Students will identify models of and/or solve problems involving multiplication and/or division situations.

Examples of multiplication or division models might include, but are not limited to

- Repeated addition: 4 bags of cookies with 8 in each bag. How many cookies are there? (8 + 8 + 8 + 8 = 32) Multiplicative comparison (also known as scalar model): Sam has 8 baseball cards. Elise has 8 times as many. How many does Elise have? Array: A marching band has 8 rows with 7 students in each row. How many band members are there? Combination: How many different combinations of one flavor of ice cream and one topping can be made from 4 different flavors and 5 different toppings? Measurement: If there are 35 bugs all together and Robbie puts 5 bugs in each jar, how many jars does he need to hold all of the bugs? Partitive: Robbie has 35 bugs and 7 jars. He will put all of the bugs in jars. If he puts the same number of bugs in each jar, how many bugs are in each jar?

Example:

Nathan paid $2 for each of the 3 books he bought at a bookstore. He can use the expression 3 X 2

to find the total amount he paid for the 3 books. Which of the following is equal to 3 X 2?

A. 3 + 3 + 3 ★

B. 2 + 2 + 2

C. 3 + 2 + 3

D. 2 X 3 + 3

Number: Operations, Problems, and Statistics:

Students will recognize equivalent representations of equations or expressions by using number properties, including the commutative, associative, distributive, and identity properties for multiplication and division and the zero property of multiplication.

Example:

Isabella cannot remember the product of 9 X 8.

Which of the following is another expression that Isabella could use to find the product of 9 X 8?

A. (9 X 5) + (9 X 3) ★

B. (9 X 4) + (9 X 2)

C. (9 X 1) + (4 X 2)

D. (9 X 2) + (8 X 6)

Number: Operations, Problems, and Statistics:

Students will identify the inverse of a multiplication or division equation.

Students will apply the inverse property to solve real-world problems and to check the solution of a problem involving multiplication or division.

Example:

A group of 24 people is getting on a roller coaster. Each car of the roller coaster can hold 4 people. Which equation could be used to find the number of roller coaster cars needed to hold all 24 people?

A. 24 + 4 =

B. 24 X 4 =

C. + 4 = 24

D. X 4 = 24 ★

Number Fractions:

Students will represent a fraction or a mixed number by a graphic representation or identify a fraction or mixed number from its graphic representation.

Example:

Rosalyn drew three figures and shaded parts of each figure.

(PICTURE OF A FRACTION MODEL WILL APPEAR HERE)

Which mixed number is represented by the shading of the three figures above?

A. 2 1/4

B. 2 3/4

C. 3 1/4

D. 3 1/2

Number Fractions:

Students will compare or order fractions using graphic representations or other strategies, such as benchmark fractions (0, 1/10, 1/5, 1/4, 1/3, 1/2, 2/3, 3/4 and 1)

Example:

Two windmills are pictured below. On Windmill A, 1/2 of the blades are shaded gray.

On Windmill B, 2/3 of the blades are shaded gray.

Windmill A 1/2 Windmill B 2/3

(PICTURE OF A FRACTIONAL MODEL ON A WINDMILL WOULD APPEAR HERE)

Which inequality below correctly compares the fractions of blades that are shaded gray?

A. 2/3< 1/2

B. 2/3 > 1/2 ★

C. 3/2 < 2/1

D. 3/2 > 2/1

Number Fractions:

Students will identify equivalent forms of fractions and mixed numbers.

Example:

Ramona filled 10 party balloons with air. She noticed that 4/10 of the balloons were striped, as shown below.

Which fraction is equivalent to 4/10?

A. 2/5 ★

B. 2/3

C. 2/4

D. 2/8

Geometry and Measurement:

Students will describe, analyze, compare, and classify two-

dimensional shapes using sides and angles—including acute, obtuse, and right angles.

Example:

Andrew bought the frame shown below for his sports picture.

(A PICTURE OF A FIVE SIDED FRAME WOULD BE HERE)

Which best describes the shape of the frame?

A. parallelogram

B. pentagon ★

C. rhombus

D. trapezoid

Geometry and Measurement:

Students will identify polygons which have been composed or decomposed from other polygons.

