This is a level 3 number activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.
A PDF of the student activity is available.
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multiply with multiples of ten
FIO, Level 3, Number, Book 2, Pitoitoi Pecks, page 14
The context in this activity uses personification to engage students in the problem.
The activity focuses on multiplying and dividing by multiples of 10. It builds on the understanding of multiplying by 10 developed earlier in Booked! The students need to be able to see how multiplying and dividing by multiples of 10 affects the place value of the digits in the factors involved. This is a vital strategy for students if they are to progress into the advanced multiplicative stage of strategy thinking.
The expression 7 x 200 in question 1a can be thought of as 7 x 2 x 100, which becomes 14 x 100. Now the place value effect of x 100 can be used to move the 14 two places to the left and make 1 400.
Question 1b involves the expression 30 x 200. Have the students explore splitting these numbers into factors of 10 or 100. The expression then becomes 3 x 10 x 2 x 100. This can be rearranged into 3 x 2 x 10 x 100, which equals 6 x 1 000 = 6 000. Guide the students to the realisation that they can reposition the factors to group the multiples of 10 together.
In question 1c, the challenge is extended in the expression 365 x 200. This can become 365 x 2 x 100 and 730 x 100 = 73 000 as the digits move 2 places to the left.
Question 3 involves division by multiples of 10 in the equation 8 000 ÷ 200 = . Challenge the students to attempt a mental strategy for solving this. Some possibilities include:
• 80 hundreds ÷ 2 hundreds = 80 ÷ 2 = 40
• 800 x 10 ÷ 200 = 800 ÷ 200 x 10
= 4 x 10
= 40
If the students do not come up with the strategies, show them some. Explain that the idea behind the strategies is to split the numbers into factors of 10 so that we can use the place value positions as we multiply or divide.
As an extension, the students could use the personification in this activity as a model for other number stories that they could research and present to a group of classmates. They must be able to solve the problems they produce and ensure that they are sensible and can be explained to the group.
Answers to Activity
1. a. About 1 400
b. About 6 000
c. About 73 000
2. a. About 4 000
b. About 28 000
3. 40