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MATHEMATICS

Grade 5: Unit 0

Review of Grade 4 Skills

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Pacing Chart – Unit 0

Grade 4

Unit 4 SLO

#

Grade 4 Student Learning Objective Grade 4

NJSLS

Grade 5

NJSLS

Unit in Grade

5

1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and

perpendicular and parallel lines and identify these in two-dimensional figures. 4.G.A.1 5.G.B.3 4

2 Classify two-dimensional figures based on the presence or absence of parallel or

perpendicular lines, or the presence or absence of angles of a particular size;

recognize right angles as a category, and identify right, acute, obtuse, equilateral,

isosceles, and scalene triangles.

4.G.A.2 5.G.B.4 4

3 Draw lines of symmetry and identify line-symmetric figures.

4.G.A.3 4

4 Explain angles as geometric shapes formed by two rays sharing a common

endpoint and explain the relationship between a one-degree angle, a circle, and

angle measure.

4.MD.C.5a,

5b

4

5 Measure angles in whole number degrees using a protractor and sketch angles of

specific measures. 4.MD.C.6 4

6 Solve addition and subtraction problems to find unknown angles on a diagram in

real world and mathematical problems using a symbol for an unknown angle

measure.

4.MD.C.7 4

7 Write and solve each equation (including any of the four operations) in order to

solve multi-step word problems, using a letter to represent the unknown; interpret

remainders in context and assess the reasonableness of answers using mental

computation with estimation strategies.

4.OA.A.3 * 5.OA.A.1 1

8 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

4.NBT.B.4 * 5.NBT.B.5*

5.NBT.B.6

5.NBT.B.7*

1, 2, 4

1

1 , 3, 4

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Grade 5

Unit New Jersey Learning Standards

4

4.G.A.1.

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-

dimensional figures.

4.G.A.2.

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of

angles of a specified size. Recognize right triangles as a category, and identify right triangles.

4.G.A.3.

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the

line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

4.MD.C.5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand

concepts of angle measurement.

4.MD.C.5a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by

considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns

through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

4.MD.C.5b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.C.6.

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure

4.MD.C.7.

Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is

the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real

world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

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Grade 5

Unit New Jersey Learning Standards

1

1, 2, 3, 4

4.NBT.B.4

Fluently add and subtract multi-digit whole numbers using the standard algorithm.[Grade 4 expectations in this domain are limited

to whole numbers less than or equal to 1,000,000.]

4.OA.A.3.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including

problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the

unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

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Mathematical Practices

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

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Grade: Five

Unit: 0 (Zero) Topic:

Review of Grade 4 Skills

NJSLS:

4.G.A.1, 4.G.A.2, 4.G.A.3, 4.MD.C.5a,b, 4.MD.6, 4.MD.C.7, 4.MD.C.7, 4.OA.A.3, 4.NBT.B.4

Unit Focus:

• Draw and identify lines and angles, and classify shapes by properties of their lines and angles

• Understand concepts of angle and measure angles (Geometric measurement)

• Use the four operations with whole numbers to solve problems

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

New Jersey Student Learning Standard:

4.G.A.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-

dimensional figures.

Student Learning Objective 1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines and

identify these in two-dimensional figures.

Modified Student Learning Objectives/Standards:

M.EE.4.G.A.1: Recognize parallel lines and intersecting lines.

MPs Evidence Statement

Key/ Clarifications

Skills, Strategies & Concepts Essential Understandings/

Questions

(Accountable Talk)

Tasks/Activities

MP 5

MP 7

4.G.1

In Grade 5 students understand that

attributes belonging to a category of

two- dimensional figures also

belong to all subcategories of that

category. For example, all

rectangles have four right angles

and squares are rectangles, so all

squares have four right angles.

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. They are classified by size.

The Geometry of Letters

Making Roads

Be an Expert

Angle Sort

Moving Around Town

What’s the point?

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Develop a clear understanding that a

point, line, and plane are the core

attributes of space objects, and real-

world situations can be used to think

about these attributes.

Enforcing precise geometrical

vocabulary is important for

mathematical communication.

Example:

How many acute, obtuse and right

angles are in this shape?

