Mathematics Pacing Resource Document
5.C.5
Standard: 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number.
Teacher Background Information:
Students need to develop a fundamental understanding that the multiplication of a fraction by a whole number could be represented as repeated
addition of a unit fraction (e.g., 2 x (1/4) = 1/4 + ¼)
This standard extends student’s work of multiplication from earlier grades. In fourth grade, students worked with recognizing that a fraction such as
3/5 actually could be represented as 3 pieces that are each one-fifth (3 x (1/5)). This standard references both the multiplication of a fraction by a
whole number and the multiplication of two fractions. Visual fraction models (area models, tape diagrams, number lines) should be used and created
by students during their work with this standard.
As they multiply fractions such as 3/5 x 6, they can think of the operation in more than one way.

3 x (6 ÷ 5) or (3 x 6/5)

(3 x 6) ÷ 5 or 18 ÷ 5 (18/5)
Students create a story problem for 3/5 x 6 such as,


Isabel had 6 feet of wrapping paper. She used 3/5 of the paper to wrap some presents. How much does she have left?
Every day Tim ran 3/5 of mile. How far did he run after 6 days? (Interpreting this as 6 x 3/5)
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.5
Standard: 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number.
Teacher Background Information:
Example:
Three-fourths of the class is boys. Two-thirds of the boys are wearing tennis shoes. What fraction of the class are boys with tennis shoes?
This question is asking what 2/3 of ¾ is, or what is 2/3 x ¾. What is 2/3 x ¾, in this case you have 2/3 groups of size ¾
(a way to think about it in terms of the language for whole numbers is 4 x 5 you have 4 groups of size 5. The array model is very
transferable from whole number work and then to binomials.)
Student 1
I drew a rectangle to represent the whole class.
The four columns represent the fourths of a class.
I shaded 3 columns to represent the fraction that
are boys. I then split the rectangle with horizontal
lines into thirds. The dark area represents the
fraction of the boys in the class wearing tennis
shoes, which is 6 out of 12. That is 6/12, which
equals 1/2.
Student 3
Fraction circle could be used to model student
thinking. First I shade the fraction circle to show the ¾
and then overlay with 2/3 of that?
Student 2
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Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.5
Standard: 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number.
Teacher Background Information:
Connecting representation to the procedure for three problems involving multiplication.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.5
Standard: 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number.
Teacher Background Information:
Solutions to a multiplication problem when
The parts must be subdivided.
Modeling multiplication of fractions with counters
The area model for modeling fraction
multiplication has several
advantages. First, it works for
problems in which partitioning a
length can be challenging. Second, it
provides a powerful visual to show
that a result can be quite a bit smaller
than either of the fractions used or
that if the fractions are both close to
1, then the result is also close to one.
Third, it is a good model for
connecting to the standard algorithm
for multiplying fractions.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.5
Standard: 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number.
Teacher Background Information:
Notice that the same four partial products can be found in the area model.
Process Standards to Emphasize with Instruction of 5.C.5:
5.PS.2: Reason abstractly and quantitatively.
5.PS.4: Model with mathematics.
5.PS.5: Use appropriate tools strategically.
5.PS.7: Look for and make use of structure.
5.PS.8: Look for and express regularity in repeated reasoning.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.5
Standard: 5.C.5: Use visual fraction models and numbers to multiply a fraction by a fraction or a whole number.
Lesson Plans/Print Activities:
Web-based Practice:

Math Expressions Lessons:
o Unit 9: Lessons 1-5

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-c-overview Multiplication of a Whole Number by a Fraction

https://www.engageny.org/resource/grade-5-mathematics-module-4topic-e-overview Multiplication of a Fraction by a Fraction

http://www.shodor.org/interactivate/activities/FractionQuiz/ Online
quiz
http://www.k-5mathteachingresources.com/supportfiles/multiplyingfractionsbydividingrectangles5.nf4a.pdf Multiplication of
fractions. Lesson seed

http://www.math-play.com/Multiplying-FractionsMillionaire/Multiplying-Fractions-Millionaire.html Multiplication of
fractions millionaire game
http://www.cpalms.org/Public/PreviewResource/Preview/27870
Modeling Fraction Multiplication

http://www.arcademics.com/games/snow-sprint/snow-sprint.html
Multiplication of fractions game





http://www.khanacademy.org/math/arithmetic/fractions/multiplyin
g_fractions/v/multiplying-fractions-and-whole-numbers Multiplying
fractions lessons
Understand multiplication of fractions by whole numbers
LZ2696, LZ2971, LZ3026, LZ2927, LZ2938, LZ2939, LZ3076
http://www.cpalms.org/Public/PreviewResource/Preview/38419
Multiplying fractions with an area model
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.5
Item Bank:
1) Makayla said, "I can represent 3 ×
2
2
with 3 rectangles each of length ."
3
3
2
2
2
2
× 3 can be thought of as of 3. Is 3 copies of the same as of 3?”
3
3
3
3
2
a. Draw a diagram to represent of 3.
3
2
2
b. Explain why your picture and Makayla’s picture together show that 3 × = × 3.
3
3
Connor said, “I know that
c. What property of multiplication do these pictures illustrate?
[www.illustrativemathematics.org] Solution at https://www.illustrativemathematics.org/illustrations/321
2) What is 2/3 of 15 marbles?
A. 10 marbles
B. 9 marbles
Indianapolis Public Schools
C. 8 marbles
D. 5 marbles
[NAEP 1990 Grade 12] Answer: A
Curriculum and Instruction
Mathematics Pacing Resource Document
5.C.5
Item Bank:
3) Gregory is installing tile on a rectangular floor.

He is using square tiles.

The length of a side of each tile is

1
foot.
2
The area of the floor is 22 square feet.

The width of the floor is 4 feet.
Use the grid to model the rectangular floor that Gregory is installing.
What is the length, in feet, of the floor? ________________ feet
[Delaware Dept. of Education] Answer: 5
1
feet
2
4) Illustrative Mathematics task Folding Strips of Paper https://www.illustrativemathematics.org/illustrations/965
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
(Also aligned to 5.C.3)
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools
Curriculum and Instruction