1. Routines for Reasoning
Capturing Quantities –
Multi-step decimal problem

2. Purpose
Today we are learning how to find quantities and relationships in word problems and diagrams. We are going to build diagrams to help us understand a math problem dealing with fractions and decimals. We are going to talk to others to clarify our own thinking about the math problem.

3. Thinking Goals Think about a problem like a mathematician.
Thinking Questions:
What can be measured, what can be counted?
What relationships can I find?
How can I represent my thinking?

4. Jen went to the book fair. She bought 3 gel pens and a book
Jen went to the book fair. She bought 3 gel pens and a book. The book cost $5.95. She gave the cashier $ The cashier gave her 30 cents back. How much did one gel pen cost?
What can be counted?
What can be measured?

5. Jen went to the book fair. She bought 3 gel pens and a book
Jen went to the book fair. She bought 3 gel pens and a book. The book cost $5.95. She gave the cashier $ The cashier gave her 30 cents back. How much did one gel pen cost?
“We can count/measure __________________.”

6. Jen went to the book fair. She bought 3 gel pens and a book
Jen went to the book fair. She bought 3 gel pens and a book. The book cost $5.95. She gave the cashier $ The cashier gave her 30 cents back. How much did one gel pen cost?
What relationships between numbers to do you see?

7. Jen went to the book fair. She bought 3 gel pens and a book
Jen went to the book fair. She bought 3 gel pens and a book. The book cost $5.95. She gave the cashier $ The cashier gave her 30 cents back. How much did one gel pen cost?
“One relationship I see is ________________.”

8. Jen went to the book fair. She bought 3 gel pens and a book
Jen went to the book fair. She bought 3 gel pens and a book. The book cost $5.95. She gave the cashier $ The cashier gave her 30 cents back. How much did one gel pen cost?
What might a diagram of this problem look like?

9. Jen went to the book fair. She bought 3 gel pens and a book
Jen went to the book fair. She bought 3 gel pens and a book. The book cost $5.95. She gave the cashier $ The cashier gave her 30 cents back. How much did one gel pen cost?
“We showed _____ by ______.”
We used the ____ relationship to _____.”

10. Jen went to the book fair. She bought 3 gel pens and a book
Jen went to the book fair. She bought 3 gel pens and a book. The book cost $5.95. She gave the cashier $ The cashier gave her 30 cents back. How much did one gel pen cost?
“We showed _____ by ______.” We used the ____ relationship to _____.”

11. Reflection Question: “Working Backwards on a math problem helps me to …”