denville township school district...shark swimathon brainpopjr (lv)- adding and subtracting tens;...

ROCHELLE PARK TOWNSHIP SCHOOL DISTRICT

Math 3-5 Curriculum Guide

BOE Approval: 02/12/2015

2



Table of Contents

DTSD Mission Statement 3

Department Vision 3

Affirmative Action Compliance Statement 3

Curriculum and Planning Guides

Grade 3 Units 4 – 35

Grade 4 Units 35 – 64

Grade 5 Units 65 - 96

STANDARDS FOR MATHEMATICAL PRACTICE

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all

levels should seek to develop in their students. These practices are integrated throughout our curriculum

at all grade levels.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate Tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

INTERDISCIPLINARY THEMES

Planned interdisciplinary activities can help students to make sensible connections among subjects,

while limiting the specialist's tendency to fragment the curriculum into isolated pieces. Such activities

provide students with broader personal meaning and the integrated knowledge necessary to solve real-

world problems. Teachers are encouraged to independently and cooperatively develop lessons which

cover multiple areas simultaneously

3

MISSION STATEMENT

The Rochelle Park School District’s envisions an educational community which inspires and empowers

all students to become self-sufficient and thrive in a complex, global society

DEPARTMENT VISION

It is the firm belief of the Rochelle Park Township School District that mathematics provides students

with a common language that allows them to actively participate in collaborative problem solving

scenarios. This common language will provide our students with a foundation of a deeper understanding

of their future fiscal responsibilities within the global economy they participate in. We encourage our

students to advocate for their communities by acting as a driving force, so that we may build a more

sustainable economy in the future.

This guide is to provide focus for the learning that will take place in this course, but is completely

modifiable based upon the needs and abilities of the students and their Individual Education Plans.

Curriculum implementation follows best practice and adheres to the New Jersey Core Content

Standards. At the same time, for students with disabilities, the Individual Education Plan, specifically

the Goals and Objectives of the plan, supersede any curricular adherence or suggestion.

21ST

CENTURY THEMES & SKILLS

Embedded in much of our units of study and problem based learning projects are the 21st Century

Themes as prescribed by the New Jersey Department of Education. These themes are as follows:

Global Awareness

Financial, Economic, Business, and Entrepreneurial Literacy

Civic Literacy

Health Literacy

AFFIRMATIVE ACTION COMPLIANCE STATEMENT

The Rochelle Park Township School District are committed to the achievement of increased cultural

awareness, respect and equity among students, teachers and community. We are pleased to present all

pupils with information pertaining to possible career, professional or vocational opportunities which in

no way restricts or limits option on the basis of race, color, creed, religion, sex, ancestry, national origin

or socioeconomic status.

4



Grade: 3 Unit: Topic 1- Numeration Time Frame: 8 lessons

ENDURING UNDERSTANDINGS ESSENTIAL QUESTIONS

The base-ten numeration system is a scheme

for recording numbers using digits 0-9, groups

of ten, and place value.

Numbers can be used for different purposes,

and numbers can be classified and represented

in different ways.

The set of real numbers is infinite and ordered.

Whole numbers, integers and fractions are real

numbers. Each real number can be associated

with a unique point on the number line.

Numbers, expressions, measures, and object

can be compared and related to other numbers,

expressions, measures, and object in different

ways.

Mathematics content and practices can be

applied to solve problems.

How are greater numbers read and written?

How can whole numbers be compared and

ordered?

KNOWLEDGE SKILLS STANDARDS

Students will know:

our number system in based on

groups of ten. Whenever we get

10 in one place value, we move

to the next greater place value.

the place-value periods ones,

thousands, millions and so

forth, are used to read and write

large numbers.

place value can be used to name

numbers in different ways.

Uses of numbers include telling

how many and showing a date

or an address.

each whole number can be

associated with a unique point

on the number line. Zero is the

least whole number on the

number line and there is no

greatest number. The distance

between any two consecutive

whole numbers on a given

number line is the same.

Students will be able to:

read and write 3-digit and 4-

digit numbers.

name numbers in different

ways.

read and write numbers in the

ten and hundred thousand.

locate and compare whole

numbers on a number line.

identify the pattern on a

number line or graph scale,

and calculate missing labels.

compare 3-digit and 4-digit

whole numbers.

order 3-digit and 4-digits

whole numbers.

make an organized list to

represent information given a

problem.

3.NBT.1

3.NBT.2

5

equal distances on the number

line must correspond to equal

differences in the numbers. The

scale of some graphs is a

number line.

place value can be used to

compare whole numbers.

place value can be used to order

whole numbers.

some problems can be solved by

generating a list of outcomes

and organizing that list in a

systematic way so all outcomes

are accounted for.

VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT

digits

place value

standard form

expanded form

word form

period

compare

order

place value blocks (or Teaching

Tools 18 and 19)

number lines (Teaching Tool 10)

Teaching Tool 31

Calendar Math:

Daily depositor (ongoing)

Calendar (ongoing)

Counting Tape (ongoing)

Computations and Connections

(ongoing)

Optional Additional Resources:

Math Start Series (LV)- Earth Day

Hooray!

BrainPopJr (LV)- comparing

numbers; making ten; place value

Smartboard activities

Study Island

Formative:

homework

teacher observation

differentiated activities

quizzes

timed fact drills

end of lesson quick checks

Summative:

End of Topic test

6



Grade: 3 Unit: Topic 2- Number Sense: Addition & Subtraction Time Frame: 9 lessons


● There are multiple interpretations of addition,

subtraction, multiplication, and division of rational

numbers and each operation is related to other

operations.

● For a given set of numbers there are relationships

that are always true called properties, and these are

the rules that govern arithmetic and algebra.

● There is more than one algorithm for each of the

operations with rational numbers. Most algorithm

for operations with rational numbers both mental

math and paper and pencil, use equivalence to

transform calculations into simpler ones.

● Numbers can be approximated by numbers that are

close. Numerical calculations can be approximated

by replacing numbers with other numbers that are

close and easy to compute with mentally.

● Any number, measure, numerical expression.,

algebraic expression, or equation can be represented

in an infinite number of ways that have the same

value.

● Mathematics content and practices can be applied to

solve problems.

● How can sums and differences be found

mentally?

● How can sums and differences be estimated?


Students will know:

● some real-world problems

involving joining, separating, part-

part-whole, or comparison can be

solved using addition or subtraction

● fact families show addition and

subtraction relationships

● two numbers can be added in any

order; the sum of any number and 0

is that number; and three or more

numbers can be grouped and added

in any order

● there is more than one way to do a

mental calculation. Techniques for

doing addition or subtraction

calculations mentally involve

changing the numbers or the

expressions so the calculation is

easy to do mentally.


concrete materials and

concepts of addition to

model the Commutative,

Associative, and Identity

Properties of Addition. • recognize situations when

subtraction is used to solve a

problem and write number

sentences. • solve problems by adding with

mental math. • will solve problems by

subtracting with mental math. • round two-digit and three-digit

whole numbers to the nearest

ten or hundred , by comparing

to the number halfway

between or by using place

value.

3.NBT.1

3.NBT.2

7

● rounding is a process for finding the

multiple of 10, 100, etc. closest to a

given number.

● there is more than one way to

estimate a sum or difference.

● rounding and substituting

compatible numbers are two ways

to estimate sums and differences.

● different numerical expressions can

have the same value. Or the value

of one expression can be less than

(or greater than) the value of

another expression

● an equation shows a balance

between what is on the right side

and what is one the left side of the

equal sign

● answers to problems should always

be checked for reasonableness, and

this can be done in different ways.

Two ways are to use estimation and

when appropriate and to check the

answer against the question and

conditions in the problem.

• solve problems by estimating

sums. • solve problems by estimating

differences. • decide whether both sides of

an equation are equal and they

will determine the value of an

unknown number in an

equation. • solve word problems and

check their answers for

reasonableness.


addends sum Commutative Property of Addition Associative Property of Addition Identity Property of Addition difference fact family round estimate compatible numbers equation

two color counters

Teaching Tool 17

Teaching Tool 33

Calendar Math:


Calendar (ongoing)



(ongoing)

Exemplars- Ant in the Well;

Bulletin Board Border; Kwanza

Celebration


Math Start Series (LV)- Betcha!;

Shark Swimathon

BrainPopJr (LV)- adding and

subtracting tens; adding with

regrouping; basic adding; basic

subtraction; rounding


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test

8



Grade: 3 Unit: Topic 3- Using Place Value to Add and Subtract Time Frame: 10 lessons


There is more than one algorithm for each of

the operations with rational numbers. Some

strategies for basic facts and most algorithms

for operations with rational numbers, both

mental math and paper and pencil, use

equivalence to transform calculations into

simpler ones.

For a given set of numbers there are

relationships that are always true called

properties, and these are the rules that govern

arithmetic and algebra.



What are standard procedures for adding and

subtracting whole numbers?


Students will know:

the expanded algorithm for

adding 3-digit numbers

breaks the addition problem

into a series of easier

problems based on place

value. Answers to the

simpler problems are added

together to determine the

final sum.

models and the standard

algorithm for adding 3-digit

numbers are just and

extension to the hundreds

place of the models and

standard algorithm for adding

2-digit numbers.


subtracting 3-digit numbers

breaks the subtraction

problem into a series of

easier problems based on

place value. Answers to the

simpler problems are used to

find the final difference.

models and the standard

algorithm for subtracting 3-

digit numbers are just an

extension to the hundreds


solve 3-digit addition problems

using an expanded algorithm.

add 3-digit numbers using place

value blocks or pictures and

record the results using the

standard addition algorithm

add 3-digit numbers using

paper-and-pencil methods and

use addition to solve problems.

add 3 or more 2- and/or 3-digit

numbers using paper- and-

pencil methods and use addition

to solve problems.

draw a picture to solve a

problem.

solve 3-digit subtraction

problems by breaking them into

smaller, easier subtraction

problems.

subtract 3-digit numbers using

place value blocks or pictures

and record the results using

standard subtraction algorithm.



use subtraction to solve

problems.

3.NBT.1

3.NBT.2

3.OA.8

9

place of the models and

standard algorithm for

subtracting 2-digit numbers.

place value relationships can

help simplify subtracting

across zero.

three or more whole numbers

can be grouped and added in

any order.

information in a problem can

often be shown using a

picture or diagram and used

to understand and solve the

problem. Some problems can

be solved by writing and

completing a number

sentence or equation.



use subtraction to solve

problems.

solve problems by writing a

number sentence based on a

picture they have drawn

describing the problem.


no new vocabulary introduced

Place-value blocks or Teaching

Tool 18

Teaching Tool 34

Teaching Tool 35

Problem-solving recording sheet

(Teaching Tool 1)

Calendar Math:


Calendar (ongoing)



(ongoing)


Math Start Series (LV)- Earth Day

Hooray!; Betcha!; Shark

Swimathon

BrainPopJr (LV)- comparing

numbers; making ten; place value

adding and subtracting tens; adding

with regrouping; basic adding;

basic subtraction; rounding


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test

10



Grade: 3 Unit: Topic 4 – Meanings of Multiplication Time Frame: 5 lessons


There are multiple interpretations of addition,

subtraction, multiplication, and division of

rational numbers and each operation is related

to other operations.


relationships that are always true, called





What are different meanings of multiplication?

How are addition and multiplication related?


Students will know:

repeated addition involves

joining equal groups and is

one way to think about

multiplication.

an array involves joining

equal groups and is one

way to think about

multiplication.

some real-world problems

involving joining or

separating equal groups or

comparison can be solved

using multiplication.

two numbers can be

multiplied in any order and

the product remains the

same.

mathematical explanations

can be given using words,

pictures, numbers, or

symbols. A good

explanation should be

correct, simple, complete,

and easy to understand.


write multiplication number

sentences for given equal

group situations, using the x

symbol.

write multiplication sentences

for arrays and use arrays to

find products.

write multiplication sentences

for arrays, use arrays to find

products, and use the

Commutative Property of

Multiplication.

write math stories for given

multiplication facts.

use objects, words, pictures,

numbers, and technology to

provide a written explanation

reflecting their understanding.

3.0A.1

3.0A.3

3.0A.5

11


multiplication

factors

product

array

Commutative (Order) Property

of Multiplication

two-color counters (Teaching

Tool 17)

Calendar Math:


Calendar (ongoing)



(December and April activities)

Exemplars- A Very Fishy Story;

Carpet Caper; Checkerboard

Investigation; Harvest Dinner; Job

Hunting


Math Start Series (LV)- Too

Many Kangaroo Things to Do!

BrainPopJr (LV)- Arrays


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test

Benchmark- Topic 1-4

12



Grade: 3 Unit: Topic 5- Multiplication Facts: Use Patterns Time Frame: 7 lessons


Relationships can be described and

generalizations made for mathematical

situations that have numbers or objects that

repeat in predictable ways. For some

relationships, mathematical expressions and

equations can be used to describe how

members of one set are related to members of a

second set.



