1. From additive to multiplicative reasoning
Pick a topic that can sometimes be tough for teachers to teach.
UMI
January 20, 2018

2. Problem Solving
Sam the snake is 4 feet long. When he is fully grown, he will be 8 feet long. Sally the snake is 5 feet long. When she is fully grown, she will be 9 feet long. Which snake is closer to being fully grown. Explain how you know.

3. directions Work the problem on your own. Share in your group.
Analyze the student reasoning. Which student is correct? Why?
Share out.

4. Types of reasoning used
They are both the same distance to being fully grown. Although Sam is only 4 feet long and will be 8 feet long, Sally is 5 feet long and will be 9 feet. No matter how you look at it, they are both 4 feet away from being fully grown.
Additive Reasoning
Sally is closer to being fully grown because she is 5 feet long and will only get to 9 feet. This means she is over half of her total growth. Although Sam will only get to be 8 feet, he is exactly halfway of his total growth, and this means that Sally is further along in in growth than Sam.
Multiplicative Reasoning
Additive Reasoning: The student believes that the correct calculation for Sam is =8 and for Sally is = 9

5. Success rates from sample students
5th Grade – 11%
6th Grade – 27%
7th Grade 40%
8th Grade – 52%

6. How do we help our students go from additive to multiplicative reasoning?
Jigsaw an article from Teaching Children Mathematics, Developing Multiplicative Thinking from Additive Reasoning, September 2013.
Additive Strategies
Unit Relationships
Composite Units
Multiplicative Reasoning
Additive reasoning if used correctly helps students move to multiplicative reasoning. Let’s jigsaw to see how that works.

7. Jigsaw instructions
Supplies - Article sections for each group (Full article is on our Website.
Groups of 4 will review their assigned section and become an expert on it. (10 minutes)
Divide into new mixed groups of 4 to share your section.
Share your section with the group in this order: (15 minutes)
Additive Strategies
Unit Relationships
Composite Units
Multiplicative Reasoning 

8. Strategies to help students develop multiplicative reasoning
Present problems that guide students toward thinking
Choose numbers carefully so that the students can find a relationship.
Allow students to use different strategies to help them distinguish between methods that do and do not work.
Present students with different types of problems. (Not all multiples like 6/30 = x/40)

9. Next steps: student work
Analyze the student work on the multiplicative reasoning problem.
What is the student not understanding?
What would be your next steps with this student?
Why?

10. What topics perplex you?