Grade+7+Fractions

Who Cares? Movie

 * School Greening Project

Clip 1: Comparing Fractions Using Unit Fractions and Benchmarks
> - 11 Fraction Circles are displayed > - a random fraction is generated > - fraction can be placed in a circle or broken up into unit fractions and placed into one or more circles > - a circle is captured if more than one-half is shaded > - a circle is given to the other player if too big a fraction is added to it > - student plays against the computer > - could have progressively harder levels
 * Benchmarks 0, 1/2, 1, 3/2,...,3
 * Unit Fraction away from a Benchmark
 * Ring Toss Game
 * Marilyn Burns' Comparison Game
 * Dropball with benchmarks of 1/2 added
 * Flash Game: Two Fractions descend from top of the screen, click on the smaller one before they disappear
 * Capture One (from Marilyn Burns - could be adapted in various ways)

Clip 2: Adding Fractions with Common Denominators

 * Start - Lasagne pan at buffet table
 * Action - arranging tables, how much did two people eat, leftovers, numerical examples, choose rule
 * Wrap-up - self checking with representations

Clip 3: Adding Fractions with relatively prime denominators

 * Clock Fractions calculator

Clip 4: Adding Fractions when one denominator is a multiple of the other

 * Start - fundraising context
 * Action - subtracting mixed numbers using borrowing, conversion to improper, subtracting whole and fractional parts separately
 * Wrap-up - self checking with context

Clip 5: Adding Fractions when one denominator is not a multiple of the other
>> The user enters two fractions, which are represented as vectors on the number line. >> Tools are provided to change the scale on the number line so that the answer falls at a nameable position. >> User can use this representation to rename addends e.g., 1/3 + 1/6 = 1/2 becomes 4/12 plus 2/12 is 6/12.
 * Engaging way to determine common multiples (e.g. movable 100s chart a la Sketchpad, Graphic Euclidean Algorithm)
 * see Multiples Grid and Geom Euclid GCD pages in http://www.dynamicgeometry.com/downloads/talks/Discrete_topics_commented.gsp
 * Combining Ingredients
 * [|Fractris Game]
 * [|Adding Fractions Virtual Manipulative]
 * GSP or Flash: Number Line Addition
 * Dropball with sums
 * Ball has something like 1 1/4+2 2/5 on it and has to be placed in the correct interval
 * Burn's Comparison Game with an Addition Sentence

Clip 7: Connecting Repeated Addition of Fractions to Multiplying by a Whole Number

 * deal with half of a whole number here?
 * other questions like 3/5 of 45?

Representations

 * Baroody calls a fraction rectangle divided horizontally for one fraction and vertically for the other a cake-cutting model which can be used as a device to get a common denominator for comparing, adding and subtracting
 * Area Models - Rectangle, Circle
 * Linear Model
 * Fractions Strips, Pieces
 * Pictorial (e.g. pictures of tickets)
 * Clock model - useful for operating with fractions that can be expressed as sixtieths. For example 2/3+3/4 can be found by realizing that 2/3 of an hour is 40 minutes and three-fourths of an hour is 45 minutes. Adding we get 85 minutes or 85-sixtieths of an hour, which is equivalent to 17/12 (by looking at the number of 5 minute intervals in each).

Pascal Fractions Triangle Idea [|Price is Right Games] Illuminations Fraction Game at NCTM Pose your own Fractions problem Finding the fraction exactly between two others

When should operations like Addition and Subtraction be considered separately and when should they be considered together? Burns recommends doing them together. Which representations are most useful? Do we want a fractions calculator for the toolbox? I have yet to find a good one online.

Baroody, Arthur. __Fostering Children's Mathematical Power: An Investigative Approach to K-8 Mathematics Instruction.__ ISBN 0-8058-3105-3