Draw and identify points, lines, line

segments, rays, angles (right, acute,

obtuse), and perpendicular and parallel

lines.

Name and identify attributes of two-

dimensional figures.

Distinguish between lines, line

segments, and rays.

SPED Strategies:

Let the student use concrete materials

and manipulatives (shapes, rulers,

geoboards) to draw points, lines, line

How can lines, angles, and shapes be

described, analyzed, and classified?

What is the difference between a

point, ray, line, and line segment?

How are points, lines, line segments,

rays, and angles related?

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segments, rays, angles, and identify

two-dimensional figures.

Create an interactive math journal to

demonstrate growth in math writing

and reasoning.

Create flip books with pictures,

academic vocabulary and examples.

Use different learning modalities to

introduce and practice drawing points,

lines, segments, rays, angles,

perpendicular and parallel lines and

identify two-dimensional figures (short

videos, songs, manipulatives).

ELL Strategies:

Demonstrate comprehension of lines,

rays, types of angles and perpendicular

and parallel lines by identifying and

drawing them in two-dimensional

figures after reading problems written

in L1 (student’s native language)

and/or using gestures, models and

selected, single words.

Use direct instruction for vocabulary

with visuals or concrete

representations.

Scaffold questioning to guide

connections, analysis, and mastery.

Let students choose the language they

prefer for arithmetic computation and

discourse.

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New Jersey Student Learning Standard: 4.G.A.2: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles

of a specified size. Recognize right triangles as a category, and identify right triangles.

Student Learning Objective 2: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the

presence or absence of angles of a particular size; recognize right angles as a category, and identify right, acute, obtuse, equilateral, isosceles, and

scalene triangles.

Modified Student Learning Objectives/Standards:

M.EE.4.G.A.2: Describe the defining attributes of two-dimensional shapes.

MPs Evidence Statement

Key/ Clarifications

Skills, Strategies & Concepts Essential Understandings/

Questions

(Accountable Talk)

Tasks/Activities

MP 5

MP 7

4.G.2

• A trapezoid is defined

as “A quadrilateral with

at least one pair of

parallel sides.”

• Tasks may include

terminology:

equilateral, isosceles,

scalene, acute, right,

and obtuse.

In Grade 5 students classify two-

dimensional figures in a hierarchy

based on properties.

Classify triangles based on the

presence or absence of perpendicular

lines and based on the presence or

absence of angles of a particular size.

Classify quadrilaterals based on the

presence or absence of parallel or

perpendicular lines and based on the

presence or absence of angles of a

particular size.

Two-dimensional or plane shapes have

many properties that make them

different from one another.

Students should become familiar with

the concept of parallel and

perpendicular lines. Two lines are

How are geometric objects different

from one another?

How are quadrilaterals alike and

different?

What are the difference between

triangles, quadrilaterals, pentagons,

hexagons, and octagons?

How are triangles alike and different?

How can angle and side measures

help us to create and classify

triangles?

How can shapes be classified by their

angles and lines?

How can the attributes of sides be

used to classify quadrilaterals?

What Shape am I?

Is it Possible?

Thoughts about

Triangles

My Many Triangles

Classify Two-

Dimensional Shapes

Sorting Shapes

Defining Attributes of

Rectangles and

Parallelograms

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parallel if they never intersect and are

always equidistant. Two lines are

perpendicular if they intersect in right

angles (90º).

Parallel and perpendicular lines are

shown below:

Polygons can be described and

classified by their sides and angles.

Identify triangles, quadrilaterals,

pentagons, hexagons, and octagons

based on their attributes.

Have a clear understanding of how to

define and identify a right triangle.

TEACHER NOTE: In the U.S., the

term “trapezoid” may have two

different meanings. Research identifies

these as inclusive and exclusive

definitions. The inclusive definition

states: A trapezoid is a quadrilateral

with at least one pair of parallel sides.

The exclusive definition states: A

trapezoid is a quadrilateral with

exactly one pair of parallel sides. With

this definition, a parallelogram is not a

How can triangles be classified by the

measure of their angles?

How can we sort two-dimensional

figures by their angles?

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trapezoid. (Progressions for the

CCSSM: Geometry, June 2012.)

