Content Standard(s):
Mathematics MA2019 (2019) Grade: 5 12. Apply and extend previous understandings of multiplication to find the product of a fraction times a whole number or a fraction times a fraction.

a. Use a visual fraction model (area model, set model, or linear model) to show (^{a} /_{b} ) x q and create a story context for this equation to interpret the product as a parts of a partition of q into b equal parts.

b. Use a visual fraction model (area model, set model, or linear model) to show (^{a} /_{b} ) x (^{c} /_{d} ) and create a story context for this equation to interpret the product.

c. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

d. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths to show that the area is the same as would be found by multiplying the side lengths.

Unpacked Content

Evidence Of Student Attainment:

Students:

Given a fraction times a whole number,

use visual models to illustrate the product to develop the procedure (a/b) × q.
Create a story context for the equation (a/b) × q. Given a fraction times a fraction,

Use visual models to illustrate the product to develop the procedure (a/b) × (c/d).
Create a story context for the equation (a/b) × (c/d).
Given a rectangle with two fractional side lengths,

Use an area model to illustrate and find the rectangular area.
Find the area by tiling it with unit squares of the appropriate unit fraction.
Given a rectangle with fractional side lengths including mixed numbers,

Use an area model to illustrate and find the rectangular area to lead to answers in the form of whole numbers or mixed numbers.
Example: Using an area model, a rectangle with dimensions of 1 1/2 x 1 2/3 will have partial products of 1, 1/2, 1/3, and 1/6 and the sum of the partial products will give an area of 2 sq units. Use an area model to find the area of a rectangle by tiling the rectangle with unit squares.
Example: Using an area model, a rectangle with dimensions 1 1/2 x 1 1/3 will be tiled with unit squares of 1/6 size showing the tiled partial products as 6/6, 3/6, 2/6, and 1/6 for a total area of 12/6 sq units, so it would take 12 tiles of size 1/6 units to cover the area of the rectangle.Teacher Vocabulary:

Fraction
Fraction model
Whole number
Area
Area model
Linear model
Set model
Tiling
Unit squares
Equation Knowledge:

Students know:

How to write an equation involving repeated addition with fractions as a multiplication equation of a whole number times the fraction.
Example: 2/9 + 2/9 + 2/9 + 2/9 = 4 x 2/9 = 8/9.
The relationship of partial products to an area model when multiplying by two whole numbers.
Area of a rectangle is determined by multiplying side lengths and is found in square units. Skills:

Students are able to:

Use previous understandings of multiplication to
Find products of a fraction times a whole number and products of a fraction times a fraction.
Use area models, linear models or set models to represent products.
Create a story context to represent equations (a/b) × q and (a/b) × (c/d) to interpret products.
Find area of rectangles with fractional side lengths and represent products as rectangular areas.
Find the area of a rectangle by tiling the area of a rectangle with unit squares. Understanding:

Students understand that:

Any whole number can be written as a fraction.
The general rule for multiplication involving fractions can be justified through visual models.
A variety of contextual situations can be represented by multiplication involving fractions.
Tiling with unit squares can be used to find the area of a rectangle with fractional side lengths. Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.5.12.1: Define proper fraction.
M.5.12.2: Multiply fractions using denominators between 2 and 5.
M.5.12.3: Identify proper and improper fractions.
M.5.12.4: Recall basic multiplication facts.
M.5.12.5: Model changing a whole number to a fraction.
M.5.12.6: Partition a rectangle into rows and columns of same-size squares, and count to find the total number of them.
M.5.12.7: Label the numerator and denominator of a fraction.
M.5.12.8: Count the area squares for the length and width.
M.5.12.9: Identify the width and length of a rectangle.

Prior Knowledge Skills:

Solve real-word problems involving multiplication of fractions and mixed numbers.
Write equations to represent the word situation.
Use visual fraction models to represent the problem.
Alabama Alternate Achievement Standards

AAS Standard: M.AAS.5.12 Determine the product of unit fractions with unlike denominators (limited to denominators of 2, 3, 4, 10) using visual models.

Mathematics MA2019 (2019) Grade: 5 14. Model and solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models, drawings, or equations to represent the problem.

