Chapter 10

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Practicing Procedures or Doing MathematicsA look at tasks for developing fractional number sense

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Mathematical Routine:Open Number Line

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Conversation in Mathematics

• Describe this student’s understanding around fractions.

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High vs. Low Level Tasks

• Pedagogy

Over-reliance on rote memorization is a mental cul-de-sac ---Donald M. Blais

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The Patio

Karen was going to install tile on her patio, which was 15 feet long and 10 feet wide. How many square tiles will she need to purchase?

A Dinner Party Ms. Lopez wanted to have a dinner party and invite 24

people. The tables she plans to rent are square and seat one person on each side. Each table costs $10.

1. If Ms. Lopez put the tables together into a rectangle so that all the guests are able to visit, what are all the different configurations she can make to fit all her guests? How many tables would she need to rent for each way?

2. Which way would be the cheapest? Which way would be the most expensive?

3. How long would the sides of each table be?4. Which configuration would make the most sense? Why?

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Low-level tasks

High Level Tasks

Tasks that demand engagement with concepts and that stimulate students to make

purposeful connections to meaningful or relevant mathematics

--Stein et al (2000) p. 11

Tasks that require students to perform a memorized procedure in a routine manner lead to one type of opportunity for students’ thinking

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Task Sort

• Low Level Tasks • High Level Tasks

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Memorization

• Procedures without connections

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Procedures with Connections

• Doing Mathematics

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Fraction Number Sense

• Content

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Task: Using the tools provided, come up with as many different ways to model 2/3.

• Dummy

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Creating a Fraction Kit

• Task:• You will create your own fraction kits. You will

be creating one whole, halves, thirds, fourths, fifths, sixths, eighths, tenths, and twelfths.

• As you are completing this task, think about what children need to know and understand to be able to make their own kits.

• Note: Consult the text if you are having trouble with fifths.

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Create a Fraction/Percent Circle

• Dummy

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Equivalents

• Task:• Using your fraction kits, find as many ways to

show 1/2.

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Games

• Race to 1:• Make a fraction spinner with the fractions that you want

to use. Fraction dice can also be used. Spin the spinner, or roll the dice and place that size piece on top of the whole. The second player places his pieces below the whole. The first person to get exactly one whole wins. Combinations of pieces (like 2 fourths for one half) can be used. If the last piece goes over the whole, then that player looses his/her turn.

• This game can be easily modified to incorporate addition and subtraction of fractions.

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Creating an Inquiry Lesson

• Take a typical fractional number sense lesson from the curriculum of your choice, or take one of the topics from the text, and create an inquiry lesson around that focus. Make sure that it is a high level task.