SPED Strategies:

Demonstrate comprehension by orally

classifying two-dimensional figures

based on the presence or absence of

parallel or perpendicular lines, and

specific angles (obtuse, acute, right)

using key, technical vocabulary in

simple sentences.

Use real-life examples and concrete

materials as needed to classify two-

dimensional figures. Identify if they

are right, acute, obtuse, equilateral,

isosceles, and scalene triangles.

Offering learners choices can develop

self-determination, instill pride, and

increase the level in which they feel

connected to their learning. One way

to offer choice is to let students decide

the sequence of some components of

their learning. Menus from which

students may choose tasks are one way

to offer such academic choice.

ELL Strategies:

Have students explain their thinking

process aloud in their native language

to a classmate while solving a

problem.

Using L1 (student’s native language)

create an interactive math journal to

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New Jersey Student Learning Standard:

4.G.A.3: Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into

matching parts. Identify line-symmetric figures and draw lines of symmetry.

Student Learning Objective 3: Draw lines of symmetry and identify line-symmetric figures.

Modified Student Learning Objectives/Standards:

M.EE.4.G.3: Recognize that lines of symmetry partition shapes into equal areas.

MPs Evidence Statement Key/

Clarifications

Skills, Strategies & Concepts Essential Understandings/

Questions

(Accountable Talk)

Tasks/Activities

MP 5

MP 7

4.G.3

Symmetry should be reviewed in

Grade 5 Unit 4.

Gain a conceptual understanding that a

line of symmetry will split a figure into

two equal parts.

Recognize a line of symmetry for a

two-dimensional figure as a line across

the figure, so that the figure can be

folded along the line into matching

parts.

What is symmetry?

How are symmetrical figures created?

How are symmetrical figures used in

art work?

How can you determine the lines of

symmetry in a figure? What do they

tell us?

How can you prove that a shape is

symmetrical?

Superhero Symmetry

Line Symmetry

A Quilt of Symmetry

The Rest of the Shape

Finding Lines of

Symmetry

Decoding ABC

Symmetry

utilize as a reference and utilize

cognates.

Accept and elicit student ideas and

suggestions for ways to extend games.

Scaffold complex concepts and

provide leveled problems for multiple

entry points.

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Develop an understanding that each

half of a figure is a mirror image of the

other half.

Draw lines of symmetry.

Folding cut-out figures will help

students determine whether a figure has

one or more lines of symmetry.

Identify figures and letters of the

alphabet that have lines of symmetry.

SPED Strategies:

Demonstrate and explain orally and in

writing how to draw lines of symmetry

and identify line-symmetric figures

using key vocabulary in simple

sentences.

Practice identifying and drawing lines

of symmetry by using technology.

Use direct instruction for vocabulary

with visual or concrete representations.

Model in small groups how to identify

and draw a line of symmetry.

ELL Strategies:

Demonstrate and explain orally and in

writing how to draw lines of symmetry

and identify line-symmetric figures in

L1 (student’s native language) and/or

use gestures, drawings and selected

single words.

How is symmetry used in areas such as

architecture and art? In what areas is

symmetry important?

Polygons with an odd number of sides

have lines of symmetry that go from a

midpoint of a side through a vertex.

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Peer Coach - Allow ELL students to

talk to a peer in their native language

when necessary to clarify

understanding and clear up

misunderstandings.

Provide sufficient wait time to allow

the student to process the meanings in

their native language.

New Jersey Student Learning Standards:

4.MD.C.5: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle

measurement.

4.MD.C.5a: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of

the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-

degree angle,” and can be used to measure angles.

4.MD.C.5b: An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Student Learning Objective 4: Explain angles as geometric shapes formed by two rays sharing a common endpoint and explain the

relationship between a one-degree angle, a circle, and angle measure.

Modified Student Learning Objectives/Standards: M.EE.4.MD.C.5: Recognize angles in geometric shapes.

MPs Evidence Statement

Key/ Clarifications

Skills, Strategies & Concepts Essential Understandings/

Questions

(Accountable Talk)

Tasks/Activities

MP 2

4.MD.5 Review this standard in Grade 5

Unit 4.

Develop a clear understanding that

angles are geometric shapes composed

of two rays that are infinite in length,

share a common endpoint, and result

What is an angle?

