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Keansburg School DistrictCurriculum Management System

Believe, Understand, and Realize GoalsMathematics: Grade 3 - College and Career Ready (CCR)

Board Approved:

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Keansburg School DistrictCurriculum System

English Language Arts

Keansburg Public Schools

Board of Education

Mrs. Judy Ferraro, PresidentMs. Kimberly Kelaher-Moran, Vice President

Ms. Delores A. BartramMs. Ann Marie BestMs. Ann Commarato

Mr. Michael DonaldsonMr. Robert Ketch

Mrs. Patricia Frizell

District Administration

Mr. Gerald North, SuperintendentDr. Thomas W. Tramaglini, Director of Curriculum, Instruction, & Funding

Ms. Michelle Derpich, Secondary Supervisor of Curriculum & InstructionDr. Brian Latwis, Supervisor of Pupil Personnel Services

Mrs. Donna Glomb, Elementary Supervisor of Curriculum & InstructionMrs. Michelle Halperin-Krain, Supervisor of Data & Assessment

Ms. Corey Lowell, Business Administrator

Curriculum Development CommitteeBarbara Leary

Maryann Underhill Nancy Varley

Stephanie Puglisi

Cynthia LongoLauren Paduano Jonna ViggianoMary Fabiano

Anne O’FlinnRosemarie Hummer

Ashley SzotakSilvia Shoiab

Mr. Craig Palmer, Principal – Port Monmouth Elementary School

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Non-Negotiables

Graduatesthat are

prepared and

inspired to make positive

contributions to society

Believe, Understand, and Realize Goals



Mission/Vision Statement

The mission of the Keansburg School District is to ensure an optimum, safe teaching and learning environment which sets high expectations and enables all students to reach their maximum potential. Through a joint community-wide

commitment, we will meet the diverse needs of our students and the challenges of a changing society.

Beliefs

We believe that:

All children can learn. To meet the challenges of change, risk must be taken. Every student is entitled to an equal educational opportunity. It is our responsibility to enable students to succeed and become the best that they can be. All individuals should be treated with dignity and respect. The school system should be responsive to the diversity within our total population. The degree of commitment and level of involvement in the decision-making processes, from the student,

community, home and school, will determine the quality of education. Decisions should be based on the needs of the students. Achievement will rise to the level of expectation. Students should be taught how to learn. The educational process should be a coordinated system of services and programs.

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Curriculum Philosophy

The curriculum philosophy of the Keansburg School District is progressive. We embrace the high expectations of our students and community towards success in the 21st Century and beyond. At the center of this ideal, we believe that all of our students can be successful. The following are our core beliefs for all curricula:

All district curricula: Balances policy driven trends of centralization and standardization with research and what we know is good for our students. Balances the strong emphasis on test success and curriculum standards with how and what our students must know to be

successful in our community. Embraces the reality that our students differ in the way they learn and perform, and personalizes instruction to meet the

needs of each learner. Are aligned to be developmentally appropriate. Provides teachers the support and flexibility to be innovative and creative to meet the needs of our students.

Mathematics Goals

To deliver a curriculum that is:

Pertinent for the success of all of our students and useful for teachers in the 21st Century. Problem-based, where students understand the importance of mathematical concepts and applications. Socially, emotionally, and academically driven with regards to statute and code, while focusing on what is best for each of the

students in our school district to achieve successful outcomes. Significant in the processes of growth and development, and relevant to the students. Differentiated with regards to our students’ abilities and needs. Embedded with teaching responsibility, respect, and the value of hard work and self-pride over time. Designed with both content knowledge and experiences which:

o Are aligned from one grade level to the next, with scaffolded underpinnings of similar concepts for success.o Engage our diverse population for positive outcomes.o Build and support the language of mathematics.o Develop educational and mathematical independence over time.

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Common Core Standards for Mathematics

OPERATIONS AND ALGEBRAIC THINKING

Represent and solve problems involving multiplication and division.

1. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1

4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ÷ 3, 6 × 6 = ?.

Understand properties of multiplication and the relationship between multiplication and division.

5. Apply properties of operations as strategies to multiply anddivide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3× 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

6. Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Multiply and divide within 100.

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English Language Arts7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and

division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

NUMBER AND OPERATIONS IN BASE TEN

Use place value understanding and properties of operations to perform multi-digit arithmetic.4

1. Use place value understanding to round whole numbers to the nearest 10 or 100.

2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

3. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

NUMBER AND OPERATIONS—FRACTIONS

Develop understanding of fractions as numbers.

1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.

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English Language Artsa.Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and

partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

MEASUREMENT AND DATA

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

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English Language Arts2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and

liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Represent and interpret data.

3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets

4.Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

5.Recognize area as an attribute of plane figures and understand concepts of area measurement.

a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.

b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

6.Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

7.Relate area to the operations of multiplication and addition.

a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

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English Language Artsb. Multiply side lengths to find areas of rectangles with whole- number side lengths in the context of solving

real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum ofa × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

8. Solve real world and mathematical problems involving perimetersof polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

GEOMETRY

Reason with shapes and their attributes.

