Grades 7/8 Breakout Session 4B
Session Goals
• to continue to develop our math talk
learning community
• to deepen understanding of proportional
reasoning
• to solve open tasks related to operations
with fractions
Minds On
Mental Strategies for Multiplying
• Identify the relationships within and among
the following sets of expressions:
14 x 8
28 x 4
56 x 2
16 x 25
8 x 50
4 x 100
6 x 3.5
3 x 7.0
28 x 500
14 x 1000
0.5 x 16
1.0 x 8
0.8 x 7.5
0.4 x 15
0.2 x 30
Minds On (continued)
Halving and Doubling
• Why does this strategy work for multiplying
whole numbers and decimals?
• Would the same strategy work for dividing
whole numbers and decimals?
• Explore the halving and doubling strategy
with fractions (Mental Strategies for
Multiplying Fractions handout)
Discussion
• What did you notice?
• What other knowledge/skills are required
to use this strategy for dividing fractions?
• Would you always use this strategy when
multiplying or dividing fractions? Explain.
Action
Reasoning about Division of Fractions
• Marian solved
and 16 by 8 to get
by dividing 15 by 3
.
• Explain, using more than one
representation if possible, why dividing
numerators and dividing denominators
‘works’ to divide fractions.
Action (continued)
Whole Group Discussion
• Why does dividing numerators and
dividing denominators to divide fractions
make sense?
Action (continued)
Making Sense of Operations with Fractions
• Work with a partner to solve two or three
of the open tasks on the handout
• For each task, represent your thinking in
more than one way
Consolidation
Reflecting on the Open Tasks
• What makes each task open?
• How does each task support both students
who may struggle with fractions and those
who may require a challenge?
• How might this kind of proportional
reasoning about fractions help students
develop a deeper understanding of
operations with fractions?
Enjoy a wonderful
break 