highlight for the mini lesson. You will continue to model/introduce/use the strategies throughout the year.
Students can create their own problem solving strategy icons or bookmarks as well as refer to a class anchor chart of strategies.
During classroom instruction, teachers can engage students in discourse about their problem solving strategy.
Day 16 Problem Solving Protocol VA Process Goals: Problem Solving, Communication
There are processes that can be used to help solve problems.
Students will be introduced to a problem solving protocol. Students will become familiar with the protocol steps.
Develop and post a problem solving protocol.
Post the protocol in the classroom for student reference.
Consider trying a problem as a class to model how the protocol is used. The emphasis should be on the steps, so it may be easiest to select content that is readily accessible to all learners.
Step 1: Read and quietly think on your own – release your pencils. Step 2: Talk about the problem. What is your plan to solve? Pick your strategy. Step 3: Share your strategy. Step 4: Solve the problem and communicate your thinking.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 17 Rubric Familiarization VA Process Goals: Reasoning, Connections
There are tools mathematicians use to monitor and assess their work or behavior.
Students understand how to use a rubric to assess themselves/ their work.
Create a class rubric that is not math related. The topic should be something relevant to an everyday student activity in the classroom or school. Examples include: Lunchroom behavior Morning routine Dismissal Cubbie/desk organization
Day 18 Reflection/ Self-Monitoring VA Process Goal: Reasoning
Mathematicians modify their work as needed.
Students reflect upon and revise their work to demonstrate their full understanding.
Introduce a criteria chart and rubric for self- monitoring of work.
Sample Rubric:
Rubric & Problem Solving Protocol Create an anchor chart with “How to Self-Correct or Modify Your Work”
Help students develop a clear understanding of the criteria and how upcoming math tasks will be scored. Emphasize how this is similar to the revisions they do during the writing process.
Mini Lesson Key Ideas Essential Understandings
Anchor Charts/Supports Resources Teacher Notes
Day 19 Collaboration (Task) VA Process Goal: Communication
Mathematicians can work collaboratively on a problem solving task to learn important math concepts.
Students understand that they can work with others to solve problems and learn new information.
Review roles that pairs or small groups should follow/hold when working together on a task. Examples: Materials manager Recorder Reporter Time keeper
Develop an anchor chart with roles/procedures for group work on a task/problem. Self-assess/reflect upon collaborative work experiences. Students can use the problem solving protocol together (See Day 16).
Save time at the end of the lesson to debrief the experience. What went well? What could be improved next time they are working in a group?
Day 20
Process Goals
VA Process Goals: Problem Solving, Reasoning, Communication, Connections, & Representation
“The content of the mathematics standards is intended to support the following five process goals for students: *becoming mathematical problem solvers *communicating mathematically *reasoning mathematically *making mathematical connections and *using mathematical representations to model and interpret practical situations.”
-2009 Mathematics Standards of Learning
Student-friendly process goals poster (can be a poster for the classroom and/or a small version can be taped to desks or in math journals) Process Goals bookmark (click on picture to the left to access the file for the poster and bookmark)
Students should be engaged in process goals throughout every mathematical task and lesson throughout the year.
VDOE Technical Assistance Document
to be used in conjunction with the VDOE Curriculum Framework (click title above to link to document)
Virginia Mathematics Standards of Learning
Curriculum Framework 2009 Introduction
The 2009 Mathematics Standards of Learning Curriculum Framework is a companion document to the 2009 Mathematics Standards of Learning and
amplifies the Mathematics Standards of Learning by defining the content knowledge, skills, and understandings that are measured by the Standards
of Learning assessments. The Curriculum Framework provides additional guidance to school divisions and their teachers as they develop an
instructional program appropriate for their students. It assists teachers in their lesson planning by identifying essential understandings, defining
essential content knowledge, and describing the intellectual skills students need to use. This supplemental framework delineates in greater specificity
the content that all teachers should teach and all students should learn.
Each topic in the Mathematics Standards of Learning Curriculum Framework is developed around the Standards of Learning. The format of the
Curriculum Framework facilitates teacher planning by identifying the key concepts, knowledge and skills that should be the focus of instruction for
each standard. The Curriculum Framework is divided into three columns: Understanding the Standard; Essential Understandings; and Essential
Knowledge and Skills. The purpose of each column is explained below.
Understanding the Standard
This section includes background information for the teacher (K-8). It contains content that may extend the teachers’ knowledge of the standard
beyond the current grade level. This section may also contain suggestions and resources that will help teachers plan lessons focusing on the standard.
Essential Understandings
This section delineates the key concepts, ideas and mathematical relationships that all students should grasp to demonstrate an understanding of the
Standards of Learning. In Grades 6-8, these essential understandings are presented as questions to facilitate teacher planning.
Essential Knowledge and Skills
Each standard is expanded in the Essential Knowledge and Skills column. What each student should know and be able to do in each standard is
outlined. This is not meant to be an exhaustive list nor a list that limits what is taught in the classroom. It is meant to be the key knowledge and skills
that define the standard.
The Curriculum Framework serves as a guide for Standards of Learning assessment development. Assessment items may not and should not be a
verbatim reflection of the information presented in the Curriculum Framework. Students are expected to continue to apply knowledge and skills
from Standards of Learning presented in previous grades as they build mathematical expertise.
FOCUS K–3 STRAND: NUMBER AND NUMBER SENSE GRADE LEVEL K
Students in grades K–3 have a natural curiosity about their world, which leads them to develop a sense of number. Young children are motivated to
count everything around them and begin to develop an understanding of the size of numbers (magnitude), multiple ways of thinking about and
representing numbers, strategies and words to compare numbers, and an understanding of the effects of simple operations on numbers. Building on
their own intuitive mathematical knowledge, they also display a natural need to organize things by sorting, comparing, ordering, and labeling objects
in a variety of collections.
Consequently, the focus of instruction in the number and number sense strand is to promote an understanding of counting, classification, whole
numbers, place value, fractions, number relationships (“more than,” “less than,” and “equal to”), and the effects of single-step and multistep
computations. These learning experiences should allow students to engage actively in a variety of problem solving situations and to model numbers
(compose and decompose), using a variety of manipulatives. Additionally, students at this level should have opportunities to observe, to develop an
understanding of the relationship they see between numbers, and to develop the skills to communicate these relationships in precise, unambiguous
terms.
K.1 The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more,
fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
A set is a collection of distinct elements or items.
A one-to-one correspondence exists when two sets
have an equal number of items.
Strategies for developing the concept of one-to-one
matching involve set comparisons without
counting. Hands-on experiences in matching
items between two sets by moving, touching, and
aligning objects, using one-to-one
correspondence, enable visual as well as
kinesthetic comparisons of the number of items in
the two sets.
Students can also count to make comparisons between
two sets without matching the sets, using one-to-
one correspondence.
Students are generally familiar with the concept of
more, but have had little experience with the term
less. It is important to use the terms together to
build an understanding of their relationship. For
example, when asking which group has more,
follow with which group has less and vice versa.
All students should
Understand how quantities relate to each other,
which leads to an understanding of how
numbers are related to each other.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Match each member of one set with each member of another
set, using the concept of one-to-one correspondence to
compare the number of members between sets, where each
set contains 10 or fewer objects.
Compare and describe two sets of 10 or fewer objects, using
the terms more, fewer, and the same.
Given a set of objects, construct a second set which has more,
fewer or the same number of objects.
K.2 The student, given a set containing 15 or fewer concrete objects, will
a) tell how many are in the set by counting the number of objects orally;
b) write the numeral to tell how many are in the set; and
c) select the corresponding numeral from a given set of numerals.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Counting involves two separate skills: verbalizing the
list of standard number words in order (“one,
two, three, ”) and connecting this sequence
with the objects in the set being counted, using
one-to-one correspondence. Association of
number words with collections of objects is
achieved by moving, touching, or pointing to
objects as the number words are spoken. Objects
may be presented in random order or arranged for
easy counting.
Kinesthetic involvement (e.g., tracing the numbers,
using tactile materials, such as sand, sandpaper,
carpeting, or finger paint) facilitates the writing
of numerals.
Articulating the characteristics of each numeral when
writing numbers has been found to reduce the
amount of time it takes to learn to write numerals.
Zero (0) is both a number and a digit. As a number, it
plays a central role in mathematics as the additive
identity of the integers, real numbers, and many
other algebraic structures. As a digit, zero is used
as a placeholder in systems.
Conservation of number and cardinality principle are
two important milestones in development to
attaching meaning to counting.
The cardinality principle refers to the concept that the
last counted number describes the total amount of
the counted set. It is an extension of one-to-one
correspondence.
All students should
Read and write numerals from 0 through 15.
Understand that the total number of objects can
be found by counting.
Understand that the last counted number
describes the total amount in the set.
Understand that if the set is empty, it has 0
elements.
Understand that changing the spatial arrangement
of a set of objects does not change the total
amount of the set.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Count orally the number of objects in a set containing 15 or
fewer concrete objects, using one-to-one correspondence,
and identify the corresponding numeral.
Identify written numerals from 0 through 15 represented in
random order.
Select the numeral from a given set of numerals that
corresponds to a set of 15 or fewer concrete objects.
Write the numerals from 0 through 15.
Write a numeral that corresponds to a set of 15 or fewer
concrete objects.
Construct a set of objects that corresponds to a given numeral,
including an empty set.