1.Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

2.Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

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Grade 3 Scope and Sequence

September

Adding and subtracting Skip counting Add up to four two-digit numbers Place value, increasing and decreasing Time Money

October Estimating to nearest 10 and 100 Adding and Subtracting within 1000 using different algorithms Understanding multiples of 10

November Introducing concept of multiplication and dividing Problem solving with equal groups and arrays Beginning study of facts up to 100

December Complete study of multiplication facts up to 100 Continue problem solving with equal groups and arrays

January Relationship between division and multiplication Associative and distributive property

February

Problem Solving with all four operations Order of operations Multi-step problems Explanations of patterns in numbers and arithmetic

March Geometric measurement of area Relating area to multiplication and division Perimeter

April

Fractions as numbers (denominators 2,3,4,6, and 8) Equivalent Fractions Fractions on a number line Fractions as whole numbers Comparing Fractions

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May Measuring liquid volume, mass Problem solving with liquid volume and mass Represent and interpret data with bar graphs and picture graphs

June Measuring Time

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Subject/Grade/Level:Mathematics/Grade 3

Timeline: September

Topic(s): Adding and Subtracting

Significance of Learning Goal(s): A fluent knowledge of addition and subtraction is necessary to progress through the mathematics curriculum.

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Specific Learning Objective(s)

The Students Will Be Able To:Suggested Activities

Instructional Tools / Materials / Technology / Resources /

Assessments and Assessment Models

2 CPI:2.NBT.5,6,8,9

EQ: How can fluent knowledge of addition and subtraction facts help me progress in mathematics?

Concept(s):understand how to add and subtract fluently using strategies, base-ten knowledge, properties of operations, and the relationship between operations; understand why addition and subtraction strategies work

SWBAT: Use place value and

operations to add and subtract mentally and in written form

Explain addition and subtraction strategies using various modeling forms

Meets Standard:EM 1.2: Patterns on a number grid: skip counting using base ten model, adding and subtracting using patterns on the grid, finding odd and even numbers using patterns on the grid, finding missing numbers using patterns on the grid, creating own number grids using patterns, increasing and decreasing numbers using vertical and horizontal movement. EMJ: 2, Elements 6, 12, Math Masters 2, Skills Links 1

EM 1.7: Using the number grid to find difference: EMJ 10, 11; HL 1.7; Skill Link 7, SRB 8,9

Assessment Assistant Goal 1a, 1b

Exceeds Standard:

Typical Assessment Question(s) or Task(s):

Games: Beat the calculator, number top-it, addition top-it, calculator computation game, Place Value Safari, Name that Number

Literature Links:12 Ways to Get to 11, Eve MerriamMath Curse, Jo Sciezka26 Letters and 99 Cents, Tana HobanHundred Grids, Number lines, Name collection boxes, EM student Journal, Number decks

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English Language Arts1.6: Many names for a number: representing numbers using various models: EMJ 8, SRB 14-15, HL 1.6, Skill Link 15, Elements 11, MM 2111.8: Skip counting, adding, and subtracting using the calculator: EMJ 13, Skill Link 8

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Timeline: September

Topic(s): Skip Counting

Significance of Learning Goal(s): Students understand the base-ten number system as they increase and decrease according to a given pattern

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The Students Will Be Able To:

Suggested ActivitiesInstructional Tools / Materials /

Technology / Resources / Assessments and Assessment

Models

1 CPI:2.NBT.2

EQ:How does an understanding of repeated patterns in the base-10 system help students to develop strategies to solve advanced algebraic equations?

Concept(s):Understand place value and repeated patterns in the base-10 numbers system

SWBAT: Count within 1000 Skip-count by 2s, 5s, 10s,

1000s, or any given pattern

Meets Standard:EM 1.2: Review patterns on a number grid—coloring numbers based on specific criteria, MJ page 11, SL page 7, HL 1.1, Elements page 6EM 1.8: Using a calculator to skip count—MJ page 13, SL page 1, SRB 202

Daily Mental Math Review with number line, calculators, and number grids.

Exceeds Standard:

Number grid puzzles with numbers exceeding 100: EM MJ pg. 2Enrichment Activity: TE 53—counting back past zero on the number line


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Timeline: September

Topic(s): Add up to four two-digit numbers

Significance of Learning Goal(s): Many circumstances in life call for the addition of more than two addends

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Models

CPI:

2.NBT.6

EQ:Under what circumstances might one need to add more than two addends?

Concept(s):Use place value understanding and properties of operations to add and subtract

SWBAT: Add up to four two-digit

numbers using various strategies.

Meets Standard:

EM 2.9: Animal Clutches and number stories with up to four addends—Students locate and use data in order to solve number story problems that include three or more addends. EM TE 140-144, SRB 242-243, MJ 54-57, SL 22, Elements 25, HL 2.9

Exceeds Standard:


Math For Real World Literature—Magic Squares, Colleen AdamsTraveling Around the United States, Barbara Linde

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What are strategies that can help when adding more than two addends

EM 2.9: Students write number stories with up to four addends using Animal Clutches poster—Using HL 2.9, students create their own number stories and have partners solve using addition skillsThree Addends Games: SRB 234, MM page 33Number Puzzles: MM page 34, SL 23, MM page 31 (Blank Number Puzzles)

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Timeline: September

Topic(s): Place Value, Increasing and Decreasing

Significance of Learning Goal(s): Students use place value to efficiently and accurately complete algorithms for various number operations and check for reasonableness using estimation.

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Models

CPI:

2.NBT.1, 4

EQ:How does an understanding of place value help one to efficiently increase and decrease numbers and establish a foundation for secured number sense?

Under what

Concept(s):Understand place value and use it to compare whole numbers and increase and decrease numbers.

