The purpose of this activity is to engage students in a practical investigation that leads to comparing fractions and/or decimals quantitatively.
The background knowledge and skills that need to be established before and/or during this activity are outlined in the diagram below:
- Measuring lengths
Measure your foot length and your height.
- Calculating a fraction from a proportion
Jane’s feet are 21 cm long and she is 147 cm tall. Express the length of her feet as a fraction of her height.
- Calculating percentages
If Al gained 36 out of a possible 60 marks in a test, what percentage score did he achieve?
- Comparing quantities, such as heights
Bill is 165 cm tall and Bob is 140 cm. How much taller is Bill than Bob?
- Expressing a proportion as a percentage
Bill is 165 cm tall and Bob is 140 cm. What percentage of Bill’s height is Bob?
This activity may be carried out with step by step guidance, or by allowing the student to follow their own method of solution. The approach should be chosen in sympathy with students' skills and depth of understanding.
The arithmetic approach (show more)
- The student is able to use numerical techniques to solve a problem comparing or fractions quantitatively.
Prompts from the teacher could be:
- What will you measure your head and height with?
- Measure your head and height.
- Find, as a fraction or decimal, the ratio of your height to head height.
- We have been told that a 20% hero has a ratio of 7.3 and that a 100% hero has a ratio of 8.5. Where does your ratio fit? Explore!
The conceptual approach (show more)
- The student is able to use original techniques to solve a problem comparing decimals or fractions.