K.2 The student, given a set containing 15 or fewer concrete objects, will
a) tell how many are in the set by counting the number of objects orally;
b) write the numeral to tell how many are in the set; and
c) select the corresponding numeral from a given set of numerals.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Conservation of number is the understanding that the
number of objects remains the same when they
are rearranged spatially.
K.3 The student, given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through
tenth, and the ordered position of each object.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Understanding the cardinal and ordinal meanings of
numbers are necessary to quantify, measure, and
identify the order of objects.
An ordinal number is a number that names the place
or position of an object in a sequence or set (e.g.,
first, third). Ordered position, ordinal position,
and ordinality are terms that refer to the place or
position of an object in a sequence or set.
The ordinal position is determined by where one starts
in an ordered set of objects or sequence of
objects.
The ordinal meaning of numbers is developed by
identifying and verbalizing the place or position
of objects in a set or sequence (e.g., the student’s
position in line when students are lined up
alphabetically by first name).
All students should
Use ordinal numbers to describe the position of
objects in a sequence.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Identify the ordinal positions first through tenth using ordered
sets of ten concrete objects and/or pictures of such sets
presented from
left-to-right;
right-to-left;
top-to-bottom; and/or
bottom-to-top.
K.4 The student will
a) count forward to 100 and backward from 10;
b) identify one more than a number and one less than a number; and
c) count by fives and tens to 100.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Counting skills are essential components of the
development of number ideas; however, they are
only one of the indicators of the understanding of
numbers.
Counting forward by rote advances the child’s
development of sequencing. The natural numbers
are 1, 2, 3, 4…. The whole numbers are 0, 1, 2, 3,
4…. Students should count the whole numbers 0,
1, 2, 3, 4,.
Counting backward by rote lays the foundation for
subtraction. Students should count backward
beginning with 10, 9, 8, through 3, 2, 1, 0.
Counting forward and backward leads to the
development of counting on and counting back.
The patterns developed as a result of skip counting are
precursors for recognizing numeric patterns,
functional relationships, and concepts underlying
money, time telling, and multiplication. Powerful
models for developing these concepts include, but
are not limited to, counters, hundred chart, and
calculators.
Skip counting by fives lays the foundation for reading
a clock effectively and telling time to the nearest
five minutes, counting money, and developing the
multiplication facts for five.
Skip counting by tens is a precursor for use of place
value, addition, counting money, and multiplying
by multiples of 10.
All students should
Use the correct oral counting sequence in both
forward and backward counting situations.
Understand that skip counting can be used to
count a collection of objects.
Describe patterns in skip counting and use those
patterns to predict the next number or
numbers in the skip counting sequence.
Understand that numeric relationships include one
more than, one less than, two more than, two
less than, etc.
Understand benchmarks of five and ten.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Count forward from 0 to 100.
Count backward from 10 to 0.
Recognize the relationship of one more than and one less than a
number using objects (i.e., five and one more is six; and
one less than ten is nine).
Group 100 or fewer objects together into sets of fives or tens
and then count them by fives or by tens.
Investigate and recognize the pattern of counting by fives to
100, using a variety of tools.
Investigate and recognize the pattern of counting by tens to
100, using a variety of tools.
K.4 The student will
a) count forward to 100 and backward from 10;
b) identify one more than a number and one less than a number; and
c) count by fives and tens to 100.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Calculators can be used to display the numeric
patterns that result from skip counting.
K.5 The student will identify the parts of a set and/or region that represent fractions for halves and fourths.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
A fraction is a way of representing part of a whole (as
in a region/area model) or part of a group (as in a
set model).
In each fraction model, the parts must have the same
area.
The fractional parts of a set model are subsets of an
equal number. For example, in a set of ten cubes,
each half would be a subset of five cubes.
Informal, integrated experiences with fractions at this
level will help students develop a foundation for
deeper learning at later grades. Understanding the
language of fractions furthers this development
(e.g., fourths means “four equal parts of a whole”
or 1
4 represents one of four parts of equal size
when a pizza is shared among four students).
All students should
Understand that fractional parts are equal shares
of a whole region or a whole set.
Understand that the fraction name (half, fourth)
tells the number of equal parts in the whole.
Understand that the fraction name (half, fourth) of
the set model is a subset of the whole set with
equal numbers.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Recognize fractions as representing parts of equal size of a
whole.
Given a region, identify half and/or a fourth of the region.
Given a set, identify half and/or a fourth of the set.
FOCUS K–3 STRAND: COMPUTATION AND ESTIMATION GRADE LEVEL K
A variety of contexts are necessary for children to develop an understanding of the meanings of the operations such as addition and subtraction.
These contexts often arise from real-life experiences in which they are simply joining sets, taking away or separating from a set, or comparing sets.
These contexts might include conversations, such as “How many books do we have altogether?” or “How many cookies are left if I eat two?” or “I
have three more candies than you do.” Although young children first compute using objects and manipulatives, they gradually shift to performing
computations mentally or using paper and pencil to record their thinking. Therefore, computation and estimation instruction in the early grades
revolves around modeling, discussing, and recording a variety of problem situations. This approach helps students transition from the concrete to the
representation to the symbolic in order to develop meaning for the operations and how they relate to each other.
In grades K–3, computation and estimation instruction focuses on
relating the mathematical language and symbolism of operations to problem situations;
understanding different meanings of addition and subtraction of whole numbers and the relation between the two operations;
developing proficiency with basic addition, subtraction, multiplication, division and related facts;
gaining facility in manipulating whole numbers to add and subtract and in understanding the effects of the operations on whole numbers;
developing and using strategies and algorithms to solve problems and choosing an appropriate method for the situation;
choosing, from mental computation, estimation, paper and pencil, and calculators, an appropriate way to compute;
recognizing whether numerical solutions are reasonable;
experiencing situations that lead to multiplication and division, such as equal groupings of objects and sharing equally; and
performing initial operations with fractions.
FOCUS K–3 STRAND: COMPUTATION AND ESTIMATION GRADE LEVEL K
K.6 The student will model adding and subtracting whole numbers, using up to 10 concrete objects.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Whole numbers are 0, 1, 2, 3, 4, 5, 6, and so on.
Addition is the process of combining or joining sets.
Subtraction can be viewed as a taking away or
separating process or as comparing to find the
difference between two sets.
Counting on from the larger set to determine the sum
of the combined sets is a strategy for finding a
sum.
Counting backward from the larger set to determine
the difference between two sets is a strategy for
subtraction.
Number relationships, including the following, help
students develop strategies for adding and
subtracting.
Instant recognition of the amount in a set of
objects that are arranged in a familiar
pattern such as the dots on number cubes
One more than, one less than, two more than,
two less than
All students should
Understand that addition means putting things
together and that subtraction is the inverse of
addition and means to separate things out.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Combine two sets with known quantities in each set, and count
the combined set using up to 10 concrete objects, to
determine the sum, where the sum is not greater than 10.
Given a set of 10 or fewer concrete objects, remove, take away,
or separate part of the set and determine the result.
FOCUS K–3 STRAND: MEASUREMENT GRADE LEVEL K
Measurement is important because it helps to quantify the world around us and is useful in so many aspects of everyday life. Students in grades K–3
should encounter measurement in many normal situations, from their daily use of the calendar and from science activities that often require students
to measure objects or compare them directly, to situations in stories they are reading and to descriptions of how quickly they are growing.
Measurement instruction at the primary level focuses on developing the skills and tools needed to measure length, weight/mass, capacity, time,
temperature, area, perimeter, volume, and money. Measurement at this level lends itself especially well to the use of concrete materials. Children can
see the usefulness of measurement if classroom experiences focus on estimating and measuring real objects. They gain deep understanding of the
concepts of measurement when handling the materials, making physical comparisons, and measuring with tools.
As students develop a sense of the attributes of measurement and the concept of a measurement unit, they also begin to recognize the differences
between using nonstandard and standard units of measure. Learning should give them opportunities to apply both techniques and nonstandard and
standard tools to find measurements and to develop an understanding of the use of simple U.S. Customary and metric units.
Teaching measurement offers the challenge to involve students actively and physically in learning and is an opportunity to tie together other aspects
of the mathematical curriculum, such as fractions and geometry. It is also one of the major vehicles by which mathematics can make connections
with other content areas, such as science, health, and physical education.
K.7 The student will recognize a penny, nickel, dime, and quarter and will determine the value of a collection of pennies and/or
nickels whose total value is 10 cents or less.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Involvement in varied activities such as physically
manipulating coins and making comparisons
about their sizes, colors, and values is prerequisite
to the skills of coin recognition and valuation.
Counting money helps students gain an awareness of
consumer skills and the use of money in everyday
life.
A variety of classroom experiences in which students
manipulate physical models of money and count
forward to determine the value of a collection of
coins are important activities to ensure
competence with using money.
Students need experiences to develop the concept that
a nickel has a value of five cents even though it is
one object.
All students should
Develop common referents for identifying
pennies, nickels, dimes, and quarters.
Understand the value of a collection of coins
whose value is 10 cents or less.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Describe the properties/characteristics (e.g., color, relative size)
of a penny, nickel, dime, and quarter.
Identify a penny, nickel, dime, and quarter.
Identify that a nickel is the same value as five pennies.
Count a randomly placed collection of pennies and/or nickels
(or models of pennies and/or nickels) whose value is 10
cents or less, and determine the value of the collection.
K.8 The student will identify the instruments used to measure length (ruler), weight (scale), time (clock: digital and analog;
calendar: day, month, and season), and temperature (thermometer).
