4th Grade Math - Cicero Public School District 99 · 4th Grade Math Unit 2: Describing the Shape of the Data Investigation 1: Representing Multiplications with Arrays 2.1 Are students

Session Essential QuestionsContent

StandardsPractices Assessments

Sample

Lessons/ActivitiesVocabulary Resources

Interdisciplinary

ConnectionsPrior Knowledges

1.1 How can students demonstrate

the use arrays to model

multiplication problems and find

multiples of a number?+B19

4.OA.3

4.OA.4

4: Model with

mathematics.

5: Use appropriate

tools.

Teacher Observation

(TO)- Do students

generate examples of

arrays of familiar

objects and find the

products represented

by these arrays?

10 minute Math:

Today's Number

*multiplication

*array

*dimension

Resource Masters

(M)

Things That Come in

Arrays (M1), One-

Centimeter Grid

paper (M2)

Family Letter

(M4,6,and 8) 1.2 How can students use arrays to

model multiplication problems

and find factors of a 2 digit

number using arrays?

4.OA.3

4.OA.4

4: Model with

mathematics.

5: Use appropriate

tools.

TO- Do students use

what they know about

multiplication to find all

the arrays for a given

number and label the

dimensions of each

array?

10 minute Math:

Today's Number

*factor One-Centimeter Grid

paper (M2)

1.3 How can students use arrays to

model multiplication problems

and identify features of a prime,

composite, and square numbers?

4.OA.3

4.OA.4

4: Model with

mathematics.

5: Use appropriate

tools.

7: Look for and make

use of structure.

TO- Teacher's discretion 10 minute Math:

Today's Number

*prime number

*composite

number

*square number

One-Centimeter Grid

paper (M2)

1.4 How can students use know

multiplication combinations to

solve more difficult

combinations?

4.OA.3

4.OA.4


use of structure.

TO- Can students use

Array Cards to find the

products of pairs of

numbers from 1 x 2 to

12 x 12?

10 minute Math:

Today's Number

*multiplication

combination

Array Cards in TK (M9-

M29)

Factor Pairs (M30)

Unit 1: Factors, Multiples, and Arrays

4th Grade Math

*Addition

*Multiplication

combinations with

products to 50

*Skip counting

*Recognize arrays

Investigation 1: Representing Multiplications with Arrays

Unit 1 1



Sample


Interdisciplinary



Investigation 1: Representing Multiplications with Arrays1.5 How can students manipulate

large arrays into smaller arrays?

4.OA.3

4.OA.4


use of structure.

TO- Can students

determine the product

represented by

incomplete or partially

covered arrays?

Assessment:

Representing 8 x 6

(M31)

10 minute Math:

Today's Number

Math Workshop:

Using Arrays to

Multiply

1A: Array Picture

Problems

1B: Factor Pairs

1C: Assessment:

Representing 8 X 6

M2 (as needed)

Assessment Checklist

(M32)

Writing about

Mathematical

Thinking: SAB p. 11-

12

1.6A Can students solve word

problems that involve

multiplicative comparisons?

4.OA.1

4.OA.2

4.OA.3

1: Make sense of

problems and

persevere in solving

them.

2: Reason abstractly

and quantitatively.

TO- Can students solve

multiplicative

comparison problems

using either

multiplication or

division equations?

10 minute Math:

Today's Number

Multiplicative

Comparison

Problems M (C2)

More Multiplicative

Comparison

Problems M (C3)

2.1 Can students use known


identify multiplications not yet

known fluently?

4.OA.4 7: Look for and make

use of structure.

TO-Can students use

knowledge of

multiplication

combinations they

know to find ones they

do no know?

10 minute Math:

Quick Images

*product Quick Images: Seeing

Numbers (M33)



determine the products of more

difficult combinations?

4.OA.4 7: Look for and make

use of structure.

TO- Are students to use

multiplication

combinations they

know to help them

solve and commit to

memory the ones they

do not know fluently?

10 minute Math:

Quick Images

Multiplication cards

(M35-40 and TK)

As needed: Blank


(M41), Practicing

with Multiplication

Cards explanation

(M42)2.3 Can students identify whether

one number is a factor or a

multiple of another?

4.OA.4 2: Reason abstractly

and quantitatively.


use of structure.

TO- Can students

identify whether a

number is multiple of a

given factor?

10 minute Math:

Quick Images

*multiple

*factor

Multiple Cards (M46-

49 and TK)

Multiple Turn Over

(M45)

Multiple Turn Over

Recording Sheet

*Addition

*Multiplication

combinations with

products to 50

*Skip counting

*Recognize arrays

*Addition

*Multiplication

combinations with

products to 50

*Skip counting

Investigation 2: Multiplication Combinations

Unit 1 2



Sample


Interdisciplinary



Investigation 1: Representing Multiplications with Arrays2.4 Can students use known


determine the products of more

difficult combinations?


and quantitatively.


use of structure.

TO-At teacher's

discretion

10 minute Math:

Quick Images

Math Workshop:

Multiplication

Combinations

2A: Multiplication

Cards

2B: Factor Pairs

2C: multiple Turn Over


(M35-40 and TK)

Array Cards (M9-M29

and TK)

Multiple Cards (M46-

49 and TK)

Multiple Turn Over

(M45)

Multiple Turn Over

Recording Sheet

2.5 Can students solve multiplication

combinations using one or more

strategies?


and quantitatively.


use of structure.

TO- Are students

demonstrating fluency

with multiplication

combinations?

Assessment:

Multiplication

Combinations (M51)

10 minute Math:

Quick Images

Math Workshop:

Multiplication

Combinations

2A: Multiplication

Cards

2B: Factor Pairs

2C: multiple Turn Over

Multiplication

Combinations (M51)

As optional: M52

3.1 Can students identify the factors

of 100?

How can students use skip

counting to help them identify

multiples of a number.

1: Make sense of

problems and


them.


and quantitatively.


use of structure.

TO- Are students able

to use knowledge of

multiplication

combinations and

reasoning to generate

factors of

100/200/300?

10 minute Math:

Quick Images

One-Centimeter Grid

paper (M2)

Four 100 Charts

(M53)

300 Chart (M54)

*Addition

*Multiplication

combinations with

products to 50

*Skip counting

Investigation 3: Finding Factors

Unit 1 3



Sample


Interdisciplinary



Investigation 1: Representing Multiplications with Arrays3.2 How were students able to use

their knowledge of the factors of

100 to find factors of multiples of

100.

Can students use known


find related multiplication

combinations for a given

product?

1: Make sense of

problems and


them.


and quantitatively.


use of structure.

TO- Are students able

to use knowledge of

multiplication

combinations and

reasoning to generate

factors of

100/200/300?

10 minute Math:

Counting Around the

Class

One-Centimeter Grid

paper (M2)

Four 100 Charts

(M53)

300 Chart (M54)

3.3 How can students determine the

factors of a number?

4.OA.1

4.OA.2

4.OA.4

1: Make sense of

problems and


them.


and quantitatively.

3: Construct viable

arguments and

critique the reasoning

of others.


use of structure.

TO- Can students

identify, represent, and

explain why the factors

of 16 are the same as

48?

10 minute Math:

Counting Around the

Class

One-Centimeter Grid

paper (M2)

Writing about

Mathematical


41

3.4 How can students determine the

factors of a number?

How will students use

representations to show that a

factor of a number is also a factor

of its multiples?

4.OA.4 1: Make sense of

problems and


them.


and quantitatively.


use of structure.

End Of Unit

Assessment: M55-M56

10 minute Math:

Counting Around the

Class

*Addition

*Multiplication

combinations with

products to 50

*Skip counting

Unit 1 4



Sample


Interdisciplinary

Connections

Prior

Knowledges

1.1 Can students record and organize

data in a box and describe the

shape of the data distribution?

4.NBT.4 1: Make sense of

problems and


them.

6: Attend to precision.

Teacher Observation

(TO)- Can students

organize the data?

Can students describe

the shape of the data?

10 minute Math:

Broken Calculator

data

bar graph

line plot

Resource Masters

(M)

1.2 Can students measure heights

and use the data to describe the

heights?

4.NBT.4

4.MD.2

5: Use appropriate

tools.

6: Attend to precision

TO- Can students

measure carefully,

trying to be as accurate

as possible?

10 minute Math:

Broken Calculator

outlier

range

1.3 Can students collect heights and

create a representation

comparing 2 data sets?

4.NBT.4

4.MD.2

5: Use appropriate

tools.


TO- Do students

organize and represent

the data clearly?

Do students create

graphs that make the

data sets easy to

compare?

10 minute Math:

Broken Calculator

data

representation

Height Data from a

First-Grade Class

(M5)

Centimeter Grid

Paper (M6)

1.4 Can students collect heights and

create a representation

comparing 2 data sets?

4.OA.3

4.OA.4

3: Construct viable

arguments and


of others.

5: Use appropriate

tools.


To-Do students create

graphs that show the

data clearly and make it

easy to compare the

two sets of data? Do

students draw some

conclusions about how

much taller a fourth

grader is than a first

grader?

10 minute Math: Quick

Survey

Writing about

Mathematical

Thinking: SAB p. 7

1.5 Are students able to find and

compare the medians of the

heights?

4.MD.2 3: Construct viable

arguments and


of others.

5: Use appropriate

tools.


TO- Can students

choose a method that

makes sense for finding

the median?

Assessment:

Comparing Numbers of

Cavities (M7-8)


Survey

median Cavity Data from a

Fourth-Grade Class

(M9)

4th Grade Math

Unit 2: Describing the Shape of the Data


Label a graph.

How to measure

in inches.

How to use the

measuring tool

to measure

something

longer than the

measuring tool.

How to set/label

two graphs on

one sheet of

paper to

compare the

data.

What is typical

and atypical in a

data set.

Unit 2 5



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math


Investigation 1: Representing Multiplications with Arrays2.1 Are students able to create a

survey question to compare 2

groups?


problems and


them.

TO- Is the survey

question clear? Will it

give students the

information they are

interested in? How will

they record and keep

track of whom they

asked?

10 minute Math:

Broken Calculator

survey

numerical data

Writing about

Mathematical


12

2.2 Are students able to collect data

for their survey question with 2

groups?

4.NBT.4 3: Construct viable

arguments and


of others.


TO- Are students able to

come up with and use

an organized system for

recording and keeping

track of responses? Do

students work together

to collect the data?

10 minute Math:

Broken Calculator

Assessment

Worksheet (M10)

2.3 Can students discuss how to

create representations to easily

compare 2 sets of data?

3: Construct viable

arguments and


of others.


TO- Do students create

a representation or

representations that

allow for an easy

comparison of the data

sets?


Survey

line plot

bar graph

2.4 Are students able to use their

representations to develop

conclusions about their data?