What patterns can be used to find certain

multiplication facts?


Students will know:

there are patterns in the

products for multiplication

facts with factors of 2 and

5.



facts with a factor of 9.



facts with factors 0 and 1.



facts with factors of 2, 5

and 9.

patterns can be used to find

products involving factors

of 10.

basic facts and place-value


products when one factor is

a multiple of 10.

sometimes the answer to

one problem/question is

needed to find the answer

to another

problem/question.


use patterns to multiply with 2

and 5 as factors.

use patterns to multiply with 9

as a factor.

use patterns and properties to

multiply with 0 and 1 as

factors.

use patterns to find products

with factors of 2, 5 and 9.

use patterns to multiply with

10 as a factor.

use basic multiplication facts

and number patterns to

multiply by multiples of 10.

solve for one problem and use

the solution to complete a

second problem.

3.OA.3

3.OA. 9

3. NBT.3

13


multiples

identify (one) property of

multiplication

zero property of multiplication

Teaching Tool 36

Two-color counters (Teaching

Tool 17)

Teaching Tool 37

Teaching Tool 38

Hundred chart (Teaching Tool 7)

Teaching Tool 39

Calendar Math:


Calendar (ongoing)



(April activities)




Hunting


Math Start Series (LV)- Too

Many Kangaroo Things to Do!

BrainPopJr (LV)- Mutiplying by

zero and one


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test

14



Grade: 3 Unit: Topic 6 -Multiplication Facts: Use Known Facts Time Frame: 9 lessons












simpler ones.



rational numbers, and each operation is related




How can unknown multiplication facts be

found using known facts?


Students will know:

the disruptive property can be

used to break a large array into

two smaller arrays.

three or more numbers can be

grouped and multiplied in any

order.

basic multiplication facts with

3 as a factor can be found by

breaking apart the unknown

fact into known facts. The

answers to the known facts are

added to get the final product.




fact into known facts. The




6 or 7 as a factor can be found

by breaking apart the unknown

facts into known facts. The




use the distributive property to

simplify multiplication

problems by breaking apart

large arrays that represent

multiplication facts into

smaller arrays that represent

other multiplication facts.

use known facts to find

products with 3 as a factor.

use known facts and doubles to

find products with 4 as a factor.

use known facts to find

products with 6 and 7 as

factors.

use known facts and doubles to

find products with 8 as a factor.

multiply three numbers and use

the associative property of

multiplication.

use known facts and patterns to

find products.

3.OA.3 3.OA5 3.OA.8 3.MD.7.c 3.MD.8

15




facts into known facts. The



patterns and known facts can

be used to find unknown

multiplication facts.

finding the number of

combinations that are possible

between the members of one

group and the members of

another group is one meaning

of multiplication.

some problems can be solved

by the first finding and solving

a sub-problem(s) and then

using that answer(s) to solve

the original problem.

use objects, pictures, and

multiplication to find the

number of possible

combinations of data or objects

in a problem.

solve multiple-step problems.


Distributive Property

Associative (Grouping) Property

of Multiplication

Teaching Tool 40

Two Color Tiles

Teaching Tool 16

Teaching Tool 17

Two color counters

Calendar Math:


Calendar (ongoing)



(January, February, and April

activities)




Hunting


Math Start Series (LV)- Too Many

Kangaroo Things to Do!


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test

16



Grade: 3 Unit: Topic 7 - Meanings of Division Time Frame: 6

lessons








What are different meanings of division?

How is division related to other operations?


Students will know:


involving joining or

separating equal groups or

comparison can be solved

using division.

sharing involves separating

equal groups and is one way

to think about division.

repeated subtraction

involves separating equal

groups and is one way to

think about division.

any division problem can be

thought of as a

multiplication fact with a

missing factor. Then, an

answer can be found using a

multiplication table.

sharing and repeated

subtraction both involve

separating equal groups and

are two ways to think about

division.

frequently word problems

can be solved by writing

equations that represent the

quantitative relationships

involved.

information in a problem

can often be shown by using

objects to act it out or by

using a picture or diagram in

order to understand and

solve the problem.


use models to solve division

problems involving sharing

and record solutions using

division number sentences.

use models to solve division

problems involving repeated

subtraction and record

solutions using division

number sentences.

use multiplication tables to

find answers to division

problems.

solve word problems by

writing equations that

represent the problem

situations.

write and solve number

stories involving division.

solve problems by using

objects and drawing a

picture.

3.0A.2

3.0A.3

3.0A.4

3.0A.6

3.0A.9

17


division


Tool 17); Teaching Tool 41

multiplication table (Teaching

Tool 9)

division sentence cards (one per

group)

Calendar Math:


Calendar (ongoing)



(March)

Exemplars- Camping; Cookie

Cutters; Is Dan Losing His

Marbles?; M&M Cookie

Combos;


Math Start Series (LV)- Divide

and Ride

BrainPopJr (LV)- Repeated

Subtraction; Making Equal

Groups


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test

18



Grade: 3 Unit: Topic 8- Division facts Time Frame: 9 lessons





to the other operations.

For a given set of numbers, there are




Any number, measure, numerical expression,

algebraic expression, or equation can be

represented in an infinite number of ways that

have the same value.

Mathematical situations and structures can be

translated and represented abstractly using

variables, expressions, and equations.



How can an unknown division fact be found

by thinking of a related multiplication fact?


Students will know:

multiplication and division

have an inverse

relationship.

the inverse relationship

between multiplication and

division can be used to find

division facts; every

division fact has a related

multiplication fact.

pattern and known facts

can be used to find

unknown multiplication

facts. Division facts can be

found by thinking of a

related multiplication fact.

any number (except 0)

divided by itself is equal to

1. Any number divided by

1 is that number. Zero

divided by any number

(except 0) is zero. Zero

cannot be a divisor.


give a multiplication fact, state

a related division fact and vice

versa.

give quotients for division

facts with divisors 2, 3, 4 and

5.


facts with divisors of 6 and 7.


facts with divisors of 8 and 9.

use previously learned skills to

solve multiple-step problems.

learn how to use

multiplication and division

facts to decide whether both

sides of an equation are equal.

They will also learn to

determine the value of an

unknown in an equation.

use patterns and fact families

to find answers to division

facts with 0 and 1.

3.OA.3

3.OA.7

19

different numerical

expressions can have the

same value. Or, the value

of one expression can be

less than (or greater than)

the value of the other

expression.

an equation shows a

balance between what is on

the right side and what is

on the left side of the equal

sign.

some problems can be

solved by first finding and

solving one or more sub-

problems and then using

the answer(s) to solve the

original problem.


can be often be shown by

using a picture or diagram

and used to understand and

solve the problem. Some

problems can be solved by

writing and completing a

number sentence or

equation.

use multiplication and division

facts to solve problems.

solve division problems

involving sharing and repeated

subtraction by drawing a

picture and writing a number

sentence.


dividend

divisor

quotient


Tool 17)

Calendar Math:


Calendar (ongoing)



(April and May activities)

Exemplars- Camping; Cookie

Cutters; Is Dan Losing His

Marbles?; M&M Cookie Combos;


Math Start Series (LV)- Divide

and Ride

BrainPopJr (LV)- Repeated

Subtraction; Making Equal

Groups


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test


20



Grade: 3 Unit: Topic 9- Understanding Fractions Time Frame: 8 lessons


● The set of a real numbers is infinite and ordered.

Whole numbers, integers, and fractions are real



● Numbers can be approximated by numbers that

are close. Numerical calculations can be

approximated by replacing numbers with other

numbers that are close and easy to compute with

mentally. Some measurements can be

approximated using known referents as the unit

in the measurement process.

● Mathematics content and practices can be applied

to solve problems

● What are different interpretations of a

fraction?


Students will know:

● a region can be divided into

equal-sized parts in different

ways. Equal-sized parts of a

region have the same area but

not necessarily the same shape.

● a fraction describes the division

of a whole number (region, set

segment) into equal parts. The

bottom number in a fraction

tells how many equal parts the

whole is divided into. The top

number tells how many equal

parts are indicated. A fraction

is relative to the size of the

whole.

● finding a unit-fractional part of

a whole is the same as dividing

the whole denominator of the

fraction.

● some points between whole

numbers on a number line can

be labeled with fractions or

mixed numbers. The

denominator of the fraction can

be determined by counting the

number of equal parts between

two consecutive whole

numbers.


● identify regions that have

been divided into equal-sized

parts and divide regions into

equal-sized parts.

● associate the model, symbol,

and words used to describe a

fractional part of a whole

region.



fractional part of a set.

● find a fractional part of a set.

● identify fractional parts and

mixed numbers on a number

line.

● use benchmark fractions to

estimate fractional parts.



fractional part of the length

of an object.

● make a table and look for a

pattern to solve a problem.

3.NF.1 3.NF.2 3.NF.2a 3.NF.2b 3.OA.3

21

● fractions can be approximated

by other fractions that are close.

● some problems can be solved by

reordering and organizing data

in a table and by finding and

using numerical patterns in the

table. VOCABULARY RESOURCES/MATERIALS ASSESSMENT/PROJECT

halves thirds fourths fifths sixths eighths tenths twelfths fraction unit fraction numerator denominator mixed numbers benchmark fractions

centimeter grid paper

(Teaching Tool 11) Teaching Tool 45 crayons two Color counters Teaching Tool 17 8 1/2 inch X 1 inch paper strips number lines fraction Strips (Teaching Tool

22)

Calendar Math:


Calendar (ongoing)



(ongoing)

*use February calendar pieces

Exemplars- Disappearing

Cookies; Post Office Display


Math Start Series (LV)- Jump

Kangaroo Jump!

BrainPopJr (LV)- Basic Parts

of a Whole; More Fractions


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test

22



Grade: 3 Unit: Topic 10- Fraction Comparison and Equivalence Time Frame: 9

lessons


Numbers, expressions, measures, and objects


expressions, measures, and objects in different

ways.

The set of real numbers in infinite and ordered.










What are different ways to compare fractions?


Students will know:

if two fractions have the same

denominator, the fraction with

the greater numerator is the

greater fraction.


numerator, the fraction with

the lesser denominator is the

greater fraction.

fractions can be compared to

each other by comparing them

to benchmark numbers such

as 0, ½, and 1.

number lines can be used to

compare fractions with like

denominators or like

numerators.

a fraction is relative to the size

of the whole. Models can be

used to compare fractional

amounts.

number lines can be used to



numerators.


use models and quantitative

reason to compare fractions

with the same denominator.

use models and reasoning

to compare fractions with

the same numerator.

use benchmark numbers to

compare fractions with the

same numerator or the

same denominator.

use number lines to



numerators.

use models to find

equivalent fractions.

use number lines to identify


use fraction strips and

number lines to find

fraction names for whole

numbers.

compare and order

fractions to solve problems.

3.NF.2

3.NF.3

3.NF.3.a

3.NF.3.c

3.NF.3.d

23

equivalent fractions name the

same point on a number line.

if a fraction aligns with a

whole number on a number

line or to a whole number

fraction strip, the whole

number is equivalent to that

fraction.

the same fractional amount

can be represented by an

infinite set of different but


equivalent fractions name the

same point on a number line.

if a fraction aligns with a

whole number on a number

line or to a whole number

fraction strip, the whole

number is equivalent to that

fraction.


often be shown using a picture

or diagram and used to

understand and solve the

problem.

draw a picture to solve

problems.


equivalent fractions

simplest form

Fraction models: strips

(Teaching Tool 22- 2 sets per

pair)

Number lines (Teaching Tool

10)

Calendar Math:


Calendar (ongoing)



(ongoing)

*use February calendar pieces

Exemplars- Disappearing

Cookies; Post Office Display


Math Start Series (LV)- Jump

Kangaroo Jump!

BrainPopJr (LV)- Equivalent

Fractions; Mixed Numbers


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test

24



Grade: 3 Unit: Topic 11- Two Dimensional Shapes and Their Attributes Time Frame: 9

lessons


Two and three dimensional objects with or

without curved surfaces can be described,

classified, and analyzed by their attributes. An

object’s location in space can be described

quantitatively.



How can two-dimensional shapes be

described, analyzed, and classified?