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Many experiences in measuring physical objects,
using nonstandard and standard units of measure,
help to develop an intuitive understanding of
measurement and will help students connect a
tool with its purpose in measuring.
Selecting from among various measuring instruments
and determining which can be used to solve
various real-life problems are introduced at this
level.
A precursor to connecting tools to a type of
measurement is an introduction to the concepts of
length, weight, time, and temperature.
All students should
Identify an appropriate measuring tool for a given
unit of measure.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Identify a ruler as an instrument to measure length.
Identify different types of scales as instruments to measure
weight.
Identify different types of clocks (analog and digital) as
instruments to measure time.
Identify the components of a calendar, including days, months,
and seasons.
Identify different types of thermometers as instruments used to
measure temperature.
K.9 The student will tell time to the hour, using analog and digital clocks.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Many experiences in relating time on the hour to daily
routines and school schedules (e.g., catching the
bus, lunch time, recess time, and resource time)
help students develop personal referents for time.
Making sense of telling time to the nearest hour is
reinforced when students recognize the positions
of the hands on an analog clock and identify the
corresponding time to the hour.
All students should
Apply an appropriate technique, depending on the
type of clock, to determine time to the nearest
hour.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Tell time on an analog clock to the hour.
Tell time on a digital clock to the hour.
K.10 The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or
more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter,
colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Length is the distance between two points.
Height is the vertical length of a perpendicular to its
base.
Weight is a measure of the heaviness of an object.
Temperature is the degree of hotness or coldness of an
object (e.g., a body) or environment.
Students need to identify the attribute that they are
measuring (e.g., length, height, weight,
temperature) before they begin to measure.
Multiple hands-on experiences are needed to gain the
ability to compare the attributes of objects.
All students should
Compare and order objects according to their
attributes.
Develop an understanding of measuring with
nonstandard and standard units of measure.
Recognize attributes (length, height, weight,
temperature) that can be measured.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Compare and describe lengths of two objects (as shorter or
longer), using direct comparison or nonstandard units of
measure (e.g., foot length, hand span, new pencil, paper
clip, block).
Compare and describe heights of two objects (as taller or
shorter), using direct comparison or nonstandard units of
measure (e.g., book, hand span, new pencil, paper clip,
block).
Compare and describe weights of two objects (as heavier or
lighter), using direct comparison or nonstandard units of
measure (e.g., book, cubes, new pencil, paper clip, block).
Compare and describe temperatures of two objects or
environment (as hotter or colder), using direct comparison.
FOCUS K–3 STRAND: GEOMETRY GRADE LEVEL K
Children begin to develop geometric and spatial knowledge before beginning school, stimulated by the exploration of figures and structures in their
environment. Geometric ideas help children systematically represent and describe their world as they learn to represent plane and solid figures
through drawing, block constructions, dramatization, and verbal language.
The focus of instruction at this level is on
observing, identifying, describing, comparing, contrasting, and investigating solid objects and their faces;
sorting objects and ordering them directly by comparing them one to the other;
describing, comparing, contrasting, sorting, and classifying figures; and
exploring symmetry, congruence, and transformation.
In the primary grades, children begin to develop basic vocabulary related to figures but do not develop precise meanings for many of the terms they
use until they are thinking beyond Level 2 of the van Hiele theory (see below).
The van Hiele theory of geometric understanding describes how students learn geometry and provides a framework for structuring student
experiences that should lead to conceptual growth and understanding.
Level 0: Pre-recognition. Geometric figures are not recognized. For example, students cannot differentiate between three-sided and four-sided
polygons.
Level 1: Visualization. Geometric figures are recognized as entities, without any awareness of parts of figures or relationships between
components of a figure. Students should recognize and name figures and distinguish a given figure from others that look somewhat the same.
(This is the expected level of student performance during grades K and 1.)
Level 2: Analysis. Properties are perceived but are isolated and unrelated. Students should recognize and name properties of geometric figures.
(Students are expected to transition to this level during grades 2 and 3.
K.11 The student will
a) identify, describe, and trace plane geometric figures (circle, triangle, square, and rectangle); and
b) compare the size (larger, smaller) and shape of plane geometric figures (circle, triangle, square, and rectangle).
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
An important part of the geometry strand in grades K
through 2 is the naming and describing of figures.
Children move from their own vocabulary and
begin to incorporate conventional terminology as
the teacher uses geometric terms.
A plane geometric figure is any plane, closed figure.
Circles and polygons are examples of plane
geometric figures.
Presentation of triangles, rectangles, and squares
should be made in a variety of spatial orientations
so that students do not develop the common
misconception that triangles, rectangles, and
squares must have one side parallel to the bottom
of the page on which they are printed.
The van Hiele theory of geometric understanding
describes how students learn geometry and
provides a framework for structuring student
experiences that should lead to conceptual growth
and understanding.
Level 0: Pre-recognition. Geometric figures
are not recognized. For example, students
cannot differentiate between three-sided
and four-sided polygons.
Level 1: Visualization. Geometric figures are
recognized as entities, without any
awareness of parts of figures or
relationships between components of a
figure. Students should recognize and
name figures and distinguish a given
figure from others that look somewhat the
same (e.g., “I know it’s a rectangle
because it looks like a door, and I know
All students should
Use their knowledge of plane figures to help them
systematically represent and describe their
world.
Identify the characteristics of plane geometric
figures (circle, triangle, square, and
rectangle).
Compare the size and shape of plane
geometric figures by using strategies to sort
and/or group and begin to refine the
vocabulary used to explain their strategies.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Identify a circle, triangle, square, and rectangle.
Describe the characteristics of triangles, squares, and
rectangles, including number of sides and number of
angles.
Describe a circle using terms such as round and curved.
Trace a circle, triangle, square, and rectangle.
Compare and group plane geometric figures (circle, triangle,
square, and rectangle) according to their relative sizes
(larger, smaller).
Compare and group plane geometric figures (circle, triangle,
square, and rectangle) according to their shapes.
Distinguish between examples and nonexamples of identified
geometric figures (circle, triangle, square, and rectangle).
K.11 The student will
a) identify, describe, and trace plane geometric figures (circle, triangle, square, and rectangle); and
b) compare the size (larger, smaller) and shape of plane geometric figures (circle, triangle, square, and rectangle).
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
that a door is a rectangle.”)
Level 2: Analysis. Properties are perceived,
but are isolated and unrelated. Students
should recognize and name properties of
geometric figures (e.g., “I know it’s a
rectangle because it is closed; it has four
sides and four right angles.”).
A polygon is a geometric figure that
has sides that are line segments;
is simple (its sides do not cross);
is closed; and
is two-dimensional (lies in a plane).
A triangle is a polygon with three angles and three
sides. Children should be shown different types of
triangles such as equilateral, isosceles, scalene,
right, acute, and obtuse; however, they are not
expected to name the various types.
A quadrilateral is a polygon with four sides.
A rectangle is a quadrilateral with four right angles.
A square is a rectangle with all four sides of equal
length.
A circle is a closed curve with all points in one plane
and the same distance from a fixed point (the
center).
Early experiences with comparing and sorting figures
assist students in analyzing the characteristics of
plane geometric figures.
K.11 The student will
a) identify, describe, and trace plane geometric figures (circle, triangle, square, and rectangle); and
b) compare the size (larger, smaller) and shape of plane geometric figures (circle, triangle, square, and rectangle).
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Attribute blocks, relational attribute blocks, and
tangrams are among the manipulatives that are
particularly appropriate for sorting and comparing
size.
Clay, straws, and paper and scissors are
several manipulatives that are appropriate
for constructing geometric figures.
K.12 The student will describe the location of one object relative to another (above, below, next to) and identify representations of
plane geometric figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Representations of circles, squares, rectangles, and
triangles can be found in the students’
environment at school and at home. Students
should have opportunities to identify/classify
things in their environment by the type of figures
those things represent.
Children are often confused when a figure such as a
square is rotated: they frequently refer to the
rotated square as a diamond. Clarification needs
to be ongoing — i.e., a square is a square
regardless of its location in space; there is no such
geometric figure as a diamond.
All students should
Understand that objects can have different
orientations in space.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Identify pictorial representations of a circle, triangle, square,
and rectangle, regardless of their position and orientation
in space.
Describe the location of one object relative to another, using
the terms above, below, and next to.
FOCUS K–3 STRAND: PROBABILITY AND STATISTICS GRADE LEVEL K
Students in the primary grades have a natural curiosity about their world, which leads to questions about how things fit together or connect. They
display their natural need to organize things by sorting and counting objects in a collection according to similarities and differences with respect to
given criteria.
The focus of probability instruction at this level is to help students begin to develop an understanding of the concept of chance. They experiment with
spinners, two-colored counters, dice, tiles, coins, and other manipulatives to explore the possible outcomes of situations and predict results. They
begin to describe the likelihood of events, using the terms impossible, unlikely, equally likely, more likely, and certain.
The focus of statistics instruction at this level is to help students develop methods of collecting, organizing, describing, displaying, and interpreting
data to answer questions they have posed about themselves and their world.
K.13 The student will gather data by counting and tallying.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Data are pieces of information collected about people
or things. The primary purpose of collecting data
is to answer questions.
Tallying is a method for gathering information. Tally
marks are used to show how often something
happens or occurs. Each tally mark represents one
occurrence. Tally marks are clustered into groups
of five, with four vertical marks representing the
first four occurrences and the fifth mark crossing
the first four on a diagonal to represent the fifth
occurrence.