SWBAT: Use place value to increase

and decrease whole numbers up to 3-digits

Use <, >, and = to record the results of comparisons

Meets Standard:1) Students read and write numbers with 3-digit place value; identify place values; increase and decrease specific place values; explain procedures for increasing and decreasing—Use place value flip chart to review place value concepts, use base-ten blocks to build three digit numbers on place value mats, MJ 104, SL 43, SRB Place Value Essay page 18, MM 56 (review), Elements 432) Review and use symbols to compare numbers: Everyday Math 1.10, SL 10 and 47, MJ 15, Money Grab Game SRB 230, Number Top-It up to 5 digits SRB 226-227, MM 59-60, HL 5.2 and MM 264.

Exceeds Standard:


How much is a Million? KelloggIf you Made MillionA Million Fish More or LessCount to a Million…How Much How Many How Far How Heavy How Long How Tall is 1000?

Math For Real World Literature (including Teacher’s Guide and Reproducible):A Trip Around the World, Carrie O’DonaldCounting with an Abacus, Patricia J. MurphyAt the Football Game (Symbols for Comparison), Joanne Matter

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English Language Artscircumstances might one use place value to compare multi-digit numbers?

Open Ended Question: Saving Money for Video Game (students compare saved money with earned money). Online District Resources

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Timeline: September

Topic(s): Time

Significance of Learning Goal(s): Students accurately read and write times on digital and analog clocks. Students accurately calculate elapsed time.

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Models

CPI:3.MD.1

EQ:How can using

a digital or analog clock

help me accurately

manage my time efficiently?

How can calculating

elapsed time help me

schedule daily activities and

responsibilities?

Concept(s):Tell time using an analog or digital clock; calculate elapsed time

SWBAT:Read and record times presented on analog and digital clocks to the nearest minute.Explain the meaning of common phrases associated with time (half-past, quarter-past, quarter-to).Calculate

Meets Standard:1) Students accurately set clocks for times

given by teacher or partner. Everyday Math 1.4, SRB page 156-161, Elements page 7, Skill Link 2, MM 4, 209, MJ pg. 4,

2) Students write down the time when displayed on a Judy Clock.

3) Solve word problems involving elapsed time.

Exceeds Standard:

1) Students create word problems with real-life application involving elapsed time. Students use classroom schedule to become familiar with the time associated with different activities.

2) Accurately estimate the duration of daily activities.


Additional Materials: Judy Clocks

Games: Race Around the ClockTime Flash Cards; I Have/ Who Has?

Literature:A Day with the Baker. Kathleen CollinsThe History of Space Exploration. Greg Moskal

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English Language ArtsA Weekend in the City. Colleen Adams

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Timeline: September

Topic(s): Money

Significance of Learning Goal(s): Students will need to add amounts of money and make change in order to participate in the economic marketplace.

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CPI:

2.MD.8

EQ:How will knowledge of currency help one to succeed in the global marketplace?

Concept(s):Work with money: add amounts of money and make change

SWBAT: Solve word problems

involving dollars, quarters, dimes, nickels, and pennies

Use dollars and cents notation

Meets Standard:

EM 1.9 : representing amounts of money with dollar and cent notation; comparing amounts of money. Math Journal pg. 15-16, Elements 13, SRB page 236, Skill link 9-11, Homelinks 213EM 1.10: using number stories to solve problems involving money Math Journal page 18-19, Elements 14, SRB 238, Homelink MM 215

Exceeds Standard:

Solve Open-Ended question involving making, saving, and spending money; explain how they got their answer.Write number stories that involve money.


Game: Buyer/Vender Game (math masters 7-8Pick a Coin (SRB 230)Money BingoEM money flashcards

Literature:A Shopping Trip, Barbara LindeA Price of a Pioneer Journal, Barbara LindeWorking at the Farmers Market, Barbara LindeLets Have a Bake Sale, Frances RuffinPigs Will be Pigs, Amy Axelrod

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English Language ArtsKeansburg School DistrictCurriculum Management System


Timeline: October

Topic(s): Estimating to nearest 10 and 100

Significance of Learning Goal(s): Students will be able to determine the reasonableness of a answer when an exact answer is not necessary

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Models

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CPI: 3.NBT.1 Round whole numbers to nearest 10 and 100EQ: How can estimation help me evaluate the reasonableness of my exact calculations?

What are some specific real-life situations where estimation is a valuable tool?

How can

Concept(s):Place value understanding can be used to round all numbers to the nearest 10 and 100

SWBAT: Use place value

understanding to round numbers to the nearest 10 and 100

Meets Standard:1) Introduce Rounding numbers song/ poem; SRB 166-1702) Number card game: students use number cards made by teacher to round numbers to the nearest 10 and 100.3) Number line activity: students visualize standard rounding rules using classroom number line4) 1.10: Determine when a situation needs an exact answer or an estimation—Stationary store activity (SRB page 238); MJ page 18: Stationary Store Poster

Exceeds Standard:

2.7: Making ballpark estimates for addition problems (MJ 46-47, MM 29)Creating number stories determining if one has enough to make a purchase (SRB 238)


Literature: Our New Fish Tank, Kathleen Collins

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English Language Artsknowing addition and subtractions algorithms help me in various careers?

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Timeline: October

Topic(s): Adding and Subtracting within 1000 using different algorithms

Significance of Learning Goal(s):

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15 CPI: 3.NBT.2

EQ: How can one use algorithms to add and subtract large numbers?

