Keep your shirt on - Number sense link
This is a level 4 number activity from the Figure It Out series. It is focused on rounding to the nearest whole number and using mental strategies to solve multiplication problems. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers’ notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Round to the nearest whole number.
- Use mental strategies to solve multiplication problems.
Keep your shirt on
Achievement objectives
NA4-1: Use a range of multiplicative strategies when operating on whole numbers.
Required materials
- Figure It Out, Link, Number Sense, Book One, "Keep your shirt on", page 23
See Materials that come with this resource to download:
- Keep your shirt on activity (.pdf)
Activity
This activity encourages students to use rounding to simplify the process of calculating in multiplication and division contexts.
The error caused by rounding accumulates, so it would be a good idea to display the estimated answer and then the adjusted, accurate answer to help the students develop an awareness of this fact.
Question 1 recording may look like this:
How I estimated |
How I adjusted the estimate |
|---|---|
$15.95 can be thought of as $16 |
This is 5c too much. |
|
|
$16 x 25 = $16 x 100, then divide by 4 = $1,600 ÷ 4 = $400 |
This is 5c x 25 too much ($1.25). $400 − $1.25 = $398.75 is therefore the accurate answer. |
Question 2 is a great opportunity to ask the students to look for connections between question 1 and each part of question 2 to find easy ways of calculating the answers.
List the final equation for question 1 and then all the open equations for each part of question 2:
- 1: 25 x $15.95 = $398.75
- 2a: 25 x $19.95 = ?
- 2b: 75 x $15.95 = ?
- 2c: 23 x $15.95 = ?
- 2d: 25 x $7.95 = ?
Ask the students to look for things that are the same and things that are different between the questions. Encourage them to use these observations to find easy ways of getting a solution.
For example, Question 2a can be solved by adding $4 x 25 to question 1 because the shirts are $4.00 more but the same number (25) is being purchased. Question 2b is three times the answer to question 1. Question 2c is two lots of $15.95 less than question 1. Question 2d is 25 x $8 less than question 1 ($15.95 – $8.00 = $7.95). Question 3b asks for the approximate cost, so make sure that the students use rounded amounts in their calculations. The 50 shirts will cost approximately $600, so they could find the cost of one shirt by dividing by 100 and then doubling. The equation for this is $600 ÷ 100 x 2 = $12. They could also divide by 10 and then by 5: $600 ÷ 10 = $60, then $60 ÷ 5 = $12.
Alternatively, if they look at it simply as 600 ÷ 50, they may realise that they can divide both numbers by 10 and get 60 ÷ 5 = 12.
Encourage the students to report on two or three ways of thinking through the problems. Help them to form a recording model that accurately reflects the language they use.
1.
Methods will vary. You could calculate your answer like this:
16 x 25 = 4 x 100
= 400
so:
15.95 x 25 = 400 – (25 x 0.05)
= 400 – 1.25
= 398.75
2.
Answers may vary. Possible methods include:
a. Take the answer to question 1 and add 25 x 4 = $100 to make up for the price increase. 398.75 + 100 = $498.75.
b. Multiply the answer to question 1 by 3: 398.75 x 3 = $1,196.25.
c. Take 2 x $15.95 from the answer to question 1:
- 398.75 – 31.90 = $366.85
d. Take 25 x 8 = $200 from the price in question 1: 398.75 – 200 = $198.75
3.
a. The exact answer is $598.13. (25 x 15.95 = 398.75. Half of $398.75 is $199.38. 398.75 + 199.38 = $598.13)
b. Approximately $12. (The exact answer is $11.96.) $598.13 is nearly $600. 600 ÷ 50 = 12.
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