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### Math Tools Grades 3–12 (2nd edition)

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.