Students may use transformations to compose or decompose polygons.

Example:

(NO EXAMPLE PROVIDED)

Geometry and Measurement:

Students will identify lines of symmetry and/or reflections. Students will identify congruent polygons.

Students will identify two-dimensional shapes composed of congruent polygons.

Example:

(NO EXAMPLE PROVIDED)

Number: Operations, Problems, and Statistics:

Students may extend numeric or graphic patterns beyond the next step, or find one or more missing elements in a numeric or graphic pattern.

Students will identify the rule for a pattern or the relationship between numbers.

Example:

Allison is making lemonade for a party. The table below shows the number of lemons she will need to make several pitchers of lemonade.

LEMONS NEEDED FOR LEMONADE

Number of Pitchers Number of Lemons

2 10

5 25

8 40

9 ?

According to the relationship shown in the table, how many lemons will Allison need to make 9 pitchers of lemonade?

A. 5

B. 15

C. 45 ★

D. 65

Geometry and Measurement:

Students will select appropriate units, strategies, or tools to solve problems involving perimeter.

Students will solve real-world problems involving perimeter.

Example:

The perimeter of a flower garden is 20 feet, as shown below.

(PICTURE OF RECTANGLE FLOWER GARDEN HERE WITH 3 ON ONE SIDE, X ON BOTTOM SEGMENT)

If the width of the flower garden is 3 feet, what is its length,

*x*?

A. 17 feet

B. 10 feet

C. 7 feet

D. 6 feet ★

Geometry and Measurement:

Students will find the measure of objects to the nearest whole or fractional parts of linear units such as 1/4, 1/2, and 3/4

of an inch.Students will find the measure of objects to the nearest whole millimeter and/or centimeter.

Example:

(NO EXAMPLE PROVIDED)

**Geometry and Measurement:**

Students will identify the time displayed on an analog clock to the nearest minute or quarter hour.

Students will determine the amount of time elapsed.

Example:

Trina went to see a play. The clock below shows the time that Trina got to the theater.

(PICTURE OF A CLOCK DISPLAYING 7:45)

If the play started at 8:00, how many minutes did Trina wait at the theater before the play started?

A. 45 minutes

B. 30 minutes

C. 15 minutes ★

D. 5 minutes

**Number: Operations, Problems, and Statistics:**

Students will represent, identify, compare, and/or order numbers through the hundred thousands place in real-world contexts. Students will compute sums and differences of numbers through the hundred thousands.

Students may use some of the following estimation strategies: chunking, using a reference, unitizing, benchmarks, clustering, reasonableness, compatible numbers, grouping, rounding, etc., when representing and computing numbers through the hundred thousands.

Example:

Ms. Tanaka is ordering calendars for the students at 4 elementary schools. The table below shows the number of students at each of the schools.

**STUDENTS IN ELEMENTARY SCHOOLS**

Name of School Number of Students

Greendale 1,789

Name of School Number of Students

Jones Park 1,032

Shady River 2,115

Wakefield 1,992

Which is the

**best**estimate of the total number of calendars Ms. Tanaka needs to order for all 4 schools?

A. 4,000

B. 5,000

C. 7,000 ★

D. 8,000

**Number: Operations, Problems, and Statistics:**

Nonroutine problems will be solved in situations where tables, charts, lists, and patterns could be used to find the solution.

Example:

Mr. Jarrell has 4 students in his chess club. He will put them in pairs to play a game of chess. The chart below shows the names of the students in the club.

**STUDENTS IN CHESS CLUB**

Charles Erin Gayle Paco

What is the total number of different pairs of two students that can be made?

Charles Erin Gayle Paco

A. 8

B. 6 ★

C. 4

D. 2

**Number: Operations, Problems, and Statistics:**

Students may identify the correct display of a given set of data. Students will analyze and draw conclusions about data displayed in the form of frequency tables, bar graphs, pictographs, and line plots.

Students will analyze data to supply missing data in frequency tables, bar graphs, pictographs, and line plots.

Example:

(NO EXAMPLE AVAILABLE)