4.NBT.4

4.MD.2

3: Construct viable

arguments and


of others.

TO- Can students draw

conclusions from their

data?

10 minute Math:

Broken Calculator

conclusion Writing about

Mathematical


12

2.5 Can students describe and

construct theories about 3 sets of

data?

4.NBT.4

4.MD.2

3: Construct viable

arguments and


of others.



use of structure.

TO- Can students find

the median for Mystery

Data B? Are students

supporting their

theories with plausible

reasons, using what

they already know

about the height of

living objects and the

characteristics of the

data set?

10 minute Math:

Broken Calculator

Looking at Mystery

Data C (M15)

Mystery Data C Table

and Line Plot (M16)

Writing about

Mathematical

Thinking: SAB p. 20

Investigation 2: Using Data to Compare

Label a graph.

How to measure

in inches.

How to use the

measuring tool

to measure

something

longer than the

measuring tool.

How to set/label

two graphs on

one sheet of

paper to

compare the

data.

What is typical

and atypical in a

data set.

Unit 2 6



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math


Investigation 1: Representing Multiplications with Arrays2.6 Can students examine different

possibilities for what data sets

with the same median and

highest and lowest values could

look like?


arguments and


of others.



use of structure.

TO-Can students make

an accurate line plot?

Do students compare

different aspects of the

shape of the data? (ex.

Highest and lowest

values, outliers, median,

how is the data

concentrated, etc.)

10 minute Math:

Broken Calculator

value

2.7 Can students use the data as

evidence to answer questions

that require them to make

decisions based on the data?


arguments and


of others.


TO-Are students able to

gather information from

the line lots in order to

draw conclusions about

the data?


Survey

3.5 Can students create and use

data to answer questions?


arguments and

critique the

reasoning of others.

6: Attend to

precision.

End Of Unit

Assessment: M18-

M21

10 minute Math:

Broken Calculator

Label a graph.

How to measure

in inches.

How to use the

measuring tool

to measure

something

longer than the

measuring tool.

How to set/label

two graphs on

one sheet of

paper to

compare the

data.

What is typical

and atypical in a

data set.

Investigation 3: Finding and Comparing Probabilities

Unit 2 7



Sample


Interdisciplinary

Connections

Prior

Knowledges

1.1 Can students represent a

multiplication problem with

pictures, diagrams, or models?

4.OA.3

4.NBT.5

4: Model with

mathematics.

5: Use appropriate

tools.

7. Look for and make

use of structure.

Teacher Observation

(TO)- How are students

solving 14 X 12? Are

they breaking apart one

of the factors and

multiplying both parts

by the other factor?

10 minute Math:

Seeing Numbers

multiplication Resource Masters

(M)


(M9-M14)

1.2 Can students use arrays to model

multiplication?

Are students using/developing

strategies for multiplying that

involve breaking apart numbers?

4: Model with

mathematics.


use of structure.

TO- Do students notice

that in order to make a

rectangle by combining

two arrays, one of the

dimensions must be the

same on both? Are

students considering

either factor as a

starting place for

combining arrays?

10 minute Math:

Seeing Numbers

Array cards (Tool kit)

Printable array cards

(M17-M37)

1.3 Can students use arrays to model

multiplication?




4.NBT.5 2: Reason abstractly

and quantitatively.

4: Model with

mathematics.

TO- When part of an

array is covered, can

students visualize what

other arrays will

complete a match? Can

students record their

matches correctly with

an equation?

10 minute Math:

Seeing Numbers

Math Workshop: Using

Arrays to Model

Multiplication

1A: Small Array/Big

Array

1B: Breaking Up arrays

1C: Solving

Multiplication

equation Small Array/Big

Array game

directions (M38-

M39)

Small Array/Big

Array Recording

Sheet (M40)



(M17-M37)1.4 Can students use arrays to model

multiplication?




4.OA.3

4.OA.4


and quantitatively.

4: Model with

mathematics.

TO- Can students

identify the larger array

that is created when the

two smaller ones are

combined? Can

students break a larger

array into two smaller

arrays, maintain on one

of the dimensions?

10 minute Math:

Seeing Numbers


Arrays to Model

Multiplication

1A: Small Array/Big

Array


1C: Solving

Multiplication

Problems


Array game

directions (M38-

M39)

Small Array/Big

Array Recording

Sheet (M40)



(M17-M37)

Unit 3: Multiple Towers and Division Stories

4th Grade Math


addition

subtraction

basic X facts 0-

12

dividend

quotient

divisor

Unit 3 8



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Representing Multiplications with Arrays1.5 Can students use arrays to model

multiplication?




4.OA.4

4.NBT.5


and quantitatively.

4: Model with

mathematics.

Assessment:

Solving 18 X 7 (M43)

10 minute Math:

Seeing Numbers


Arrays to Model

Multiplication

1A: Small Array/Big

Array


1C: Solving

Multiplication

Problems


Array game

directions (M38-

M39)

Small Array/Big

Array Recording

Sheet (M40)



(M17-M37)

2.1 How will students solve division

story problems?

4.OA.4

4.NBT.6

1: Make sense of

problems and


them.


and quantitatively.

5: Use appropriate

tools.

TO- What known

multiplication or division

relationships do

students use to solve

these division

problems? Are

students able to solve

division story problems

by acting out the

situation, showing either

the grouping or the

number being divided?

10 minute Math:

Counting Around the

Class

division

2.2 How are dividends, divisors,

quotients, and remainders

related? How can a remainder

affect the answer in a division

word problem?

4.OA.3

4.OA.4

4.NBT.6

1: Make sense of

problems and


them.


and quantitatively.


solve 44 ÷ 8 by using

number relationships

that they know, such as

8 X 5 and 8 X 6? Are

students able to

determine what to do

with remainders in the

context of the problem

situation?

10 minute Math:

Counting Around the

Class

remainder

Investigation 2: Division addition

subtraction

basic X facts 0-

12

dividend

quotient

divisor

Unit 3 9



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Representing Multiplications with Arrays2.3 How can a remainder affect the

answer in a division word

problem? Can

students represent a division

problem with pictures, diagrams,

or models?

4.OA.3

4.NBT.6

1: Make sense of

problems and


them.


and quantitatively.

3. Construct viable

arguments and


of others.

TO- Are students using

known multiplication

relationship in solving

division problems? Do

students recognize that

the answer to the

question posed in the

problem may be

different from the

answer as expressed in a

division equation do to

the remainder?

10 minute Math:

Counting Around the

Class

Math Workshop:

Division Stories

2A: Small Array/Big

Array

2B: More Division

Stories



(M17-M37)

Writing about

Mathematical

Thinking: SAB p. 28



solve division problems? How

can a remainder affect the

answer in a division word

problem?

4.OA.3

4.NBT.6

1: Make sense of

problems and


them.


and quantitatively.

3. Construct viable

arguments and


of others.


use of structure

TO- How do students

find the missing factor?

(By using known

multiplications, skip

counting, repeated

addition) Are students

able to write

multiplication equations

that represent the

problem accurately?

10 minute Math:

Seeing Numbers

Math Workshop:

Strategies for Division

2A: Missing Factors

2B:Small Array/Big

Array

2C: More Division

Stories

factor Writing about

Mathematical

Thinking: SAB p. 31



solve division word problems?


problems and


them.


and quantitatively.


use of structure.

TO- Are students

recognizing and using

the relationship

between the numbers in

each pair of problems?

10 minute Math:

Seeing Numbers

Math Workshop:

Strategies for Division

2A: Missing Factors

2B: Related

Multiplication and

Division Problems



(M17-M37)

addition

subtraction

basic X facts 0-

12

dividend

quotient

divisor

Unit 3 10



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Representing Multiplications with Arrays2.6 Are students able to create a

story problem to represent a

division expression? Can students

use known multiplication

combinations to solve division

problems?


problems and


them.


and quantitatively.


use of structure.

Assessment:

Writing and Solving a

Division Problem, M46

10 minute Math:

Seeing Numbers

3.1 Can students understand the

effect of multiplying by a multiple

of 10? Can students find

multiples of 2-digit numbers?


problems and


them.

5: Use appropriate

tools.


use of structure.


generate sequences of

the multiples of 2-digit

numbers? Do students

easily calculate the 10th

multiple in the sequence

and use it to find other

multiples?

10 minute Math:

Counting Around the

Class

multiple

factor

Writing about

Mathematical

Thinking: SAB p. 39



of 10? Are

students able to represent a

multiplication problem with

pictures, diagrams, or models?

4.OA.1

4.OA.2

4.OA.4

4.NBT.5

4: Model with

mathematics.

5: Use appropriate

tools.


use of structure.


one of the available

tools to create a visual

representation of the

factors?

Are students able to use

their representation to

explain the

mathematical

relationship between

the two problems?

10 minute Math:

Counting Around the

Class

Math Workshop:

Multiplying Groups of

10

2A: Multiplying by

Multiples of 10: What

Happens?

2B: Multiple Towers

Writing about

Mathematical

Thinking: SAB p. 46

Investigation 3: Multiplying 10s addition

subtraction

basic X facts 0-

12

dividend

quotient

divisor

Unit 3 11



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Representing Multiplications with Arrays3.3 Can students understand the


of 10?

4.OA.1

4.OA.2

4.OA.4

4.NBT.5

4: Model with

mathematics.

8: Look for and

express regularity in

repeated reasoning.

TO- Do students solve

the second problem in

each pair by relating it

to the first?

Can students create a

story problem that

represents one of the

pairs of the problems?

10 minute Math:

Counting Around the

Class

Math Workshop:


10

2A: Multiples of 10:

Related Problems

2B: Story Problems

About 10s

2C: Multiplying by

Multilples of 10: What

Happens?

Writing about

Mathematical

Thinking: SAB p. 47



of 10? Are

students able to use diverse

strategies to answer

multiplication combinations to 12

X 12?

4.OA.4

4.NBT.5


use of structure.

8: Look for and


repeated reasoning.

Assessment:

Multiplication

Combinations (M50)

10 minute Math:

Counting Around the

Class

Math Workshop:


10

2A: Multiples of 10:

Related Problems

2B: Story Problems

About 10s

4.1 Can students determine the

effect on the product when a

factor is doubled or halved?

Are students able to represent a

multiplication or division problem

with pictures, diagrams, or

models?

4.OA.1

4.OA.2

4.NBT.5

4.NBT.6


use of structure.

8: Look for and


repeated reasoning.

TO- Are students

recognizing that in each

problem, one or two

factors have been

doubled?

Can students make

representations that

show the doubling or

double/half

relationship?

10 minute Math:

Seeing Numbers

doubled

halved

Writing about

Mathematical


54

Investigation 4: Strategies for Multiplication

addition

subtraction

basic X facts 0-

12

dividend

quotient

divisor

Unit 3 12



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Representing Multiplications with Arrays4.2 Are students developing



Can students use arrays to model

multiplication?

