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Teaching 4.NF.B.4 .a.b.c – Understand a Fraction a/b as a Multiple of 1/b – Multiply Fraction by a Whole Number

 

multiplying fractions whole numbersNumber & Operations – Fractions – 4th Grade

Build fractions from unit fractions.

CCSS.Math.Content.4.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
CCSS.Math.Content.4.NF.B.4.a
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).
CCSS.Math.Content.4.NF.B.4.b
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.)
CCSS.Math.Content.4.NF.B.4.c
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?

Teacher Notes
How does repeated addition of fractions relate to multiplication of a fraction by a whole number?
Fractions can be thought of as parts of a whole or as individual units.  Multiplying a fraction by a whole number yields the number of unit fractions or individual units.
After teaching how multiplying is the same as repeated addition with fractions, explaining to students how multiplying a whole number by a fraction will always result in a lower whole number by using an example with half. Example: One half of four is two, correct? This is the same as one half times four which equals two.

Student Knowledge Goals

I know that multiplication is repeated addition.
I know that adding unit fractions is the same as multiplying a unit fraction by a whole number.
I can explain how a fraction is a multiple of another fraction using models, drawings, or equations.

Vocabulary
No new vocabulary

Lessons
Engage NY Module 5 G-35 – Represent the multiplication of n times a/b as (n × a)/b using the associative property and visual models.
Engage NY Module 5 G-36 – Represent the multiplication of n times a/b as (n × a)/b using the associative property and visual models.
Engage NY Module 5 G-37 – Find the product of a whole number and a mixed number using the distributive property.
Engage NY Module 5 G-38 – Find the product of a whole number and a mixed number using the distributive property.
Engage NY Module 5 G-39 – Solve multiplicative comparison word problems involving fractions.
Engage NY Module 5 G-40 – Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots.
Multiplying Fractions – Various Lessons

Student Video Lessons
Learn Zillion – Understand multiplication of fractions by whole numbers
Virtual Nerd – Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Online Problems and Assessments
Khan Academy – Questions and Video Lessons
Multiply unit fractions by whole numbers using number lines
Multiply unit fractions and whole numbers: sorting
Multiply unit fractions by whole numbers
Multiply fractions by whole numbers using number lines
Multiply fractions and whole numbers: sorting
Multiply fractions by whole numbers
Multiply unit fractions by whole numbers: word problems
Multiply fractions by whole numbers: word problems
Multiply fractions and mixed numbers by whole numbers in recipes

Online Games
Multiply Fractions

Printables
Multiplying Fractions
Assessment Task 1
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Assessment Task 4
Assessment Task 5
Assessment Task 6
Assessment Task 7
Assessment Task 8

 

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