MA.5.FR.2.3

When multiplying a given number by a fraction less than 1 or a fraction greater than 1, predict and explain the relative size of the product to the given number without calculating.

Clarifications

Clarification 1: Instruction focuses on the connection to decimals, estimation and assessing the reasonableness of an answer.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 5
Strand: Fractions
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.5.FR.2.AP.3: Explore the impact on the size of the product when multiplying a given number by a fraction less than 1 or by a whole number.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Multiplying by a Fraction Greater Than One:

Students are asked to describe the size of a product of a fraction greater than one and a whole number without multiplying.

Type: Formative Assessment

Multiplying by a Fraction Less than One:

Students are asked to describe the size of a product of a fraction less than one and a whole number without multiplying.

Type: Formative Assessment

More Than or Less Than Two Miles:

Students are asked to reason about the size of the product of fractions and whole numbers presented in context.

Type: Formative Assessment

Estimating Products:

Students are given three products, each involving a whole number and a fraction, and are asked to estimate the size of the product and explain their reasoning.

Type: Formative Assessment

Lesson Plans

Real-World Fractions:

This lesson focuses on providing students with real-world experiences where they will be required to multiply fractions. Students will be required to use visual fraction models or equations to represent the problem.  This is a practice and application lesson, not an introductory lesson.

Type: Lesson Plan

Multiplying a Fraction by a Fraction:

In this lesson, students will solve problems related to training for a marathon to apply and make sense of multiplying fractions. The student will complete a function table to help illustrate patterns in the numerator/denominator relationships. This lesson utilizes the linear model as a concrete representation and moves towards the standard algorithm (a/b) x (c/d) = ac/bd.

Type: Lesson Plan

Looking for Patterns in a Sequence of Fractions:

Students generate and describe a numerical pattern using the multiplication and subtraction of fractions.

Type: Lesson Plan

Original Student Tutorial

Scaling Up to Escape:

Try to escape from this room using multiplication as scaling in this interactive tutorial.

Note: this tutorial is an introductory lesson on multiplying a given number without calculating before working with fractions.

Type: Original Student Tutorial

Problem-Solving Tasks

Running a Mile:

The solution uses the idea that multiplying by a fraction less than 1 results in a smaller value. The students need to explain why that is so.

Type: Problem-Solving Task

Reasoning about Multiplication:

This is a good task to work with kids to try to explain their thinking clearly and precisely, although teachers should be willing to work with many different ways of explaining the relationship between the magnitude of the factors and the magnitude of the product.

Type: Problem-Solving Task

Grass Seedlings:

The purpose of this task is to gain a better understanding of multiplying with fractions. Students should use the diagram provided to support their findings.

Type: Problem-Solving Task

Fundraising:

This problem helps students gain a better understanding of multiplying with fractions.

Type: Problem-Solving Task

Comparing a Number and a Product:

The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one. As written, this task could be used in a summative assessment context, but it might be more useful in an instructional setting where students are asked to explain their answers either to a partner or in a whole class discussion.

Type: Problem-Solving Task

Calculator Trouble:

This particular problem deals with multiplication. Even though students can solve this problem by multiplying, it is unlikely they will. Here it is much easier to answer the question if you can think of multiplying a number by a factor as scaling the number.

Type: Problem-Solving Task

MFAS Formative Assessments

Estimating Products:

Students are given three products, each involving a whole number and a fraction, and are asked to estimate the size of the product and explain their reasoning.

More Than or Less Than Two Miles:

Students are asked to reason about the size of the product of fractions and whole numbers presented in context.

Multiplying by a Fraction Greater Than One:

Students are asked to describe the size of a product of a fraction greater than one and a whole number without multiplying.

Multiplying by a Fraction Less than One:

Students are asked to describe the size of a product of a fraction less than one and a whole number without multiplying.

Original Student Tutorials Mathematics - Grades K-5

Scaling Up to Escape:

Try to escape from this room using multiplication as scaling in this interactive tutorial.

Note: this tutorial is an introductory lesson on multiplying a given number without calculating before working with fractions.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorial

Scaling Up to Escape:

Try to escape from this room using multiplication as scaling in this interactive tutorial.

Note: this tutorial is an introductory lesson on multiplying a given number without calculating before working with fractions.

Type: Original Student Tutorial

Problem-Solving Tasks

Running a Mile:

The solution uses the idea that multiplying by a fraction less than 1 results in a smaller value. The students need to explain why that is so.

Type: Problem-Solving Task

Reasoning about Multiplication:

This is a good task to work with kids to try to explain their thinking clearly and precisely, although teachers should be willing to work with many different ways of explaining the relationship between the magnitude of the factors and the magnitude of the product.

Type: Problem-Solving Task

Grass Seedlings:

The purpose of this task is to gain a better understanding of multiplying with fractions. Students should use the diagram provided to support their findings.

Type: Problem-Solving Task

Fundraising:

This problem helps students gain a better understanding of multiplying with fractions.

Type: Problem-Solving Task

Comparing a Number and a Product:

The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one. As written, this task could be used in a summative assessment context, but it might be more useful in an instructional setting where students are asked to explain their answers either to a partner or in a whole class discussion.

Type: Problem-Solving Task

Calculator Trouble:

This particular problem deals with multiplication. Even though students can solve this problem by multiplying, it is unlikely they will. Here it is much easier to answer the question if you can think of multiplying a number by a factor as scaling the number.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Tasks

Running a Mile:

The solution uses the idea that multiplying by a fraction less than 1 results in a smaller value. The students need to explain why that is so.

Type: Problem-Solving Task

Reasoning about Multiplication:

This is a good task to work with kids to try to explain their thinking clearly and precisely, although teachers should be willing to work with many different ways of explaining the relationship between the magnitude of the factors and the magnitude of the product.

Type: Problem-Solving Task

Grass Seedlings:

The purpose of this task is to gain a better understanding of multiplying with fractions. Students should use the diagram provided to support their findings.

Type: Problem-Solving Task

Fundraising:

This problem helps students gain a better understanding of multiplying with fractions.

Type: Problem-Solving Task

Comparing a Number and a Product:

The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one. As written, this task could be used in a summative assessment context, but it might be more useful in an instructional setting where students are asked to explain their answers either to a partner or in a whole class discussion.

Type: Problem-Solving Task

Calculator Trouble:

This particular problem deals with multiplication. Even though students can solve this problem by multiplying, it is unlikely they will. Here it is much easier to answer the question if you can think of multiplying a number by a factor as scaling the number.

Type: Problem-Solving Task