B2.9 Use the ratios of 1 to 2, 1 to 5, and 1 to 10 to scale up numbers and to solve problems.
Activity 1: Groups Everywhere!
Step 1
Explain to students that the world around them is filled with things that come in groups, whether at school, at home, in nature, or elsewhere around them.
Place students in groups of 2 and hand out a sheet of paper that students will separate into 3 columns.
Ask students to name things that come in groups of 2, 5, and 10 and record them in their chart.
Examples
| Groups of 2 | Groups of 5 | Groups of 10 |
|---|---|---|
| Socks Mittens Eyes Legs Twins Shoes Wheels of a bicycle Ears Hands Thumbs Arms Shoulders |
Sides of a pentagon Quintuplets Toes Players on a basketball team Fingers School days in a week Cents in a nickel |
Tentacles of a squid Fingers Toes |
Step 2
Give each group about 40 interlocking cubes.
Choose a grouping suggestion from the class list (for example, 2 mittens).
Ask students to solve the problem below using interlocking cubes.
There are 5 pairs of mittens in the bin. How many mittens are there?
Ask students to represent the proportional relationship between the two quantities using an illustration, a double number line or a table of values.
Example
Give students time to solve the problem and discuss their solution with their partner.
Continue this activity with the various groupings of 2, 5, and 10 by creating problems (keeping in mind that students have about 40 interlocking cubes) and having students solve them.
Source: adapted and translated from Les mathématiques… un peu, beaucoup, à la folie!, Guide pédagogique, Édition révisée, Numération et sens du nombre, 3e année, Module 2, Série 1, Activité 1 - Des groupes tout autour de nous, p. 215-216.
Activity 2: Mixing the Juice
For track and field day, students in Ms. Guerin's class prepare juice for the runners. For each container of juice concentrate, they need to add 5 containers of water. How many containers of water will they need to add to 4 containers of juice concentrate?
This will require 20 containers of water.
Activity 3: The Notebooks
Present the following problem to students and ask them to solve it using the strategy of their choice.
The notebooks distributed to schools are sold in packs of 10.
- How many notebooks are there in 5 packs? (50 notebooks)
- If the school needs 100 notebooks, how many packs should it order?(10 packs)