4.NBT.5 7. Look for and make

use of structure.

8: Look for and


repeated reasoning.


break the numbers of

the final problem into

more manageable

parts?

Are students recognizing

the relationship

between the problems

in the set and the final

problem to be solved?

10 minute Math:

Seeing Numbers

4.3 Are students developing



Can students determine the



4.OA.1

4.OA.2

4.NBT.5

1: Make sense of

problems and


them.



use of structure.

8: Look for and


repeated reasoning.

TO- How are students

breaking apart these 2-

digit numbers to make

the problems easier to

solve.

Do students accurately

recombine all parts of

the problem to get the

final product?

Are students using

doubling and halving to

create an equivalent

problem?

10 minute Math:

Seeing Numbers

Math Workshop:

Strategies for

Multiplication

2A: Multiplication

Cluster Problems

2B: More Multiplication

Problems

2C: Array Card Games

4.4 Are students developing



Can students determine the




problems and


them.


8: Look for and


repeated reasoning.

TO- How are students

breaking apart these 2-

digit numbers to make

the problems easier to

solve.

Do students accurately

recombine all parts of

the problem to get the

final product?

Are students using

doubling and halving to

create an equivalent

problem?

10 minute Math:

Seeing Numbers

Math Workshop:

Strategies for

Multiplication

2A: Multiplication

Cluster Problems

2B: More Multiplication

Problems

2C: Array Card Games

addition

subtraction

basic X facts 0-

12

dividend

quotient

divisor

Unit 3 13



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Representing Multiplications with Arrays4.5 Are students able to solve division

problems by making groups of the

divisor?

Are students using known


solve division problems?

Did students developed strategies

for multiplying that involve

breaking apart numbers?


problems and


them.


and quantitatively.


End Of Unit

Assessment: M51-M52

10 minute Math:

Counting Around the

Class

addition

subtraction

basic X facts 0-

12

dividend

quotient

Unit 3 14



Sample


Interdisciplinary

Connections

Prior

Knowledges

1.1 Can students use units of

measurement to lengths in cm,

in, ft, yd, m?

4.NBT.4

4.MD.1

4.MD.3

5: Use appropriate

tools.

Teacher Observation

(TO)- Are students able

to measure lengths

appropriately? Are

students able to

estimate lengths using

benchmarks?

10 minute Math:

Today's Number

Area

Volume

Perimeter

Linear -

Measurement

Inch

Foot

Yard

Centimeter

Meter

Benchmark

Resource Masters

(M)

1.2 Are students able to determine

when to estimate or us exact

measurements when needed?

4.NBT.4

4.MD.1

5: Use appropriate

tools.


relationships among

measurement tools?

Can students use and

read measurement tools

accurately?

10 minute Math:

Today's Number

Millimeter

Standard System

Metric System

Kilometer

Estimate

1.3 Can students find the perimeter

using standard units?

4.NBT.4

4.MD.1

4.MD.2

4.MD.3

5: Use appropriate

tools.

TO- Can student identify

and measure the

perimeter of objects?

Can students position

measurement tool

correctly?

10 minute Math:

Today's Number

Math Workshop:

Measuring Length

1A: Perimeter

Problems

1B: LogoPaths Activity:

Missing Measures

(optional)

1C: Assessment: How

Long Is Our Classroom?

Perimeter Writing about

Mathematical

Thinking: SAB p. 8

4th Grade Math


*Linear

Measurement

*Perimeter

*2-D shapes

*Attributes of

Triangles and

Quadrilaterals

*Right Angles

*Area of

rectangles and

other shapes

through

decomposition

Unit 4: Size, Shape, and Symmetry

Unit 4 15



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math




using standard units and identify

possible causes of measurement

errors?

4.OA.3

4.OA.4

5: Use appropriate

tools.


10 minute Math:

Today's Number

Math Workshop:

Measuring Length

1A: Perimeter

Problems


Missing Measures

Writing about

Mathematical


13


using standard units and identify

possible causes of measurement

errors?

4.NBT.4

4.MD.1

4.MD.2

4.MD.3

5: Use appropriate

tools.

10 minute Math:

Today's Number

Math Workshop:

Measuring Length

1A: Perimeter

Problems


Missing Measures

(optional)

1C: Assessment: How

Long Is Our Classroom?

1D: Mapping 100 Feet

2.1 Can students define a polygon by

their attributes?

4.G.1

4.G.2

6: Attend to precision. TO- Are students

articulating properties

such as: it has to be

closed, it has to have

line segments for sides,

the sides cannot cross?

Are students identifying

shapes that are less

familiar as polygons?

What attributes do

students pay attention

to as they make their

rules?

10 minute Math:

Quick Images

Polygon

Line Segment

Endpoint

Vertex (Vertices)

Orientation

TO- Do students have a

sense of how long the

path of 100 feet long

will be? Do students

position the measuring

tool to get the most

accurate

measurements? Can

students accurately

keep track of the length

and calculate the total

measurement?

Investigation 2: Polygons of Many Types

*Linear

Measurement

*Perimeter

*2-D shapes

*Attributes of

Triangles and

Quadrilaterals

*Right Angles

*Area of

rectangles and

other shapes

through

decomposition

Unit 4 16



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



2.2 Are students able to make new

polygons by combining polygons?

Can students identify the number

of sides for various polygons?

4.G.1 6: Attend to precision. TO- Can students

combine two or more

polygons to make a new

shape that is a closed

figure? Do students

trace around the outside

edge of the polygonal

shapes and correctly

count the number of

sides?

10 minute Math:

Quick Images

Trapezoid

Equilateral

Triangle

Parallelogram

Hexagon

2.3A Are students able to identify lines

(parallel, perpendicular), angles

(right, acute, obtuse) and right

triangles?

4.G.1

4.G.2

4.MD.3

4.G.1

4.G.2

5: Use appropriate

tools.


TO- Do students

understand that an

angle that turns through

n one-degree angles is

said to have an angle

measure of n degrees?

10 minute Math:

Quick Images

Point

line

ray

line segment

perpendicular

lines

parallel lines

angle

right angle

acute angle

obtuse angle

right triangle

Shape Cards (M19-

20)

2.3 Are students able to make new

polygons by combining polygons?

Can students identify the number

of sides for various polygons by

their attributes?

4.MD.3

4.G.1

4.G.2

5: Use appropriate

tools.


TO- Can students

combine two or more

polygons to make a new

shape that is a closed

figure? Do students

trace around the outside

edge of the polygonal

shapes and correctly

count the number of

sides?

10 minute Math:

Quick Images

Math Workshop:

Working With

Polygons

3A: Guess My Rule with

Shape Cards

3B: Making Polygons

3C: LogoPaths Activity:

600 Steps (optional)

Side

Angle

Right Angle

Parallel

*Linear

Measurement

*Perimeter

*2-D shapes

*Attributes of

Triangles and

Quadrilaterals

*Right Angles

*Area of

rectangles and

other shapes

through

decomposition

Unit 4 17



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



2.4 Can students use vocabulary

words to describe attributes and

properties of quadrilaterals?

4.G.1

4.G.2

3. Construct viable

arguments and


of others.


TO- What geometric

terms do students use

to state their rules? Can

students combine two

or more polygons to

make a new shape that

fits the given

description?

10 minute Math:

Quick Images

Quadrilateral Writing about

Mathematical

Thinking: SAB p. 29

2.5 Can students use vocabulary

words to describe attributes and

properties of quadrilaterals?

Can students indentify

relationships between squares

and rectangles?

4.G.1

4.G.2

3. Construct viable

arguments and


of others.


Assessment: What is a

Quadrilateral?

10 minute Math:

Quick Images

Square

Rectangle

3.1 Can students identifying right

angles as 90 degrees?

Can students measure acute

angles by using 90 degrees?

4.NBT.4

4.MD.6

4.MD.7

5: Use appropriate

tools.

TO- Do students easily

reognize the shape of a

right angle? Can

students find

combinations of angles

that fit into a 90-degree

angle exactly?

10 minute Math:

Today's Number

Angle

Degree

Right Angle

Equilateral

Triangle

Investigation 3: Measuring Angles

*Linear

Measurement

*Perimeter

*2-D shapes

*Attributes of

Triangles and

Quadrilaterals

*Right Angles

*Area of

rectangles and

other shapes

through

decomposition

Unit 4 18



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



3.2 Can students measure acute


Can students use known angles to

measure other angles?

4.NBT.4

4.MD.6

4.MD.7

5: Use appropriate

tools.

TO- Are students using


90-degree to reason

about the number of

degrees of the angles in

the Power Polygon

pieces?

10 minute Math:

Today's Number

Math Workshop:

Measuring and

Building Angles

2A: How Many

Degrees?

2B: Building Angles


600 Steps, other

Polygons (optional)

Acute

Obtuse

Writing about

Mathematical


43

3.3 Can students measure acute


Can students use known angles to

measure other angles?

4.NBT.4

4.MD.6

4.MD.7

5: Use appropriate

tools.


draw polygons

containing only 90-

degree angles that have

more than four sides?

10 minute Math:

Today's Number

Math Workshop:

Measuring and Building

Angles

2A: How Many

Degrees?

2B: Assessment:

Building Angles


600 Steps, other

Polygons (optional)

Assessment Checklist

(M22)

3.4A Can students draw lines, parts of

lines, and angles?

Are students able to use the

relationship between the degree

measure of an angle and circular

arcs?

Are students able to use a

protractor to measure angles?

4.NBT.4

4.MD.5.a

4.MD.5.b

4.MD.6

4.G.1

5: Use appropriate

tools.


Images

protractor

*Linear

Measurement

*Perimeter

*2-D shapes

*Attributes of

Triangles and

Quadrilaterals

*Right Angles

*Area of

rectangles and

other shapes

through

decomposition

Unit 4 19



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



4.1 Can students find the area of

symmetrical designs?

4.MD.3

4.G.2

4.G.3

5: Use appropriate

tools.

TO- Can students create

a symmetrical design?

Do students understand

that area is the measure

of the whole surface of

the design? How do

students find the area?

10 minute Math:

Quick Images

Symmetrical Writing about

Mathematical

Thinking: SAB p. 52

4.2 Can students find the area of

symmetrical designs?

Can students identify the large

the unit of area, the a smaller the

umber of units needed to

measure the area?

4.MD.3

4.G.2

4.G.3

5: Use appropriate

tools.

TO- How do students

determine area?

10 minute Math:

Quick Images

4.3 Can students identify the area of

polygons by decomposing

shapes?

4.MD.3

4.G.2

4.G.3

5: Use appropriate

tools.

