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Math CAMPPP 2011

Math at the Beach!!!Grade 5-8

Sandra Fraser

Erik Teather

Proportional ReasoningBreakout 1

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What time is it?

The numbers were cut off of this clock.

On your own, determine what time the clock is showing.

After a few minutes, share

your thinking with your table.

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Discussion

• What mathematical concepts came out of that clock problem?

• Was there proportional reasoning involved?

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The Palm Trees

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This year, they were measured again. Now they are:Large Tree: 12 m tallSmall Tree: 9 m tall

The two palm trees were measured last year.Large Tree: 8 m tallSmall Tree: 5 m tall

Which palm tree grew more?

The Families

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Which family has more girls?

A B

The Life Preservers

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A

B

Which group has more duck life preservers?

Proportional Reasoning

• There are 2 different ways to interpret these problems:– Additive Thinking– Multiplicative Thinking

• Discuss the differences between them and whether there’s an appropriate time to use each one.

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Reflection

• How did your thinking change during these problems?

• Which questions were asked which helped promote your thinking?

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Responding to Students inthe Moment• How do we respond to students in class?• What questions do we ask to promote

student thinking?• Are our questions funneling (to arrive at

the teacher’s thinking) or focusing (to focus students on their own thinking)?

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Questioning

• Look through the DI Question Cards (or Mathematical Processes on Computers)

• Have you used any of these questions before?

• Which ones do you like?

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The Marker Problem

• You have more than 20 markers. When you give them out in groups of 3, there is exactly one marker leftover. How many markers could there be?

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Video – Marker Problem

• Group 6 Video– How did the group interact?– Were they thinking additively or

multiplicatively?– What did they know?– Did the manipulatives help their thinking?– What question would you like to ask them?

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Video – Marker Problem

• Group 4 Video– How did the group interact?– Were they thinking additively or

multiplicatively?– What did they know?– Did the manipulatives help their thinking?– What question would you like to ask them?

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Responding to Students

• We will now look at a few student samples.• How do you think they solved the problem?

– Additive Thinking– Multiplicative Thinking

• Decide what question you would want to ask this student if you were there while they were working on the problem.

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Responding to Students

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What question would you want to ask this student?

23, 26, 29, 32, 35, …

Responding to Students

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What question would you want to ask this student?

19, 22, 25, 28, 31, …

Responding to Students

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There are 22 markers.I put them into 7 groups of 3 and there is one more left over.

What question would you want to ask this student?

Responding to Students

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What question would you want to ask this student?

3 3 3 3 3 3 3

6 9 12 15 18 21

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22+ + + + + + +

Responding to Students

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What question would you want to ask this student?

3 x 3 = 93 x 3 = 9

18 + 3 = 21 + 1 = 22

Responding to Students

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What question would you want to ask this student?

3 x 7 = 21 + 1 = 22 + 3 = 25

What did we learn?

…about the mathematics?

…about teaching mathematics?

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Learning Goals(Did we meet them?)• To explore the differences between

multiplicative and additive thinking (within proportional reasoning)

• To reflect on the ways in which we respond to students in the moment.

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Activity

• Make up your own proportional reasoning task.

• Create 2 solutions:– Additive thinking– Multiplicative thinking

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