Students will know:

lines and line segments are

sets of points in space that

can be used to describe

parts of other geometric

lines, shapes, and solids.

an angle is formed by two

rays with a common

endpoint. Angles can be

classified by their size.

plane shapes have many

properties that make them

different from one another.

polygons can be described

and classified by their sides

and angles.

polygons can be put

together or taken apart to

make other polygons.


solved by breaking apart or

changing the problem into

simpler ones, solving the

simpler ones, and using

those solutions to solve the

original problem.

commonalities in attributes

of objects or situations can

be found and used to make

and test generalizations

about relationships.


identify lines and line

segments and explore their

different relationships

identify and classify angles in

relation to right angles

identify and classify polygons

identify and classify triangles

identify and classify

quadrilaterals

create new shapes by

combining shapes or by

separating shapes

make a new shape by cutting

apart a shape and rearranging

the pieces

solve a problem by first

solving a simpler problem

identify commonalities among

objects or situations to make

and test generalizations

3.G.1 3.G.2

25


point line line segment intersecting lines parallel lines ray angle vertex right angle perpendicular acute angle obtuse angle polygon side vertex diagonal triangle quadrilateral pentagon hexagon octagon decagon equilateral triangle isosceles triangle scalene triangle right triangle acute triangle obtuse triangle trapezoid parallelogram rectangle rhombus square

ruler or straight edge 2 pipe cleaners or 2 strips of paper

and 1 paper fastener Dot Paper (Teaching Tool 14) Teaching Tool 43 scissors glue Teaching Tool 44 Polygons B, H, K, M, N, O from

polygons (Teaching Tool 29) 1 inch grid paper ( Teaching Tool

12) tape polygons (Teaching Tool 29) two color tiles (Teaching Tool 16)

Calendar Math:


Calendar (ongoing)



(ongoing)

*use April calendar pieces


Math Start Series (LV)- Hamster

Champs

BrainPopJr (LV)- Plane Shapes


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test

26



Grade: 3 Unit: Topic 12 - Time Time Frame: 5 lessons


Some attributes of objects are measurable and

can be quantified using unit amounts.



How can lengths of time be measured and

found?


Students will know:

time can be expressed

using different units that

are related to each other.

the minute hand takes 5

minutes to move from one

number to the next on a

typical clock face. The

minute hand takes 1 minute

to move from one mark to

the next on a typical clock

face.

there are different units for

measuring time. Many

clock times can be

expressed in more than one

way.

the duration of an event

can be measured if one

knows the start and end

times for the event.

some problems with the

initial data point unknown

can be solved by starting

with the end result,

reversing the steps and

processes, and working

backward to the initial data

point.


tell time to the nearest half

hour and quarter hour using

analog and digital clocks, and

identify times as A.M. and

P.M.

tell to the nearest minute using

analog and digital clocks.

perform simple conversations

for units of time.

find elapsed time in intervals

of minutes.

use the strategy work

backward to solve problems.

3.MD.1

27


hour

half hour

quarter hour

minute

seconds

A.M.

P.M.

elapsed time

clock face (Teaching Tool 25)

calendar (Teaching Tool 26)

Calendar Math:


Calendar (ongoing)



(ongoing)

Clock Activities (October;

November; December; March)

Exemplars: Busy Day; To the

Detail


Math Start Series (LV)- Game

Time!; Rodeo Time

BrainPopJr (LV)- Calendar and

Dates; Parts of a Clock; Time to

the Minute; Time to the Quarter

and Half Hour


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test


28



Grade: 3 Unit: Topic 13- Perimeter Time Frame: 5 days


Some attributes of objects are measurable and




How can perimeter be measured and found?


Students will know:

the distance around a

figure is its perimeter. To

find the perimeter of a

polygon, add the lengths of

the sides.

in a given measurement

situation, the type of

measuring Tool and the

measurement units it

contains determine the

appropriateness of the

Tool.

to find the perimeter of a

polygon, add the lengths of

the sides.

shapes can be made with a

given perimeter. Different

shapes can have the same

perimeter.


solved by making a

reasoned first try for what

the answer might be and

then, through additional

reasoning, arrive at the

correct answer.


use standard units to find the

perimeter of a shape.

select appropriate Tools and

units to find perimeter.

use standard units to find the

perimeter of a common shape.

match shapes to a given

perimeter and learn that

different shapes can have the

same perimeter.

solve a problem through the

process of try, check, and

revise.

3.MD.8

29


perimeter

mile

centimeter grid paper (Teaching

Tool 11)

inch ruler (or Teaching Tool 24)

yardstick

measuring tape

string

Teaching Tool 46

straws

craft sticks

tooth picks

colored chalk

Calendar Math:


Calendar (ongoing)



(ongoing)

Measurement (January pgs 78-80)


Math Start Series (LV)- Racing

Around

BrainPopJr (LV)- Perimeter


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative: End of Topic test

30



Grade: 3 Unit: Topic 14 - Area Time Frame: 10 lessons


Some attributes of objects are measureable and




What does area mean?

What are different ways to find the area of a

shape?


Students will know:

the amount of space inside a

shape is its area, and area can

be estimated or found using

square units.

square units can be used to

create shapes with given

areas.

standard measurements units

are used for consistency in

finding and communicating

measurements.

the amount of space inside a

shape is its area and area can

be estimated or found using

square units. Formulas exist

for finding the area of some

polygons.

the area of rectangles can be

used to model the Distributive

Property.

the area of some irregular

shapes can be found by

breaking apart the original

shape into other shapes for

which the areas can be found.

there are relationships

between the perimeter and

area of a polygon.

equal-area parts of a figure

can be used to model unit

fractions.


by breaking apart or changing

the problem into simpler ones,

solving the simpler ones, and

using those solutions to solve

the original problem.


measure the area of a shape

by counting the number of

square units that cover a

region.

use square units to make

figures with given areas.

use standard units of area

and counting to measure

the area of a shape.

find the area of rectangles

by counting square units or

by using a formula.

use the areas of rectangles

to model the Distributive

Property.

solve complex problems

asking for the area of

irregular shapes.

find the area of irregular

shapes.

compare different

rectangles with same area

to discover the change in

perimeter.

select appropriate units

and Tools for measuring

the area of given items.

3.MD.5

3.MD.5.a

3.MD.5.b

3.MD.6

3.MD.7

3.MD.7.a

3.MD.7.b

3.MD.7.c

3.MD.7.d

3.MD.8

3.G.2

31

in a given measurement

situation, the type of

measuring Tool and the

measurement units it contains

determine the appropriateness

of the Tool.


area

square units


(Teaching Tool 11); tracing

shapes (circle) (per pair)

1 –inch grid paper (Teaching

Tool 12)

index cards (per pair)

scissors (per pair)

Calendar Math:


Calendar (ongoing)



(ongoing)

Measurement Activities

(January 78-80)


Math Start Series (LV)-

Bigger, Better, Best!

BrainPopJr (LV)- Area


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test

32



Grade: 3 Unit: Topic 15- Liquid, Volume, Mass Time Frame: 5 lessons


● Some attributes of objects are measurable and


● Mathematics content and practices can be applied

to solve problems.

● What are the customary units for measuring

capacity and weight?

● What are the metric units for measuring capacity

and mass?


Students will know:

● capacity is a measure of the

amount of liquid a container

can hold.

● mass is a measure of the

quantity of matter in an

object. Weight and mass are

different.

● the weight of an object is a

measure of how heavy an

object is.

● information in a problem can

often be shown using picture



problem. Some problems

can be solved by writing and

completing a number



● choose an appropriate unit and

Tool, estimate, and measure in

cups, pints, quarts, and gallons.

● identify objects which hold

about a cup, a pint, a quart, or a

gallon.



milliliters and liters.

● identify objects that hold about a

liter or a milliliter.



grams and kilograms.

● identify objects with a mass of

about one gram or one kilogram.



ounces, pounds, and tons.

● identify objects that weigh about

an ounce, a pound, or a ton. draw a picture to solve a problem

involving units of capacity and

mass.

3.MD.2

33


capacity cup pint quart gallon milliliter liter mass gram kilogram weight ounce pound ton

Teaching Tool 47 liter containers water sand rice pan balance dollar bill stapler

Calendar Math:


Calendar (ongoing)



(ongoing)

Measurement Activities (February

pgs 91-93; March pgs 105-106;

April pgs 120-121)


Math Start Series (LV)- Room for

Ripley

BrainPopJr (LV)- Cups, Pints,

Quarts, Gallons; Grams and

Kilograms; Ounces, Pounds, and

Tons


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative: End of Topic test

34



Grade: 3 Unit: Topic 16- Data Time Frame: 6 lessons


Some questions can be answered by collecting

and analyzing data, and the question to be

answered determines the data that needs to be

collected and how best to collect it. Data can

be represented visually using tables, charts and

graphs. The type of data determines the best

choice of visual representation.



How can data be represented, interpreted and

analyzed?


Students will know:

line plots allow data to be

compared more easily than

in a list or a table.

line plots can be used to

organize and represent data

generated by measuring

lengths.

each type of graph is most

appropriate for certain

kinds of data. Pictographs

and bar graphs help to

compare data.

the key for a pictograph

determines the number of

pictures needed to

represent each number in a

set of data.

in a bar graph, the scale

determines how long the

bar needs to be to represent

each number in a set of

data.


solved by making, reading

and analyzing a graph.


use a line plot to organize the

results of an experiment

generate data by measuring

lengths to the nearest fourth of

an inch and make line plots to

organize their data and draw

conclusions.

read and interpret data from a

pictograph and a bar graph.

make a pictograph from a

table or tally chart.

make a bar graph to represent

the data in a table or tally

chart.

solve problems by using tables

and graphs to draw

conclusions.

3.MD.3

3.MD.4

35


line plot

pictograph

key

bar graph

scale

line Plots (Teaching Tool 48)

rulers (Teaching Tool 24)

reading pictographs and bar

graphs (Teaching Tool 49)

making Pictographs (Teaching Tool

50) centimeter Grid paper (Teaching

Tool 11) sandwich Survey (Teaching Tool 30)

Calendar Math:


Calendar (ongoing)



(ongoing)

Graph Activities- (September pgs

28-29; October pgs 44-45;

January pgs 84-85; March pgs

112-113; May pgs 134-135)


Math Start Series (LV)-

Lemonade For Sale

BrainPopJr (LV)- Pictographs;

Tally Charts and Bar Graphs


Study Island

Formative:

homework

teacher observation


quizzes

timed fact drills


Summative:

End of Topic test


End of the year test

36



Grade: 4 Unit: Topic 1- Multiplication and Division Time Frame: 10 Lessons





to the other operations.

Relationship can be described and



repeat in predicable ways.


relationships that are always true called


arithmetic and equations

Some strategies for basic facts use equivalence

to transform calculations into simpler ones.






How can patterns and properties be used to

find some multiplication facts?

How can unknown multiplication facts be

found by breaking them into known facts?

How can unknown division facts be found by

thinking about a related multiplication fact?


Students will know:


involving joining or separating

equal groups or comparison can be

solved using multiplication.

Repeated addition and arrays

involve joining equal groups and

are two ways to think about

multiplication.

there are patterns in the products

for multiplication facts with factors

of 2, 5, and 9.

two numbers can be multiplied in

any order. The product of any

number and 0 is zero. The product

of any number and 1 is that

number.

basic multiplication facts with 3,

4, 6, 7, or 8 as a factor can be

found by breaking apart the

unknown fact into known facts.



recognize multiplication as

repeated addition of equal

groups used in equal

groups used in arrays.

use products with factors

of 2, 5, and 9.

use multiplication

properties to simplify

computations.

use the Distributive

Property to find products

of the factors of 3,4, 6, 7,

and 8 by breaking apart

problems into simpler

problems.

recognize patterns and be

able to continue the

pattern.

use and draw models to

solve division problems.

use arrays to write and

4.OA.1

4.OA.2

4.OA.3

4.OA.4

4.OA.5

37

identifying elements that repeat in

a predictable way.

some real-world problems involve

joining or separating equal groups

or comparison can be solved using

division.

Sharing and repeated subtraction

involve separating equal groups

and are two ways to think about

multiplication.

multiplication and division have an

inverse relationship. The inverse

relationship between multiplication

and division can be used to find

division facts: every division fact

has a related multiplication fact.

any number (except 0) divided by

itself is equal to 1. Any number

divided by 1 is that number. Zero

divided by any number (except 0)

is zero. Zero cannot be a divisor.

information in a problem can often

be shown using a picture or

diagram and used to understand

and solve the problem. Some

problems can be solved by writing

and completing a number sentence

or equation.

complete multiplication

and division fact families.

use multiplication facts

with 0 and 1 to learn about

special division rules with

0 and 1.

identify multiplication

facts related to division

facts in order to solve

division problems.

draw pictures to problem

solve multiplication

situations and use their

pictures to write number

sentences.


array

product

factors

multiple


Multiplication

Zero Property of Multiplication

Identity Proper

Identity Property of Multiplication


inverse operations

fact family


place-value blocks

crayons

colored pencils

colored chalk

markers

hundred chart

index cards

counters

Calendar Math Aug/Sept

Calendar pieces, Counting

Tape, Daily Depositor

Formative

Homework

Teacher observation

Differentiated activities

Quizzes

Summative

Topic test

38



Grade: 4 Unit: Topic 2- Generate and Analyze Patterns Time Frame: 6 Lesson


Patterns, Relationships, and Functions.




repeat in predictable ways.

