Fraction wafers

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Purpose

These exercises and activities are for students to use independently of the teacher to practice number properties.

Achievement Objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Specific Learning Outcomes
  • Divide items into equal pieces
  • Share by dealing pieces
  • Use the symbols for the mixed numbers and improper fractions
Description of Mathematics

Proportions and Ratios, EA (Stage 5)

Required Resource Materials
  • Practice exercises with answers (PDF or Word)
  • Homework with answers (PDF or Word)
Activity

Prior knowledge 

  • The activity ‘fraction circles’ (Book 7, pages 9 and 10) as well as fair shares (Book 7, pages 2 to 4) should have already been taught
  • Identify that in a fraction, all the pieces are the same size
  • Recognise symbols for 1/2, 1/4 etc
  • The link between the number of equal pieces an item is cut into, and the name of the fraction

Background

There are a several significant ideas that arise in this activity, and need to be addressed in the teaching that precedes these activities.

  1. It cannot be assumed that students have the skill to accurately divide a shape into equal pieces – if there are no marks or guides to work from. In the process of halving, students pass through a developmental process. A child’s understanding of one half develops through as number of stages before it can be represented precisely. As a continuous quantity, involving tasks like cutting lengths of string, these stages are:
    • One half as a multiple sequence of subdivisions, (where preschoolers simply do not know when to stop cutting…);
    • One half as a single subdivision where there is gross inequality in each part (the whole is simply cut into 2 parts);
    • One half as a single subdivision with remainder (here some attention to equality is made with the first cut, then ‘a remainder’ is usually cut off the large piece and discarded;
    • One half as a single subdivision into 2 equal parts that uses all of the material (here eye movements and/or a finger movements are used to check the relative size of the pieces before cutting, and the size of the pieces is checked after cutting).
      Cutting into 4, 3 and 5 pieces all require different strategies for success
  1. The concept of the fraction as 5 items each cut into 2 pieces is being created here. This can lead to a confusion between proper fractions and mixed numbers (3/4 and 3 3/4) as the numerator is seen as the 3 wholes…
    Working with cutting shapes and dividing written lines should be included with the written problems.

Comments on the Exercises

Exercise 1
Asks students to draw pictures to help solve problems that involve a number of people sharing equally a set of items. For example, 4 people share 3 bags of popcorn between them.  How much of a bag will each person get. In this questions there are more people than items so the answers are less than 1.

Exercise 2
Asks students to draw pictures to help solve problems that involve a number of people sharing equally a set of items. But in these questions the answers are greater than 1.

 

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Level Two