Multiplicative Comparison Problems and Strip Diagrams Tuesday September 27, 2011 Common Core Leadership in Mathematics (CCLM)

Learning Intentions & Success Criteria We are learning to… Understand how to solve multiplication comparison problems and use tape (strip) diagrams to illustrate the solutions. We will be successful when…. Clearly explain the mathematical content in 4OA.2 and be able to provide examples of the mathematics.

Revisiting Multiplicative Comparison Problems Connie ran 50 meters Melissa ran 200 meters On your slate, write three problems using this information: Larger quantity unknown Smaller quantity unknown Compare quantity unknown

Standard 4.OA.2 Read standard 4.OA.2 Divide your slate in half. On one side, rephrase this standard and on the other side, provide an example. Share with your partner.

Sense Making…. Share with your shoulder partner a few ideas that struck you as critical to developing a sound understanding of multiplicative comparison problems. 5 minute partner share Whole group discussion. Give them a situation like: The second paragraph is difficult to understand. We have to help them make sense of this. Blue hat $10 Red hat $30 Larger quantity unknown: The red hat costs $10. The blue hat cost 3 times as much as the red hat. How much does the blue hat cost? Smaller quantity unknown: The blue hat cost $30. The cost of the blue hat is three times as much as the red hat. How much does the red hat cost? Compare quantity unknown: The red hat cost $10 and the blue hat costs $30. The blue hat is how many times as expensive as the red hat?

Tape Diagram A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as strip diagrams, bar model, fraction strip or length model. CCSSM Glossary p. 87

A Parking Lot Problem A fourth grade class counted the number of vehicles that went by the front entrance of the school between 9 o'clock and 10 o'clock. The total number of vehicles counted was156. There were 3 times as many passenger cars as trucks. How many passenger cars and how many trucks were counted? Use a tape diagram to illustrate and solve this problem. Ask teachers to draw the strip diagram before showing them the sample.

Farmer problem A farmer has 7 ducks. He has 5 times as many chickens as ducks. How many more chickens than ducks does he have? On your slate, draw a diagram to help you solve this problem. Record your thinking. (Singapore Math Primary Mathematics volume 3A, page 46, problem 4) 1 unit is 7 ducks Chickens are 5 units so 5 x 7 ducks 35 chickens 35 – 7 = 28 more chickens

Let’s Look at Some Student Problems Solve the problems (from Singapore Mathematics 3A) with your partner. How did the tape diagram help you think multiplicatively?

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

Reflecting on the Practices with mc cullum graphic. Discussions about which practices we saw/did today. How does clustering the practices help you with this discussion? Be explicit.

Learning Intentions & Success Criteria We are learning to… Understand how to solve multiplication comparison problems and use tape (strip) diagrams to illustrate the solutions. We will be successful when…. Clearly explain the mathematical content in 4OA.2 and be able to provide examples of the mathematics.