For some relationships, mathematical

expressions and equations can be used to

describe how members of one set are related to

members of a second set. Practices, Processes,

and Proficiencies.



How can patterns be used to describe how two

quantities are related?

How can a relationship between two quantities

be shown using a table?


Students will know:

patterns, relationships, and

functions

some patterns consist of

shapes or numbers arranged in

a unit that repeats.

some sequences of geometric

objects change in predicable

ways that can be described

using mathematical rules.

some real world quantities

have a mathematical

relationship; the value of one

quantity can be found if you

know the value of the other

quantity.

some real world quantities

have a mathematical


quantity can be found if the

value of the other quantity is

known.

patterns can be used to

identify some relationships

some sequences of geometric

objects change in predicable

ways that can be described

using mathematical rules.


identify and extend repeating

geometric or repeating number

patterns

identify and extend whole

number patterns involving

addition and subtraction.

extend tables of ordered pairs for

situations involving

multiplication, addition, or

subtraction.

find a rule and extend the table,

given a table of number pairs.

extend patterns of cubes or tiles.

use the strategies Act It Out and

Use Reasoning to solve problem.

4.OA.5

39


by using objects to act out the

information in the problem.


by reasoning about the

conditions in the problem.


compare

divide

multiply

regroup

repeating pattern

pattern blocks or tangram pieces,

recording sheets: Number

Sequences, two-color counters,

Recording Sheet: Writing Rules for

Situations, Cubes, centimeter grid

paper, two –color counters

Calendar Math Aug/Sept Calendar

pieces, Counting tape, Daily

Depositor

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

40



Grade: 4 Unit: Topic 3- Place Value Time Frame: 6 Lessons


The Base Ten Numeration System The Base Ten

Numeration System is a scheme for recording numbers

using digits 0-9, groups of ten, and place value.

Comparison and Relationships. Numbers, expressions,

measures, and objects can be compared and related to

other numbers, expressions, measures and objects in

different ways.

Numbers can be approximated by numbers that are

close.

Mathematics content and practices can be applied to

solve problems.

How are greater numbers read and

written?

How can whole numbers be compared

and ordered?


Students will know:

our number system is based on

groups of ten. Whenever we get 10

in one place value, we move to the

next greater place value.

in a multi-digit whole number, a

digit in one place represents tem

times what it would represent in

the place immediately to its right.

place value can be used to compare

and order number.

rounding whole numbers is a

process for for finding the multiple

of 10, 100, and so on the the

closest number.


generating a list of outcomes and

organizing that list in a systematic

way so all outcomes are accounted

for.


students will read and write

3 digit and 4 digit numbers.

students will learn how

digits within a multi-digit

whole number relate to each

other by their place value.

students will compare

whole number through

hundred thousands.

students will apply their

knowledge of place value to

compare and order numbers.

students will show place

value to round whole

numbers.

students will systematically

find and record all possible

outcomes for a situation.

4.NBT.1

4.NBT.2

4.NBT.3


odd

even

period

number line

digits

place value

standard form, expanded form,

word form

compare

place-value blocks

recording sheet: Comparing and

Ordering Whole Numbers

number lines,

Calendar Math: Oct. Calendar

pieces, coin counter, Daily

Depositor , measurement lesson

Teacher Manual pg.36-38

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

41



Grade: 4 Unit: Topic 4- Addition and Subtraction of Whole Number Time Frame: 6 Lessons


Any number, measure, numerical expression, algebraic

expression, or equation can be represented in an

infinite number of ways that have the same value.

There is more than one algorithm for each of the

operations with rational numbers. Some strategies for

basic facts and most algorithms for operations with

rational numbers, both mental math and paper and

pencil, use equivalence to transform calculations into

simpler ones.


close. Numerical calculations can be approximated by

replacing numbers with other numbers with other

numbers that are close and easy to compute mentally.

Some measurements can be approximated using

known referents as the unit in the measurement

process.


solve problems.

How can sums and differences of

whole numbers be estimated?

What are standard procedures for

adding and subtracting whole numbers?


Students will know:

representing numbers and

numerical expressions in

equivalent forms can make

some calculations easy to do

mentally.

there is more than one way to

do a mental calculation.

the standard addition and

subtraction algorithms for

multi-digit numbers break the

calculation into simpler

calculations using place value

starting with the ones, then the

tens, and so on.



Each estimation technique

gives a way to replace numbers

with other numbers that are

close and easy to compute with

mentally.


apply a variety of methods to

add and subtract whole

numbers mentally.

round whole numbers to

estimate sums and

differences.

add numbers to hundreds and

thousands with and without

regrouping.

subtract numbers to

thousands with and without

regrouping.

subtract numbers with zeros

to thousands.

use a picture or diagram to

translate an everyday

situation into a number


4.NBT. 3

4.NBT.4

4.OA.3

42


often be shown using a picture





completing a number sentence

or equation.


breaking apart

compensation

counting on

Commutative Property of Addition

Associative Property of Addition

Identity Property of Addition

Inverse Operations

place-value blocks

place-value chart

Calendar Math: October

calendar pieces, coin counter,

clock, Daily Depositor, Counting

Tape measurement lesson


Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

43



Grade: 4 Unit: Topic 5- Number Sense: Multiplying by 1-Digit Numbers Time Frame:6 Lessons



operations with rational numbers. Some

strategies for basic facts and most algorithms for

operations with rational numbers, both mental

and paper and pencil, use equivalence to


Relationship can be described and

generalizations made for mathematical situations

that have numbers or objects that repeat in

predictable ways. For some relationships,

mathematical expressions and equations can be

used to describe how members of one set are

related to members of a second set.

Numbers can be approximated by numbers that


approximated by replacing numbers that are

close and easy to compute mentally. Some

measurements can be approximated using known

referents as the unit in the measurement process.



How can some products be found mentally?

How can products be estimated?


Students will know:

making an array with place-value

blocks provides a way to

visualize and find products.

provides a way to visualize and

find products. A 2-digit by 1-

digit multiplication calculation

can be broken into simpler

problems: a basic fact and a 1-

digit number times a multiple of

10. Answers to the simpler

problems can be added to give

the product.

there is more than one way to do

a mental calculation. Techniques

for doing multiplication


changing the numbers or the

expression so the calculation is

easy to do mentally.


use arrays to multiply by 10

and 100.

multiply by multiples of 10

and 100.

break apart factors to

multiply.

use compensation to multiply

mentally.

use rounding to estimate

products.

decide if the answer to a

problem is reasonable.

4. NBT.3

4.NBT.5

4.OA.3

44

basic facts and place value


products when one factor is 10 or

100.

rounding is one way to

estimating products.

answers to problems should

always be checked for

reasonableness and this can be

done in different ways. Two

ways are to use estimation and to

check the answer against the

question and conditions in the

problem.


partial products

compensation

place-value blocks

1/4-inch grid paper

multiplication recording sheet

rounding recording sheet.

Calendar Math :

October/November calendar

pieces, Counting Tape, Daily

Depositor, measurement lesson


Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

45



Grade: 4 Unit: Topic 6- Multiplying by 1 Digit Numbers Time Frame: 6 Lessons


Algorithms: There is more than one algorithm

for each of the operations with rational

numbers. Most algorithm for operations with

rational numbers, both mental math and paper

and pencil, use equivalence to transform

calculations into simpler ones

Equivalence: Any number, measure, numerical

expression, algebraic expression, or equation

can be represented in an infinite number of

ways that have the same value.

Practices, Processes, and Proficiencies:



How can arrays be used to find products?

What is a standard procedure for multiplying

multi digit numbers?


Students will know:

there is an expanded algorithm

for multiplying where numbers

are broken apart using place

value and the parts are use to

find partial products. The partial

products are then added together

to find the product.

the standard multiplication

algorithm is just a shortened way

of recording the information in

the expanded multiplication

algorithm


algorithm is a shortcut for the

expanded algorithm. Regrouping

is used rather than showing all

partial products.

the standard algorithm for

multiplying three digit by one

digit numbers is just an extension

to the hundreds place of the

algorithm for multiplying two

digits by one digit numbers.


multiply using arrays and an

expanded algorithms.

connect the expanded and

standard algorithms for

multiplication.

multiply 2 digit by 1 digit

numbers.

multiply 3 and 4 digit by 1

digit number

multiply by 1 digit numbers.

evaluate problems for missing

or extra information

4.NBT.5,

4.NBT.3,

4.OA.3

46

the standard algorithm for

multiplication involves breaking

apart numbers using place value,

finding partial products, and then

adding partial products to get the

final product. The process is the

same regardless of the size of the

factors.

different numerical expressions

can have the same value. Or, the

value of one expression can be

less than (or greater than) the

value of the other expression.

Information in a problem can

often be shown using a picture or

diagram and be used to


problem. Some problems can be

solved by writing and

completing a number sentence or

equation.


product

array

factor

rounding

Place-value blocks.

Calendar Math October or Nov.

calendar pieces, counting tape,

Daily Depositor, measurement

lesson Teacher Manual pg.52-54

Exemplar; “A Very Fishy Story”

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

47



Grade: 4 Unit: Topic 7- Number Sense: Multiplying by 2-Digit Numbers Time Frame:5 Lessons



operations with rational numbers. Most

algorithms for operations with rational numbers,

both mental math and paper and pencil, use

equivalence to transform calculations into simpler

ones.



that have numbers or objects that repeat or are

arranged in predictable ways. For some


equations can be used to describe how members

of one set are related to members of a second set.




numbers that are close and easy to compute


approximated using known referents as the unit in

the measurement process.

Mathematics content and practices can be applied

to solve problems.

How can greater products be found

mentally?

How can greater products be estimated?


Students will know:

making an array with place-

value blocks provides a way

to visualize and find

products.



mentally multiply a two-digit

number by a multiple of 10

or 100.

products can be estimated by

replacing numbers with other

numbers that are close and

easy to multiply mentally.



solving a sub-problem(s) and

then using that answer(s) to

solve the original problem.


multiply 2-digit numbers by

multiples of 10, using arrays.

use mental math to multiply

2-digit numbers.

use rounding to estimate.

use compatible numbers to

estimate.

solve multi-step problems.

4.NBT.3

4.NBT.5

4.OA.3

48


compatible numbers

¼-inch grid paper

place-value blocks

colored pencils

colored markers

crayons

¼-inch grid paper transparency

calculators

colored chalk,

Calendar Math: Dec Calendar

pieces, counting tape, clock,

measurement lesson Teacher

Manual pg.66-68

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

49



Grade: 4 Unit: Topic 8- Developing Fluency: Multiplying by 2-Digit Numbers

Time Frame: 5 Lessons



the operations with rational numbers, both



simpler ones.



How can arrays be used to find greater

products?

What is a standard procedure for multiplying

multi-digit numbers?


Students will know:


multiplying by two-digit numbers is

just an extension of the expanded

algorithm for multiplying with one-

digit numbers.

making an array with place-value

blocks provides a way to visualize and

find products using an expanded

algorithm.

the standard algorithm for multiplying

a two-digit number by a multiple of 10

is just an extension of the algorithm

for multiplying multi-digit numbers by

a one-digit number.

the standards multiplication algorithm

is a shortcut for the expanded

algorithm. Regrouping is used rather

than showing all partial products.

sometimes the answer to one

problem/question is needed to find the

answer to another problem/question.


multiply 2-digit factors

with arrays.

multiply using arrays and

an expanded algorithm

with partial products.

multiply 2-digit factors by

multiples of 10.

multiply two 2-digit

numbers.

solve problems that involve

two questions.

4.NBT.5

VOCABULARY RESOURCES/MATERIALS ASSESSMENT/

PROJECT

No New Vocabulary Introduced

¼-inch grid paper


colored pencils

crayons

colored chalk

tape

Calendar Math: Dec Calendar

pieces, counting tape, clock,

measurement lesson Teacher

Manual pg.66-68

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

50



Grade:4 Unit: Topic 9- Number Sense Dividing by One Digit Divisors Time Frame:6 Lessons


Patterns, Relations, and Functions. Relationships

can be described and generalizations made for

mathematical situations that have numbers or

objects that repeat in predicable ways. For some


equations can be used to describe how members of

one set are related to members of a second set

Estimation. Numbers can be approximated by

numbers that are close. Numerical calculations can

be approximated by replacing numbers with other





Operation Meanings and Relationships. There are

multiple interpretations of addition, subtraction,

multiplication and division of rational numbers,

and each operation is related to other operations.

Practices, Processes and Proficiencies.


to solve problems.

What are different meanings of division?

How can mental math and estimation be

used to divide?


Students will know:

basic math facts and place-

value patterns can be used to

dive multiples of 10 and 100

by one digit numbers.

substituting compatible

numbers is an efficient

technique for estimating

quotients

mentally multiplying by

different powers of 10 will

help you arrive at an estimate

for a quotient of a multi-digit

division problem.

the remainder when dividing

must be less than the divisor.