Unpacked Content

Evidence Of Student Attainment:

Students:

Use a variety of strategies, including models, pictures, tables, and patterns to solve problems that provide a context for multiplying fractions and mixed numbers. Teacher Vocabulary:

Fraction
Models
Mixed number
Multiplication Knowledge:

Students know:

Contextual situations for multiplication.
How to use an area model to illustrate the product of two whole numbers and its relationship to partial products and extend this knowledge to illustrate products involving fractions and mixed numbers. Skills:

Students are able to:

Solve real-word problems involving multiplication of fractions and mixed numbers.
Write equations to represent the word situation.
Use visual fraction models to represent the problem. Understanding:

Students understand that:

A variety of strategies are used to model and solve problems that provide a context for multiplying fractions and mixed numbers.
Solutions are interpreted based on the meaning of the quantities and the context of the problem situation. Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.5.14.1: Define improper fraction, mixed number, fraction, equations, numerator, denominator.
M.5.14.2: Multiply proper fractions with common denominators 2-10.
M.5.14.3: Solve problems using whole numbers.
M.5.14.4: Write number sentences for word problems.
M.5.14.5: Identify key terms to solve multiplication word problems. Examples: times, every, at this rate, each, per, equal/equally, in all, total.
M.5.14.6: Recall basic multiplication facts.

Prior Knowledge Skills:

Divide unit fractions by a whole number and whole numbers by unit fractions.
Use visual models to illustrate quotients.
Create story contexts for division.
Use relationship between multiplication and division to explain quotients.
Alabama Alternate Achievement Standards

AAS Standard: M.AAS.5.14 Use a model to solve multiplying a whole number by a unit fraction of 1/2, 1/3, and 1/4.

Mathematics MA2019 (2019) Grade: 5 15. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and illustrate using visual fraction models, drawings, and equations to represent the problem.

b. Create a story context for a unit fraction divided by a whole number, and use a visual fraction model to show the quotient.

c. Create a story context for a whole number divided by a unit fraction, and use a visual fraction model to show the quotient.

Unpacked Content

Evidence Of Student Attainment:

Students:

Solve real-world problems involving division of a unit fraction by a non-zero whole number, or division of a whole number by a unit fraction.
Justify solutions using visual models, drawings, and equations to represent the problem context.
Explain quotients using the relationship between multiplication and division.
Create a story context for a unit fraction divided by a whole number and use models to illustrate the quotient.
Create a story context for a whole number divided by a unit fraction and use models to illustrate the quotient. Teacher Vocabulary:

Unit fraction
Whole number
Division
Dividend
Divisor
Quotient
Equation
Multiplication
Factor
Fraction models Knowledge:

Students know:

Contextual situations involving division with whole numbers and unit fractions. Strategies for representing a division problem with a visual model. Skills:

Students are able to:

Use previous understandings of operations to
Divide unit fractions by a whole number and whole numbers by unit fractions.
Use visual models to illustrate quotients.
Create story contexts for division.
Use the relationship between multiplication and division to explain quotients. Understanding:

Students understand that:

A variety of contextual situations are represented with division of a whole number by a fraction or a fraction by a whole number.
Quotients resulting from division of a whole number by a fraction or a fraction by a whole number can be illustrated and justified with a visual model.
The relationship between multiplication and division can be used to justify quotients resulting from division of a whole number by a fraction or a fraction by a whole number. Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.5.15.1: Define quotient.
M.5.15.2: Multiply a fraction by a whole number.
M.5.15.3: Recognize key terms to solve word problems. Examples: times, every, at this rate, each, per, equal/equally, in all, total.
M.5.15.4: Recall basic multiplication and division facts.
M.5.15.5: Express whole numbers as fractions.
M.5.15.6: Recognize fractions that are equivalent to whole numbers.
M.5.15.7: Recall basic multiplication and division facts.
M.5.15.8: Solve word problems involving multiplication of a fraction by a whole number.
M.5.15.9: Recognize key terms to solve word problems.
M.5.15.10: Recall basic multiplication and division facts.

Prior Knowledge Skills:

Find products of a fraction times a whole number and products of a fraction times a fraction.
Use area models, linear models or set models to represent products.
Create a story context to represent equations (a/b) × q and (a/b) × (c/d) to interpret products.
Find area of rectangles with fractional side lengths and represent products as rectangular areas.
Find the area of a rectangle by tiling the area of a rectangle with unit squares.
Alabama Alternate Achievement Standards

AAS Standard: M.AAS.5.15 Use a model to solve dividing a whole number by a unit fraction of 1/2.