What are the real-life circumstance within which one might apply this skill?

How can

Concept(s):Fluently add and subtract within 1000 using strategies and algorithms based on place value properties of operations and/or the relationship between addition and subtraction

SWBAT:Fluently add and subtract whole numbers within 1000 using different strategies and algorithms based on place value properties of operations and/or the relationship between addition and subtraction

Meets Standard:1) Review how basic facts are used to solve problems involving larger numbers; EM lesson 2.2, MJ pg. 30-32, MM pg. 223, SRB page 224-225, Skill Link pg. 14, Elements 18f

2) Introduce partial sums algorithm for 2 and 3-digit numbers (model with base-ten and practice); Everyday Math lesson 2.7, MM page 29, MJ 46-48, MM 228, Skill Link 19-20, Elements 21

3) Review traditional addition algorithm; Assessment Assistant created materials

4) Introduce trade-first algorithm (regrouping-model with base-ten and practice); Everyday Math lesson 2.8: MM page 30, MJ 50-52, HL MM 229, Skill Link 20-21, Elements 23-24

5) Fact families/ fact triangles (show relationship


Games: What’s My Rule? Fishing (TE 89, 108); Fact Triangle flashcards, Addition Top-It, Beat the Calculator, Name that Numbers, Three Addends, I have/ Who has?, Two-Fisted Coin Addition, Make Seven

Literature:Working at the Post Office, Barbara LindeTour de France, Joseph SaviolaTraveling around the United States, Barbara Linde

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English Language Artsknowing addition and subtractions algorithms help me in various careers?

between addition and subtraction; Everyday Math lesson 2.1: SRB 44-45 (addition table), MJ page 29, MM 17-18 (Math Journal Activity Pages 1,2), HL 222, Skill Link page 12-13, Elements 17

6) Introduce algebraic reasoning using function tables: What’s My Rule? And Frames and Arrows. Continue review of basic facts/ relationship between addition and subtraction; Everyday Math Lesson 2.3, MM 19 and 224, MJ 34, SRB 176-177, SRB 178-180, Skill Link 13, 16, Elements page 15-16, 18

Exceeds Standard:1) EM 2.4, 2.5, 2.6, 2.9: Use diagrams to explore real-life situations where one would apply addition and subtraction algorithms: part/part/total, change diagram, comparison diagram, quantity/quantity difference2) Teach two-rule functions using double frames and arrows (MM 15).3) Students create function tables and frames and arrows for partners to solve.

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Timeline: October

Topic(s): Understanding multiples of 10

Significance of Learning Goal(s): Knowledge of place value is necessary to understand how to multiply one-digit whole numbers by ten.

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CPI: 3.NBT.3

EQ: How can I use my knowledge of place value and properties of operations to increase whole numbers by multiples of 10?

Concept(s):You can use place value and properties of operation to multiple one-digit whole numbers by multiples of ten.

SWBAT:Multiply one-digit whole numbers by multiples of 10, using place value and properties of operations.

Meets Standard:Introduce the concept of multiplication using multiples of 10, 100, and 1000: students use base-ten blocks to model multiplication number sentences, students use arrays to model multiplication number sentences, students use decimal grids to shade groups of 10 and 100.

Exceeds Standard:

Students apply concepts of multiples of 10, 100, and 1000 by solving money number stories using dimes and 1 and 10 dollar bills.


Activity:Extended Fact Families on Pumpkins.I Have/ Who Has?

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Timeline: November

Topic(s): Introducing concept of multiplication and dividing

Significance of Learning Goal(s): Students will gain an understanding of the circumstances in life when one must use multiplication or divisions. Students should understand that it is easier to multiply than to repeatedly add.

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Models

CPI:

3.OA.1-43.OA. 5-6

EQ:What are the

circumstances in which one

must use multiplication

and division to solve a

problem?

Concept(s):Multiplying means repeated addition of equal groups; Division is dividing objects into equal groups;Division is related to multiplication on account of it being an unknown factor problem

SWBAT:

Understand that multiplication means repeated addition of equal groups; recognize number stories that require multiplication; recognize that multiplication is a shortcut to repeated addition

Meets Standard:Students read number stories involving equal stories and draw representation that demonstrate the model of multiplication; student fill in labels on the multiplication diagrams identifying groups and numbers in each group; find the product of number stories. Math Journal 83-84, SRB 239, MM 41, 22, 248, Skill Link 32, Elements 35

Exceeds Standard:Students will write their own number stories that involve equal groups (MJ 84)Students will solve other students’ number problems.Students fill in blank multiplication tables (MM 41)


Literature: Each Orange Had Eight Slices, Paul Ganti, Jr.Sea Squares, Joy HumeHow Many Legs?, Christine Laley

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Timeline: November

Topic(s): Problem solving with equal groups and arrays

Significance of Learning Goal(s): Students will understand what situations in life require multiplication; students understand they can only multiply when there are equal groups.

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Models

CPI:3.OA. 1-9

EQ: Under what circumstances do I apply the operation of multiplication?

Concept(s):When there are equal groups of objects, multiplication can be used to find the total; multiplication is repeated addition of equal groups

SWBAT:Explain the definition of multiplication; write and solve number models to represent and solve multiplication number stories and arrays.