The nature of the question

asked determines how to

interpret and use the

remainder.


use basic facts and patterns

of zero to solve division

problems with 3 digit

dividends and 1 digit

divisors.

use compatible numbers and

rounding to estimate

quotients.

estimate quotients of multi-

digit division problems

using multiplication facts

and place value concepts.

divide whole numbers by 1

digit divisors resulting in

quotients with remainders

use words and models to

represent multiplication and

division problems accurately

4.NBT.6

4.NBT.5

4.OA.2

4.OA.3

51

some real – world problems

involving joining equal

groups, separating equal

groups, or comparison can be

solved using multiplication;

others can be solved using

division.



picture or diagram and used




completing a number


draw pictures and write

related number sentences to

solve problems


divisor

multiple

factor

quotient

product

division

remainder

two color counters

Calendar Math: January


Daily Depositor , measurement

lesson Teacher Manual 81-82

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

52



Grade: 4 Unit: Topic 10- Developing Fluency: Dividing by 1-Digit Divisors Time Frame: 7 Lessons



subtraction, multiplication, and division of rational

numbers, and each operation is related to the other

operations.


operations with rational numbers. Most algorithms

for operations with rational numbers, both mental






close and easy to compute mentally.


solve problems.

How can repeated subtraction be used to

model division?

What is the standard procedure for

dividing multi-digit numbers?


Students will know:

repeated subtraction can be

modeled and solved using

division.

repeated subtraction

situations can be solved

using a division algorithm

different form the standard

algorithm.

the sharing interpretation

of division can be used to

model the standard division

algorithm.

the standard division

algorithm breaks the


calculations using basic

facts, place value, the

relationship between

multiplication and division,

and estimation.

the relationship between

multiplication, division,

and estimation can help

determine the place value

of the largest digit in a

quotient.


use repeated subtraction to

model division.

record division as repeated

subtraction.

use place value to understand

the algorithm of long division.

use the standard algorithm to

divide 2-digit by 1-digit

numbers.


divide 3-digit numbers by 1-

digit numbers.


divide 3-digit numbers by 1-

digit numbers and properly

decide where to begin

dividing.

estimate and find quotients for

4-digit dividends and 1-digit

divisors.

identify the hidden question in

a multi-step problem. Then

use the answer to that hidden

question to solve the original

problem.

4.NBT.6

4.OA.3

53



solving a sub-problem(s)

and then using that

answer(s) to solve the

original problems.


No New Vocabulary

Introduced

two-color counters

place-value blocks

blank recording sheet

Calendar Math: January calendar

pieces, counting tape, Daily

Depositor, measurement lesson

Teacher Manual pg.81-82,

Exemplar “Camping”

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

54



Grade: 4 Unit: Topic 11- Fraction Equivalence and Ordering Time Frame: 7 Lessons



and numbers can be classified and represented

in different ways.








ways.



How can the same fractional amount be named

using symbols in different ways?

How can fractions be compared and ordered?


Students will know:

every counting number is

divisible by 1 and itself, and some

counting numbers are also

divisible by other numbers.

some counting numbers have

exactly two factors; others have

more than two.

the product of any nonzero

number and any other nonzero

number is divisible by each

number and is called a multiple of

each number.

the same fractional amount can be

represented by an infinite set of

different by equivalent fractions.

Equivalent fractions are found by

multiplying or dividing the

numerator and denominator by

the same nonzero number.


denominator, the fraction with the

greater numerator is the greater

fraction. If two fractions have the

same numerator, the fraction with

the lesser denominator is the

greater fraction.


learn how to find factors of

a number.

learn to identify prime and

composite numbers.

find multiples of a number.

use models and computation

to find equivalent fractions

using a number line.

use benchmark fractions to

compare fractions with

unlike denominators.

use common denominators

and equivalent fractions to

order fractions with unlike

denominators.

write to explain whether an

answer is correct or not.

4.OA.4

4.NF.1

4NF.2

55

ordering 3 or more numbers is

similar to comparing 2 numbers

because each number must be

compared to the other numbers.

mathematical explanations can be

given using words, pictures,

numbers, or symbols. A good

explanation should be correct,

simple, and easy to understand.


fraction

denominator

numerator

benchmark fraction

equivalent fractions

prime number composite number


color tiles

fraction models: strips

strips of paper

number lines

Calendar Math: February


coin counter, graph,

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

56



Grade: 4 Unit: Topic 12- Adding and Subtracting Fractions and Mixed Numbers

with Like Denominators Time Frame: 11 Lessons


There is more than algorithm for each of the

operations with rational numbers. Some





simpler ones.















What does it mean to add and subtract

fractions and mixed numbers with like

denominators?

What is a standard procedure for adding and

subtracting fractions and mixed numbers with

like denominators?

How can fractions and mixed numbers be

added and subtracted on a number line?


Students will know:

a model can be used to add

two or more fractions

when adding fractions with

like denominators, you are

adding portions of the

same size. So you can add

the numerators without

changing the denominator.

one way to add mixed

numbers is to add the

fractional parts and then

add the whole number

parts. Sometimes whole

numbers or fractions need

to be renamed.


use models to add fractions

with like denominators.

use computational procedures

to add fractions with like

denominators and solve

problems.

use models to subtract

fractions with like

denominators.

use computational procedures

to subtract fractions with like

denominators and solve

problems.

use the number line to add and

subtract fractions with like

denominators.

4.NF.3

4.NF.3a

4.NF.3c

4.NF.3d

57

one way to subtract mixed

numbers is to subtract the

whole number parts.

Sometimes whole numbers

or fractions need to be

renamed.

models can be used to

show different ways of

adding and subtracting

mixed numbers.

positive fractions can be

added or subtracted by

locating a fraction on the

number line and then

moving to the right to add

or to the left to subtract.

fractional amounts greater

than 1 can be represented

using a whole number and

a fraction. Whole number

amounts can be represented

as fractions. When the

numerator and

denominator are equal, the

fraction equals 1.

a fractional amount can be

decomposed into a sum of

fractions in more than one

way.


can often be shown using a

diagram and used to solve

the problem. Some



number sentence or

equation.

identify and write mixed

numbers as improper fractions

as mixed numbers.

use models to add and subtract

mixed numbers.

use models and computational

procedures to add mixed

numbers.

use models and computational

procedures to subtract mixed

numbers.

decompose fractions and

represent them as

compositions of fractions in a

variety of ways.

will draw a picture and write

an equation to solve a

problem.


mixed number

improper fraction

fraction models: strips and circles

colored pencils

Calendar Math: February calendar

pieces, counting tape, coin

counter, graph,

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

58



Grade: 4 Unit: Topic 13- Extending Fraction Concepts Time Frame: 10 Lessons


Numbers, expressions, measures, and objects can

be compared and related to other numbers,


ways.


Whole numbers, integers and fractions are real


with a unique point on a number line.





The base 10 numeration system is a scheme for

recording numbers using digits 0-9, groups of 10

and place value.


to solve problems.

How is decimal numeration related to whole

numbers numeration?

How can decimals be compared and

ordered?

How are fractions and decimals related?


Students will know:

physical representations and

symbols can be used to

develop the understanding that

a/b = a x 1/b.

models can be used to find the

product of a whole number and

a fraction.

to multiply a fraction by a

whole number, one must

multiply the whole number by

the numerator of the fraction

and then divide the product by

the denominator of the

fraction.

the decimal is another name for

a fraction.

each fraction, mixed number,

and decimal can be associated

with a unique point on the

number line.


use unit fractions and

multiplication to describe

fractions that are multiples of

unit fractions.

multiply a fraction by a whole

number using models.

multiply a whole number and

a fraction to solve problems.

understand how to write

fractions as decimals and

decimals as fraction.

learn to locate and name

fractions and decimals on a

number line.

understand how to use

equivalent fractions to write

fractions as decimals.

use models and place-value

charts to represent decimals to

the hundredths. They will

read and write decimals in

expanded, standard, and word

form.

4.NF.4a,b,c

4.NF.5

4.NF.6

4.NF.7

4.MD.2

59

every fraction can be

represented by an infinite

number of equivalent fractions,

but each fraction is represented

by the same decimal or an

equivalent form.

decimal numeration is just an

extension of whole number

numeration.


compare and order numbers.


be shown with a picture or

diagram and used to

understand and used to

understanding and solve the

problem.

use models and place-value

charts to compare decimals to

hundredths. They will use

greater than and less than

symbols to order decimal

numbers.

Use place-value charts to

read, write, and compare

decimal, tenths and

hundredths using money.

solve problems using the

strategy Draw a Picture.


unit fraction

decimal point

hundredth, tenth

fraction strips, decimal models

(Teaching Tool 17), number lines

(Teaching Tool 14), Decimal

Place Value (Teaching Tool 31),

Decimal Place- Value Table

(Teaching Tool 32). Bills and

coins (Teaching Tool 19) place-

value charts (Teaching Tool 10)

rulers (Teaching Tool 20 or 21)

Calendar Math: March calendar


counter, measurement, graph,

Exemplar: ‘Disappearing

Cookies”

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

60



Grade: 4 Unit: Topic 14- Measurement Units and Conversions Time Frame: 11 Lessons




Some measurements can be approximated

using know referents as the unit in the

measurement process.

Relationships can be described and generalized

made for mathematical situations that have

numbers or objects that repeat in predictable

ways. For some relationships, mathematical

expressions and equations can be used to

describe how members of one set are related to

members of a second set.



What are customary and metric units for

measuring length, capacity, and weight/mass,

and how are they related?


Students will know:

length can be estimated and

measured in different systems

(customary, metric) and using

different units in each system

that are related to each other.

capacity is a measure of the

amount of a liquid a container

can be measured in different

systems (customary, metric) and

using different units in each

system that are related to each

other.

the weight of an object is a

measure of how heavy an object

is.

mass is a measure of the

quantity of matter in an object.

Weight and mass are different

measures.

time can be expressed using

different units that are related to

each other.

length can be estimated in

different measurement systems.


estimate and measure length

by choosing the most

appropriate unit of length.

estimate fluently with

customary capacity units

(cups, pints, quarts, and

gallons). They will compare

the relative sized of capacity

measurements.

estimate fluently and

measure with units of

weight.

convert between customary

units.

solve and explain the

answers to each problem in

writing.

estimate and measure length

to the nearest centimeter, and

choose the most appropriate

metric unit for measuring

length.

estimate fluently with

milliliters and liters. They

will measure capacity using

these metric units.

4.MD.1

4.MD.2

61

relationships between

customary measurement units

can be expressed as a function

(e.g., 12 inches to 1 ft or 12 in =

1ft.) Relationships exist that

enable you to convert between

customary units of the same

attribute by multiplying or

dividing.

relationships between metric

units can be expressed as a

function (e.g. 10mm to 1 cm or

10mm =1cm). Relationships

exist that enable you to convert

between metric units of the

same attribute by multiplying or

dividing.

mathematical explanations can

be given using words, pictures,



simple, complete, and easy to

understand.

some problems with the initial

data point unknown can be

solved by starting with the end

result by reversing the steps and

processes to work backward to

find the initial data point.

estimate and measure with

units of mass – grams and

kilograms.

convert between metric

units.

compare several different

units of time and freely

convert from one unit of

time to another.

solve problems that require

finding the original times,

measurements, or quantities

that led to a result that is

given.


inch

foot

yard

mile

capacity

weight

ounce

pound

ton

millimeter

centimeter

decimeter

meter

kilometer

milliliter

liter

mass

gram

kilogram

rulers

yardstick

masking tape

examples of a cup, pint, quart,

gallon containers

place-value blocks

tag board

eyedropper

1-liter bottle

Calendar Math: March calendar


counter, graph, measurement

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

62



Grade: 4 Unit: Topic 15- Solving Measurement Problems Time Frame: 5 lessons


Some attributes of objects are measurable and can

be quantified using unit amounts.




collected and how best to collect it. Data can be

represented visually using tables, charts, and




to solve problems.

What do area and perimeter mean and how

can each be found?

How can line plots and other tools help to

solve measurement problems?


Students will know:


applying the formula for the

perimeter of a rectangle or the

formula for the area of a

rectangle.

some measurement problems can

be represented and solved using

models.

making change is often easiest

by counting from the smaller

amount to the larger amount.

some data can be represented

using a line plot and the line plot

can be used to answer certain

questions about the data.


breaking apart or changing the

problem into simpler ones.

Recording information in a table

can help one understand and

solve some problems.


use the formulas for the

perimeter and area of

rectangles to solve real-

world problems.

use diagrams to show data

and analyze how the

quantities are related to solve

real-words measurement

problems.

solve real-world problems

that involve money and

giving change by counting.

construct line plots using

given data and use the line

plot to answer questions

about the data set.

break a problem into smaller,

more manageable pieces and

find a pattern to fit.

