- Home
- Canvas Guide
Partial Progress - Circles (browser only)
Multiplication and Division
Objectives
To understand doubling and halving as inverses.
To double and halve 2-digit numbers.
Resources
📄 Mystery machine A, B and C | 📄 Blank Mystery Machines | 📄 Mystery Machines Doubling And Halving | 1–20 bead string | Two sets of 20 small plastic cubes, each in a container (40 cubes in total)
Vocabulary
double | halve
Today's Lesson
Introduction
Show your student the two containers of 20 cubes. Say: Because each set of cubes is the same amount, the two of them are a double.
Then ask your student to move the two containers closer together, and establish that 20 and 20 is 40. So, double 20 is 40.
Then repeat for halving: establish we now know there are 40. Ask your student to move the two containers away from each other. Show that one of the sets is half of the total amount.
Repeat this process until your student becomes confident with the concept.
Ask: Can we write a number sentence to show double 20? Write 20 + 20 = 40.
Remind your student that this shows us that double 20 is 40 and half 40 is 20.
Explain: So, halving is the opposite, or inverse, of doubling. Remember that doubling is the same as multiplying by 2, and halving is the same as dividing by 2.
Watch this video which shows how doubling and halving are the opposites of each other, and how to use a 0-100 number line to record this visually.
Ask your student to record halving and doubling facts for other numbers on paper.
Access 📄 Mystery Machines A, B and C and show your student Machine A only. Explain that they need to use what they know about the relationship between halving and doubling to work out what the Mystery Machine is doing to the numbers.
Give your student time to think and discuss with you what the mystery machine has done, before working out that it has doubled the number.
Show Mystery Machine B to agree that it has halved the number.
Show Mystery Machine C and note that this time we can see the number coming out of the machine, but not going in. We can see that the mystery number was doubled, so what was the number? Agree that we need to find the number which is half 62 (as double the mystery number is 62).
Your student may know that half of 60 is 30. Give them a chance to say this and then model partitioning 62 into 60 + 2 to calculate half.
Main Activity
Ask your student to work through 📄 Mystery machines doubling and halving, working out the missing number or operation.
Then ask your student to make some Mystery Machines for friends/peers to solve! Use the 📄 Blank mystery machines to do this.