TO- Do students

recognize a turn of 90-

degrees? Do students

use congruence or

symmetry in their

explanation?

10 minute Math:

Quick Images

Math Workshop:

Finding Area

3A: Crazy Cakes


Mazes (optional)

4.4 Can students identify the area of


shapes?

4.MD.3

4.G.2

4.G.3

5: Use appropriate

tools.

TO- How do students

find area? Do students

decompose shapes into

smaller to find area?

10 minute Math:

Quick Images

Math Workshop:

Finding Area

2A: Crazy Cakes


Mazes (optional)

2C: Measuring Area on

Geoboards

Square Unit

Pentagon

Writing about

Mathematical


64

Investigation 4: Finding Area

*Linear

Measurement

*Perimeter

*2-D shapes

*Attributes of

Triangles and

Quadrilaterals

*Right Angles

*Area of

rectangles and

other shapes

through

decomposition

Unit 4 20



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



4.5 Are students able to find the area

of a rectangle?

Are students able to find the area

of a rectangle using are of a

triangle?

4.NBT.4

4.MD.3

5: Use appropriate

tools.

TO- How do students

determine area?

10 minute Math:

Today's Number

Math Workshop:

Finding Area

3A: LogoPaths Activity:

Mazes (optional)

3B: Measuring Area on

Geoboards

3C: Area of Rectangles

Writing about

Mathematical


68

4.6 Are students able to find the area

of a rectangle?

Can students identify the area of


shapes?

4.NBT.4

4.MD.3

4.G.3

5: Use appropriate

tools.

TO- How do students

decompose shapes?

How are students

finding the area of

rectangles? How are

students finding the

area of triangles?

10 minute Math:

Today's Number

4.7 Can students identifying right

angles as 90 degrees?

Can students measure acute


Can students identify the area of


shapes?

4.NBT.4

4.MD.3

4.G.1

4.G.2

1: Make sense of

problems and


them.


and quantitatively. 6:

Attend to precision.

End-of-unit-

assessment:

10 minute Math:

Today's Number

*Linear

Measurement

*Perimeter

*2-D shapes

*Attributes of

Triangles and

Quadrilaterals

*Right Angles

*Area of

rectangles and

other shapes

through

decomposition

Unit 4 21



Sample


Interdisciplinary

Connections

Prior

Knowledges

1.1 Can Students read, write, and

sequence numbers to 1,000?

4.NBT.1

4.NBT.2

4.NBT.4


use of structure.

Teacher Observation

(TO)- Are students able

to read and write

numbers up to 1,000?

Are students familiar

with the structure of the

number system in the

hundreds?

10 minute Math:

Broken Calculator

Activity: Making a

1,000 Book

Place Value Resource Masters

(M)



4.NBT.2

4.NBT.4

5: Use appropriate

tools.


use of structure.

TO- Ares students able

to read and write

numbers in the

hundreds? Do the

students use landmark

numbers to help them

locate other numbers?

10 minute Math:

Broken Calculator

Writing about

Mathematical

Thinking: SAB p. 2

1.3 Can Students add and subtract

multiples of 10, 100, 1,000?

Can Students read, write, and


4.NBT.2

4.NBT.4

5: Use appropriate

tools.


use of structure.

TO- Can students easily

add and subtract

multiples of 10 and 100,

starting at any number?

10 minute Math:

Practicing Place Value

Activity: Changing

Places (M15)

Changing Places

(M15)

Changing Places

Recording Sheet

(M12)

Change Cards for

Changing Places

(M10-11)1.4 Can Students use multiples of 10

and 100 to find the difference

between any 3-digit number and

1,000?

Can Students represent addition

and subtraction on a number

line?

4.OA.3

4.OA.4

5: Use appropriate

tools.


use of structure.

TO- If students are

either adding up or

subtracting back, what

size are the "chunks" of

numbers that they use?

Do students make use of

landmark numbers at

"stopping-off places"

(e.g., 540+60=600)

10 minute Math:


1.5A Can students round numbers to

the nearest ten and the nearest

hundred?

Can students write numbers to

1,000 in expanded form?

4.NBT.2

4.NBT.3

5: Use appropriate

tools.


use of structure.

TO- Can students round

2- or 3-digit numbers to

the nearest ten or

nearest hundred?

10 minute Math:


expanded form

less than

greater than

4th Grade Math

*Solving

addition and

subtraction

problems with 2-

digit and 3-digit

numbers

*Composition of

numbers to

1,000

*Addition

*Variety of

subtraction

situations

*Addition and

subtraction

combinations

*Addition and

subtraction

relationships


Unit 5: Landmarks and Large Numbers

Unit 5 22



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math




multiples of 10, 100, and 1,000?

Can Students use multiples of 10



1,000?

4.NBT.2

4.NBT.4

4.MD.2

5: Use appropriate

tools.


use of structure.


read and write 3-digit


recognize the value of

digits in numbers? Can

students add multiples

of 10 mentally?

10 minute Math:

Broken Calculator

Math Workshop: The

Number System to

1,000

1A: Changing Places

1B: How Many Miles to

1,000?

1C: Assessment:

Numbers to 1,000

Digit Cards (M16-18)

and also in tool kit.

Assessment

Numbers to 1,000

(M19)

Assessment checklist

(M20)



Can Students use multiples of 10



1,000?

4.NBT.2

4.NBT.4

4.MD.2

5: Use appropriate

tools.


use of structure.


read and write 3-digit


recognize the value of

digits in numbers? Can

students add multiples

of 10 mentally?

10 minute Math:

Broken Calculator

Math Workshop: The

Number System to

1,000

1A: Changing Places

1B: How Many Miles to

1,000?

1C: Assessment:

Numbers to 1,000

Digit Cards (M16-18)

and also in tool kit.

Assessment

Numbers to 1,000

(M19)

Assessment checklist

(M20)

2.1 Can Students add 3 and 4-digit

numbers?

Can Students identify, describe,

and compare addition strategies

by focusing on how each strategy

starts?

4.NBT.2

4.NBT.4

4.MD.2

3: Construct viable

arguments and


of others.


8: Look for and


repeated reasoning.

TO- Do students have at

least one addition

strategy that they can

use accurately and

efficiently? Can


strategies and solutions

clearly?

10 minute Math:


Addition

Strategies

Investigation 2: Adding it Up

*Solving

addition and

subtraction

problems with 2-

digit and 3-digit

numbers

*Composition of

numbers to

1,000

*Addition

*Variety of

subtraction

situations

*Addition and

subtraction

combinations

*Addition and

subtraction

relationships

Unit 5 23



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math




numbers?

Can Students identify, describe,



starts?

4.NBT.4

4.MD.2

3: Construct viable

arguments and


of others.


8: Look for and


repeated reasoning.


least one addition

strategy that they can

use accurately? Do

students use the same

strategy for every

addition problem, or do

they choose a strategy

based on the number

relationships in the

problem?

10 minute Math:

Broken Calculator

2.3 Can Students identify, describe,



starts?

Can Students develop arguments

about why two addition

expressions are equivalent?

Can Students use story contexts

and representations to support

explanations about equivalent

addition expressions?

4.NBT.4

4.MD.2

3: Construct viable

arguments and


of others.


8: Look for and


repeated reasoning.


some or all of the starter

problems mentally, or

do they need to write

them down and break

them apart? Can

students accurately

follow through one of

the starts to solve the

final problem?

10 minute Math:

Broken Calculator

2.4 Can Students use clear and

concise notation to record

addition and subtraction

strategies?

Can Students understand the

meaning of the steps and

notation of the U.S. algorithm for

addition?

4.NBT.4

4.MD.2


8: Look for and


repeated reasoning.

TO- Can students

explain Solution1,

adding by place? Can

students explain the U.S.

algorithm, especially

what they "carried" 1

means and where it

comes from?

10 minute Math:


Writing about

Mathematical

Thinking: SAB p. 29

*Solving

addition and

subtraction

problems with 2-

digit and 3-digit

numbers

*Composition of

numbers to

1,000

*Addition

*Variety of

subtraction

situations

*Addition and

subtraction

combinations

*Addition and

subtraction

relationships

Unit 5 24



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



2.5 Can Students find combinations

of 3-digit numbers that add to

1,000?

4.NBT.4

4.MD.2


and quantitatively.

TO- Do students make

one 3-digit number and

then figure out how

much more they need to

get to 1,000? Do

students use place

value, such as focusing

on the 100s first as a

way of getting close to

1,000, and then filling in

the 10s and 1s?

10 minute Math:


Close to 1,000 (M21)

Close to 1,000

Recording Sheet

(M22)


numbers?

Can Students find combinations


1,000?

4.NBT.4

4.MD.2


and quantitatively.


Assessment: Solving

Addition Problem in

Two Ways (M23)

10 minute Math:

Broken Calculator




structure of 10,000 and its

equivalence to one thousand 10s,

one hundred 100s and ten

1,000s?

4.NBT.1

4.NBT.2

4.NBT.4

1: Make sense of

problems and


them.


use of structure.

TO- Can students

identify the first and the

last number on each

chart? Do students

notice and understand

the pattern of numbers

throughout the 100

chart? Can students

identify some numbers

in the middle of each

chart?

10 minute Math:

Broken Calculator




structure of 10,000 and its

equivalence to one thousand 10s,

one hundred 100s and ten

1,000s?

4.NBT.1

4.NBT.2

4.NBT.4

1: Make sense of

problems and


them.

TO- Do students use


the number of 100s in

10,000? Can students

keep track of the groups

of 10s as they work their

way up to 10,000?

10 minute Math:

Broken Calculator

Writing about

Mathematical

Thinking: SAB p. 39

Investigation 3: Working with Numbers to 10,000

*Solving

addition and

subtraction

problems with 2-

digit and 3-digit

numbers

*Composition of

numbers to

1,000

*Addition

*Variety of

subtraction

situations

*Addition and

subtraction

combinations

*Addition and

subtraction

relationships

Unit 5 25



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math





Can Students add and subtract


Can Students recognize the place

value of digits in large numbers?

4.NBT.2

4.NBT.4

1: Make sense of

problems and


them.

TO- Can students

accurately read and

write numbers in the

thousands? Can

students identify the

pace values in a 3- or 4-

digit number? Do

students recognize

which digits of their

starting number will

change as the result of

their computation?

10 minute Math:

Broken Calculator


numbers?





1,000?

4.NBT.2

4.NBT.4

4.MD.2

1: Make sense of

problems and


them.

TO- Can students add

numbers in the

hundreds and

thousands? Do

students have at least

one addition strategy

that they can use

accurately? Do

students use clear and

concise notation? Do

students use their

chosen strategies

efficiently, combining

larger "chunks" of

numbers and using a

minimum number of

steps?