4MD.2

4MD.3

4MD.4


perimeter

area

line plot

bills and coins

recording sheet: Line Plot Data

Calendar Math: April/May


measurement, Daily Depositor,

measurement,

Exemplar: “Carpet Caper”

“Harvest Dinner”

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

63



Grade: 4 Unit: Topic 16- Lines, Angles and Shapes Time Frame: 11 Lessons


Geometric Figures: Two- and three-

dimensional objects with or without curved

surfaces can be described, classified and

analyzed by their attributes.

Measurement: Some attributes of objects are

measurable and can be quantified using unit

amounts.



How can lines, angles, and shapes be

described, analyzed and classified?

How are angles measured, added and

subtracted?


Students will know:

point, line and plane are the

core attributes of space

objects, and the real world

situations can be used to think

about these attributes

line segments and rays are sets

of points that describe parts of

lines, shapes, and solids.

Angles are formed by two

intersecting lines or by rays

with a common endpoint and

are classified by size.

two-dimensional or plane

shapes have many properties

that make them different from

one another. Polygons can be

described and classified by

their sides and angles

some shapes can be reflected

across one or more lines

passing through the shape so

the shape folds into itself

exactly.

the measure of an angle

depends upon the fraction of

the circle cut off by its rays

the unit for measuring the size

of an opening of an angle is 1

degree


identify and describe points,

lines, and planes

learn geometric terms to

describe parts of lines and

types of angles

use unit angles and fractions

of a circle to find angle

measurement

use a smaller angle to

measure a larger angle by

repeating the unit

measure and draw angles

find unknown angle

measures by adding and

subtracting

learn to identify polygons

learn to identify and classify

triangles

identify quadrilaterals

determine if a plane figure

has line symmetry and if so,

how many lines of

symmetry it has

solve problems by making

and testing generalizations

4.G.1

4.G.2

4.G.3

4.MD.5

4.MD.5a

4.MD.5b

4.MD.6

4.MD.7

64

angle measures can be added

or subtracted

commonalities in attributes of

objects or situations can be

found and used to make

generalizations about

relationships


point, line, plane, parallel lines,

intersecting lines, perpendicular

lines, line segment, ray, angle,

right angle, acute angle, obtuse

angle, straight angle, degree, unit

angle, angle measure, protractor,

polygon, side, vertex, triangle,

quadrilateral, pentagon, hexagon,

octagon, equilateral triangle,

isosceles triangle, scalene

triangle, right triangle, acute

triangle, obtuse triangle, rhombus,

trapezoid, parallelogram,

rectangle, square, symmetric, line

of symmetry

centimeter ruler(Teaching Tool

4), dot paper (Teaching Tool 7),

clock face (Teacher Tool 23),

pattern blocks (Teacher Tool

25), recording sheet, blank

protractors (Teaching Tool 34),

rulers (Teaching Tool 21),

polygons (Teaching Tool 25),

Calendar Math: January


coin counter,

Formative

Homework

Teacher observation


Quizzes

Summative

Topic test

65



Grade: 5 Unit: Topic 1- Place Value Time Frame: 6 lessons


The base ten numeration system is a scheme for

recording numbers using digits 0-9, groups of

ten, and place value.


numbers can be classified and represented in

different ways.



expressions, measures and objects in different

ways.



How are whole numbers and decimals written,

compared, and ordered?


Students will know:

numbers can be used to tell

how many.( 1-1,1-4)

our number system is

based on groups of ten.

Whenever we get 10 in one

place, we move to the next

greater place value. (1-1,1-

2,1-3,1-4)


compare and order whole

numbers and decimals.(1-

5)


identifying elements that

repeat in a predictable way.

(1-6)


write the standard expanded,

and word forms of whole

numbers in the billions and

identify the value of digits in

whole numbers. (1-1)

represent decimals (tenths and

hundredths) as fractions.

Students also represent

fractions with denominators of

10 and 100 as decimals. (1-2)

represent decimals

(thousandths) as fractions and

fractions with denominators of

1,000 as decimals. (1-3)

write decimals in standard

form, word form, and

expanded from though

thousandths. (1-4)

Students compare and order

decimals through thousandths.

(1-5)

look for patterns with decimal-

number sets in order to solve

problems. (1.6)

5.NBT.1

5.NBT.3a

5.NBT.3.b

66


digits

value

standard form

expanded form

word form

equivalent decimals

Calendar Math:

Daily Depositor

Counting Tape and Daily Decimal

A Fraction a Day

Exemplar:

Chocolate Chip Cookie Rubric

Interactive Learning Recording

Sheet ( Teaching Tool 4)

Fraction Model Strips ( Teaching

Tool 5)

10x10x10 cube

place value chart (Teaching Tool

6)

Comparing and ordering decimals

( Teaching Tool 7)

Problem Solving: Look for a

Pattern ( Teaching Tool 8)

Optional:

Hand-On Standards : Algebra:

Lessons 1-4

Formative

Daily Common core review

Informal observation


Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

67



Grade: 5 Unit: Topic 2- Adding and Subtracting Decimals Time Frame: 8 lessons



the operations with rational numbers, both


equivalence to transfer calculations into simpler

ones.

The set of numbers is infinite and ordered.

Whole numbers and decimals are real numbers.

Each real number can be associated with a

unique point on a number line.





mentally.




repeat in predictable ways.


applied to solve problems

How can sums and differences of decimals be

estimated?

What are the standard procedures for adding

and subtracting whole numbers and decimals?


Students will know:


do a mental calculation.

Techniques for doing

addition or subtraction


changing the numbers so the

calculation is easy to do

mentally. (2-1)

a number line can be used to

round whole numbers and

decimals by making it easy to

see which multiple of 10,

100, etc. a number is closest

to. (2-2)



Each estimation technique

gives one way to estimate by




compute sums and

differences mentally using

the Commutative and

Associative Properties of

Addition, compatible

numbers, and compensation.

(2-1)

round whole numbers

though millions and

decimals through

thousandths. (2-2)

use rounding and compatible

numbers to estimate sums

and differences of whole

numbers and decimals (2-3)

will add and subtract

decimals in tenths and

hundredths using models.

(2-4)

5.NBT.4

5.NBT.7

68

easy to compute with

mentally. (2-3)

models and algorithms for

adding and subtracting multi-

digit decimals are just an

extension of models and

algorithms for adding or

subtracting multi-digit whole

numbers. (2-4)



diagram and used to solve a



completing a number

sentence or equation. (2-5)

adding or subtracting multi-

digit decimals is similar to

adding or subtracting multi-

digit whole numbers. (2-6,2-

7)


by first finding and solving a

sub-problem(s) and then

using that answer(s) to solve

the original problem. (2-8)

use pictures and write

equations to help them solve

problems. (2-5)

compute sums of decimals

involving tenths,

hundredths, and

thousandths. (2-6, 2-7)

use multiple steps to solve a

variety of problems. (2-8)


Commutative Property

Associative Property

compensation

compatible numbers

rounding

Calendar Math:

Daily Depositor

Counting Tape and Daily

Decimal

A Fraction a Day

Exemplar:

Holiday Fair

Place value materials

Teaching Tool (1, 9, 10, 11, 12)

Problem Solving Recording

Sheet

Optional:

Hands-On Standards: Number

and Operations: Lesson 5,6,13

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

69



Grade: 5 Unit: Topic 3- Multiplying Whole Numbers Time Frame: 9 lessons


For a given set of numbers there are relationships,

that are always true called properties, and these are

the rules that govern arithmetic and algebra.

: Relationships can be described and


that have numbers or objects that repeat in

predictable ways.


close. Numerical calculations can be



mentally.



different ways.

Each operation with rational numbers has more

than one algorithm. Most algorithms for operations

with rational numbers. Both mental math and

paper and pencil, use equivalence to transform

calculations into simpler ones.


to solve problems.

What are the standard procedures, for

estimating and multiplying whole

numbers?


Students will know:

the properties of multiplication

can be used to simplify

computation and to verify

mental math and paper and

pencil algorithms. ( 3-1)



products when one factor is a

multiple of 10 or a multiple of

100. ( 3-2)


estimate a product.

each estimation technique

gives one way to estimate by



easy to compute with mentally.

(3-3)


identify and apply the

commutative Associative,

Associative, Identify, and

Zero Properties of

Multiplication.(3-1)

mentally compute products of

whole numbers using place-

value patterns, and the

properties of multiplication.

(3-2)

use rounding or compatible

numbers to estimate products

of whole numbers. (3-3)

use exponential notation.(3-4)

use the Distributive Property

to simplify expressions and

solve equations.(3-5)

5.NBT.2

5.NBT.5

5.NBT.6

70

some numbers can be

represented using a base

number and an exponent.(3-4)

the properties of multiplication

can be used to simplify

computation and to verify

mental math and paper and

pencil algorithms. ( 3-5 & 3-8)


algorithm breaks the


calculations using place value

starting with the ones, then the

tens, and so on. (3-6 & 3-7)



diagram and used to solve the

problem.(3-9)


by writing and completing a

number sentence or equation.

(3-9)

use partial products or the

traditional algorithm to

multiply multi-digit numbers

by a one-digit number. (3-6)

multiply two-digit numbers.

(3-7)

multiply two-digit numbers by

factors with more than two

digits. (3.8)

use diagrams and write

equations to solve problems.

(3.9)



Multiplication

Associative Property of

Multiplication

Identity Property of Multiplication

Zero Property of Multiplication


factors

product

multiple

overestimate

underestimate

partial product

base

exponent

power

exponential notation

expanded form

standard form

squared

cubed

Calendar Math:

Daily Depositor


A Fraction a Day

Arrays & Factor Figures

Exemplar:

The Great Pizza Dilemma

Two-color counters ( Teaching

Tool 13)

Exponents (Teaching Tool 14)

Distributive Property ( Teaching

Tool 15 and 18)

Straightedges,

colored pencils,

small grid paper ( Teaching Tool

16)

Problem-solving Recording sheet

( Teaching Tool 1)

Optional:

Hands-On Standards: Algebra:

Lesson 5,6,7

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

71



Grade: 5 Unit: Topic 4- Dividing by 1-Digit Divisors Time Frame: 7 lessons


Relationships can be described and generalizations

made for mathematical situations that have numbers

or objects that repeat in predictable ways. For some


equations can be used to describe how members of

one set are related to members of a second set.


operations with rational numbers. Some strategies

for basic facts and most algorithms for operations

with rational numbers, both mental math and paper

and pencil, use equivalence to transfer calculations

into simpler ones.










value.


solve problems

What is the standard procedure for

division and why does it work?


Students will know:



divide multiples of 10, 100

and so forth by one-digit

numbers. (4-1)

there is more than one way

to estimate a quotient.

Substitute compatible


technique for estimate

quotients. (4-2)

answers to problems

should always be checked

for reasonableness and this

can be done in different

ways. Two ways are to use


find the quotient of a division

problem whose dividend is a

multiple of 10, where division

involves a basic fact. (4-1)


numbers to estimate quotients

of whole numbers. (4-2)

check problems for

reasonableness by using

various methods, including

estimation and checking their

final answer. (4-3)

find quotients using the model

of sharing money. (4-4)

5.NBT.6

72

estimation and to check the

answer against the question

in the problem. (4-3)

the sharing interpretation

of division and money can

be used to model the

standard division

algorithm. (4-4, 4-5, 4-6)


can often be shown using a

diagram and used to solve

the problem. Some



number sentence or

equation. (4-7)

divide three-digit whole

numbers by one-digit divisors.

(4-5)

divide with zeros in the

quotient. (4-6)

use pictures and equations to

help them represent

remainders in a problem. (4-7)


dividend

divisor

quotient

Calendar Math:

Daily Depositor


A Fraction a Day

Arrays and Factor Figures

April Graphing

Exemplar:

Making a Fair Decision

Multiplication Table

Bills and Coins

Number cubes

Teaching Tool (1,17, 18)

Problem Solving Recording Sheet

Optional:

Hands-On Standards: Numbers &

Operations: Lesson 7,8,15

Algebra: Lesson 8

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

73



Grade: 5 Unit: Topic 5- Dividing by 2-digit divisors Time Frame: 8 lessons





repeat in predictable ways. For some



members in one set are related to members of a

second set.





with mentally. Some measurements can be




the operations with rational numbers. Most

algorithms for operations with rational

numbers, both mental math and paper and

pencil, use equivalence to transform


Doing mathematics involves a variety of

processes including problem solving,

reasoning, communicating, connecting, and

representing.

What is the standard procedure for dividing

with two-digit divisors?


Students will know:

using basic facts and

patterns can be helpful in

dividing by multiples of 10

( 5-1)

there was more than one

way to estimate a quotient.

Substituting compatible


technique for estimating

quotients. (5.2, 5.7)

using area models and

arrays can help understand

the algorithm for dividing

by 2-digit divisors. ( 5-3)


find the quotients of division

problems whose dividends and

divisors are multiples of 10,

where the division involves a

basic fact.(5-1)

use estimation to find

approximation solutions to

division problems with two-

digit divisors using compatible

numbers. (5-2)

use arrays and area models to

model division. (5-3)

find quotients with a two-digit

divisor that is a multiple of ten.

