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- Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
- Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
- Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
Remarks
Examples of Opportunities for In-Depth FocusThis standard represents an important step in the multi-grade progression for multiplication and division of fractions. Students extend their developing understanding of multiplication to multiply a fraction by a whole number.
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
- Assessment Limits :
Fractions may only be multiplied by a whole number. Denominators of given fractions are limited to: 2, 3, 4, 5, 6, 8, 10, 12, 100. - Calculator :
None
- Context :
Allowable
- Test Item #: Sample Item 1
- Question:
Daniella fills a container with soil by using a bowl. The bowl holds
cup of soil. Daniella uses 13 full bowls of soil to fill the container.How many cups of soil does the container hold?
- Difficulty: N/A
- Type: EE: Equation Editor
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Educational Games
Formative Assessments
Students use a visual fraction model to explain how many one sixths are in 
and record their work with an equation.
Type: Formative Assessment
Lesson Plans
Original Student Tutorials
Problem-Solving Tasks
Tutorial
STEM Lessons - Model Eliciting Activity
Students will develop a model for choosing a balloon party planner and rank them from best to worst.
The students will be able to use prior knowledge of addition of multi-digit whole numbers, multiplication and division facts and concepts, math calculations with money and time, understanding fractions, and problem solving skills to solve a non-routine MEA (Model Eliciting Activity) that requires real-world application of mathematical skills.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
Students use a visual fraction model to explain how many one sixths are in and record their work with an equation.
Students are asked to multiply a fraction by a whole number and to represent the product with a visual fraction model.
Students are asked to multiply a fraction by a whole number to solve a word problem and to represent the product with a visual fraction model.
Students are asked to multiply an improper fraction by a whole number to solve a word problem and use a visual model or equation to represent the problem.
Original Student Tutorials Mathematics - Grades K-5
Help Buffy the Baker multiply a fraction by a whole using models in this sweet interactive tutorial.
This is part 3 of a 4-part series. Click below to open other tutorials in the series.
Help Buffy multiply fractions by whole numbers using the standard algorithm in addition to visual fraction models in this bakery-themed, interactive tutorial.
This is part 4 of a 4-part series. Click below to open other tutorials in the series.
Find the total amounts of repeated fraction quantities by multiplying a fraction by a whole number using visual models that represent real-world problems and cookies in this interactive tutorial.
Student Resources
Original Student Tutorials
Help Buffy multiply fractions by whole numbers using the standard algorithm in addition to visual fraction models in this bakery-themed, interactive tutorial.
This is part 4 of a 4-part series. Click below to open other tutorials in the series.
Type: Original Student Tutorial
Help Buffy the Baker multiply a fraction by a whole using models in this sweet interactive tutorial.
This is part 3 of a 4-part series. Click below to open other tutorials in the series.
Type: Original Student Tutorial
Find the total amounts of repeated fraction quantities by multiplying a fraction by a whole number using visual models that represent real-world problems and cookies in this interactive tutorial.
Type: Original Student Tutorial
Educational Games
This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.
Various levels of difficulty make this game appropriate for multiple age and ability levels.
Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.
Multiplication/Division: The multiplication and addition of whole numbers.
Percentages: Identify the percentage of a whole number.
Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.
Type: Educational Game
Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.
Type: Educational Game
Problem-Solving Tasks
This task provides a familiar context allowing students to visualize multiplication of a fraction by a whole number. This task could form part of a very rich activity which includes studying soda can labels.
Type: Problem-Solving Task
The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and use this burgeoning understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.
Type: Problem-Solving Task
Tutorial
In this Khan Academy video visual fraction models are used to represent the multiplication of a whole number times a fraction.
Type: Tutorial
Parent Resources
Problem-Solving Tasks
This task provides a familiar context allowing students to visualize multiplication of a fraction by a whole number. This task could form part of a very rich activity which includes studying soda can labels.
Type: Problem-Solving Task
The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and use this burgeoning understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.
Type: Problem-Solving Task