When data are presented in an organized manner,
students can describe the results of their
investigation (i.e., identifying parts of the data
that have special characteristics, including
categories with the greatest, the least, or the same
number of responses).
In the process of gathering data, students make
decisions about what is relevant to their
investigation (e.g., when collecting data on their
classmates’ favorite pets, deciding to limit the
categories to common pets).
When students begin to collect data, they recognize
the need to categorize, which helps develop the
understanding of “things that go together.”
Categorical data are used when constructing
picture graphs and bar graphs.
All students should
Pose questions and gather data.
Understand how data are collected and presented
in an organized manner by counting and
tallying.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Use counting and tallying to gather data on categories
identified by the teacher and/or student (e.g., favorites,
number of days of various types of weather during a given
month, types of pets, types of shoes).
K.14 The student will display gathered data in object graphs, picture graphs, and tables, and will answer questions related to the
data.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Object graphs are graphs that use concrete materials to
represent the categorical data that are collected
(e.g., cubes stacked by the month, with one cube
representing the birthday month of each student).
Picture graphs are graphs that use pictures to show
and compare information.
Tables are an orderly arrangement of data in which the
data are arranged in columns and rows in an
essentially rectangular format. Tables may be
used to display some type of numerical
relationship or organized lists (e.g., input/output
functions, tables showing one candy costs five
cents and two candies cost 10 cents).
Students represent data to convey results of their
investigations at a glance, using concrete objects,
pictures, and numbers to give a “picture” of the
organized data.
When data are displayed in an organized manner,
children can describe the results of their
investigations.
Graphs can be used to make connections between
mathematics and social studies and/or science
(e.g., job areas and the different people that work
in these areas: health — doctors and nurses;
education — teachers and principals).
Statements representing an analysis and interpretation
of the characteristics of the data in the graph (e.g.,
similarities and differences, least and greatest, the
categories, and total number of responses) should
be asked.
All students should
Understand that data can be represented using
concrete objects, pictures, and graphs.
Understand that different types of representations
emphasize different things about the same
data.
Understand that picture graphs use pictures to
show and compare information; object graphs
use concrete materials to represent
categorical data; and tables can be used to
show an orderly arrangement of data in
columns and rows.
Answer questions related to the gathered data
from object graphs, picture graphs, and
tables.
Relate their ideas about the data to concepts such
as part-part-whole and number relationships.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Display data by arranging concrete objects into organized
groups to form a simple object graph.
Display gathered data, using pictures to form a simple picture
graph (e.g., a picture graph of the types of shoes worn by
students on a given day).
Display gathered data in tables, either in rows or columns.
Answer questions related to the gathered data displayed in
object graphs, picture graphs, and tables by:
Describing the categories of data and the data as a
whole (e.g., the total number of responses) and its
parts.
Identifying parts of the data that represent numerical
relationships, including categories with the greatest,
the least, or the same.
FOCUS K–3 STRAND: PATTERNS, FUNCTIONS, AND ALGEBRA GRADE LEVEL K
Stimulated by the exploration of their environment, children begin to develop concepts related to patterns, functions, and algebra before beginning
school. Recognition of patterns and comparisons are important components of children’s mathematical development.
Students in kindergarten through third grade develop the foundation for understanding various types of patterns and functional relationships through
the following experiences:
sorting, comparing, and classifying objects in a collection according to a variety of attributes and properties;
identifying, analyzing, and extending patterns;
creating repetitive patterns and communicating about these patterns in their own language;
analyzing simple patterns and making predictions about them;
recognizing the same pattern in different representations;
describing how both repeating and growing patterns are generated; and
repeating predictable sequences in rhymes and extending simple rhythmic patterns.
The focus of instruction at the primary level is to observe, recognize, create, extend, and describe a variety of patterns. These students will experience
and recognize visual, kinesthetic, and auditory patterns and develop the language to describe them orally and in writing as a foundation to using
symbols. They will use patterns to explore mathematical and geometric relationships and to solve problems, and their observations and discussions of
how things change will eventually lead to the notion of functions and ultimately to algebra.
K.15 The student will sort and classify objects according to attributes.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
To classify is to arrange or organize a set of materials
according to a category or attribute (a quality or
characteristic). An object has many attributes
such as color, size, shape, thickness, etc.
General similarities and differences among objects are
easily observed by children entering kindergarten,
who are able to focus on any one attribute. The
teacher’s task is to move students toward a more
sophisticated understanding of classification in
which two or more attributes connect or
differentiate sets, such as those found in nature
(e.g., leaves with different colors and different
figures).
All students should
Understand that the same set of objects can be
sorted and classified in different ways.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Sort objects into appropriate groups (categories) based on one
attribute.
Classify sets of objects into groups (categories) of one attribute.
Label attributes of a set of objects that has been sorted.
Name multiple ways to sort a set of objects.
K.16 The student will identify, describe, and extend repeating patterns.
UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)
ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS
Pattern recognition is a fundamental cornerstone of
mathematics, particularly algebra.
In a repeating pattern, the core of the pattern is the
string of elements that repeats. By identifying the
core, students demonstrate their understanding of
the pattern.
Students should recognize that the sound pattern
‘snap, clap, snap, clap’ is the same in form as the
color pattern ‘red, blue, red, blue’.
Pattern recognition and the extension of the pattern
allow students to make predictions.
The simplest types of patterns are repeating patterns.
The patterns can be oral, such as the refrain in
“Old MacDonald’s Farm” (“e-i-e-i-o”), or
physical with clapping and snapping patterns, or
combinations of both, such as is found in songs
like the “Hokey Pokey.” In each case, students
need to identify the basic unit of the pattern and
repeat it. Opportunities to create, recognize,
describe, and extend repeating patterns are
essential to the primary school experience.
Sample repeating patterns (repeating the core) are
ABABABAB;
ABCABC;
AABBAABBAABB;
AABAAB;
AABCAABC; and
ABACABAC.
All students should
Understand that patterns are a way to recognize
order and organize their world and to predict
what comes next in an arrangement.
Understand that the sound pattern ‘snap, clap,
snap, clap’ is the same in form as the color
pattern ‘red, blue, red, blue’.
The student will use problem solving, mathematical
communication, mathematical reasoning, connections, and
representations to
Observe and identify the basic repeating pattern (core) found in
repeating patterns of common objects, sounds, and
movements that occur in practical situations.
Identify the core in a repeating pattern.
Extend a repeating pattern by adding at least two repetitions to
the pattern.
Create a repeating pattern.
Compare similarities and differences between patterns.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
Learning Progressions The following pages are the Learning Progressions for the curriculum. More information about the Learning Progressions can be found on VISION. The Grading and Assessment, Module 3: Learning Progressions is about what Learning Progressions are, how they were developed, and how they are used to support instruction and build student learning.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.1 SOL K.1: The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence. Learning Target: I can compare two sets of objects and describe a set as having more, fewer, or the same quantity of objects. I can create a set of objects which has more, fewer, or the same quantity as a given set.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can count the objects in the two sets and compare the two sets by describing the number as greater than, less than, or the same. *Students begin to develop an understanding of the values associated with numbers.
Proficient
I can compare two sets of objects and describe a set as having more, fewer, or the same quantity of objects. I can create a set of objects which has more, fewer, or the same quantity as a given set.
Intermediate
I can describe two sets of objects as having the same quantity or not.
Beginner
I can match the members from one set to the members of the other set.* *This develops the strategy of one-to-one matching to compare sets and one-to-one correspondence when two sets have an equal number of items.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.2 SOL K.2: The student, given a set containing 15 or fewer concrete objects, will
a) tell how many are in the set by counting the number of objects orally; b) write the numeral to tell how many are in the set; and c) select the corresponding numeral from a given set of numerals.
Learning Target: I can identify the number of objects in a set by counting the objects orally, selecting the numeral, and writing the numeral that matches the number of objects in the set. I can create a set of objects that matches a number from 0 through 15.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can create a set of objects that is greater than or less than a given number, or I can select or write a number that is greater than or less than a given number.* *This LT focuses on writing or selecting a number equal to the quantity in a set. The Advanced Proficient level extends this to identifying the relationship
between numbers by exploring greater than or less than a given number.
Proficient
I can identify the number of objects in a set by counting the objects orally, selecting the numeral, and writing the numeral that matches the number of objects in the set. I can create a set of objects that matches a number from 0 through 15.
Intermediate
I can recognize, select, and write the numerals that match the numbers I am counting.
Beginner
I can count orally from 0 through 15. I understand that the numbers I am counting tells me how many objects are in a set.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.3 SOL K.3: The student, given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object. Learning Target: I can identify the ordinal positions for each object in a set of 10 objects that are in order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top).
Learning Progression
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can identify the ordinal positions for each object in a set of objects that are placed in order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top), and at any starting point in the set. For example:
Proficient
I can identify the ordinal positions for each object in a set of 10 objects that are in order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top).
Intermediate
I can count* the ten objects that are placed in an order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top). *This is about cardinal numbers or counting numbers.
Beginner
I can organize a set of ten objects in order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top).
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.4ac SOL K.4: The student will:
a) count forward to 100 and backward from 10; c) count by fives and tens to 100.
Learning Target: I can count forward to 100 by ones, fives, and tens and I can count backward from 10. I can identify the patterns of counting by ones, fives, and tens using different models (hundreds chart, number line, etc.).
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can relate counting to 100 in different ways and counting backwards from 10 to real-life situations (counting money, rocket launch, etc.).