(5-4)

5.NBT.6

74

dividing by 2 digit divisors

is just an extension of the

steps for dividing with 1-

digit divisors. Estimation

and place value can help

determine the placement of

digits in the quotient. (5-

4;5-5;5-6)

some real-world quantities

have a mathematical

relationship; the value of

one quantity cab be found

if you know the value of

the other quantity. Patterns

can sometimes be used to

identify the relationship

between quantities. (5.5)

dividing with multi-digit is

just an extension of the

steps for dividing with 1

and 2-digit divisors,

Estimation and place value

can help determine the

placement of digits in the

quotient.(5-7)


solved by writing and

completing a number

sentence or equation. (5-8)

find one-digit quotients where

the divisor is a two-digit

number. (5-5)

divide a three-digit number by a

two-digit number to find a two-

digit quotient (5-6)

solve problems involving

division of numbers with 4 or 5

digits by 2-digit divisors with an

estimate, or by using a

calculator when the exact

answer is needed. . (5-7)

determine which information is

missing identify extraneous

information in problems. (5-8)



Calendar Math:

Daily Depositor


A Fraction a Day

Exemplar:

Fish Dilemma

grid paper

calculator

Problem Solving Recording Sheet

( Teaching Tool 1)

Optional:

Hands-On Standards: Number and

Operations: Lesson 18,19

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

75



Grade: 5 Unit: Topic 6- Multiplying Decimals Time Frame: 7 lessons




numbers or objects that repeat in predictable ways.

For some relationships, mathematical expressions

and equations can be used to describe how


second set.


close. Numerical calculations can be







operations with rational numbers. Most algorithms

for operations with rational numbers, both mental




to solve problems.

What are the standard procedures for

estimating and finding products involving

decimals?


Students will know:

patterns can be used to mentally

multiply decimals by 10, 100,

and 1,000. ( 6-1)

rounding and compatible

numbers can be used to estimate

the product of a whole number

and a decimal. (6-2)

compare each factor to 1 as a

way of determining if you have

placed the decimal point

reasonably.

( 6-3)


algorithm involving decimals is

an extension of the standard

algorithm for multiplying whole

numbers. (6-4)


mentally multiply decimals by

10,100, and 1,000.(6-1)


numbers to estimate products

of whole numbers and

decimals. Students also

identify estimates as

overestimates or

underestimates. (6-2)

will use number sense and

place value to multiply

decimals. (6-3)

find products of whole

numbers and decimals to ten

thousandths. (6-4)

use a standard algorithm to

multiply a whole number and

a decimal. (6-5)

5.NBT.2

5.NBT.7

76

the steps for multiplying whole

numbers by decimals are similar

to the steps for multiplying two

whole numbers. Place value

determines the placement of the

decimal point in a product.. (6.5)

steps for multiplying decimals

are similar to steps for

multiplying whole numbers.

Place value determines the

placement of the decimal point in

a product. The product of two

decimals less that one is less than

either factor..(6.6)


first finding and solving a sub-

problem(s) and then using that

answer to solve the original

problem .(6.7)

will use the standard

algorithm to multiply

decimals by decimals (6-6)

find the hidden question or

questions to solve multiple-

step problems. (6-7)



Calendar Math:

Daily Depositor


Decimal

A Fraction a Day

Graph and Measurement Nov.

Whole Day Celebration Feb.

Exemplar:

M&M Cookie Combos

Multiplying decimals by

10,100,and 1,000 (Teaching Tool

19)

Estimating the product of a

decimal and a whole number

(Teaching Tool 20)

Decimal Grids (Teaching Tool

21)

Colored pencils

Multiplying a whole number and

a decimal ( Teaching Tool 41)

Multiplying Two Decimals

(Teaching Tool 22)

Optional:


and Operations: Lesson 7

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

77



Grade: 5 Unit: Topic 7- Dividing Decimals Time Frame: 7 lessons


The base-ten numeration system is a scheme

for recording numbers using digits 0-9, groups

of 10, and place value.










expressions, measures and objects in different

ways.




for operations with rational mumbers, both


equivalence to transfer calculations into simpler

ones.







What are the standard procedures for

estimating and finding quotients involving

decimals?


Students will know:

place-value patterns can be

used to mentally divide

decimals by 10,100, or 1000

(7-1)

estimating quotients for whole

number divisors and dividends

can be applied to calculations

with decimal dividends and

divisors. Substitute compatible

numbers can be used in most

cases. (7-2)


mentally divide decimals by

10, 100, or 1000. (7-1)

will learn to estimate

quotients involving decimals,

and to use reasoning to

understand how the size of

the quotient relates to the

dividend and divisor. (7-2)

will learn how to use

reasoning to correctly place

the decimal point in a

quotient. (7-3)

5.NBT.6

78

the location of decimal points

in decimal division

calculations can sometimes be

decided by reasoning about the

relative size of the given

numbers. (7-3)

the standard division algorithm

involving decimals is an

extension of the standard

algorithm for dividing whole

numbers. (7-4)

a number divided by a decimal

can be represented as an

equivalent calculation using

place value to change the

divisor to a whole number. (7-

5, 7-6)


by first finding and solving a

sub-problem(s) and then using

that answer(s) to solve the

original problem. (7-7)

find quotients where the

dividend and/or the quotient

is a decimal. (7-4)

divide whole numbers by

decimals. (7-5)

find quotients of two

decimals. (7-6)

use multiple steps to solve a

variety of problems. (7-7)



Calendar Math:

Daily Depositor


Decimal

A Fraction a Day

Graph and Measurement Nov.

Whole Day Celebration Feb.

Exemplar:

Busy Day

Calculator

Decimal Models

Decimal Grids


Sheet

Optional:


and Operations: Lesson 17

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

79



Grade: 5 Unit: Topic 8- Numerical Expressions, Patterns

and Relationships Time Frame: 9 lessons




numbers or objects that repeat in predictable ways.

For some relationships, mathematical expressions

and equations can be used to describe how


second set.

For a given set of numbers, there are relationships

that are always true, called properties, and these

are the rules that govern arithmetic and algebra.

Any number, measure, numerical expression.

Algebraic expression, or equation can be

represented in an infinite number of ways that have

the same value.




Rules of arithmetic and algebra can be used

together with notions of equivalence to transform

equations so solutions can be found.


to solve problems.

How are the values of an algebraic

expression and a numerical expression

found?


Students will know:

some mathematical phrases can

be represented using a variable in

an algebraic expression.(8-1)

there is an agreed upon order for

which operations in a numerical

expression are performed. (8-2)

to simplify a numerical

expression, first compute within

parenthesis. Second, evaluate all

terms with exponents.Then do

any multiplication and division

calculations from left to right

followed by any addition and

subtraction calculations from left

to right

( 8-3; 8-4)


write numerical expressions

with variables to represent

relations expressed

verbally.(8-1)

use given values for

variables to evaluate

numerical or algebraic

expressions with three or

more numbers and two or

more operations. (8-2)

use the order of operations

to simplify and solve basic

algebraic expressions. (8-3)

use the order of operations to

evaluate expressions with

whole numbers decimals.

5.OA.1

5.OA.2

5.OA.3

80

patterns can sometimes be used to

identify a relationship between

two quantities. Some real-world

quantities have a mathematical


quantity can be found if you know

the value of the other quantity.

(8-5;8-6)

patterns that repeat in predictable

ways may be used to identify

relationships. (8-7)

some mathematical phrases can

be represented using a variable in

an algebraic expression.(8-8)


using objects to act out the actions

in the problem. Some problems

can be solved by reasoning about

the conditions in the

problem.(8.9)

(8-4)

study completed tables to

determine a rule and write an

expression. (8-5)

study completed tables to

determine a rule and write an

expression. (8-6)

extend patterns in a table

using given rules and will

then look for the relationship

between corresponding terms

in the sequences. (8-7)

translate words into algebraic

expressions. (8.8)

solve problems by showing

how to act our the problem.

Students also use

information given in the

problem to draw conclusions.

(8.9


variable

algebraic expression

corresponding

sequence

term

order of operations

Calendar Math:

Daily Depositor


Decimal

A Fraction a Day

Sept. calendar

Jan. graphing

Exemplar:

Party Seating

counters

Place-value blocks (Teaching

Tool 24)

Optional:


Lessons 9

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

81



Grade: 5 Unit: Topic 9- Adding and Subtracting Fractions Time Frame: 10 lessons





value.

The set of numbers is infinite and ordered. Whole

numbers and decimals are real numbers. Each real

number can be associated with a unique point on a

number line.

Numbers can be used for different purposes, and


different ways.


operations with rational numbers. Some strategies

for basic facts and most algorithms for operations

with rational numbers, both mental math and paper

and pencil, use equivalence to transfer calculations

into simpler ones.








solve problems.

What does it mean to add and subtract

fractions with unlike denominators?

What is a standard procedure for

adding and subtracting fractions with

unlike denominators?


Students will know:

the same fractional amount can be

represented by an infinite set of

different but equivalent fractions.

Equivalent fractions are found by

multiplying or dividing the

numerator and the denominator by

the same nonzero number. (9-1)

a fraction is in simplest form when

1 is the only common factor of the

numerator and denominator (9-2)

mathematical explanations can be

given using words, pictures,



simple, complete and easy to

understand. (9-3)


write equivalent fractions.

(9-1)

identify fractions that are

in simplest form and find

the simplest form of a

fraction. (9-2)

explain how they estimated

fractional amounts of

objects. (9-3)

will use a number line to

estimate sums and

differences of fractions. (9-

4)

5.NF.1

5.NF.2

82

a number line can be used to

determine the nearest half or whole

a fraction is closest to. (9-4)

all non-zero whole numbers have

common multiples, including at

least one. Sometimes the least

common multiple of two numbers is

one of the numbers (9-5)

fractions with unlike denominators

can be added or subtracted by

replacing fractions with equivalent

fractions with like denominators.

The product of the denominators of

two fractions is a common

denominator of both (9-6, 9-7, 9-8,

9-9)


be shown using a diagram and used

to solve a problem. Some problems

can be solved by writing and

completing a number sequence or

equation.(9-10)

will determine the least

common multiples and

least common multiples of

numbers. (9-5)

will find common

denominators for fractions

with unlike denominators.

(9-6)

will use models and

computational procedures

to add fractions with unlike

denominators. (9-7)

will use models and

computational procedures

to subtract fractions with

unlike denominators. (9-8)

will solve problems

involving addition and

subtraction of fractions. (9-

9)

will draw a picture and

write an equation to solve a

problem (9-10)


Equivalent fractions

Simplest form

Benchmark fraction

Common multiple

Least common multiple (LCM)

Common denominator

Least common denominator (LCD)

Calendar Math:

Daily Depositor


Decimal

A Fraction a Day

Sept & Mar. graphing

Jan. measurement

Exemplar:

Disappearing Cookies

Calculator

Fraction Models

Number lines

(Teaching Tool 5, 25, 26, 28)

Hundred Charts


Sheet

Optional:


and Operations: Lesson 1,2,3,

8,9,10

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

83



Grade: 5 Unit: Topic 10- Adding and Subtracting Mixed Numbers Time Frame: 7 lessons














with.


Whole numbers, fractions, and mixed numbers

are real numbers. Each real number can be

associated with a unique point on the number

line. .



What does it mean to add and subtract mixed

numbers?

What is a standard procedure for adding and

subtracting mixed numbers


Students will know:

fractional amounts greater than

1 can be represented using a

whole number and a fraction.

Whole number amounts can be

represented as fractions. When

the numerator and

denominator are equal, the

fraction equals 1. Fractions

greater than 1 can be named

using a whole number and a

fraction of an improper

fraction.(10-1)

sums and differences of mixed

numbers can be estimated by

rounding the mixed number to

the nearest whole number. .

(10-2)


write improper fractions as

mixed numbers and mixed

numbers as improper fractions

and they place them on a

number line. (10-1)

estimate sums and differences

of fractions and mixed

numbers by rounding to the

nearest whole number.(10-2)

will use models to add and

subtract mixed numbers. (10-

3)

will use models and

computational procedures to

add mixed numbers. (10-4)

will use models and


subtract mixed numbers. (10-5)

5.NF.1

5.NF.2

84

models can be used to show

different ways of adding and

subtracting mixed numbers.

( 10-3)

one way to add mixed numbers

is to utilize a number line to

model and find common

denominators. Sometimes

whole numbers or fractions

need to be renamed. (10.4)

one way to subtract mixed

numbers is to utilize a number

line to model and find

common denominator.

Sometimes whole numbers or

fractions need to be renamed..