10 minute Math:


Math Workshop: 2A:

Planning a Road Trip

2B: Changing Places on

the 10,000 Chart

2C: Close to 1,000

*Solving

addition and

subtraction

problems with 2-

digit and 3-digit

numbers

*Composition of

numbers to

1,000

*Addition

*Variety of

subtraction

situations

*Addition and

subtraction

combinations

*Addition and

subtraction

relationships

Unit 5 26



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math




numbers?





1,000?

4.NBT.2

4.NBT.4

4.MD.2

1: Make sense of

problems and


them.

TO- Can students add

numbers in the

hundreds and

thousands? Do

students have at least

one addition strategy

that they can use

accurately? Do

students use clear and

concise notation? Do

students use their

chosen strategies

efficiently, combining

larger "chunks" of

numbers and using a

minimum number of

steps?

10 minute Math:


Math Workshop: 2A:

Planning a Road Trip

2B: Changing Places on

the 10,000 Chart

2C: Close to 1,000

3.6A Can Students understand place-

value concepts to 1,000,000?

Can Students use >, =, and < to

compare numbers to 1,000,000?

Can Students write numbers to

1,000,000 in expanded form?

Can Students round numbers to

1,000,000?

4.NBT.1

4.NBT.2

4.NBT.3

1: Make sense of

problems and


them.

TO- Do students write

the correct value for

each digit?

Do students “skip” an

addend when the digit is

0?

10 minute Math:


4.1 Can Students understand the

action of subtraction problems?

Can Students represent

subtraction situations?

Can Students represent addition

and subtraction on a number

line?

4.NBT.2

4.NBT.4

4: Model with

mathematics.


show the action of the

subtraction problem

with representation?

Do students have at

least one efficient

strategy for solving

these problems? What

strategies are students

using?

10 minute Math:

Broken Calculator

*Solving

addition and

subtraction

problems with 2-

digit and 3-digit

numbers

*Composition of

numbers to

1,000

*Addition

*Variety of

subtraction

situations

*Addition and

subtraction

combinations

*Addition and

subtraction

relationships

*Solving

addition and

subtraction

problems with 2-

digit and 3-digit

numbers

*Composition of

numbers to

1,000

*Addition

*Variety of

subtraction

situations

*Addition and

subtraction

combinations

*Addition and

Investigation 4: Subtraction

Unit 5 27



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



4.2 Can Students solve subtraction

problems by breaking numbers

apart?





1,000?

4.NBT.2

4.NBT.4

4: Model with

mathematics.

TO- Do Students

interpret the problems

correctly; that is, do

they know that they are

finding the difference

and not combining two

amounts? What

strategies do students

use? How do students

keep track of their

strategies as they are

showing their solutions?

Are students able to

write a story problem

that represents a

subtraction solution?

10 minute Math:

Broken Calculator

Math Workshop:

Subtraction Story

Problems

2A: Solving Subtraction

Problems

2B: What's the Story

2C: Close to 1,000

Subtraction

Strategies

Writing about

Mathematical

Thinking: SAB p. 57



apart?





1,000?

4.NBT.2

4.NBT.4

4: Model with

mathematics.

TO- Do Students

interpret the problems

correctly; that is, do

they know that they are

finding the difference

and not combining two

amounts? What


use? How do students

keep track of their

strategies as they are

showing their solutions?


write a story problem

that represents a

subtraction solution?

10 minute Math:

Broken Calculator

Math Workshop:

Subtraction Story

Problems

2A: Solving Subtraction

Problems

2B: What's the Story

2C: Close to 1,000

Subtraction

Strategies

*Solving

addition and

subtraction

problems with 2-

digit and 3-digit

numbers

*Composition of

numbers to

1,000

*Addition

*Variety of

subtraction

situations

*Addition and

subtraction

combinations

*Addition and

subtraction

relationships

Unit 5 28



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



4.4A Can students understand the

meaning of the steps and

notation of the U.S. algorithm for

subtraction?

Can students use clear and

concise notation for recording


strategies?

4.NBT.2

4.NBT.4

8: Look for and


repeated reasoning.

TO- Do students

understand how the

numbers are broken

apart to show

regrouping? Can

students use this

algorithm to solve

subtraction problems?

Do they understand the

shorthand notation of

the algorithm?

10 minute Math:


4.4 Can Students understand the

action of subtraction problems?

Can Students develop arguments

about how the differences

represented by two subtraction

expressions are related?

Can students use story contexts

and representations to support

explanations about related

subtraction expressions?

4.NBT.2

4.NBT.4

1: Make sense of

problems and


them.


the starter problems

mentally? Which starter

problems do student

choose to solve the final

problem? If the choose

the start that changes

one of the numbers to a

landmark, can they

accurately follow

through by making an

adjustment for the

change?

10 minute Math:


*Solving

addition and

subtraction

problems with 2-

digit and 3-digit

numbers

*Composition of

numbers to

1,000

*Addition

*Variety of

subtraction

situations

*Addition and

subtraction

combinations

*Addition and

subtraction

relationships

Unit 5 29



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math





apart?

Can Students add 3 and 4-digit

numbers?

4.NBT.2

4.NBT.4

4.MD.2

1: Make sense of

problems and


them.


least one strategy they

can use efficiently? Do


strategies clearly and

concisely? Is their

computation accurate?

What strategies do

students use? Can

students write amounts

of money accurately?

Do students look for

ways to balance positive

score with negative

scores? Can students

combine positive an

negative numbers?

10 minute Math:


Math Workshop:

Solving Addition and

Subtraction Problems

2A: Which Is Farther?

How Much Farther?

2B: Money Problems

2C: Close to 1,000: Plus

and Minus

2D: Assessment:

Numbers to 10,000



apart?


numbers?

4.NBT.2

4.NBT.4

4.MD.2

1: Make sense of

problems and


them.


least one strategy they

can use efficiently? Do


strategies clearly and

concisely? Is their

computation accurate?

What strategies do

students use? Can

students write amounts

of money accurately?

Do students look for

ways to balance positive

score with negative

scores? Can students

combine positive an

negative numbers?

10 minute Math:


Math Workshop:

Solving Addition and

Subtraction Problems

2A: Which Is Farther?

How Much Farther?

2B: Money Problems

2C: Close to 1,000: Plus

and Minus

2D: Assessment:

Numbers to 10,000

*Solving

addition and

subtraction

problems with 2-

digit and 3-digit

numbers

*Composition of

numbers to

1,000

*Addition

*Variety of

subtraction

situations

*Addition and

subtraction

combinations

*Addition and

subtraction

relationships

Unit 5 30



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math





apart?


numbers?

Can students use clear and

concise notation for recording


strategies?


problems and


them.


and quantitatively.

8: Look for and


repeated reasoning.


strategies efficiently to

solve addition

problems? Can students

use strategies efficiently

to solve subtraction

problems?

End-of-Unit Assessment

(M29)

10 minute Math:

Broken Calculator

Unit 5 31



Sample


Interdisciplinary

Connections

Prior

Knowledges

1.1 Can students find the fractional

parts of a rectangular area?

Can students interpret the

meaning of the numerator and

the denominator of a fraction?

4.NBT.2

4.NF.1

4.NF.3.a

4.NF.3.b

1: Make sense of

problems and


them.


and quantitatively.

Teacher Observation

(TO)-Can students find ¼

and ¾ of a rectangle?

Can students explain

how they know that it is

¼, either by

demonstrating that it is

composed of 6 out of 24

squares or by showing

that it is 1 of 4 equal

pieces?

10 minute Math:


Fraction,

Denominator

Numerator

Resource Masters

(M)



Are students able to identify

relationships between unit

fractions when one denominator

is a multiple of the other (e.g.,

halves and fourths, thirds and

sixths)

Can students identify equivalent

fractions?

4.NBT.2

4.NF.3.a

4.NF.3.b

1: Make sense of

problems and


them.


and quantitatively.


and ⅓ and ⅙ of a 4X6

rectangle? Can students

identify ⅓ as one of

three equal parts of a

whole (and ⅙ as 1 out of

6 equal parts)?

Can students use correct

fraction notation for the

parts they identify?

10 minute Math:


Thirds

Sixths

1.3 How are fractions used in

problem-solving situations?

4.NBT.2

4.NF.3.d

4: Model with

mathematics.


fractional parts of 24

objects and/or group of

objects represented by

fractions with

numerators greater than

1?

Can students use

representations to show

that they have identified

the correct quantity?

10 minute Math:


4th Grade Math


*Fractions

*Fraction

relationships

*Equal shares

*Fractions as

part of a whole

*Numerator and

Denominator

*Halves,

Fourths, Eights

*Thirds and

Sixths

*Simple

Equivalent

Fractions (Halves

and Fourths)

*Mixed

Numbers

*Decimal

Fractions as

money (0.25,

0.5)

Unit 6: Fraction Cards and Decimal Squares

Unit 6 32



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math





Are students finding fractional

parts of a group?

Are students comparing the same

fractional parts of different-sized

wholes?

4.OA.3

4.OA.4

4: Model with

mathematics.

TO- Can students

interpret the meaning of

a fraction in the context

of area?

Which of the fractional

parts are students able

to find easily?

What strategies are

students using to find

fractional parts of the

5X12 rectangle?

10 minute Math:


Math Workshop:

Finding Fractions of a

5X12 Rectangle, M11.



Are students able to write, read,

and apply fraction notation?

4.NBT.2

4.NF.1

4.NF.3.a

1: Make sense of

problems and


them.


and quantitatively.

4: Model with

mathematics.

TO- Can students divide

a rectangle into

fractional parts and

identify each of the

fractions that they

draw?

Can students write an

equations that

represents the sum of all

the fractional parts

equaling 1?

Assessment: Identifying

and Comparing

Fractions (M12)

10 minute Math:


Writing about

Mathematical

Thinking: M12

*Fractions

*Fraction

relationships

*Equal shares

*Fractions as

part of a whole

*Numerator and

Denominator

*Halves,

Fourths, Eights

*Thirds and

Sixths

*Simple

Equivalent

Fractions (Halves

and Fourths)

*Mixed

Numbers

*Decimal

Fractions as

money (0.25,

0.5)

Unit 6 33



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



1.6 Can students use representations

to add fractions that sum to 1?

Can students add fractions with

the same and related

denominators?

4.NBT.2

4.NF.3.a

4.NF.3.b


and quantitatively.

TO- Are students adding

fractions by using what

they know about

representing fractions

and reasoning from

their knowledge of

equivalent fractions and

fraction combinations?

Can students add

fractions with like

denominators mentally

and explain how they

know what the sum is?

Can students solve

problems with sums

greater than 1?

10 minute Math:


Math Workshop:

Fractions

2A: Adding fractions

2B: Combinations That

Equal 1

2C: Finding Fractions of

a Rectangle

2D: Story Problems

About a Class

1.7 Can students estimate sums of

fractions?