Proficient
I can count forward to 100 by ones, fives, and tens and I can count backward from 10. I can identify the patterns of counting by ones, fives, and tens using different models (hundreds chart, number line, etc.).
Intermediate
I can understand that I can count in equal groups to get to the target number more quickly.
Beginner
I can count to 100 by ones and backward from 10.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.4b SOL K.4: The student will: b) identify one more than a number and one less than a number. Learning Target: I can identify one more than a number and one less than a number and show the relationship using objects.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can identify two more than a number, two less than a number, three more than a number, three less than a number, and show the relationship using objects.
Proficient
I can identify one more than a number and one less than a number and show the relationship using objects.
Intermediate
I can identify one more than a given number and one less than a given number on a hundreds chart or a number line.
Beginner
I can count the number of objects in a set and identify that number on a hundreds chart or a number line.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.5 SOL K.5: The student will identify the parts of a set and/or region that represent fractions for halves and fourths. Learning Target: I can show (represent) halves and fourths as parts of sets and parts of regions.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can represent fourths as parts of halves.
Proficient I can show (represent) halves and fourths as parts of sets and parts of regions.
Intermediate I can show (represent) fourths as parts of a region and as part of a set by using manipulatives..
Beginning I can show (represent) halves as parts of a region and part of a set by using manipulatives.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.6 SOL K.6: The studentwill model adding and subtracting whole numbers, using up to 10 concrete objects. Learning Target: I can use manipulative to model and describe addition and subtraction.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can describe how addition and subtraction are alike and how they are different.
Proficient I can use manipulatives to model and describe addition and subtraction.
Intermediate I can take away a set of objects from a given set and use counting backward OR counting on to find the difference.
Beginning I can combine two sets of concrete objects and count on to find a sum.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.7 SOL K.7: The student will recognize a penny, nickel, dime, and quarter and will determine the value of a collection of pennies and/or nickels whose total value is 10 cents or less. Learning Target: I can identify and describe a penny, nickel, dime, and quarter and determine the value of a collection of coins (10 cents or less)
and equivalent amounts (a nickel is the same as 5 pennies).
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can create a collection of coins based on clues (for example: Create a collection of coins whose value is 23 cents and includes at least 2 nickels).
Proficient
I can identify and describe a penny, nickel, dime, and quarter and determine the value of a collection of coins (10
cents or less) and equivalent amounts (a nickel is the same as 5 pennies).
Intermediate
I can recognize and identify a penny, nickel, dime, and quarter.
Beginner
I can understand that coins represent a specific value of money.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.8 SOL K.8: The student will identify the instruments used to measure length (ruler), weight( scale), time (clock: digital and analog; calendar: day, month, and season), and temperature (thermometer). Learning Target: I can identify instruments used to measure length, weight, time, and temperature.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can identify a non-standard instrument to measure length, weight, and/or temperature.
Proficient
I can identify instruments used to measure length, weight, time, and temperature.
Intermediate
I can identify the instruments that are used for measurement. (i.e. I can identify a ruler, a scale, a clock, a calendar, and a thermometer).
Beginner
I understand that length, weight, time, and temperature can be measured.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.9 SOL K.9: The student will tell time to the hour, using analog and digital clocks. Learning Target: I can tell time to the hour on an analog and digital clock and relate the time to daily routines.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can name a time based on clues (for example: What time of day could it be if the hour hand is on the 6 and you are eating dinner?).
Proficient
I can tell time to the hour on an analog and digital clock and relate the time to daily routines.
Intermediate
I can use the hour hand on an analog clock to determine time to the nearest hour.
Beginner
I can recognize an analog and digital clock as a tool to measure time.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.10 SOL K.10: The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: Length (shorter, longer), height (shorter, taller), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block. Learning Target: I can compare and measure objects using foot length, hand span, new pencil, paper clip, and/or block.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can investigate how nonstandard units may be equivalent; i.e. how many hand spans “equal” a foot length?
Proficient I can compare and measure objects using foot length, hand span, new pencil, paper clip, and/or block.
Intermediate I can measure objects using foot length, hand span, new pencil, paper clip, and/or block and tell how many measures the object is (3 hand spans, 2 foot lengths).
Beginning I can compare objects and tell which is longer, taller, heavier, hotter.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.11a SOL K.11: The student will:
a) identify, describe, and trace plane geometric figures (circle, triangle, square, and rectangle); and…
Learning Target: I can name geometric shapes and tell how they are different.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can tell how squares and rectangles are different and how they are alike.
Proficient I can name geometric shapes and tell how they are different.
Intermediate I can describe the size of bgeometric shapes.
Beginning I can sort, identify, and trace geometric shapes.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.11b SOL K.11: The student will: b) compare the size (larger, smaller) and shape of geometric figures (circle, triangle, square, and rectangle). Learning Target: I can tell (compare) which shape is larger and which is smaller.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can put three or more shapes in order by size.
Proficient I can tell (compare) which shape is larger and which is smaller.
Intermediate I can tell (compare) which shape is larger.
Beginning I can tell (compare) which shape is smaller.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.12 SOL K.12: The student will describe the location of one object relative to another and identify representations of plane geometric figures regardless of their positions in space. Learning Target: I can describe the location of one object relative to another and identify representations of plane geometric figures regardless of their positions in space.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can place an object above or below or next to another object.
Proficient
I can identify a triangle, circle, square, and rectangle and describe if one of them is above or below or next to another one.
Intermediate I can identify a triangle, circle, square, and rectangle.
Beginning I can describe an object as above or below or next to another object.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.13 SOL K.13: The student will gather data by counting and tallying. Learning Target: I can collect answers to a question, keep track of the answers by using tally marks, and organize the answers in categories.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can combine my data with another set of data for the same question and show the combined data by counting and tallying.
Proficient
I can collect answers to a question, keep track of the answers by using tally marks, and organize the answers in categories.
Intermediate
I can gather data for a question (i.e. Did you bring lunch? How many pets do you have? What type of shoes are you wearing?).
Beginner
I can count by fives and use tally marks to represent the different numbers.
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.14 SOL K.14: The student will display gathered data in object graphs, picture graphs, and tables, and will answer questions related to the data. Learning Target: I can analyze data I have displayed in graphs and tables.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can create multiple ways to represent data and develop questions to analyze the data.
Proficient I can analyze data I have displayed in graphs and tables.
Intermediate I can display data using pictures as counting devices.
Beginning I can display data by arranging manipulatives/objects or into groups (object graph).
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.15 SOL K.15: The student will sort and classify objects according to attributes. Learning Target: I can sort and classify a set of objects in at least two different ways and explain my reasoning.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can sort and classify a set of objects in multiple ways and justify the most efficient way for a real-life situation (for example, sorting food at a grocery store).
Proficient
I can sort and classify a set of objects in at least two different ways and explain my reasoning.
Intermediate
I can sort and classify a set of objects in at least one way.
Beginner
I can identify characteristics of objects (color, size, shape, etc.).
Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K
LP K.16 SOL K.16: The student will identify, describe, and extend repeating patterns. Learning Target: I can compare the similarities and differences between patterns.
Learning Progression The student will use problem solving, mathematical communication,
mathematical reasoning, connections, and representations at each level of the learning progression.
Advanced Proficient
I can find examples of repeating patterns in real life situations and connect it to other repeating patterns. (i.e. the colors on a checkerboard – red, black, red, black is a repeating pattern that looks like the AB-AB pattern)
Proficient
I can compare the similarities and differences between patterns.
Intermediate
I can identify the core of a repeating pattern and extend the pattern (by two repetitions or more).
Beginner
I can recognize repeating patterns around me and in practical situations.
NCSM Great Tasks K-5 (available in all LCPS Elementary Schools)
VA SOL Alignment
Kindergarten Math
Domino Addition and Subtraction
Launch
SOL K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; b) write the numeral to tell how many are in the set; and c) select the corresponding numeral from a given set of numerals.
Activity
SOL K.1 The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.
Counting Sheep
Launch
SOL K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; d) write the numeral to tell how many are in the set; and e) select the corresponding numeral from a given set of numerals.
Activity SOL K.3 The student, given an ordered set of ten objects and/or
pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object.
How Big is Your Foot?
Launch & Activity
SOL K.10 The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block.
1st Grade Math
Bunny Hip Hop
Launch
SOL 1.1 The student will a) count from 0 to 100 and write the corresponding numerals;
and b) group a collection of up to 100 objects into tens and ones and
write the corresponding numeral to develop an understanding of place value.
Activity
SOL 1.2 The student will count forward by ones, twos, fives, and tens to 100 and backward by ones from 30.
When does it Happen?
Launch & Activity
SOL 1.8 The student will tell time to the half-hour, using analog and digital clocks.
Ten is our Friend!
Launch
SOL 1.5 The student will recall basic addition facts with sums to 18 or less and the corresponding subtraction facts.
Activity SOL 1.6 The student will create and solve one-step story and picture
problems using basic addition facts with sums to 18 or less and the corresponding subtraction facts.
2nd Grade Math
Creative Cards
Launch & Activity
SOL 2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism).
Piggy Banks
Launch & Activity
SOL 2.10 The student will a) count and compare a collection of pennies, nickels, dimes, and
quarters whose total value is $2.00 or less; and b) correctly use the cent symbol (¢), dollar symbol ($), and
decimal point (.).
Show What You Know!
Launch
SOL 2.2 The student will a) identify the ordinal positions first through twentieth, using an
ordered set of objects; and b) write the ordinal numbers.
Activity
SOL 2.8 The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs.
