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Fraction Towers Building
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Fraction Towers Building
Use fractions to describe and compare coloured parts of cube towers. Simplify fractions where possible and show your reasoning.
Representing fractions with towers
1.A 15-cube tower contains 6 orange cubes, 4 purple cubes and 5 white cubes. Write the fraction of the tower represented by each colour, in simplest form.
2.Simplify the fractions 8/20, 9/12 and 14/21. Show a common factor used for each.
3.Mere's 10-cube tower has 4 green cubes. Freya's 15-cube tower has 6 green cubes. Which tower has the greater proportion of green cubes?
- Mere's tower
- Freya's tower
- They have equal proportions
4.Justify your choice by comparing 4/10 and 6/15. Include one method, such as simplifying or finding a common denominator.
Equivalent fractions and ordering
5.A tower has 20 cubes. How many cubes must be blue for blue to make up 3/5 of the tower? Write an equivalent fraction with denominator 20.
6.Arrange these fractions from smallest to largest: 5/12, 2/3, 3/4 and 7/8.
7.Draw two cube towers to show why 3/6 and 5/10 represent the same fraction. Use equal-sized cubes within each tower and clearly distinguish the shaded or coloured cubes from the unshaded ones.
Fractions beyond the tower
8.Give a New Zealand example of sharing or measuring where a fraction such as 2/5 or 3/4 would be useful. Explain what the numerator and denominator would describe.
9.A student says, “Using cube towers helps me see that 4/8 and 1/2 are equivalent.” Explain why this statement is mathematically correct using a fraction or a tower description.
2 printable pages
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