Can students use representations

to add fractions that sum to 1?

Can students add fractions with

the same and related

denominators?

4.NBT.2

4.NF.2

4.NF.3.a


and quantitatively.

TO- Are students adding

fractions by using what

they know about

representing fractions

and reasoning from

their knowledge of

equivalent fractions and

fraction combinations?

Can students add

fractions with like

denominators mentally

and explain how they

know what the sum is?

Can students solve

problems with sums

greater than 1?

10 minute Math:


Math Workshop:

2A: Adding fractions

2B: Combinations That

Equal 1

2C: Finding Fractions of

a Rectangle (5 X 12

and 10 X 10)

*Fractions

*Fraction

relationships

*Equal shares

*Fractions as

part of a whole

*Numerator and

Denominator

*Halves,

Fourths, Eights

*Thirds and

Sixths

*Simple

Equivalent

Fractions (Halves

and Fourths)

*Mixed

Numbers

*Decimal

Fractions as

money (0.25,

0.5)

Unit 6 34



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



1.8A Can students use visual

representations to subtract

fractions

with like denominators?

Can students subtract fractions

with like denominators?

4.NF.3.a

4.NF.3.d

1: Make sense of

problems and


them.

4: Model with

mathematics.

5: Use appropriate

tools.

TO- Are they using

rectangles or making

drawings that

match the context of the

problem? Are they

maintaining equal sized

parts?

Are students continuing

to reason about the size

of fractions?


Survey

2.1 Can students interpret the



Can students represent fractions

greater than 1?

Can students find fractional parts

of a rectangular area?

4.NF.1

4.NF.2

3: Construct viable

arguments and


of others.


representations of

fractions that range

from 0/2 to 2½,

including improper

fractions? Are students

recognizing that

fractions in which the

numerator and the

denominator are the

same equal 1?

Do students recognize

some equivalent

fractions and use this

understanding to create

their representations?


Survey

How to Make

Fraction Cards

(M19), Blanks for

Fraction Cards (M16-

18)

Investigation 2: Ordering Fractions

*Fractions

*Fraction

relationships

*Equal shares

*Fractions as

part of a whole

*Numerator and

Denominator

*Halves,

Fourths, Eights

*Thirds and

Sixths

*Simple

Equivalent

Fractions (Halves

and Fourths)

*Mixed

Numbers

*Decimal

Fractions as

money (0.25,

0.5)

Unit 6 35



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math







greater than 1?

Can students find fractional parts

of a rectangular area?

4.NF.2 3: Construct viable

arguments and


of others.


representations of

fractions that range

from 0/2 to 2½,

including improper

fractions? Are students

recognizing that

fractions in which the

numerator and the

denominator are the

same equal 1?


some equivalent

fractions and use this

understanding to create

their representations?


Survey

Writing about

Mathematical

Thinking: SAB p. 31




Can students identify equivalent

fractions?

Can students order fractions and

justify their order through

reasoning about fraction

equivalencies and relationships?

4.NF.1

4.NF.2

3: Construct viable

arguments and


of others.

TO- How do students

decide which fraction is

greater?

Are students paying

attention to the value

and meaning of both the

numerator and

denominator?

Are students recognizing

equivalent fractions?


Survey

Writing about

Mathematical

Thinking: SAB p. 35

*Fractions

*Fraction

relationships

*Equal shares

*Fractions as

part of a whole

*Numerator and

Denominator

*Halves,

Fourths, Eights

*Thirds and

Sixths

*Simple

Equivalent

Fractions (Halves

and Fourths)

*Mixed

Numbers

*Decimal

Fractions as

money (0.25,

0.5)

Unit 6 36



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



2.4 Can students identify equivalent

fractions?

Can students compare fractions

to the landmarks 0, ½, 1, and 2?

4.NF.2 7. Look for and make

use of structure.

TO- How do students

decide whether a

fraction is less than ½ or

more than ½?


fractions that are

equivalent to 0, 1, and

2?

Can students sort the

fractions by reasoning

about fraction

equivalencies and other

fraction relationships

they know?


Survey

Landmarks

2.5 Can students order fractions and







using a number line?

4.NF.1

4.NF.2

4.NF.3.a

5: Use appropriate

tools.

TO- How do students

order fractions?

How do students decide

about the order of

fractions that are close

in size but have different

denominators?


Survey

Math Workshop:

Comparing Fractions

3A: Making a Fraction

Number Line

3B: Capture Fractions

Capture Fractions

(M20-M21)

2.6 Can students order fractions and







using a number line?

4.NF.1

4.NF.2

5: Use appropriate

tools.

TO- How do students

order fractions?

How do students decide

about the order of

fractions that are close

in size but have different

denominators?


Survey

Math Workshop:

Comparing Fractions

3A: Making a Fraction

Number Line

3B: Capture Fractions

Writing about

Mathematical

Thinking: M23

*Fractions

*Fraction

relationships

*Equal shares

*Fractions as

part of a whole

*Numerator and

Denominator

*Halves,

Fourths, Eights

*Thirds and

Sixths

*Simple

Equivalent

Fractions (Halves

and Fourths)

*Mixed

Numbers

*Decimal

Fractions as

money (0.25,

0.5)

Unit 6 37



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



2.7A Can students make a line plot to

display a data set of

measurements

involving fractions?

Can students add and subtract

mixed numbers with like

denominators using

representations and reasoning

about

fractions and the operations?

4.NF.3.c

4.MD.4

5: Use appropriate

tools.

TO- When students use

the information from

the table to complete

the line

plot can they correctly

plot the data? Are

students’ statements

about the data

accurate?

What strategies are

students using to solve


problems?


Survey

3A.1 Can students multiply a whole

number and a fraction?

Can students use visual models to

solve word problems involving

multiplication of a whole number

and a fraction?

4.NF.4.a

4.NF.4.b

4.NF.4.c

4: Model with

mathematics.

TO- What

representations and


use to

solve the problems? Can

students write a

multiplication equation

for the problem?

10 minute Math:


Decimal

3A.2 Can students multiply a fraction

and a whole number?

Can students use visual models to

solve word problems involving

multiplication of a fraction and a

whole number?

4.NF.4.a

4.NF.4.b

4.NF.4.c

4: Model with

mathematics.

TO- What strategies do


the problems? Can

students write a


for the problem? Can

students decide

whether their answers

to the problems are

reasonable?

10 minute Math:


Math Workshop

2A: Multiplying

Fractions and Whole

Numbers (SAB p. 44F)

2B: More Multiplying

Fractions and Whole

Numbers (SAB 44G)

Investigation 3: Working With Decimals

*Fractions

*Fraction

relationships

*Equal shares

*Fractions as

part of a whole

*Numerator and

Denominator

*Halves,

Fourths, Eights

*Thirds and

Sixths

*Simple

Equivalent

Fractions (Halves

and Fourths)

*Mixed

Numbers

*Decimal

Fractions as

money (0.25,

0.5)

Unit 6 38



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



3A.3 Can students multiplying fractions

and whole numbers?

Are students using visual models

to solve word problems involving

multiplication of a fraction and a

whole number?

4.NF.4.a

4.NF.4.b

4.NF.4.c

4: Model with

mathematics.

What strategies do


the problems? Can

students write a


for the problem? Can

students decide

whether their answers

to the problems are

reasonable?

Assessment:

Multiplying

with Fractions, M41

10 minute Math:


Math Workshop:

Multiplying with

Fractions

2A: Multiplying

Fractions and Whole

Numbers

2B: More Multiplying

Fractions and Whole

Numbers

2C: Multiplying with

Fractions

3.1 How will students identify

everyday uses of fractions and

decimals?

Can students read and write

tenths and hundredths?

4.NF.5

4.NF.6

4.NF.7

4.MD.2

5: Use appropriate

tools.


TO- Can students

represent the numbers

on the 10 X 10 square?

Do students read and

understand the meaning

of the decimal

numbers?

10 minute Math:


3.2 Can students read and write


Can students order decimals and


reasoning about representations

and meaning of the numbers?

4.NF.6

4.NF.7

5: Use appropriate

tools.


Can students represent

tenths and hundredths

as part of the square?

Can students use the

representations and/or

reason about the

meaning of the decimal

numbers to compare

them? Can students

determine the value of

each number?

10 minute Math:


*Fractions

*Fraction

relationships

*Equal shares

*Fractions as

part of a whole

*Numerator and

Denominator

*Halves,

Fourths, Eights

*Thirds and

Sixths

*Simple

Equivalent

Fractions (Halves

and Fourths)

*Mixed

Numbers

*Decimal

Fractions as

money (0.25,

0.5)

Unit 6 39



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



3.3 Can students identify decimal and

fraction equivalents?

4.NF.5

4.NF.6

4.NF.7

5: Use appropriate

tools.


use of structure.

TO- Can students fill in

the 10X 10 square to

represent the decimal?

Are students examining

their partially filled

squares to choose a

decimal card that will fill

the square? How are

students combining the

decimals to show the

total?

10 minute Math:


Fill Two Activity (M28)

3.4 Can students estimate the sums

of decimal numbers?

Can students use representations

to combine tenths and

hundredths?

4.NF.7

4.MD.2

4: Model with

mathematics.

5: Use appropriate

tools.

TO- Do students make

reasonable estimates?

Do students keep track

of the meaning of each

digit (i.e., which digit

represents tenths, which

represent hundredths,

and which represent

whole numbers)?

10 minute Math:


3.5 Can students read and write






4.NF.7

4.MD.2

4: Model with

mathematics.

TO- Do students notice

whether their sum is or

is not reasonable? Do

students keep track of

the meaning of each

digit (i.e., which digit

represents tenths, which

represent hundredths,

and which represent

whole numbers)? Are

students able to add the

numbers accurately?

10 minute Math:


Math Workshop:

Comparing and

Combining Decimals

1A: Decimal Compare

1B: Fill Two

1C: Making Your Own

Running Logs

Writing about

Mathematical


58

*Fractions

*Fraction

relationships

*Equal shares

*Fractions as

part of a whole

*Numerator and

Denominator

*Halves,

Fourths, Eights

*Thirds and

Sixths

*Simple

Equivalent

Fractions (Halves

and Fourths)

*Mixed

Numbers

*Decimal

Fractions as

money (0.25,

0.5)

Unit 6 40



Sample


Interdisciplinary

Connections

Prior

Knowledges

4th Grade Math



3.6 Can students read and write tenths

and hundredths?





4.NF.7

4.MD.2

4: Model with

mathematics.

Continuation of same

assessments from

session 3.5

10 minute Math:


Math Workshop:

Comparing and

Combining Decimals

1A: Decimal Compare

1B: Fill Two

1C: Making Your Own

Running Logs

3.7 Can students identify fractional

parts of a group?