Meets Standard:Introduce number stories where either addition or multiplication can be used; explain and relate the two operations; act out classroom situations where equal groups are used to solve problems: EM 4.1—Guide to solving number stories, MM22, Multiplication Diagram MM41, SRB Essay 65-66, SRB Variety Poster page 239; Math Journal 83; Elements 35-36, Skill Link 32-33, MM 248

Exceeds Standard:

Students create their own multiplication number stories using SRB variety Poster page 239; Partners solve created number stories. Math Journal 84.


Sea Squares, Joy HulmEach Orange Had Eight SlicesOne Hundred Hungry Ants, Eleanor PinczesHow Many Legs, Christine Lalley

Games:Division Arrays: SRB 207Array Bingo: SRB 197

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English Language ArtsStudents solve Open-Ended questions creating multiple arrays to determine all possible arrangments of equal groups. OE questions: Third Grade Parade, Ants Marching, Assembly chairs.

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Timeline: November

Topic(s): Beginning study of facts up to 100

Significance of Learning Goal(s): Students will fluently solve multiplication problems with factors up to 10. Students will understand that there are a variety of strategies to help them develop fluency with basic facts

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CPI:3.OA.73.OA.9

EQ:What

strategies can I use to

help me achieve fact power? How

will fact power benefit me in real life situations and

future math learning

Concept(s): There are many shortcuts and tricks that one can use to quickly learn basic facts

SWBAT: understand the number patterns and rules that will help them memorize 0s, 1s, 2s, 5s, 9s, and 10

Meets Standard:Introduce all of the rules and patterns that help students quickly learn a large number of their basic facts.Everyday Math Lesson 4.5: Teacher created classroom poster showing the 0s rule, the identity rule, doubles, 5s pattern, multiples of ten, 9 patterns, and commutative property.HL page 252, Elements 39

Begin Weekly Fact Practice Homework and Quizzes

Exceeds Standard:

Teacher will demonstrate the 11s pattern for students


Songs: Schoolhouse Rock Basic Facts Songs (Available on YouTube)Multiplication Songs CD (3rd grade resources)

Games:Platter Facts: Math Binder TemplateDisappearing Numbers: Skip Counting (begin with all numbers on the board and erase them while students continue to skip count by memory)Fact Power Game (EM T250)

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Timeline: December

Topic(s): Complete study of facts up to 100

Significance of Learning Goal(s): Automaticity is necessary for a variety of real life situations and future mathematics success

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CPI:3.OA.7

EQ:What

strategies can I use to

help me achieve fact power? How

will fact power benefit me in real life situations and

future math learning?

Concept(s):

Repeated study is necessary for basic fact automaticity.

SWBAT:

Use a variety of different games, activities, and study strategies to memorize basic facts.

Meets Standard:

Classroom Activities for Practice and Reinforcement of Math Facts:

1. Around the World: Fact competition2. I Have, Who Has?3. Platter Facts4. Fact Triangles (MJ Activity Sheet 3,4)5. Continental Hop6. Timed multiplication drills where students

chart individual progress and identify areas for practice

Exceeds Standard:

Students create flashcards for home study; students identify personal remediation needs and choose study strategies to achieve proficiency.


Games:Multiplication BingoMultiplication BaseballFactor BlasterFactor BingoPigBeat the Calculator

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English Language ArtsStudents analyze and graph results of weekly timed quizzes and practice.

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Timeline: December

Topic(s): Continue problem solving with equal groups and arrays

Significance of Learning Goal(s): Students will understand what situations in life require multiplication; students understand they can only multiply when there are equal groups.

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Models

CPI:3.OA. 1-9

EQ: Under what

circumstances do I apply the operation of

multiplication?

Concept(s):When there are equal groups of objects, multiplication can be used to find the total; multiplication is repeated addition of equal groups

SWBAT:Explain the definition of multiplication; write and solve number models to represent and solve multiplication number stories and arrays.

Meets Standard:1. Students understand the steps involved in solving number stories. Everyday Math 4.1: Math Masters pg.22—guide to solving number stories;2. Students will be able to complete diagram with information from number stories. MM page. 41—mulitplication/division diagrams3. Students solve multiplication numbers stories—Math journal page 83. Use Variety Store poster on SRB page 239.Additional Practice: MM page 248 and Elements page 35.

Exceeds Standard:

1. Students write and solve their own number stories using Variety Store Poster and Diagrams. Math Journal page 84.


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Timeline: January

Topic(s): Relationship between division and multiplication

Significance of Learning Goal(s): Students will understand what situations in life require multiplication; students understand they can only multiply when there are equal groups. Students will understand that sometimes they will need to use division to find number of groups or numbers in each group

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Models

CPI:3.OA. 1-9

EQ: Under what

circumstances do I apply the operation of

multiplication? When do I

use division to help me solve equal groups

number stories?

Concept(s):Multiplication and division are related as operations involving equal groups.

SWBAT:

SWBAT represent multiples of equal groups; solve multiplication number stories using arrays and number models; understand that division is the opposite of multiplicaiton

Meets Standard:

1. Students solve multiplication stories that include totals and they must find number in each group. Math Journal page 87. MM page 82, MJ page 90, MM page 250.

2. Students continue to use diagrams to solve multiplication number stories that may include total and not part values. Math Masters 41, MJ 92, MM 251.

Additional Resources: Elements pages 36, 37, 38.

