1CATHY SHIDE, CONSULTANT

TO INFINITY AND BEYOND . . .

GOING BEYOND ANSWER GETTING

OBJECTIVES

• Integrate the math practices with word problems • teachers and students going beyond “answer getting”

•Use different modes of representation to solve problems with a focus on Fractions, Ratios, and Percents

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PROBLEM #1

Cathy and Joan started out with the same number of coins. Cathy lost 15 coins and Joan gained 36. How many more coins does Joan have than Cathy?

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“TAPE DIAGRAM”

“A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model.”

Also referenced in “Visual Fraction Model” definition.

- CCSSM (Glossary) p. 87

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6.RP.3

Students were creating spirit necklaces to sell for a fundraiser. A necklace takes twice as many purple beads as white beads and 4 times as many purple beads as black beads. One necklace takes 28 beads. What is the number of each color of beads?

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7.RP.3

A class had 32 students and twenty-five percent were boys. When some new boys joined the class, the percentage of boys increased to 40%. How many new boys joined the class?

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7.RP.3

Two students were running for school president. Student A received 65% of the votes and had 900 more votes than Student B. How many students voted?

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5.NF.4

The fundraising committee made 400 pizzas. The students sold 5/8 of the pizzas and took 1/5 of the remainder for a party. How many pizzas did the committee have left to sell?

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GROUP PROBLEM SOLVING

Work with your colleagues to create:• A manipulative model with your color tiles• A tape diagram (bar model) of your

problem• An equation • A verbal description of your thought

process• What other questions can be answered

about your situation/problem?

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WHAT DO YOU KNOW? WHAT CAN YOU ANSWER?

A cran-apple mixture is made up of 3 parts apple juice and 1 part cranberry juice. The company will use 5 gallon containers for the cran-apple mixture.

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WHAT ARE THE MATH PRACTICES?

•Look at your Bulleted List of Math Practices•What practices have you been engaged in?

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ANSWER GETTING VS. LEARNING MATH

• USA:How can I teach my kids to get the answer to

this problem? Use mathematics they already know. Easy, reliable, works

with bottom half, good for classroom management.

• Japanese:How can I use this problem to teach the

mathematics of this unit?

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Phil Daro, Writer of CCSS in Mathematics, Slide 16, http://www.cmc-math.org/resources/downloads/Daro%20PS%20Conference.ppt

POSING THE PROBLEM

• Whole class: pose problem, make sure students understand the language, no hints at solution• Focus students on the problem situation, not

the question/answer game. Hide question and ask them to formulate questions that make situation into a word problem• Ask 3-6 questions about the same problem

situation; ramp questions up toward key mathematics that transfers to other problems

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Phil Daro, Writer of CCSS in Mathematics, Slide 80, http://www.cmc-math.org/resources/downloads/Daro%20PS%20Conference.ppt

WHAT PROBLEM TO USE?

• Problems that draw thinking toward the mathematics you want to teach. NOT too routine, right after learning how to solve.

• Ask about a chapter: what is the most important mathematics students should take with them? Find a problem that draws attention to this mathematics

• Begin chapter with this problem (from lesson 5 thru 10, or chapter test). This has diagnostic power. Also shows you where time has to go.

• Also near end of chapter, while still time to respond

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Phil Daro, Writer of CCSS in Mathematics, Slide 81, http://www.cmc-math.org/resources/downloads/Daro%20PS%20Conference.ppt

REFLECTIONS

•What were the big ideas in this session?

•How can I implement the ideas from this session?

•What do I still need?

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