How are a circle and an angle related?

How can we measure angles using

wedges of a circle?

Turn, Turn, Turn

The Water Sprinklers

Build an Angle Ruler

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from the rotation of one ray around the

endpoint.

Become aware that the unit for

measuring the size of the opening of

an angle is 1 degree.

Angle Measurement: An angle that

turns through n at one-degree angles is

said to have an angle measure of n

degrees.

As the rays of an angle extend, the

degree of the angle does not change,

but the distance between the rays

increases.

Describe an angle as measured with

reference to a circle with the center of

the circle being the common endpoint

of the rays.

Explain a ‘one-degree angle’ and its

relation to a circle; a “degree” is

defined as 1/360 (one-degree angle) of

the entire circle.

Identify angles in two-dimensional

figures.

A protractor can be used to draw and

label an angle.

How are the angles of a triangle

related?

How can angles be combined to create

other angles?

Why do we need a standard unit with

which to measure angles?

Why would one need to measure an

angle?

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SPED Strategies:

Provide students with color coded

notes and samples.

Review vocabulary and provide

students with the opportunity to

engage in hands-on activities.

Assess by multiple means, including

“show and tell” rather than written.

ELL Strategies:

Connect students’ prior knowledge

and experiences to new learning. Find

out what students already know about

a topic by making a semantic web on

the board. Write the topic in the center

of a circle and record students’

knowledge around it.

To reduce the pressure on ELL

students, let them discuss a question in

pairs for a minute before calling on a

student to give an answer. This

strategy gives everyone in the class

more time to think about the question

and form an answer. It also increases

comprehension and gives all students

more opportunities to participate in

class discussions.

Create an interactive math journal in

L1 (student’s native language) to

demonstrate growth in math writing

and reasoning.

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New Jersey Student Learning Standard:

4.MD.C.6: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Student Learning Objective 5: Measure angles in whole number degrees using a protractor and sketch angles of specific measures.

Modified Student Learning Objectives/Standards:

M.EE.4.MD.C.6: Identify angles as larger and smaller.

MPs Evidence Statement Key/

Clarifications

Skills, Strategies & Concepts Essential Understandings/

Questions

(Accountable Talk)

Tasks/Activities

MP 2

MP 5

4.MD.6

Review angles and the use of a

protractor in Grade 5 Unit 4.

Become aware of the relationship that

acute and obtuse angles have to right

angles.

Reinforce that the unit for measuring

the size of the opening of an angle is

1 degree and angles are measured in

whole number degrees.

Students should measure angles and

sketch angles.

Provide varied examples and explicit

discussions to avoid learning limited

ideas about measuring angles.

Develop a clear understanding of how

to use a protractor to measure and

draw angles in whole number degrees.

What do we actually measure when

we measure an angle?

What mathematical tool is used to

measure and draw angles?

How does knowing whether an angle

is acute or obtuse help us when using

a protractor?

What are benchmark angles and how

can they be useful in estimating angle

measures?

How do we measure an angle using a

protractor?

How can we use angle measure to

draw reflex angles?

Guess my Angle

Making Shapes

Going Different

Directions

Intersecting Roads

Activities:

Angle Barrier Game

Predicting and

Measuring Angles

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Given an angle measure, sketch the

angle.

SPED Strategies:

Describe and explain orally and in

writing how to measure angles in

whole number degrees using a

protractor and sketch angles of

specified measure using key

vocabulary in simple sentences.

Model how to measure using a

protractor. Provide student with the

opportunity to measure angles using

technology.

Use alternative methods of delivery of

instruction such as recordings and

videos that can be accessed

independently or repeated if

necessary.

ELL Strategies:

Describe and explain orally and in

writing how to measure angles in

whole-number degrees using a

protractor and sketch angles of

specified measure in L1 (student’s

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native language) and/or use gestures,

pictures and selected single words.

Let students choose the language they

prefer for arithmetic computation and

discourse.

Keep picture dictionaries in the class

and allow ELL students to create

individualized bilingual math

dictionaries.

New Jersey Student Learning Standard: 4.MD.C.7: Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the

sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and

mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Student Learning Objective 6: Solve addition and subtraction problems to find unknown angles on a diagram in real world and

mathematical problems using a symbol for an unknown angle measure.

