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Lead Teacher Term Four Fractions 11/12 November 2011

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Body Fractions Game Arm Span = 1 One arm = half What is a quarter? Make one half, three quarters, one, etc With a partner three halves In a group of four…

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Dotty Pairs Game You need two sets of cards 1-6 or dice The children play in pairs. One child takes dots, the other takes crosses. The players take turns turning over two cards or roll the dice. The numbers are used to form a fraction e.g 2 and 5 are turned over - could make two fifths or five halves. One fraction is chosen and marked on a 0-6 number line with the players identifying mark. Winner is the person who can get three uninterrupted marks on the number line. If a fraction is already marked on the number line the player misses that turn. 0123456

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Top and bottom numbers What does the bottom number in a fraction tell us? What does the top number in a fraction tell us?

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Top and bottom numbers The top number counts The bottom number tells what is being counted.

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Fraction Language Use words first then introduce symbols with care. e.g. ‘one fifth’ not 1 / 5 How do you explain the top and bottom numbers? 1 2 The number of parts chosen The number of parts the whole has been divided into

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+ = “I ate 1 out of my 2 sandwiches, Kate ate 2 out of her 3 sandwiches so together we ate 3 out of the 5 sandwiches”!!!!! 1212 2323 3535 The problem with “out of” 8686 x 24 = 2 out of 3 multiplied by 24! 2323 = 8 out of 6 parts!

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The language Importance of building conceptual understanding (Skemp – Relational vs Instrumental) Appropriate use of materials What connections have you made between fractions and proportional reasoning?

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Summary of Fractions Key Ideas 1.Use sets as well as shapes/regions from early on 2.Fraction Language - use words first and introduce symbols carefully. 3.Go from Part-to-Whole as well as Whole-to-Part 4.Division is the most common context for fractions. 5.Fractions are not always less than 1, push over 1 early. 6.Fractions are numbers as well as operators. 7.Fractions are always relative to the whole. 8.Consider the relationship between ratios and fractions 9.Use addition/skip counting to find fractions of sets then develop and apply multiplicative thinking – Fractions are really a context for add/sub and mult/div strategies

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2011 349 – Peter Hughes paper Understanding and Extending Mathematical Thinking. 6 days – 3 Saturdays, in Whangarei, first Monday of each holiday at Dargaville Primary

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