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Math Tools Grades 3–12 (2nd edition)

maths-tools-grades-3-12

Math(s) tools are ways to build mathematical practices, differentiate instruction and increase student engagement.

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Same denominator

There are three different situations to explore when adding fractions with the same denominator. Additions can be where:

  • the whole is completed (e.g. \(\frac{1}{4}\) + \(\frac{3}{4}\) = 1)
  • the total is less than one (e.g. \(\frac{2}{8}\) + \(\frac{1}{8}\) = \(\frac{3}{8}\))
  • the total is greater than one, which involves working with improper fractions and mixed numbers (e.g. \(\frac{2}{3}\) + \(\frac{2}{3}\) = \(\frac{4}{3}\) = 1\(\frac{1}{3}\))

Similarly, subtractions can be taking away from:

  • one whole (e.g. 1 – \(\frac{1}{4}\) = \(\frac{3}{4}\))
  • a fraction less than one (e.g. \(\frac{3}{8}\) – \(\frac{2}{8}\) = \(\frac{1}{8}\))
  • a number greater than one (e.g. 1\(\frac{1}{3}\) – \(\frac{2}{3}\) = \(\frac{2}{3}\))

Both additions and subtractions can be modelled with area diagrams or scenarios such as pieces of pizza. However, modelling these operations on a number line allows the use of counting forwards or backwards along the number line as a solution strategy.

The number line counting model can also help avoid the common misconception of adding the denominators as well as the numerators.

Number lines

Students solve problems requiring the addition or subtraction of fractions with the same denominator, modelling with area diagrams and a number line. Students begin to realise the strategy of adding the numerators.

Hit the apple

Using the digital learning object, students create a pair of fractions that add to one. There is a fraction bar representing each fraction and a vertical number line that monitors the progress towards the target of adding to one.