SOL 2.9 The student will recognize and describe the related facts that represent and describe the inverse relationship between addition and subtraction.
Pies for Sale
Launch SOL 2.19 The student will analyze data displayed in picture graphs,
pictographs, and bar graphs.
Activity
SOL 2.17 The student will use data from experiments to construct picture graphs, pictographs, and bar graphs.
SOL 2.19 The student will analyze data displayed in picture graphs, pictographs, and bar graphs.
3rd Grade Math
Playful Puppies
Launch
SOL 3.10 The student will a) measure the distance around a polygon in order to determine
perimeter; and b) count the number of square units needed to cover a given
surface in order to determine area.
SOL 3.20 The student will a) investigate the identity and the commutative properties for
addition and multiplication; and b) identify examples of the identity and commutative properties
for addition and multiplication.
Activity
SOL 3.5 The student will recall multiplication facts through the twelves table, and the corresponding division facts.
SOL 3.6 The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.
SOL 3.10 The student will a) measure the distance around a polygon in order to determine
perimeter; and b) count the number of square units needed to cover a given
surface in order to determine area.
SOL 3.20 The student will a) investigate the identity and the commutative properties for
addition and multiplication; and b) identify examples of the identity and commutative properties
for addition and multiplication.
Correcting the Calculator
Launch & Activity
SOL 3.1 The student will a) read and write six-digit numerals and identify the place value
and value of each digit; b) round whole numbers, 9,999 or less, to the nearest ten,
hundred, and thousand; and c) compare two whole numbers between 0 and 9,999, using
symbols (>, <, or = ) and words (greater than, less than, or equal to).
SOL 3.2 The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences. The student will use these relationships to solve problems.
Fraction Reactions
Launch & Activity
SOL 3.3 The student will a) name and write fractions (including mixed numbers)
represented by a model; b) model fractions (including mixed numbers) and write the
fractions’ names; and c) compare fractions having like and unlike denominators, using
words and symbols (>, <, or =).
4th Grade Math
Bugs, Giraffes, Elephants, and More
Launch
SOL 4.2 The student will a) compare and order fractions and mixed numbers; b) represent equivalent fractions; and c) identify the division statement that represents a fraction.
SOL 4.7 The student will a) estimate and measure length, and describe the result in
both metric and U.S. Customary units; and b) identify equivalent measurements between units within
the U.S. Customary system (inches and feet; feet and yards; inches and yards; yards and miles) and between units within the metric system (millimeters and centimeters; centimeters and meters; and millimeters and meters).
SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs.
Activity
SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs.
Does it Make Sense?
Launch
SOL 4.3 The student will a) read, write, represent, and identify decimals expressed
through thousandths; b) round decimals to the nearest whole number, tenth, and
hundredth; c) compare and order decimals; and
SOL 4.4 The student will a) estimate sums, differences, products, and quotients of whole
numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without
remainders; and d) solve single-step and multistep addition, subtraction, and
multiplication problems with whole numbers.
Activity
SOL 4.4 The student will a) estimate sums, differences, products, and quotients of whole
numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without
remainders; and d) solve single-step and multistep addition, subtraction, and
multiplication problems with whole numbers.
The Bigger Half
Launch & Activity
SOL 4.2 The student will a) compare and order fractions and mixed numbers; b) represent equivalent fractions; and c) identify the division statement that represents a fraction.
Harry’s Hike
Launch
SOL 4.2 The student will a) compare and order fractions and mixed numbers; b) represent equivalent fractions; and c) identify the division statement that represents a fraction.
Activity
SOL 4.5 The student will a) determine common multiples and factors, including least
common multiple and greatest common factor; b) add and subtract fractions having like and unlike
denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractions, using common multiples and factors;
c) add and subtract with decimals; and d) solve single-step and multistep practical problems involving
addition and subtraction with fractions and with decimals.
5th Grade Math
Packed Parking
Launch
SOL 5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.
Activity
SOL 5.5 The student will a) find the sum, difference, product, and quotient of two numbers
expressed as decimals through thousandths (divisors with only one nonzero digit); and
b) create and solve single-step and multistep practical problems involving decimals.
SOL 5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.
Finding Fractions
Launch
SOL 5.2 The student will a) recognize and name fractions in their equivalent decimal form
and vice versa; and b) compare and order fractions and decimals in a given set from
least to greatest and greatest to least.
Activity
SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.
SOL 5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical
relationship, using a variable; c) model one-step linear equations in one variable, using addition
and subtraction; and d) create a problem situation based on a given open sentence,
using a single variable.
SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition.
Varying Volumes
Launch & Activity
SOL 5.8 The student will a) find perimeter, area, and volume in standard units of measure; b) differentiate among perimeter, area, and volume and identify
whether the application of the concept of perimeter, area, or volume is appropriate for a given situation;
c) identify equivalent measurements within the metric system; d) estimate and then measure to solve problems, using U.S.
Customary and metric units; and e) choose an appropriate unit of measure for a given situation
involving measurement using U.S. Customary and metric units.
SOL 5.13 The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will
a) develop definitions of these plane figures; and b) investigate and describe the results of combining and
subdividing plane figures.
Location, Location, Location
Launch
SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.
Activity
SOL 5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical
relationship, using a variable; c) model one-step linear equations in one variable, using addition
and subtraction; and d) create a problem situation based on a given open sentence,
using a single variable.
SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition.
Mathematics Literature Connections Organized by Curriculum Units
Grade K Math Literature Connections
Unit 2: Counting
One, Two, Skip a Few: First Number Rhymes by Roberta Arenson
98,99,100! Ready or Not, Here I come! by Marilyn Bums and Teddy Slater
Unit 3: Comparing Sets
20 Hungry Piggies: A Number Book by Trudy Harris
Ten Little Rubber Ducks by Eric Carle
Ten Little Caterpillars by Bill Martin Jr
Henry the Fourth by Stuart J. Murphy
One Monday Morning by Uri Shulevitz
The Napping House by Audrey Wood
Tally O’Malley by Stewart J. Murphy
So you want to be President? By Judith St. George
The Great Graph Contest By Loreen Leedy
Unit 4: Geometry & Sorting
Dave’s Down-to-Earth Rock Shop by Stuart J. Murphy
Unit 5: Shapes in Space
Twizzlers Shapes and Patterns by Jerry Pallotta
Unit 6: Geometry & Fractions
Give Me Half by Stuart J. Murphy
Full House by Dayle Ann Dodds
Unit 7: Measuring My World
Measuring Up by J.E. Osborne
Dumpling Soup by Jama Kim Rattigan
How Big is a Foot by Rolf Myller
Big and Little by Steven Jenkins
Time to… by Bruce McMillan
Telling Time: How to Tell Time on Digital and Analog Clocks by Jules Older
Telling Time with Big Mama Cat by D. Harper
Biggest, Strongest, Fastest by Steven Jenkins
Inch by Inch by Leo Lionni
Before and After: A Book of Nature Timescapes by Jan Thornhill
Unit 8: Skip Counting & Money
Arctic Fives Arrive by Elinor J. Pinczes
26 Letters and 99 Cents by Tana Hoban
Unit 9: Combining & Separating
More or Less by Stuart J. Murphy
Animals on Board by Stuart J. Murphy
A Quarter from the Tooth Fairy by Caren Holtzman
Grade 1 Math Literature Connections
Unit 2: Sorting, Ordering, & Patterns
Twizzlers Shapes and Patterns by Jerry Pallotta
Unit 3: Developing a Base Ten System
Moira’s Birthday by Robert Munsch
Something Good by Robert Munsch
Is It Larger? Is It Smaller? By T. Hoban
One Hundred Hungry Ants by Elinor J. Pinczes
Ten Sly Piranhas: A Counting Story in Reverse by William Wise
How Many, How Many, How Many by Rick Walton
98, 99, 100! Ready or Not, Here I Come! By Marilyn Burns and Teddy Slater
Stay in Line by Teddy Slater
Unit 4: Geometry & Fractions
Three Pigs, One Wolf, and Seven Magic Shapes by Grace Maccarone
Flat Stanley by J. Brown
The Shapes We Eat by Simone T. Ribke
Give Me Half! By Stuart J. Murphy
Gator Pie by L. Mathews
Unit 5: Time & Fractions
Give Me Half by Stuart J. Murphy
Telling Time: How to Tell Time on Digital and Analog Clock by Jules Older
Before and After: A Book of Nature Timescapes by Jan Thornhill
Unit 6: Working With Data
Probably Pistachio by Stuart J. Murphy
So You Want to be President? By Judith St. George
The Great Graph Contest by Loreen Leedy
Ready, Set, Hop! By Stuart J. Murphy
