Multiplication of Fractions
Part 1
This material was developed for use by participants in the
Common Core Leadership in Mathematics (CCLM^2) project
through the University of Wisconsin-Milwaukee. Use by school
district personnel to support learning of its teachers and staff is
permitted provided appropriate acknowledgement of its source.
Use by others is prohibited except by prior written permission.
January 29, 2013
Common Core Leadership in Mathematics2 (CCLM)
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Agenda
• Project 2: Select a Common Task
• Solving Multiplication Problems Using Tape
Diagrams
• MP 5
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Understanding Multiplication of
Fractions Using Tape Diagrams
Isn’t this everything I need to know?
Common Core Partnership for Mathematics
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Multiplication and Division of
Fractions: Standards Progression
4.NF.4 Apply and extend previous understandings of multiplication to
multiply a fraction by a whole number.
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?
5.NF.3 ,5.NF.4, 5.NF.5,
5.NF.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.
5.NF.7, 6.NS.1
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Standard 4.NF.4c
• Read Standard 4.NF.4c
• Rephrase this standard and provide an
example on your slate.
• Share with your partner.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Standard 4.NF.4c
4. Apply and extend previous understandings of
multiplication to multiply a fraction by a whole
number.
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?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Standard 5.NF.6
• Read Standard 5.NF.6
• Rephrase this standard and
provide an example on your slate.
• Share with your partner.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Standard 5.NF.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.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Learning Intentions &
Success Criteria
• We are learning to…
– Understand how to solve fraction word
problems and use tape (number line)
diagrams to illustrate the solutions.
• We will be successful when….
– We can solve fraction word problems and
use tape (number line) diagrams to illustrate
the solutions.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Money, Money, Money
• David spent 2/5 of his money on a
storybook. The storybook cost $20. How
much money did he have at first?
• On your slate, draw a model to help you
solve this problem. Solve the problem.
Record your thinking.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Let’s Look at Some Sample
Problems
Solve the problems on pages 20 and
21(from Singapore Mathematics 4A) with
your partner. Record your thinking.
How did the tape diagram help you solve
complicated fraction word problems?
Now solve the problems on pp. 24-25 by
drawing tape diagrams.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Comparing Performance on TIMMS
Items (8th grade)
• Laura had $240. She spent 5/8 of it. How much
money did she have left?
Singapore 78%, United States 25%
• Penny had a bag of marbles. She gave one-third of
them to Rebecca and then one-fourth of the
remaining marbles to John. Penny then had 24
marbles left in the bag. How many marbles were
there to start with?
Singapore 81%, United States 14%
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Sense Making….
• Share with your shoulder partner a few
ideas that struck you as critical to
developing a sound understanding of
multiplication of fractions.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
The power of strip diagrams
With the aid of simple strip diagrams,
children can use straightforward reasoning
to solve many challenging story problems
conceptually.
Beckmann 2004
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Big Ideas
A Focus on Fractions
• Multiplication and division of fractions are among the
most complicated fraction concepts that elementary
students encounter.
• Instructional opportunities that students encounter
should include the meaning of multiplication and division
in a range of situations and build procedural fluency with
understanding.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
The School Problem
• There are 3 ½ times as many fifth graders at
School A as School B. There are 115 more
students at School A than at School B. How
many students are there at each school?
• Draw a tape diagram to help you solve this
problem.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments & critique reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
MP5
Use Appropriate Tools Strategically
List 3 specific examples for:
– Student Disposition: What did you do as
students that illustrate this practice?
– Teacher Actions: What experiences and
opportunities did the teachers provide to
foster the desired student dispositions?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013
Learning Intentions &
Success Criteria
• We are learning to…
– Understand how to solve fraction word
problems and use tape (number line)
diagrams to illustrate the solutions.
• We will be successful when….
– We can solve fraction word problems and
use tape (number line) diagrams to illustrate
the solutions.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013