Exceeds Standard:

1. Students write multiplication number stories


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English Language Artsusing diagrams. They will include stories that have the total value and must solve for the group value

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Timeline: January

Topic(s): Associative and distributive properties

Significance of Learning Goal(s): Knowledge of operation strategies helps students solve multiplication and division problems fluently and with ease

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CPI:3.OA.5

EQ:How do these

properties help me

develop fact automaticity?

Concept(s):

Students can learn fact families to help them solve multiplication and division facts related to number stories.

SWBAT:

Use knowledge of fact families to quickly solve multiplication and division facts.

Meets Standard:

1. Students cut out multiplication/division fact triangles 1 and 2. Activity Sheets 3 and 4 in Math Journal. Students practice individually and with partners.Additional Practice: MM page 254.

2. Students will play fact triangle flip (Directions on TE page 258)

Additional Practice: Elements page 39, 40

Exceeds Standard:

Students create fact triangle for higher level math facts. Students create fact triangles to practice facts that they need to practice.

Game: Beat the calculator (SRB page 203)


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Timeline: February

Topic(s): Problem-solving with all four operations

Significance of Learning Goal(s): Students will understand the real-life application for addition, subtraction, multiplication, and division.

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CPI:

3.OA.83.MD.3

EQ:How do I

decide what operation is needed to

solve problems?

Concept(s):

Students need to understand under what circumstances to use addition, subtraction, multiplication, or division to solve problems.

SWBAT:

Solve problems using the appropriate operation

Meets Standard:1. Students will complete part, part, total

diagrams to solve addition number stories MJ page 36-37. Student Reference book page 242-243. Additional practice: HL page 225, Elements page 19, Skill Link page 22

2. Students will complete a start, change, end model to complete addition and subtraction word problems involving deposits and withdrawals. MJ page 40-42. Additional practice: HL page 226, Elements page 20, Skill link page 17.

3. Students will complete a quantity, quantity difference model to complete subtraction number stories involving high and low temperatures around the country. Student Reference book page 244. MJ page 44. Additional practice: HL page 227.

4. Students will complete

Guide to Solving Number stories poster, MM page 22

(SmartBoard Math Word Problems)-book


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English Language Artsmultiplication/division diagrams to solve multiplication number stories. Student reference book page 239. MJ page 83. Additional practice: HL page 248, Elements page 35, Skill link page 32

5. Students will use multiplication to solve map distance number stories. MJ page 100-101.

6. Students will complete multiplication/division diagrams to solve division number stories. Students will complete equal shares and equal groups problems. MJ page 90, MJ page 92. Additional practice: HL page 250 and 251, Elements page 37, Skill link page 40.

Exceeds Standard:1. Students will create their own addition,

subtraction, multiplication, and division number stories using the appropriate diagram.MM page 21-Parts and total diagramMM page 41- Multiplication/division diagram

2. Groundworks Reasoning with Numbers book page 17-22 (Addition Number Stories)

3. Groundworks Algebraic Thinking book page 9-14 (Using graphs to solve number stories)

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Timeline: February

Topic(s): Order of operations

Significance of Learning Goal(s): Students need to understand that the order in which operations are performed will affect the final result.

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CPI:

3.OA.93.OA.8

EQ:In what order do I need to complete a

number sentence to

solve the problem

correctly?

Concept(s):The order of operations affects the resulting answer.

SWBAT:

Apply their knowledge of the order of operations to correctly solve number sentences.

Meets Standard:1. Students will compare punctuation in

sentences to parentheses in number models. Explain how different punctuation changes meaning; connect to math punctuation.

2. Solve number models with parentheses: Math Journal page 168.

3. Parentheses in Puzzles: Math Masters page 299.

4. Complete name collection boxes with parentheses: MM page 121

Additional Practice: Elements 63.

Exceeds Standard:

1. Creating original number models using parentheses.

2. Children will write number models for


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English Language Artspoints scored by basketball players from professional teams: MJ page 170, MM page 110

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Timeline: February

Topic(s): Multi-step problems

Significance of Learning Goal(s): Students will apply their knowledge of basic operations to solve a multi-step problem.

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CPI:3.OA.8

EQ:How do I decipher which operations to use and in which order to implement them to solve the multi-step word problem?

Concept(s):Knowing which operation to choose and use first.

SWBAT:

To accurately solve a multi-step problem

Meets Standard:(Groundworks)-book

Exceeds Standard: Typical Assessment Question(s) or Task(s):

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Timeline: March

Topic(s): Geometric measurement of area

Significance of Learning Goal(s): Students will develop the concept of measuring area using a variety of standard and non-standard units and make real-life applications.

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CPI:3.MD.53.MD.63.MD.7

EQ:How can I

use knowledge of multiplication and addition to measure

and calculate the area of

plane figures?

Concept(s):Using square units to measure area; count square units using standard units; use multiplication and addition to find area; use tiling to find area

SWBAT:

1. Recognize area as an attribute of plane figures and understand concepts of area measurement.2. Measure areas by counting unit squares3. Relate area to the operations of multiplication and addition

Meets Standard:1. How Big is a Foot: Introduction to

standard and non-standards of measurement; square units and square yards using template; real life application problems such as measuring room, measuring hallway/ bedroom; comparing Pattern-Block sizes by tiling equal areas (EM Lesson 3.6, EM Lesson 3.5 Exploration B) MJ 72-73, MJ 75, SRB 136-137, MM 342

2. Using Multiplication and addition to find area of plane figures: EM Lesson 3.7, MJ 77, SRB 138, Elements 31-33, Skill Link 29, 34.