Modified Student Learning Objectives/Standards: N/A

MPs Evidence Statement Key/

Clarifications

Skills, Strategies & Concepts Essential Understandings/

Questions

(Accountable Talk)

Tasks/Activities

MP 1

MP 7

4.MD.7 Review this standard in Grade 5

Unit 4.

Recognize angle measurements as

additive.

Understand that when an angle is

decomposed into non-overlapping

parts, the angle measurement of the

How are angles measured, added, and

subtracted?

How can you find an unknown angle

measurement when two other related

angle measurements are given?

Sending the Right

Signal

Measuring Angles

How Many Degrees?

Adding Up Angles

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whole is the sum of the angle

measurements of the parts.

Recognize that you can find an

unknown angle measurement by

adding or subtracting angle parts.

Understand that you can write an

equation for the unknown angle

measurement (symbol).

This standard addresses the idea of

decomposing (breaking apart) an

angle into smaller parts.

Example:

80° is decomposed as (30° + ?°).

Write an equation with a symbol for

the unknown angle measure.

Add and subtract to find unknown

angles on a diagram in real world and

mathematical problems.

Example:

The five shapes in the diagram are the

exact same size. Write an equation

How Can We Split

Angles?

Finding an Unknown

Angle

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that will help you find the measure of

the indicated angle. Find the angle

measurement.

SPED Strategies:

Demonstrate comprehension of

addition and subtraction problems of

unknown angles on a diagram in real

world and mathematical problems by

identifying the solution using key

vocabulary in simple sentences.

Elaborate on the problem-solving

process. Read word problems aloud.

Post a visual display of the problem-

solving process. Have students check

off or highlight each step as they

work. Talk through the problem-

solving process step-by-step to

demonstrate thinking process. Before

students solve, ask questions to check

for comprehension.

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Give students a few extra minutes to

process the information before giving

the signal to respond.

ELL Strategies:

Demonstrate comprehension of

addition and subtraction problems of

unknown angles on a diagram in real

world and mathematical problems by

identifying the solution in L1

(student’s native language) and/or use

gestures, pictures and selected single

words.

Interactive math journal to

demonstrate growth in math writing

and reasoning.

Highlight words/boldface words that

students should remember.

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New Jersey Student Learning Standard: 4.OA.A.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including

problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity.

Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Student Learning Objective 7: Write and solve each equation (including any of the four operations) in order to solve multi-step word

problems, using a letter to represent the unknown; interpret remainders in context and assess the reasonableness of answers using mental

computation with estimation strategies.

Modified Student Learning Objectives/Standards:

M.EE.4.OA.A.3: Solve one-step real-world problems using addition or subtraction within 100.

MPs Evidence Statement

Key/ Clarifications

Skills, Strategies & Concepts Essential Understandings/

Questions

(Accountable Talk)

Tasks/Activities

MP 1

MP 2

MP 4

MP 7

4.OA.3-1

4.OA.3-2

• Assessing

reasonableness of

answer is not assessed

here

• Tasks involve

interpreting remainders.

• See p. 30 of the OA

Progression document.

• Multi-step problems

must have at least 3

steps.

4.C.5-1

• Distinguish correct

explanation/reasoning

from that which is

flawed, and – if there is

a flaw in the argument

– present corrected

In Grade 5 students use parentheses,

brackets, or braces in numerical

expressions, and evaluate expressions

with these symbols. (Order of

Operations)

Use graphic organizers to help identify

unknowns to create equations and solve a

word problem based on clues in the word

problem.

Some operations can be used

interchangeably to create different

equations that solve the same word

problem.

Variables can be used to represent an

unknown in any part of an equation.

Emphasize the proper use of the equal (=)

sign and the improper use (3+7=10-5=5)

How do multiplication, division,

addition, subtraction, and

estimation help us solve real

world problems?

How can we find evidence in

word problems to support our

equations?

Variables can be used to

represent an unknown in any

part of an equation.

Recycling Cans

Zoo Field Trip

How Many Cookies Do

We Have?

Birthday Treats

Ice Cream Party

Carnival Tickets

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reasoning. (For

example, some flawed

‘student’ reasoning is

presented and the task

is to correct and

improve it.)

