1 CATHY SHIDE, CONSULTANT TO INFINITY AND BEYOND . . . GOING BEYOND ANSWER GETTING
Mar 26, 2015
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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