(10-5)


add or subtract mixed

numbers.(10-6)


often be shown with a picture

or diagram, which can be used




completing a number sentence

or equation.(10-7)

will solve more complex

problems involving the

addition and subtraction of

mixed numbers. (10-6)

draw a picture and write an

equation in order to accurately

solve a problem. (10-7)


improper fraction

mixed number

proper fraction

Calendar Math:

Daily Depositor


A Fraction a Day

Feb. measurement

Exemplar:

Galaxy Araca

fractional models (Teaching Tool

5)

Problem Solving recording sheet

( Teaching Tool 1)

Optional:

Hands-On Standards: Number and

Operations: Lesson 11,12

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

85



Grade: 5 Unit: Topic 11- Multiplying and Dividing Fractions and Mixed Numbers

Time Frame: 11 lessons














with.


the operations with rational numbers. Most

algorithms for operations with rational

numbers, both mental math and paper and

pencil, use equivalence to transform




What are standard procedures for estimating

and finding products and quotients of fractions

and mixed numbers?


Students will know:

a fraction describes the division of

a whole into equal parts, and it can

be interpreted in more than one

way depending on the whole to be

divided. .(11-1)

the product of a whole number and

a fraction can be interpreted in

different ways. One interpretation

is repeated addition. Multiplying a

whole number by a fraction

involves division as well as

multiplication. The product is a

fraction of the whole number. (11-

2)

rounding and compatible numbers

can be used to estimate the product

of fractions or mixed numbers.

( 11-3)


write improper fractions as

mixed numbers and mixed

numbers as improper

fractions and they place

them on a number line. (10-

1)

estimate sums and

differences of fractions and

mixed numbers by rounding

to the nearest whole

number.(10-2)

will use models to add and

subtract mixed numbers.

(10-3)

will use models and


add mixed numbers. (10-4)

5.NF.1

5.NF.2

86

a unit square can be used to show

the area of meaning fraction

multiplication. When you multiply

two fractions that are both less

than 1, the product is smaller than

either fraction. To multiply

fractions, write the product of the

denominators. (11-4;11-5))

one way to find the product of

mixed numbers is to change the

calculation to an equivalent one

involving improper fractions. (11-

6)

the relative size of factors can be

used to determine the relative size

of the product.(11-6)

the relative size of the factos can

be used to determine the relative

size of the product.(11-7)




answer(s) to solve the original

problem.( 11-8)

one way to find the quotient of a

whole number divided by a

fraction is to multiply the whole

number by the reciprocal of the

fraction (11-9)

the inverse relationship between

multiplication and division can be

used to divide with fractions.(11-

10)


be shown with a a diagram and

used to solve the problem. Some

problems can be solved by writing

and completing a number sentence

or equation. (11-11)

will use models and


subtract mixed numbers.

(10-5)

will solve more complex

problems involving the

addition and subtraction of

mixed numbers. (10-6)

draw a picture and write an

equation in order to

accurately solve a problem.

(10-7)

87


improper fraction

mixed number

proper fraction

Calendar Math:

Daily Depositor


Decimal

A Fraction a Day

Feb. measurement

Exemplar:

Deluxe Birthday Cake

fractional models ( Teaching

Tool 5)

Problem Solving recording

sheet

( Teaching Tool 1)

Optional:


and Operations: Lesson 14,16

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

88



Grade: 5 Unit: Topic 12- Volume of Solids Time Frame: 7 Lessons


Two- and three-dimensional objects with or



objects location in space can be described

quantitatively.



How can three-dimensional shapes be

represented and analyzed?

What does the volume of a rectangular prism

mean and how can it be found?


Students will know:

three-dimensional or solid figures

have length, width, and height.

Many can be described, classified,

and analyzed by their faces, edges,

and vertices. Many everyday

objects closely approximate

standard geometric solids. (12-1)

the shape of a solid can sometimes

be determined by analyzing

different views of the solid. (12-2)


breaking apart or changing the

problem into simpler ones, solving

simpler ones, and using those

solutions to solve the original

problem (12-3)

volume is a measure of the amount

of space inside a solid figure.

Volume can be measured by

counting the number of cubic units

needed to fill a three –dimensional

object (12-4, 12-5)

the volume of some objects can be

found by breaking apart the object

of into other objects from which the

volume can be found. (12-6)


using objects to act out the action in

the problem. Some problems can be

solved by reasoning about

conditions in the problem. (12-7)


will identify three

dimensional shapes

according to faces, edges,

and vertices. (12-1)

identify different views of

a solid. (12-2)

will use objects to act out

and break apart problems

into simpler ones in order

to reach a solution. (12-3)

will determine the volume

of regular solids. (12-4)

will count cubic units and

use formulas to find the

volume of rectangular

prisms. (12-5)

will find volumes of

irregular solids. (12-6)

will use objects and

reasoning to find volumes

of solid figures. (12-7)

5.MD.3

5.MD.3.a

5.MD.3.b

5.MD.4

5.MD.5

5.MD.5.a

5.MD.5.b

5.MD.5.c

89


three-dimensional shape

cube

edge

face

vertex (pl: vertices)

cone

cylinder

prism

pyramid

volume

cubic unit

Calendar Math:

Daily Depositor


Decimal

calendar for Sept., Oct., Nov.,

Jan, Feb,. Mar., Apr.

Whole day celebration Feb.

Measurement March

Exemplar:

Carpet Caper

Power Solids

Centimeter Cubes

Centimeter

Grid Paper

Unit Cubes

Folders

(Teaching Tool 1, 31, 32)

Optional:

Hands-On Standards:

Geometry: Lesson 16

Measurement: Lesson 5-9

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

90



Grade: 5 Unit: Topic 13- Units of Measure Time Frame: 7 lessons






What are customary measurement units and

how are they related?

What are metric measurement units and how

are they related?


Students will know:

relationships between measurement

units of the same length can be

expressed as an equation (e.g. 1

ft=12 in; 1 m = 100cm). (13-1)(13-

4)

relationships exist that enable you

to convert between units of length

by multiplying or dividing. (13-1)

(13-4)


units of the same capacity can be

expressed as a ratio (e.g. 1 qt. to 2

pt or 1 qt = 2 pt; 1 L to 1,000 mL or

1 L =1,000 mL) (13-2) (13-5)


to convert between units of capacity

by multiplying and dividing.

( 13-2)( 13-5)


units of weight/mass can be

expressed as a ratio (e.g 1 lb to 16

oz or 1 lb. = 16 oz; 1 kg to 1,000 g

or 1 kg= 1,000 g). (13-3) (13-6)


to convert between units of weight

or mass by multiplying or dividing.

(13-3) (13-6)




answer(s) to solve the original

problem.( 13-7)



customary length (inches,

feel, yards, and miles) to

another. (13-1)


customary capacity

(gallons, quarts, pints,

cups, and fluid ounces) to

another. (13-2)

convert from one

customary unit of weight

(ounces, pounds, and tons)

to another and apply this

skill to compare quantities.

( 13-3)

convert one metric unit of

length (kilometer, meter,

centimeter, and millimeter)

into another. (13-4)

convert from one metric

unit of capacity by

multiplying and dividing.

(13-5)

convert from one metric

unit of mass (milligrams,

grams, and kilograms) to

another. (13-6)

find the hidden question or

questions to solve multiple-

step problems. (13-7)

5.MD.1

91



Calendar Math:

Daily Depositor


Decimal

A Fraction a Day

Measurement Jan. , Feb., April

Exemplar:

Ant in the Wall

Inch and yard rulers ( or

Teaching Tool 33)

2 different colored markers

Strips of paper 1 yard long( 1

per group)

Liquid measuring cup

Empty containers ( pint, quart,

½ gallon, and gallon size)

Water

Centimeter rulers marked in

millimeters ( Teaching Tool

35) (per group)

Problem solving recording

sheet

Optional:

Hands-On Standards:

Measurement: Lessons 1-4

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

92



Grade: 5 Unit: Topic 14- Data Time Frame: 5 lessons





collected and how best to collect it. Data can

be represented visually using tables, charts, and





How can line plots be used to represent data

and answer questions?

How can numbers be used to describe certain

data sets?


Students will know:

each type of graph is most

appropriate for certain

kinds of data, A line plot

organized data on a

number line and is useful

for showing visually how a

set of data is distributed.

(14-1)(14-3)

some questions can be

answered using a survey.

An appropriate selected

sample can be used to

make predictions about a

population. Sample size is

one factor that determines

how close data from the

sample will mirror the

population. (14-2) (14-4)

mathematical explanations

can be given using words,

pictures, numbers, or

symbols. A good

explanation should be

correct, simple, complete,

and easy to understand.

(14-5)


learn and understand how to

draw line plots, interpret

points, and recognize outliers.

(14-1)

collect data and record data in

frequency tables and line

plots. Students then interpret

the results. (14-2)

learn how to make a line plot

from data in a frequency table.

(14-3)

how to use the information in

a line plot to solve problems

involving the data. (14-4)

write math explanation that

relate to line graphs that show

data changing over time. (14-

5)

5.MD.2

93


data

frequency table

line plot

outlier

sample

survey

Calendar Math:

Daily Depositor


A Fraction a Day

Graphing Sept., Nov., Jan., Mar.

& April

Exemplar:

Checkerboard Investigation

Problem-solving: Look for a

pattern ( Teaching Tool 8,

optional)

Optional:

Hands-On Standards: Data

Analysis: Lessons 1-8

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

94



Grade: 5 Unit: Topic 15- Classifying Plane Figures Time Frame: 6 lessons


Two and three-dimensional objects with or without

curved surfaces can be described, classified, and

analyzed by their attributes. An object’s location

can be described quantitatively.


to solve problems.

How can angles be measured and

classified?

How can polygons, triangles, and

quadrilaterals be described, classified and

named?


Students will know:

plane shapes have many

properties that make them

different from one another.

Polygons can be described

and classified by their sides

and angles. . (15-1)(15-

2)(15-3)

classify two-dimensional

shapes into categories

based on their properties.

(15-4)(15-5)

commonalities in attributes

of objects or situations can

be found and used to make

generalization about

relationships. (15-6))


identify and classify polygons. (15-

1)

place shapes have many properties

that make them different form one

another. (15-2)

polygons can be described and

classified by their sides and angles.

(15-2)(15-3)

classify two-dimensional shaped

into categories based on their

properties. (15-4)(15-5)

commonalities in attributes of

objects or situations can be found

and used to make generalizations

about relationships. (15-6)

5.G.3

5.G.4


polygon, regular

polygon,triangle

quadrilateral, pentagon,

hexagon, octagon, equilateral

triangle, isosceles triangle,

scalene triangle

right triangle, acute triangle

obtuse triangle, parallelogram

trapezoid, rectangle, rhombus

square, generalization

Calendar Math:

Daily Depositor


calendar for Sept., Oct., Nov., Jan,

Feb,. Mar., Apr.

Whole day celebration Feb.

Measurement March

Exemplar:

Who Owns the Most Land

Wooden sticks or straws

Teaching Tool 37

Teaching Tool 38

Scissors

Paper

Optional:

Hands-On Standards: Geometry:

Lessons 1-15

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

95



Grade: 5 Unit: Topic 16- Coordinate Geometry Time Frame: 6 lessons


Two and three-dimensional objects with or



object’s location can be described

quantitatively.


generalization made for mathematical situations

that have numbers or objects that repeat or are

arranged in predictable ways. For some



members of one set are related to members of a

second set.



How are points graphed?

How can we show the relationship between

sequences on a graph?


Students will know:

the coordinate system is a scheme

that uses two perpendicular lines

intersecting at 0 to name the

location of points in the plane.

(16-1)

the ordered pairs of the end points

of vertical and horizontal line

segments can be used to find the

length of the segments. ( 16-2)


breaking apart of changing the

problem into simpler ones. ( 16-

3)

a graph of a rule contains all of

the points on the coordinate grid

whose x- and y-coordinates

satisfy the rule. (16-4)

mathematical relationships

represented by rules can also be

represented by a graph of the rule.

Ordered pairs that satisfy the rule

can be used to graph the data. (16-

5)


identify and graph points on

a coordinate grid. (16-1)

find the distance between

two points by using ordered

pairs.. (16-2)

find the distance between

two points not on a straight

line by solving a simpler

problem. (16-3)

create and interpret

coordinate graph (16-4)

use coordinate graphs to

explore the relationship

between two rules. (16-5)

work backward to solve a

problem. (16-6)

5.G.1

5.G.2

96

some problems with the initial

data point unknown can be solved

by starting wit the end result and

reversing the steps and processes

to work backward to find the

initial data point. ( 16-6


Coordinate grid

x-axis

y-axis

origin

ordered pair

x-coordinate

y-coordinate

Calendar Math:

Daily Depositor


Decimal

Graphing Jan. and April

Exemplar:

Bulletin Board Border

Coordinate grids

10 x 10 grids ( Teaching Tool

40)

Grid paper

Optional:


Lessons 10-16

Formative




Leveled Homework

Center activities

Summative

Topic test

Quarterly benchmark

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