Can students order fractions with

like and unlike denominators?

Can students compare decimal

numbers?

Can students read, write, and

interpret decimal fractions in tenths

and hundredths?

4.NF.2

4.NF.7

1: Make sense of

problems and


them.


and quantitatively.

End Of Unit

Assessment: M31

10 minute Math:


Writing about

Mathematical

Thinking: M31

*Fractions

*Fraction

relationships

*Equal shares

*Fractions as

part of a whole

*Numerator and

Denominator

*Halves,

Fourths, Eights

*Thirds and

Sixths

*Simple

Equivalent

Fractions (Halves

and Fourths)

*Mixed

Numbers

*Decimal

Fractions as

money (0.25,

0.5)]

Unit 6 41



Sample


Interdisciplinary

Connections

Prior

Knowledges

3.1 Can students find the number of

cubes (volume) that will fit into the

box made by a given pattern?

4.NF.7 1: Make sense of

problems and persevere

in solving them.

4: Model with

mathematics.

8: Look for and express

regularity in repeated

reasoning.

Teacher Observation (TO)-

While students find the

volume of given boxes,

how close are their

predictions? Are students

able to use the pattern to

construct the box?

10 mintue Math:


Rectangular Prism Resource Masters (M)

3.2 Can students design patterns for

boxes that hold a given number of

cubes (volume)?

Can students see that cubes filling a

rectangular prism can be

decomposed into congruent layers?

4.NF.7 1: Make sense of


in solving them.

4: Model with

mathematics.



reasoning.

TO- What strategies are

students using to

complete the pattern?


figure out how many

layers the box needs? Do

students understand the

relationship between the

actual box and the

squares that appear on

the pattern?

10 mintue Math:


3.3 Can students see that cubes filling a

rectangular prism can be

decomposed into congruent layers?

Can students develop a strategy for

determining the volume of

rectangular prisms?

1: Make sense of


in solving them.

4: Model with

mathematics.



reasoning.


find the volume without

building the box? What

strategies are students

using to make the

pattern? Do students see

the relationship between

the number of layers and

the number of squares

they need to draw for

each side?

10 mintue Math: Quick

Images

Math Workshop:

1A: Finding the Volume

of More Boxes

1B: Building Boxes from

the Bottom Up

1C: Double the Number

of Cubes

Writing about

Mathematical

Thinking: SAB p. 48


*Cube

*Rectangular

Prism

*How many

cubes fit in an

open box

Unit 7: Moving Between Solids and Silhouettes

4th Grade Math

Unit 7 42



Sample


Interdisciplinary

Connections

Prior

Knowledges

1.1 Are students able to estimate 2

digit multiplication problems?

Can students multiply multiples of

10?

1: Make sense of

problems and


them.

Teacher Observation

(TO)-Are students using

multiples of 10 to make

their estimates?

10 minute Math:

Closest Estimate

estimate

multiplication

landmark

multiple

Resource Masters

(M)

Writing about

Mathematical

Thinking:

SAB p. 1

1.2 Are students able to estimate 2

digit multiplication problems?

Can student break a problem into

smaller parts to solve 2 digit

multiplication problems and

combined sub products?


problems and


them.


story problem and solve

and 2-digit by 2-digit

multiplication problem?

10 minute Math:

Closest Estimate

Writing about

Mathematical

Thinking:

SAB p. 5-6, 8

1.3 Can student break a problem into





10?



with picture or diagrams?

4.NBT.5 7. Look for and make

use of structure.

TO-Are to students able

to solve a set of

problems and using

break apart to solve 2-

digit problems?

10 minute Math:

Closest Estimate

cluster CM Grid paper

(Resource Master

(M11)

Unit 8: How Many Packages? How Many Groups

4th Grade Math

Investigation 1: Multiplication with2 Digit Numbers

*Multiplication

and Division

*Multiplication

Combinations 12

X 12

*Solve and

represent a 2-

digit and 1-digit

multiplication

problem by

visualizing or

story context

*Arrays

*Skip counting

*Relationship

between

multiplication

and division

*Remainders

Unit 8 43



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Multiplication with2 Digit Numbers1.4 Can student break a problem into





10?




4.OA.3

4.OA.4


use of structure.

TO-Can students identify

factors of numbers that

are multiples of 10?

Are to students able to

solve a set of problems

and using break apart to

solve 2-digit problems?

Can students estimate

and solve 2-digit

multiplication story

problems?

10 minute Math:

Counting Around the

Class

Math Workshop:

Multiplication Practice

2A: Factor Bingo

2B: Multiplication

Cluster Problems

2C: Assessment:

Solving Multiplication

Problems

factor Factor Bingo

Gameboards A and B

(M14-15)

Number Cards for

Factor Bingo (M16)

Factor Bingo Game

Explanation (M17)

Assessment

Checklist: Solving

Multiplication

Problems (M18)

Writing about

Mathematical


15






10?




4.OA.3

4.OA.5

4.NBT.5


use of structure.

Teacher discretion 10 minute Math:

Counting Around the

Class

Math Workshop:

Multiplication Practice

2A: Factor Bingo

2B: Multiplication

Cluster Problems

2C: Assessment:


Problems

2.1 Can student solve multiplication

problems by changing one factor

to create an easier problem?




4.OA.3

4.NBT.5

4.MD.2

3. Construct viable

arguments and


of others.


problems in which one

of the factors has been

changed to a multiple of

10?

10 minute Math:

Closest Estimate

*Multiplication

and Division

*Multiplication

Combinations 12

X 12

*Solve and

represent a 2-

digit and 1-digit

multiplication

problem by

visualizing or

story context

*Arrays

*Skip counting

*Relationship

between

multiplication

and division

*Remainders

Investigation 2: Strategies for Multiplication

Unit 8 44



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Multiplication with2 Digit Numbers2.2 Can student solve multiplication

problems by changing one factor to

create an easier problem?






10?

4.OA.3

4.NBT.5

3. Construct viable

arguments and


of others.

8: Look for and


repeated reasoning.


break apart a 2-digit

multiplication problem

to solve easily?


solve story problems

with the possibility of

rounding up?

10 minute Math:

Closest Estimate

Math Workshop:


Problems

2A: more Multiplication

Cluster Problems

2B: Problems About

Oranges

2C: Factor Bingo

2.3 Can student solve multiplication








10?

4.NBT.5 3. Construct viable

arguments and


of others.

8: Look for and


repeated reasoning.

TO- At teacher's

discretion

10 minute Math:

Closest Estimate

Math Workshop:


Problems

2A: more Multiplication

Cluster Problems

2B: Problems About

Oranges

2C: Factor Bingo

Writing about

Mathematical

Thinking: SAB p. 29

2.4A Can students multiplying a 4-digit

number by a 1-digit number?

4.OA.3

4.NBT.5

4.MD.2

3. Construct viable

arguments and


of others.

8: Look for and


repeated reasoning.


the problems

accurately?

What strategies do


the problems? Were

they able to keep track

of all the parts of the

four digit

number?

10 minute Math: Close

Estimate with 4-Digit

Numbers

*Multiplication

and Division

*Multiplication

Combinations 12

X 12

*Solve and

represent a 2-

digit and 1-digit

multiplication

problem by

visualizing or

story context

*Arrays

*Skip counting

*Relationship

between

multiplication

and division

*Remainders

Unit 8 45



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Multiplication with2 Digit Numbers2.4 Can student solve multiplication








10?

4.OA.5

4.NBT.5

3. Construct viable

arguments and


of others.

8: Look for and


repeated reasoning.

TO- Can students put

multiplication problems

into story contexts and

solve the problems?

10 minute Math:

Counting Around the

Class

Math Workshop:


Problems

2A: More

Multiplication Cluster

Problems

2B: Writing

Multiplication Story

Problems

2C: Factor Bingo

Writing about

Mathematical


32





4.OA.5

4.NBT.5

8: Look for and


repeated reasoning.

Assessment Activity

(M19)

10 minute Math:

Counting Around the

Class

Math Workshop:


Problems

2A: More

Multiplication Cluster

Problems

2B: Writing

Multiplication Story

Problems

Assessment Activity

(M19)

3.1 Are students able to solve division

problems by breaking the

problem into parts or represent

using pictures or diagrams?

4.NBT.5

4.NBT.6

4.MD.2

1: Make sense of

problems and


them.


division problems by

making groups of the

divisor?

10 minute Math:

Counting Around the

Class

divisor

division

Investigation 3: Solving Division Problems

*Multiplication

and Division

*Multiplication

Combinations 12

X 12

*Solve and

represent a 2-

digit and 1-digit

multiplication

problem by

visualizing or

story context

*Arrays

*Skip counting

*Relationship

between

multiplication

and division

*Remainders

Unit 8 46



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Multiplication with2 Digit Numbers3.2 Are students able to use multiples

of 10 or break apart into parts to


4.OA.5

4.NBT.6

1: Make sense of

problems and


them.

5: Use appropriate

tools.

TO- Can students

accurately identify

landmark multiples (5th,

10th, 20th)?


solve division problems

with 2-digit and 3-digit

numbers?

10 minute Math: Closest

Estimate


Multiples of 10

2A: Problems About

Multiple Towers

2B: Solving Division

Problems

2C: Factor Bingo

remainder 300 Chart (M20)

Factor Bingo (M14-

15)

Number Cards for

Factor Bingo (M16)

Factor Bingo

Instructions (M17)

3.3 Are students able to use multiples



4.OA.3

4.OA.5

4.NBT.6

1: Make sense of

problems and


them.

5: Use appropriate

tools.

TO- At teacher's

discretion


Estimate


Multiples of 10

2A: Problems About

Multiple Towers


Problems

2C: Factor Bingo

Writing about

Mathematical

Thinking: SAB p. 48

3.4 Are students able to use multiples



4.OA.5,

4.NBT.5,

4.NBT.6

1: Make sense of

problems and


them.

5: Use appropriate

tools.

8: Look for and


repeated reasoning.

TO- At teacher's

discretion

10 minute Math:

Counting Around the

Class


Multiples of 10

2A: Problems About

Multiple Towers


Problems

2C: Factor Bingo

Factor Bingo (M14-

15)

Number Cards for

Factor Bingo (M16)

Factor Bingo

Instructions (M17)

3.5A Can students divide a 4-digit

number by a 1-digit number?


problems and


them.


the problems

accurately?

What strategies do


the problems?

Can students accurately

express any remainders

in the context of the

problem?

10 minute Math: Close

Estimate with 4-Digit

Numbers

*Multiplication

and Division

*Multiplication

Combinations 12

X 12

*Solve and

represent a 2-

digit and 1-digit

multiplication

problem by

visualizing or

story context

*Arrays

*Skip counting

*Relationship

between

multiplication

and division

*Remainders

Unit 8 47



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Multiplication with2 Digit Numbers3.5 Are students able to use the


multiplication and division to

solve problems?