• Reasoning in these

tasks centers on

interpretation of

remainders.

4.C.6-1

• Present solutions to

multi-step problems in

the form of valid chains

of reasoning, using

symbols such as equals

signs appropriately (for

example, rubrics award

less than full credit for

the presence of

nonsense statements

such as 1 + 4 = 5 + 7 =

12, even if the final

answer is correct), or

identify or describe

errors in solutions to

multi-step problems

and present corrected

solutions

• Tasks may involve

interpreting remainders.

• Multi-step problems

must have at least 3

steps.

Relate the terms in the equation to the

context in the word problem.

Students should be able to identify the

unknown(s) in the problem and use a

variable to represent that term in context.

Solve multi-step word problems involving

any of the four operations.

Explain why an answer is reasonable, such

as using mental computation and

estimation strategies.

Provide students with a variety of

equations and have students create their

own math story that is represented in the

given equation.

SPED Strategies:

Elaborate on the problem-solving process.

Read word problems aloud. Post a visual

display of the problem-solving process.

Have students check off or highlight each

step as they work. Talk through the

problem-solving process step-by-step to

demonstrate thinking process. Before

students solve, ask questions for

comprehension, such as, “What unit are we

counting? What happened to the units in

the story?” Teach students to use self-

questioning techniques, such as, “Does my

answer make sense?”

Interactive Math Journal with samples.

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Replace unknown numbers with given

values in two-digit by two-digit

addition/subtraction sentences.

ELL Strategies:

In L1 (student’s native language), elaborate

on the problem-solving process. Read word

problems aloud. Post a visual display of the

problem-solving process. Have students

check off or highlight each step as they

work. Talk through the problem-solving

process step-by-step to demonstrate

thinking process.

Provide sufficient wait time to allow the

student to process the meaning in their first

language.

Determine the reasonableness of an answer

to an addition or subtraction problem using

estimation strategies of “more” and “less”

and the reasonableness of an answer to

division problems using estimation

strategies (e.g., repeated subtraction).

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New Jersey Student Learning Standard: 4.NBT.B.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm. [Grade 4 expectations in this domain are limited to

whole numbers less than or equal to 1,000,000.]

Student Learning Objective 8: Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Modified Student Learning Objectives/Standards: M.EE.4.NBT.4: Add and subtract two-digit whole numbers.

MPs Evidence Statement

Key/ Clarifications

Skills, Strategies & Concepts Essential Understandings/

Questions

(Accountable Talk)

Tasks/Activities

MP 7

MP 8

4.NBT.4-1

• The given addends are

such as to require an

efficient/standard

algorithm (e.g., 7263

+ 4875). Addends in

the task do not suggest

any obvious ad hoc or

mental strategy (as

would be present for

example in a case such

as 16,999 + 3,501).

• Tasks do not have a

context are not timed.

• Grade 4 expectations

in CCSSM are limited

to whole numbers less

than or equal to

1,000,000; for

purposes of

assessment, both of

the given numbers

should have 4 digits.

• Tasks are not timed.

Review using the standard algorithm to

add and subtract.

In Grade 5 students:

• Fluently multiply multi-digit whole

numbers using the standard

algorithm.

• Find whole-number quotients

of whole numbers with up to four-

digit dividends and two-digit

divisors, using strategies based on

place value, and the properties of

operations.

• Add, subtract, multiply, and divide

decimals to hundredths

Recognize the need for regrouping and not

just subtracting the smaller digit from the

larger one.

Utilize grid paper to line up similar place

values when adding and subtracting.

Fluency refers to accuracy, efficiency

(using a reasonable amount of steps and

What strategies can we use to

help us make sense of a written

algorithm?

How can we combine hundreds,

tens, and ones in two or more

numbers efficiently?

The value of a number is

determined by the place of its

digits.

Addition and subtraction

algorithms are abbreviations or

summaries of the connection

between math drawings and

written numerical work.

Why does it help to know inverse

relationships?

Computation algorithm:

Make Sense of an

Algorithm

Reality Checking

Beehive Adventure

Filling the

Auditorium

How Much Liquid

If I Had a Million

Dollars?