Bunches and Bunches of Bunnies by Mathews and Bassett
Unit 7: Combining & Separating
Rooster’s Off to See the World by Eric Carle
Round Trip by A. Jonas
Lemonade For Sale by Stuart J. Murphy
Unit 8: Measuring My World
How Do You Measure Weight? by Thomas K. and Heather Adamson
The Greedy Triangle by Marilyn Burns
Dumpling Soup by Jama Kim Rattigan
How Big is a Foot? by Rolf Myller
Big and Little by Steven Jenkins
Biggest, Strongest, Fastest by Steven Jenkins
Inch by Inch by Leo Lionni
More or Less by Stuart J. Murphy
Best Bug Parade by Stuart J. Murphy
Me and the Measure of Things by J. Sweeney
Unit 9: Applying Place Value
Shoes, Shoes, Shoes by A. Morris
Unit 10: Whole Number Computation
Animals on Board by Stuart J. Murphy
Elevator Magic by Stuart J. Murphy
Ten Black Dots by Donald Crew
Rooster’s Off to See the World by Eric Carle
Elevator Magic by Stuart J. Murphy
How High Can a Dinosaur Count? by V. Fisher
Unit 11: Skip Counting & Money
The Penny Pot by Stuart J. Murphy
Grade 2 Math Literature Connections
Unit 2: Extending Place Value
The Crayon Counting Book by Pam Munoz
Underwater Counting: Even Numbers by Jerry Pallotta
Unit 3: Computational Fluency
Growing Patterns: Fibonacci Numbers in Nature by S.G. and R.P. Campbell
Mission: Addition by Loreen Leedy
Each Orange Had 8 Slices: A Counting Book by Paul Giganti
Elevator Magic by Stuart J. Murphy
Unit 4: Applying Place Value to Computation/Problem Solving
Great Estimations by Bruce Goldstone
How Many Seeds in a Pumpkin? By Margaret McNamara and G. Brian Karas
How Many Feet? How Many Tails? A Book of Math Riddles by Marilyn Burns
Sam and the Lucky Money by K. Chinn
Balancing Act by Ellen Stoll Walsh
Betcha by Stuart J. Murphy
Unit 5: Probability & Data
Frog and Toad are Friends by A. Lobel
Polar Bear Math: Learning About Fractions from Klondike and Snow by Nagda and Bickel
Get Up and Go! By Stuart J. Murphy
Unit 6: Data & Problem Solving
So You Want to be President? By Judith St. George
Unit 7: Time & Temperature
Telling Time: How to Tell Time on Digital and Analog Clock by Jules Older
Before and After: A Book of Nature Timescapes by Jan Thornhill
Why Mosquitoes Buzz in People’s Ears: A West African Tale by V. Aardema
The Grouchy Lady Bug by Eric Carle
Chimp Math: Learning About Time from a Baby Chimpanzee by Nagda and Bickel
What Time Is It? A Book of Math Riddles by Sheila Keenan
Unit 8: Geometry & Fractions
Eating Fractions by Bruce McMillan
Give Me Half by Stuart J. Murphy
Full House by Dayle Ann Dodds
The Patchwork Quilt by Valerie Flournoy
Unit 9: Measuring My World
Inch by Inch by Leo Lionni
How Big is a Foot? By Rolf Myller
Dumpling Soup by Jama Kim Rattigan
Big and Little by Steven Jenkins
Biggest, Strongest, and Fastest by Steven Jenkins
More or Less by Stuart J. Murphy
Unit 10: Skip Counting & Money
Jelly Beans for Sale by Bruce McMillan
The Penny Pot by Stuart J. Murphy
The Coin Counting Book by Rosanne Lanczak Williams
Once Upon a Dime by Nancy Kelly Allen
Grade 3 Math Literature Connections
Unit 2: Place Value
Many Is How Many? By Illa Pondendorf
A Light in the Attic (“How Many, How Much” and “Overdues”) by Shel Silverstein
Counting on Frank by Rod Clement
How Much Is a Million? by David M. Schwartz
If You Made a Million by David M. Schwartz
Moira’s Birthday by Robert Munsch
Something Good by Robert Munsch
Unit 3: Computation With Whole Numbers (addition/subtraction)
Ten Black Dots by Donald Crews
Dealing with Addition Lynette Long
One Duck Stuck by Phyllis Root
One Gorilla by Atsuko Morozumi
A Three Hat Day by Laura Geringer
Unit 4: Money
Alexander, Who Used To Be Rich Last Sunday by Judith Viorst
Penny: The Forgotten Coin by Denise Brenna-Nelson
The Coin Counting Book by Rozanne Lanczak Williams
The Penny Pot by Stuart Murphy
Pigs Will Be Pigs: Fun With Math and Money by Amy Axelrod
Unit 5: Computation With Whole Numbers (multiplication/division)
Amanda Bean’s Amazing Dream by Cindy Neuschwander
A Remainder of One (*extension) by Elinor J. Pinczes
One Hundred Angry Ants by Elinor J. Pinczes
2 x 2 = Boo by Loreen Leedy
7 x 9 Trouble by Claudia Mills
Too Many Kangaroo Things to Do by Stuart Murphy
Divide and Ride by Stuart Murphy
Bananas Jacqueline Farmer
Centipede’s 100 Shoes by Tony Ross
Ten Times Better by Richard Michelson
Unit 6: Patterns & Data
Emma’s Christmas by Irene Trivias
The Doorbell Rang by Pat Hutchins
One Hundred Angry Ants by Elinor Pinczes
She Came Bringing Me That Little Baby Girl by Eloise Greenfield
Knots on a Counting Rope by Bill Martin Jr.
Berries, Nuts, and Seeds by Diane L. Burns
Lemonade for Sale by Stuart Murphy
Tiger Math: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda
Grapes of Math by Greg Tang
The Quilting Bee by Gail Gibbons
Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee
Unit 7: Geometry
The Important Book by Margaret Wise Brown
Three Pigs, One Wolf, and Severn Magic Shapes by Grace Maccarone
Pablo’s Tree Pat Mora
If You Were a Polygon Marcie Aboff
It Looked Like Spilt Milk by Charles G. Shaw
Mummy Math by Cindy Neuschwander
Shape Up by David Adler
A Cloak for the Dreamer by Aileen Friedman
Unit 8: Fractions, Probability, & Measurement (length) / Unit 9: Computation With Fractions
Eating Fractions by Bruce McMillan
Seven Little Hippos by Mike Thaler
Shoes, Shoes, Shoes by Ann Morris
Biggest, Strongest, Fastest Steve Jenkins
The Wolf’s Chicken Stew Keiko Kasza
A Very Improbably Story: A Math Adventure by Edward Einhorn
The Thirteen Days of Halloween Carool Greene
The Doorbell Rang Pat Hutchins
Whole-y Cow, Fractions are Fun! by Taryn Souders
Apple Fractions by Jerry Pallotta
The Hershey’s Milk Chocolate Bar Fractions BookU by Jerry Pallotta
Fraction Action by Loreen Leedy
Unit 10: Elapsed Time and Temperature
Telling Time: How to Tell Time on Digital and Analog Clocks by Jules Older
What Time is it, Mr. Crocodile? By Judy Sierra
Chimp Math by Ann Whitehead Nagda
Unit 11: Measurement
Spaghetti and Meatballs for All by Marilyn Burns
Perimeter, Area, and Volume David A. Adler
Pastry School in Paris Cindy Neuschwander
Measuring Penny (length) by Loreen Leedy
Biggest, Strongest, Fastest by Steve Jenkins
Is a Blue Whale the Biggest Thing There Is? by Robert E. Wells
Polly’s Pen Pal by Stuart L. Murphy
Spaghetti and Meatballs for All by Marilyn Burns
Room for Ripley by Stuart Murphy
Grade 4 Math Literature Connections
Unit 2: Number Sense: Whole Numbers
A Million Fish…More or Less by Patricia C. McKissack
Unit 3: Whole Number Operations & Applications (adding & subtracting)
Math Curse by Jon Scieszka and Lane Smith
The $1.00 Word Riddle Book by Marilyn Burns
Esio Trot by Roald Dahl
From Seashells to Smart Cards: Money and Currency (everyday economics) by Ernestine
Giesecke
Anno’s Magic Seeds by Mitsumasa Anno
Equal Shmequal by Virginia Kroll
Unit 4: Whole Number Operations & Applications (multiplication & division)
The King’s Chessboard by David Birch
The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan
Math Curse by Jon Scieszka and Lane Smith
Hottest, Coldest, Highest, Deepest by Steve Jenkins
In the Next Three Seconds…Predictions for the Millenium by Comp. Rowland Morgan
Ten Times Better by Richard Michelson
Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee
A Remainder of One by Elinor J. Pinczes
Counting on Frank by Rod Clement
Unit 5: Data & Statistics
The Great Graph Contest by Loreen Leedy
Unit 6: Number Sense: Rational Numbers
The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan
One Riddle, One Answer by Lauren Thompson
Icebergs and Glaciers by Seymour Simon
Tiger Math: Learning to Graph from a Baby Tiger by Ann W. Nagda and Cindy Bickel
Unit 7: Rational Number Operations
Jump, Kangaroo Jump (Math Start) by Stuart Murphy and Kevin O’Malley
Pizza Counting by Christina Dobson
Piece=Part=Portion by Gifford and Thaler
Fractions=Trouble! By Claudia Mills
Unit 8: Probability & Data Using Rational Numbers
Jumanji by Chris Van Allsburg
A Very Improbable Story by Edward Einhorn and Adam Gustavson
Pigs at Odds by Amy Axelrod and Sharon Nally
Unit 9: Patterns & Measurement
G is for Googol: A Math Alphabet Book by David M. Schwartz
How Much, How Many, How Far, How Heavy, How Long, How Tall Is 1000? by Helen
Nolan
Icebergs and Glaciers by Seymour Simon
If You Hopped Like a Frog by David M. Schwartz
Is a Blue Whale the Biggest Thing There Is? By Robert E. Wells
Biggest, Strongest, Fastest by Steve Jenkins
Unit 10: Plane Geometry & Transformations
Marvelous Math by Lee Bennett Hopkins
The Warlord’s Puzzle by Virginia Walton Pilegard
Shape Up! Fun with Triangles and Other Polygons by David Adler and Nancy Tobin
Spaghetti and Meatballs for All! by Marilyn Burns and Debbie Tilley
Chickens on the Move (Math Matters!) by Pamela Pollack
Grade 5 Math Literature Connections
Unit 2
A Remainder of One by Elinor Pinczes
My Even Day by Doris Fisher
The Grapes of Math by Greg Tang
Math Appeal by Greg Tang
Among the Odds and Evens by Prescilla Turner
Spaghetti and Meatballs for All by Marilyn Burns
Unit 3
Germs Make Me Sick by Melvin Berger
Bats on Parade by Kathi Appelt
Unit 4
Alexander Who Used to Be Rich Last Sunday by Judith Viorst
Fraction Fun by David Adler
Unit 5
Measuring Penny by Loreen Leedy
Alexander Who Used to Be Rich Last Sunday by Judith Viorst
Counting On Frank by Rod Clements
How Long? How Wide? by Brian Cleary
Millions to Measure by David Schwartz
Fractions, Decimals, and Percents by David Adler
Unit 6
The Greedy Triangle by Marilyn Burns
Sir Cumference and the Dragon of Pi by Cindy Neuschwander
Unit 7
Chimp Math, Tiger Math, Polar Bear Math, and Cheetah Math (series) by Anne Nagda
A More Perfect Union by Betsy Maestro
Model Performance Indicator Information for Curriculum Guides
Embedded in the LCPS curriculum guides are sample Model Performance Indicator (MPI) tables (below).