3. Using Geoboards to model area: EM Lesson 3.7, section 3.


A Cloak for the Dreamer, Aileen Friedman

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English Language ArtsExceeds Standard:

Open Ended Problem Solving: How much would it cost to re-carpet our classroom?

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Timeline: March

Topic(s): Perimeter

Significance of Learning Goal(s): Students will develop the concept of measuring the perimeter of plane figures and differentiating the attribute of perimeter from area.

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CPI:3.MD.8

EQ:How can I

use my knowledge of

addition to find the

perimeter of plane

figures?

Concept(s):Perimeter is the linear measurement of the length around a plane figure.

SWBAT:

Meets Standard:


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Timeline: April

Topic(s): Fractions as numbers (denominators 2, 3, 4, 6, & 8)


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CPI:

EQ:

Concept(s):

SWBAT:

Meets Standard:


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Timeline: April

Topic(s): Equivalent fractions


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CPI:

EQ:

Concept(s):

SWBAT:

Meets Standard:


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Timeline: April

Topic(s): Fractions on a number line


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EQ:

Concept(s):

SWBAT:

Meets Standard:


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Timeline: April

Topic(s): Fractions as whole numbers


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CPI:

EQ:

Concept(s):

SWBAT:

Meets Standard:


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Timeline: April

Topic(s): Comparing fractions


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CPI:

EQ:

Concept(s):

SWBAT:

Meets Standard:


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Timeline: May

Topic(s): Measuring liquid (volume, mass)


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CPI:

EQ:

Concept(s):

SWBAT:

Meets Standard:


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Timeline: May

Topic(s): Problem-solving with liquid (volume, mass)


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CPI:

EQ:

Concept(s):

SWBAT:

Meets Standard:


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Timeline: May

Topic(s): Represent and interpret data with bar graphs and picture graphs


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CPI:

EQ:

Concept(s):

SWBAT:

Meets Standard:


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Timeline: June

Topic(s): Measurement of Time


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CPI:

EQ:

Concept(s):

SWBAT:

Meets Standard:


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Alignment Matrices of Common Core State Standards

Grade Strand Standard # Standard

Sept

embe

r –

Oct

ober

Nov

embe

r –

Dec

embe

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Janu

ary

– Fe

brua

ry

Mar

ch –

Apr

il

May

- Ju

ne

3 OA 1 CC.3.OA.1 Represent and solve problems involving multiplication and division. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

3 OA 2 CC.3.OA.2 Represent and solve problems involving multiplication and division. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

3 OA 3 CC.3.OA.3 Represent and solve problems involving multiplication and division. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

3 OA 4 CC.3.OA.4 Represent and solve problems involving multiplication and division. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?.

3 OA 5 CC.3.OA.5 Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15 then 15 × 2 = 30, or by 5 × 2 = 10 then 3 × 10 = 30. (Associative property

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English Language Artsof multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal terms for these properties.)

3 OA 6 CC.3.OA.6 Understand properties of multiplication and the relationship between multiplication and division. Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

3 OA 7 CC.3.OA.7 Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of one-digit numbers.

3 OA 8 CC.3.OA.8 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).)

3 OA 9 CC.3.OA.9 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

3 NBT 1 CC.3.NBT.1 Use place value understanding and properties of operations to perform multi-digit arithmetic. Use place value understanding to round whole numbers to the nearest 10 or 100.

3 NBT 2 CC.3.NBT.2 Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (A range of algorithms may be used.)

3 NBT 3 CC.3.NBT.3 Use place value understanding and properties of operations to perform multi-digit arithmetic. Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. (A range of algorithms may be used.)

3 NF 1 CC.3.NF.1 Develop understanding of fractions as numbers. Understand a

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English Language Artsfraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)

3 NF 2 CC.3.NF.2 Develop understanding of fractions as numbers. Understand a fraction as a number on the number line; represent fractions on a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)

3 NF 2a CC.3.NF.2a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)

3 NF 2b CC.3.NF.2b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)

3 NF 3 CC.3.NF.3 Develop understanding of fractions as numbers. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)

3 NF 3a CC.3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)

3 NF 3b CC.3.NF.3b Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)

3 NF 3c CC.3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)

3 NF 3d CC.3.NF.3d Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)

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English Language Arts3 MD 1 CC.3.MD.1 Solve problems involving measurement and estimation of intervals

of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

3 MD 2 CC.3.MD.2 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of “times as much.”)

3 MD 3 CC.3.MD.3 Represent and interpret data. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

3 MD 4 CC.3.MD.4 Represent and interpret data. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

3 MD 5 CC.3.MD.5 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Recognize area as an attribute of plane figures and understand concepts of area measurement. -- a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. -- b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

3 MD 6 CC.3.MD.6 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

3 MD 7 CC.3.MD.7 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Relate area to the operations of multiplication and addition.

3 MD 7a CC.3.MD.7a Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

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English Language Arts3 MD 7b CC.3.MD.7b Multiply side lengths to find areas of rectangles with whole-number

side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

3 MD 7c CC.3.MD.7c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

3 MD 7d CC.3.MD.7d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

3 MD 8 CC.3.MD.8 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different area or with the same area and different perimeter.