4.OA.3

4.OA.5

4.NBT.5

4.MD.2

1: Make sense of

problems and


them.


solve multiplication and

division problems with 2-

digit and 3-digit

numbers?

10 minute Math:

Counting Around the

Class

3.6 Are students able to solve

multiplication problems with 2

digit numbers by making groups

of the divisor?

4.OA.5

4.NBT.5

4.NBT.6

1: Make sense of

problems and


them.


and quantitatively.

3. Construct viable

arguments and


of others.


communicate their

thinking clearly?

Assessment: End-of-the-

Unit Assessment (M21-

M22)

*Multiplication

and Division

*Multiplication

Combinations 12

X 12

*Solve and

represent a 2-

digit and 1-digit

multiplication

problem by

visualizing or

story context

*Arrays

*Skip counting

*Relationship

between

multiplication

and division

Unit 8 48



Sample


Interdisciplinary

Connections

Prior

Knowledges

1.1 Are students able to

interpreate the points

and shape of a graph in

terms of the situation

the graph represents?


find the difference

between two values on

a line graph?

4: Model with

mathematics.

Teacher Observation (TO)-

Can students answer

questions about features of

a 2 topic graph?

Can students use the motion

graph to answer questions

about what the different

parts of the graph show?


Survey

Graph

Axis

Resource Masters (M)

Writing about

Mathematical Thinking:

SAB p. 6


interperate the points

and shape of a graph in

terms of the situation

the graph represents?


identify features of a

graph that represents

quantity and those that

represent changes in

quantity?

4: Model with

mathematics.

TO- Can students classify

words or phrases that

describe speed and sketch a

graph?


Survey

Unit 9: Penny Jars and Plant Growth

4th Grade Math

*Graphing

*Temperature

*Line graphs

*Change over

time

*Individual

change on a

graph

*X-axis

*Y-axis

*Variables

*Tables


Unit 9 49



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math



find the value of one

quantity in a situation

of constant change,

given the value of the

other?


representation for a

situation of constant

change?

4.OA.3

4.OA.4


and quantitatively.

4: Model with

mathematics.


use of structure.

TO- Can students find the

number of something within X

amount of rounds given the

starting number and the

number of pennies added in

each round?

Can students make

representations of jars

situations using diagrams,

pictures, tables or graphs that

show the number of

something of each round?


Estimate

Table Represen-

tation

Penny Jar Situation Cards

(M19)

Writing about


SAB p. 15

2.2 Are students able to find

the value of one quantity

in a situation of constant

change, given the value

of the other?

Can students use tables

to represent the


two quantities of

constant change?


interpret numbers in a

table in terms of what

they represent?


representation for a

situation of constant

change?

4.OA.5

4.NBT.6


and quantitatively.

4: Model with

mathematics.


use of structure.

TO- Can students determine

the number of something

for any given round later in

the sequence?


Estimate

Writing about


SAB p. 18

Investigation 2: Penny Jars and Towers

*Graphing

*Temperature

*Line graphs

*Change over

time

*Individual

change on a

graph

*X-axis

*Y-axis

*Variables

*Tables

Unit 9 50



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Representing Multiplications with Arrays2.3 Are students able to find

the value of one quantity

in a situation of constant

change, given the value

of the other?

Can students use tables

to represent the


two quantities of

constant change?


arithmetic expression for

finding the value of one

constant?


and quantitatively.

4: Model with

mathematics.


use of structure.

TO- Can students use the

sequence to determine if

the number is doubled in

the 20th round or not?


Survey

Writing about


SAB p. 21-22


indentify points in a

graph with

corresponding values in

a table?

Can students plot

points one coordinate

grid?

4.OA.5

4.NBT.5

4.NBT.6


and quantitatively.

4: Model with

mathematics.


use of structure.

TO- Can students complete

a table and graph the

results?


Estimate

Penny Jar Talbes A and B

(M23)

*Graphing

*Temperature

*Line graphs

*Change over

time

*Individual

change on a

graph

*X-axis

*Y-axis

*Variables

*Tables

Unit 9 51



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Representing Multiplications with Arrays2.5 Are students able to



of constant change,


other?


arithmetic expression

for finding the value of

one constant?

4.OA.5

4.NBT.5

4.NBT.6


and quantitatively.


use of structure.

TO- Can students complete

a table to solve for

problems?

Can students compare

tables and graphs from 2

situations?


Estimate

Assessment Checklist: Penny

Jar Compari-sons (M27)

Writing about


SAB p. 35 & 37




of constant change,


other?




one constant?

4.OA.5

4.NBT.5

4.NBT.6


and quantitatively.


use of structure.

TO- Can students identify

whether single and double

towers can ever have a

given number of windows?

Can students make table

and graph to compare 2

situations and answer

questions?


Estimate

*Graphing

*Temperature

*Line graphs

*Change over

time

*Individual

change on a

graph

*X-axis

*Y-axis

*Variables

*Tables

Unit 9 52



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Representing Multiplications with Arrays2.7 Can students find the

steepness of graphs or

parts of graphs in

terms of rate of

change?

Can students make a

rule to relate one

variable to another in

terms of constant

change?

Can students use

symbolic letter

notation to represent

the value of one

variable in terms of

another?


and quantitatively.


use of structure.

TO- At teacher's discretion 10 minute Math: Quick

Survey

2.8 Can students make a

rule to relate one

variable to another in

terms of constant

change?

Can students use

symbolic letter

notation to represent

the value of one

variable in terms of

another?

4.OA.5

4.NBT.5

4.NBT.6


and quantitatively.


use of structure.


rules for a pattern/


Estimate

*Graphing

*Temperature

*Line graphs

*Change over

time

*Individual

change on a

graph

*X-axis

*Y-axis

*Variables

*Tables

Unit 9 53



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math


3.1 Can students identify

points in a graph with


a table?

Can students plot points

on a coordinate grid?

Can students find the


parts of graphs in terms

of rate of change?

4.OA.5

4.MD.1

4.MD.4

5: Use appropriate

tools.

TO- Can students graph a

and make prediction for

growth?

Can students use their

graphs to answers questions

about slower and faster

growth?


Survey

3.2 Can students plot

points on a coordinate

grid?



parts of graphs in

terms of rate of

change?



parts of graphs in

terms of rate of

change?

4.OA.5

4.MD.1

4.MD.4

5: Use appropriate

tools.

TO- Can students create a

new graph with similar data

and then compare the 2?


Survey

3.3 Can students identify

points in a graph with


a table?

4.OA.5

4.NBT.5

4.NBT.6

4.MD.1

5: Use appropriate

tools.

Can students create their

own story to make a graph?


Estimate

Matching Numbers, Stories,

and Graphs (M36)

Investigation 3: Collecting and Analyzing Measurements

*Graphing

*Temperature

*Line graphs

*Change over

time

*Individual

change on a

graph

*X-axis

*Y-axis

*Variables

*Tables

Unit 9 54



Sample


Interdisciplinary

Connections

Prior

Knowledges


4th Grade Math

Investigation 1: Representing Multiplications with Arrays3.4 Can students interpret

points and shape of a

graph in terms of the

situation?

Can students compare

tables, graphs, and

situations of constant

change and those with

out?

Can students plot points

on a coordinate grid?

4.NBT.5

4.NBT.6

5: Use appropriate

tools.

TO- Can students graph a

constant rate of change?


Estimate

Decrease

3.5 Can students find the


parts of graphs in

terms of rate of

change?




one constant?

Can students write and



one quantity in terms

of the constant rate?

4.OA.5

4.MD.1

1: Make sense of

problems and


them.


and quantitatively.

5: Use appropriate

tools.

TO- Can students interpret

data to match stories to

graphs?

Assessment: End-of-the-

Unit Assessment (M37-

M39)


Survey

*Graphing

*Temperature

*Line graphs

*Change over

time

*Individual

change on a

graph

*X-axis

*Y-axis

*Variables

*Tables

Unit 9 55

Unit Author Title Strand

G4U1 Tang, Greg

The Best of Times: Math Strategies

That Multiply Multiplication and Division

Investigati

on 1:

Represent

ing

Multiplica

tions with

Arrays Cushman, Jean

Do You Wanna Bet?: Your Chance to

Find Out about Probability Data Analysis and Probability

G4U2 Nagda, Ann Whitehead

Tiger Math: Learning to Graph from

a Baby Tiger Data Analysis and Probability

G4U3 Anno, Masaichiro Anno's Mysterious Multiplying Jar Multiplication and Division

G4U3 Tang, Greg 4.OA.3 4.OA.4 Multiplication and Division

G4U3 Michelson, Richard Ten Times Better Multiplication and Division

G4U4 Adler, David A.

Shape Up!: Fun with Triangles and

Other Polygons 2D Geometry and Measurement

G4U4 Burns, Marilyn The Greedy Triangle 2D Geometry and Measurement

G4U4 Burns, Marilyn

Spaghetti and Meatballs for All!: A

Mathematical Story 2D Geometry and Measurement

G4U4 Friedman, Aileen A Cloak for the Dreamer 2D Geometry and Measurement

G4U4 Tompert, Ann

Grandfather Tang's Story: A Tale

Told with Tangrams 2D Geometry and Measurement

G4U5 McKissack, Patricia C. A Million Fish … More or Less

Addition, Subtraction, and the Number

System

G4U5 Schwartz, David M. How Much Is a Million?


System

G4U5 Schwartz, David M.

On Beyond a Million: An Amazing

Math Journey


System

G4U5 Wells, Robert E. Can You Count to a Googol?


System

G4U6 Hutchins, Pat The Doorbell Rang Fractions

G4U6 Nagda, Ann Whitehead

Polar Bear Math: Learning about

Fractions from Klondike and Snow Fractions

G4U6 Adler, David A. Fraction Fun Fractions

G4U7 Clement, Rod Counting on Frank 3D Geometry and Measurement

G4U7 Pluckrose, Henry Arthur Knowabout: Capacity 3D Geometry and

G4U7 Schwartz, David M. Millions to Measure 3D Geometry and Measurement

G4U7 Macaulay, David Pyramid 3D Geometry and Measurement

G4U8 Birch, David The King's Chessboard Multiplication and Division

G4U8 Demi, Hitz

One Grain of Rice: A Mathematical

Folktale Multiplication and Division

G4U9 Schwartz, David M.

G Is for Googol: A Math Alphabet

Book General

4th Grade Math

Read Alouds 56

4th Grade Math

Read Alouds 57

Documents

4th Grade Math - Cicero Public School District 99 · 4th Grade Math Unit 2: Describing the Shape of the Data Investigation 1: Representing Multiplications with Arrays 2.1 Are students