These tables will be useful as you differentiate instruction for all of your learners, but they are especially
helpful for English Language Learners. Below are frequently asked questions about MPI.
What is a Model Performance Indicator (MPI)?
An MPI is a tool that can be used to show examples of how language is processed or produced within a
particular context, including the language with which students may engage during classroom instruction and
assessment.
Each MPI contains three main parts:
Language Function: The first part of an MPI, this shows how students are processing/producing
language at each level of language proficiency
Content Stem: This will remain consistent throughout an MPI strand and should reflect the knowledge
and skills of the state’s content standards
Support: The final part of an MPI, this highlights the differentiation that should be incorporated for
students at each language level by suggesting appropriate instructional supports for students at each
level of language proficiency
The samples provided also include an example context for language use that provides a brief descriptor of the
activity or task in which students would be engaged, while the inclusion of topic-related language helps to
support the emphasis on imbedding academic language instruction into our content-area teaching practices.
How can these sample MPIs help me?
Educators can use MPI strands in several ways:
to align students’ performance to levels of language development
as a tool for creating language objectives/targets that will help extend students’ level of language
proficiency
as a means for differentiating instruction that incorporates the language of the content area in a way that
meets the needs of students’ levels of language proficiency
An MPI strand helps illustrate the progression of language development from one proficiency level to the next
within a particular context. As these strands are examples, they represent one of many possibilities; therefore,
they can be transformed in order to be made more relevant to the individual classroom context.
Where can I get more information about WIDA, MPIs, etc.?
See My Learning Plan for several WIDA training modules
Introduction to the WIDA ELD Standards
Transforming the WIDA ELD Standards
Interpreting the WIDA ACCESS Score Report
The information above was adapted from the 2012 Amplification of the English Development Standards Kindergarten-Grade 12 resource guide and can be accessed at www.wida.us
SOL K.13 The student will gather data by counting and tallying.
Example Context for Language Use: Students will count tally marks to organize data gathered on the number of girls and the number of boys in
each of two kindergarten classrooms in the school.
COGNITIVE FUNCTION: Students at all levels of English proficiency will ANALYZE information by counting and tallying data gathered.
LIS
TE
NIN
G
Level 1
Entering
Level 2
Emerging
Level 3
Developing
Level 4
Expanding
Level 5
Bridging
Lev
el 6-R
each
ing
Apply teacher-modeled
oral directions on
counting and tallying
data gathered using
illustrated graphic
organizers in small
groups using L1 or L2
Apply teacher-modeled
oral directions on
counting and tallying
data gathered based on
simple oral commands
in small groups
Organize counting and
tallying data gathered
based on teacher-modeled
oral directions using
illustrated graphic
organizers with a partner
Organize counting and
tallying data gathered
based on teacher-
modeled oral directions
using illustrated graphic
organizers
Organize counting and
tallying data gathered
based on teacher-
modeled oral directions
SP
EA
KIN
G
Describe counting and
tallying data gathered
using teacher modeling,
illustrated graphic
organizers, and
illustrated word banks in
small groups using L1 or
L2
Present counting and
tallying data gathered
using teacher modeling,
illustrated graphic
organizers, and
illustrated word banks
with a partner
Explain counting and
tallying data gathered
using teacher modeling
and illustrated graphic
organizers with a partner
Discuss counting and
tallying data gathered
using illustrated graphic
organizers with a partner
Compare and contrast
counting and tallying
data gathered using
illustrated graphic
organizers with a
partner
RE
AD
ING
Level 1
Entering
Level 2
Emerging
Level 3
Developing
Level 4
Expanding
Level 5
Bridging
Lev
el 6-R
each
ing
Identify counting and
tallying data gathered
using illustrated graphic
organizers and illustrated
word banks in small
groups using L1 or L2
Associate with objects
the counting and tallying
data gathered using
illustrated graphic
organizers and word
banks with a partner
Develop questions about
counting and tallying data
gathered using labeled and
illustrated graphic
organizers with a partner
Categorize counting and
tallying data gathered
with using labeled and
illustrated graphic
organizers with a partner
Compare and contrast
categories of objects
from counting and
tallying data gathered
using labeled and
illustrated graphic
organizers
WR
ITIN
G Identify counting and
tallying data gathered
using illustrated word
cards in small groups
using L1 or L2
Describe counting and
tallying data gathered
using sentence frames
and illustrated word
cards with a partner
Explain counting and
tallying data gathered
using sentence fames and
illustrated word cards with
a partner
Formulate questions
about counting and
tallying data gathered
using sentence frames
with a partner
Create a chart to show
counting and tallying
data gathered with a
partner
TOPIC-RELATED LANGUAGE: Students at all levels of English language proficiency interact with grade level words and expressions such as:
data, data collection, tally marks, tallying, apply, organize, describe, present, explain, discuss, compare and contrast, identify, associate, develop,
categorize, identify, explain, formulate, create
SOL K.14 The student will display gathered data in object graphs, picture graphs, and tables, and will answer questions related to the data.
Example Context for Language Use: Students will answer questions about data gathered and displayed on a picture graph of the class’ favorite ice
cream.
COGNITIVE FUNCTION: Students at all levels of English language proficiency will EVALUATE data in tables, object graphs, or picture
graphs.
LIS
TE
NIN
G
Level 1
Entering
Level 2
Emerging
Level 3
Developing
Level 4
Expanding
Level 5
Bridging
Lev
el 6-R
each
ing
Identify data on a table,
object graph, or picture
graph based on teacher-
modeled oral directions
during whole group
instruction using
manipulatives and
illustrated examples
Identify data on a table,
object graph, or picture
graph based on teacher-
modeled oral directions
using illustrated examples
and visual supports in a
small group
Classify data on a table,
object graph, or picture
graph following one-step
oral commands using
illustrated examples in small
groups
Compare data on a table,
object graph, or picture
graph following multi-step
oral commands using visual
supports and graphic
organizers with a partner
Evaluate data on a table,
object graph, or picture
graph in response to oral
questions from the
teacher using graphic
organizers with a partner
SP
EA
KIN
G
Present data on a table,
object graph, or picture
graph based on teacher-
modeled oral directions
using manipulatives and
illustrated examples during
whole group instruction
Present data on a table,
object graph, or picture
graph following simple
oral commands using
illustrated examples and
visual supports in small
groups
Describe data on a table,
object graph, or picture
graph using visual supports
and graphic organizers in
small groups
Discuss data on a table,
object graph, or picture
graph using visual supports
and graphic organizers with
a partner
Explain data on a table,
object graph, or picture
graph using visual
supports and graphic
organizers with a partner
R
EA
DIN
G
Level 1
Entering
Level 2
Emerging
Level 3
Developing
Level 4
Expanding
Level 5
Bridging
Lev
el 6-R
each
ing
Identify data on a table,
object graph, or picture
graph based on labeled
illustrations during whole
group instruction
Identify data on a table,
object graph, or picture
graph based on labeled
illustrations in small
groups
Compare data on a table,
object graph, or picture
graph based on labeled
illustrations in a small group
Compare data on a table,
object graph, or picture
graph based on labeled
illustrations with a partner
Draw conclusions about
data on a table, object
graph, or picture graph
based on labeled
illustrations with a
partner
WR
ITIN
G Identify data on a table,
object graph, or picture
graph using labeled
illustrations and graphic
support during whole group
instruction
Describe data on a table,
object graph, or picture
graph using models and
illustrated word cards in a
small group
Explain data on a table,
object graph, or picture
graph using models and
illustrated word cards in a
small group
Compare data on a table,
object graph, or picture
graph using word banks and
illustrated graphic
organizers with a partner
Compile data on a table,
object graph, or picture
graph using word banks
and graphic organizers
with a partner
TOPIC-RELATED LANGUAGE: TOPIC-RELATED LANGUAGE: Students at all levels of English language proficiency interact with grade
level words and expressions such as gather, tables, picture graph, object graph, data, data collection, more, less, equal, identify, classify, compare,
evaluate, present, describe, discuss, explain, draw conclusions, explain, compile
top related