gradelevel/course:&grade&5& - west contra costa …€¦ · ·...

of 11 MCC@WCCUSD 10/06/13

Grade Level/Course: Grade 5 Lesson/Unit Plan Name: Multiplying Fractions Rationale/Lesson Abstract: Students will conceptually understand multiplying fractions using an area model. Students will then be able to apply their understanding of multiplying fractions to solve word problems. Timeframe: 3 Days Common Core Standard(s): 5.NF.B.4 – Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.B.6 – Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Instructional Resources/Materials: -‐Scissors -‐Transparencies -‐Fraction Area Models -‐Zip-‐lock bags


Background/Connecting Prior Knowledge: Utilize students’ prior knowledge on multiplying whole numbers using an array or area model to introduce multiplying fractions. Remind students that we use multiplication to find ‘groups of’ something. 2 x 3 is 2 groups of 3

2 x 12 is 2 groups of

12

14 x 12 is 14 of a group of

12

Activity/Lesson: Multiplying Fraction by a Whole Number 2 24 43 3or of•

Draw It

“We will begin by drawing 4 groups of 23”

“How many thirds do we have out of the four groups?” [8]

So 243

•

= 83

“Is there another way I can write 83

?” “What do you know about the fraction 83

?”

Take this opportunity to review that an improper fraction tells us that there are whole(s) within the fraction. “We can combine all the thirds and see how many wholes we have.” “How many wholes did we create?” [2] “How many thirds do we have left?” [two thirds]


∴ 243

•

= 83

or 223

Write It 243

•

“Do you notice another way we can get the answer 83

?” [4 times 2 give us 8 and we can keep the

3 as the denominator.]

“We can multiply like-terms by converting the 4 to a fraction, 41

”

As you work out the algorithm, point to the picture to show students the connection between the visual and algorithm. 2434 21 34 21 383

•

= •

•=•

=

or 223

We Do (Draw It and Write It) 3 54•

You Try (Draw It and Write It) 236

•


Multiplying Fraction by a Fraction (Build It, Draw It, Write It) Build It and Draw It Make copies of the Fraction Area Models template on to transparencies. Sets can be made for partner share or individual students. Remind students when we create an area model for a multiplication problem, one term is represented by the height and the other term is represented by the base. Since we are multiplying fractions, which is part of a whole, the area of the model/square will always equal to a one. Therefore, the height will equal to one and the base will equal to one. As students build each step to simplify the problem, have them record each step by drawing what they’ve built. Tell students to use a striped Fraction Area Model to represent one term and a dotted Fraction Area Model to represent the other term. Example #1

1 34 5•

*Remember, fraction is out of a whole. To find what is 14of 35 we can’t just make fourths out of the

35,

but we have to make fourths out of the whole.

Have students pull out the striped Fraction Area

Model for and the

dotted model for

Draw the models.

Overlay the on top of the

model. The over lapping

parts show what is of a

group of . The numerator

and the denominator is represented by the amount of pieces that creates the whole

which is 20.

=

=


Example #2 Follow the same process as Example #1.

5 26 3•

=

=

Ask students what they notice about the answer. Is this the final answer? Students should point out the fraction is not in

simplest form.

Simplify the fraction.

“Do you notice another way we can get the answer?” Allow students to discover the rule to multiplying fractions where we can multiply across the numerator and denominator to get the answer.


We Do (Build It, Draw It, Write It) 1 36 4•

You Try (Build It, Draw It, Write It) 1 42 5•

Ask students what they notice about the step where we multiply the fractions to

where we simplify the fraction.

Show students that instead of multiplying our numerator and denominator together and then decomposing it by its prime factor to simplify, we can prime factor it right

away.


Word Problems Emphasize to students that drawing a visual representation of the word problem will help them visualize what they need to find and how they need to solve it.

Sammy’s play mat is 45 of a meter long and

23 of a meter wide. Find the area of Sammy’s play

mat.

∴ The area of Sammy’s play mat is 815

We Do

There are 46 pounds of dog food in each bag. How many pounds of dog food would be in 3

bags? You Try

Zoe brought 23 of her leftover lasagna to work. She ate

34 of the leftover lasagna at lunch. How

much lasagna does Zoe have leftover?

Draw a square to

represent the length of Sammy’s play mat.

On the same model, create

horizontally to represent

the width.


Closing Display a multiplication problem using whole numbers and another problem using fractions, with answers, side-‐by-‐side. Ask students what they notice about the answers to both multiplication problems. Students may tell you that the answers are larger in value than the problem. This is true for multiplying whole numbers. For multiplying fractions, the terms of the fraction do get larger, but a larger denominator means smaller in value for a fraction.


Fraction Area Models Copy the two pages onto transparency and have students cut them out to model multiplying


Assessment:

Jack has 25 foot of a rope in his garage. He used

26 of it for his tree house. How much rope

does he have left? Which of the following response are possible solutions?

a) 2 22 3 5

•• •

b) 411

c)

d) 23 5•

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