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Common Core State Standards Vocabulary

Addition and subtraction within 5, 10, 20, 100, or 1000. Addition or subtraction of two whole numbers with whole number answers, and with sum or minuend in the range 0-5, 0-10, 0-20, or 0-100, respectively. Example: 8 + 2 = 10 is an addition within 10, 14 – 5 = 9 is a subtraction within 20, and 55 – 18 = 37 is a subtraction within 100.

Additive inverses. Two numbers whose sum is 0 are additive inverses of one another. Example: 3/4 and – 3/4 are additive inverses of one another because 3/4 + (– 3/4) = (– 3/4) + 3/4 = 0.

Associative property of addition. See Table 3 in this Glossary.

Associative property of multiplication. See Table 3 in this Glossary.

Bivariate data. Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team.

Box plot. A method of visually displaying a distribution of data values by using the median, quartiles, and extremes of the data set. A box shows the middle 50% of the data.1

Commutative property. See Table 3 in this Glossary.

Complex fraction. A fraction A/B where A and/or B are fractions (B nonzero).

Computation algorithm. A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly. See also: computation strategy.

Computation strategy. Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another. See also: computation algorithm.

Congruent. Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations).

Counting on. A strategy for finding the number of objects in a group without having to count every member of the group. For example, if a stack of books is known to have 8 books and 3 more books are added to the top, it is not necessary to count the stack

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English Language Artsall over again. One can find the total by counting on—pointing to the top book and saying “eight,” following this with “nine, ten, eleven. There are eleven books now.”

Dot plot. See: line plot.

Dilation. A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.

Expanded form. A multi-digit number is expressed in expanded form when it is written as a sum of single-digit multiples of powers of ten. For example, 643 = 600 + 40 + 3.

Expected value. For a random variable, the weighted average of its possible values, with weights given by their respective probabilities.

First quartile. For a data set with median M, the first quartile is the median of the data values less than M. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the first quartile is 6.2 See also: median, third quartile, interquartile range.

Fraction. A number expressible in the form a/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.

Identity property of 0. See Table 3 in this Glossary.

Independently combined probability models. Two probability models are said to be combined independently if the probability of each ordered pair in the combined model equals the product of the original probabilities of the two individual outcomes in the ordered pair.

Integer. A number expressible in the form a or –a for some whole number a.

Interquartile Range. A measure of variation in a set of numerical data, the interquartile range is the distance between the first and third quartiles of the data set. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the interquartile range is 15 – 6 = 9. See also: first quartile, third quartile.

Line plot. A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.3

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English Language ArtsMean. A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.4 Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21.

Mean absolute deviation. A measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing by the number of data values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean absolute deviation is 20.

Median. A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list—or the mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11.

Midline. In the graph of a trigonometric function, the horizontal line halfway between its maximum and minimum values.

Multiplication and division within 100. Multiplication or division of two whole numbers with whole number answers, and with product or dividend in the range 0-100. Example: 72 ÷ 8 = 9.

Multiplicative inverses. Two numbers whose product is 1 are multiplicative inverses of one another. Example: 3/4 and 4/3 are multiplicative inverses of one another because 3/4 × 4/3 = 4/3 × 3/4 = 1.

Number line diagram. A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.

Percent rate of change. A rate of change expressed as a percent. Example: if a population grows from 50 to 55 in a year, it grows by 5/50 = 10% per year.

Probability distribution. The set of possible values of a random variable with a probability assigned to each.

Properties of operations. See Table 3 in this Glossary.

Properties of equality. See Table 4 in this Glossary.

Properties of inequality. See Table 5 in this Glossary.

Properties of operations. See Table 3 in this Glossary.

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English Language ArtsProbability. A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).

Probability model. A probability model is used to assign probabilities to outcomes of a chance process by examining the nature of the process. The set of all outcomes is called the sample space, and their probabilities sum to 1. See also: uniform probability model.

Random variable. An assignment of a numerical value to each outcome in a sample space.

Rational expression. A quotient of two polynomials with a non-zero denominator.

Rational number. A number expressible in the form a/b or – a/b for some fraction a/b. The rational numbers include the integers.

Rectilinear figure. A polygon all angles of which are right angles.

Rigid motion. A transformation of points in space consisting of a sequence of one or more translations, reflections, and/or rotations. Rigid motions are here assumed to preserve distances and angle measures.

Repeating decimal. The decimal form of a rational number. See also: terminating decimal.

Sample space. In a probability model for a random process, a list of the individual outcomes that are to be considered.

Scatter plot. A graph in the coordinate plane representing a set of bivariate data. For example, the heights and weights of a group of people could be displayed on a scatter plot.5

Similarity transformation. A rigid motion followed by a dilation.

Tape diagram. A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model.

Terminating decimal. A decimal is called terminating if its repeating digit is 0.

Third quartile. For a data set with median M, the third quartile is the median of the data values greater than M. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the third quartile is 15. See also: median, first quartile, interquartile range.

Transitivity principle for indirect measurement. If the length of object A is greater than the length of object B, and the length of object B is greater than the length of object C, then the length of object A is greater than the length of object C. This principle applies

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English Language Artsto measurement of other quantities as well.

Uniform probability model. A probability model which assigns equal probability to all outcomes. See also: probability model.

Vector. A quantity with magnitude and direction in the plane or in space, defined by an ordered pair or triple of real numbers.

Visual fraction model. A tape diagram, number line diagram, or area model.

Whole numbers. The numbers 0, 1, 2, 3, ….5

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