Japan Trip

Destination Utah

Comparing Manti and

La Sal Mountain

Range Elevation

27 | P a g e

4.NBT.4-2

• The given subtrahend

and minuend are such

as to require an

efficient/standard

algorithm (e.g., 7263 –

4875 or 7406 – 4637).

The subtrahend and

minuend do not

suggest any obvious

ad hoc or mental

strategy (as would be

present for example in

a case such as 7300 –

6301).

• Tasks do not have a

context and are not

timed.

• Grade 4 expectations

in NJSLS are limited

to whole numbers less

than or equal to

1,000,000; for

purposes of

assessment, both of

the given numbers

should have 4 digits.

times) and flexibility (variety of strategies

learned previously if needed).

Explain why algorithms work with the use

of multiples of 10, place value, and

diagrams of arrays and area.

Computation involves taking apart and

combining numbers using a variety of

approaches.

Flexible methods of computation involve

grouping numbers in strategic ways: partial

sum, regrouping, and trade first.

One could use an alternate algorithm to

check the answer to a problem.

SPED Strategies:

In small groups students can practice

adding and subtracting facts by using

bundles, chips and other resources.

Use of grid paper to assist students with

lining up digits and emphasize place value

and the meaning of each of the digits.

Provide flashcards and or the opportunity

to practice basic facts on the computer.

Start with a students’ understanding of a

certain strategy, and then make intentional

connections for the student to the standard

algorithm. This allows the student to gain

understanding of the algorithm rather than

just memorize certain steps to follow.

A set of predefined steps

applicable to a class of problems

that gives the correct result in

every case when the steps are

carried out correctly.

Computation strategy:

Purposeful manipulations that

may be chosen for specific

problems, may not have a fixed

order, and may be aimed at

converting one problem into

another.

28 | P a g e

ELL Strategies:

Sequence orally the steps needed to add

and subtract two multi-digit whole

numbers in L1 (student’s native language)

and/or use gestures, examples, and

selected, technical words.

Have students peer tutor classmates who

are having difficulties applying standard

algorithms in addition and subtraction.

Use technology to practice adding and

subtracting single digit numbers and use

grid paper to assist students with lining up

digits.

Explain directions in L1 (student’s native

language) to ensure understanding of the

task.

29 | P a g e

Unit 4 Vocabulary

• Acute Angle

• Acute Triangle

• Additive

• Algorithm

• Angle

• Angle Extension

• Angle Measure

• Attributes

• Circle

• Classify

• Compose

• Computation

• Congruent

• Decompose

• Degree

• Diagonal

• Endpoint

• Geometry

• Hexagon

• Horizontal

• Intersecting Lines

• Length

• Line

• Line Segment

• Line of Symmetry

• Line Segment

• Mathematical Tool

• Non-Overlapping

• Obtuse Angle

• Obtuse Triangle

• Octagon

• Parallel Lines

• Parallelogram

• Pentagon

• Perpendicular Lines

• Place Value

• Plane Shapes/ Figure

• Point

• Polygon Protractor

• Quadrilateral

• Ray

• Rectangle

• Regular Polygon

• Rhombus

• Right Angle

• Right Triangle

• Shapes

• Side Measures

• Sketch

• Square

• Standard Unit

• Straight Angle

• Symmetry

• Triangle

• Trapezoid

• Two-Dimensional Figure

• Unknown Angle

• Vertex

30 | P a g e

References & Suggested Instructional Websites

Imagine Math Facts: https://www.imaginelearning.com/programs/math-facts

SuccessMaker: https://paterson1991.smhost.net/lms/sm.view

https://illuminations.nctm.org/Search.aspx?view=search&cc=1973

www.internet4classrooms.com

http://nlvm.usu.edu/en/nav/index.html

www.k-5mathteachingresources.com/

www.georgiastandards.org/Common-Core/Pages/Math-K-5.aspx

www.illustrativemathematics.org/

http://www.sebring.k12.oh.us/userfiles/28/Classes/7664/4th%20Grade%20Common%20Core%20Math%20Vocabulary%20on%20one%20sheet%

20for%20notebook-0.pdf

http://www.katm.org/flipbooks/4%20FlipBook%20Final%20CCSS%202014.pdf

http://www.sheppardsoftware.com/