The purpose of this activity is to support students in comparing ratios that do not have a common part or whole. They do so by using their knowledge of fractions, and by expressing the part-whole relationships as fractions.
Pose the following problem, using cube models.
Which ratio has the stronger taste of blueberry? How do you know?
Look for students to consider the relationships between parts and wholes when making their decision. Watch for attention to a single part, e.g. “2:3 is stronger because it has more blueberry.”
Some students may reproduce copies of the ratios until a common part or whole is found. For example, doubling 1:2 gives 2:4 which has a common number of blueberry parts as 2:3.
Ask students to create a ratio table for the comparison and record the part whole fractions.
In this case students should know which fraction, 2/5 or 1/3, is greater. If they do not know, then explore the intervention on fractions as numbers at another time. Using a calculator is one way to compare the fractions.
2/5 = 2 ÷ 5 = 0.4 and 1/3 = 1 ÷ 3 = 0.33.
Ask students to record the inequality 2/5 > 1/3 and make a statement about the ratios. For example: “2:3 has a stronger blueberry taste because it is 2/5 blueberry. 1:2 is only 1/3 blueberry.”
Next steps
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/comparing-ratios at 9:03pm on the 26th February 2024