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This activity involves carefully chosen quantities that enable the students to choose a variety of strategies to use in the fraction and decimal calculations. The calculator could be used in a variety of ways, depending on the desired learning intention.
You could encourage the students to develop a sense of a reasonable answer by asking them to do a mental estimation, discuss the mental strategy with a classmate, and then check with a calculator to see how successful they were in estimating. It is important to ensure that the calculator is not used before the estimate is made and recorded.
If you want to encourage pencil and paper strategies, the calculator could be used as a checking device.
When the learning intention involves using a calculator to solve multiplication and division with decimals and fractions, the students should use a calculator from the start.
Some interesting strategies to share with students include:

• Alien 1: Divide 104 by 2 and 2 again.
• Alien 2: Divide 140 by 10 and multiply by 2.
• Alien 3: Divide 144 by 2 and that answer by 3.
• Alien 4: Divide 48 by 4, multiply by 3, and then multiply by 100.
• Alien 5: Find 1/3 of 60 and then 1/3 of 12 and add them together.
• Alien 6: Multiply 6.5 by 2 and by 2 again.
• Alien 7: Move the digits in 33.75 two places to the left of the decimal point so that you get 3 375.
• Alien 8: Find 1/4 of 100 and 1/4 of 12 and add them together.
• Alien 9: Think of 120 as 10 x 12. Divide 10 by 5 and then multiply by 12.
• Alien 10: Find 1/2 of 72 and multiply by 100.
• Alien 11: Find 1/2 of 6 000 and 1/2 of 900 and add them together.
• Alien 12: Double and halve, that is, (3.5 x 2) x (8 ÷ 2) = 7 x 4.
 

Once again, the Numeracy Project material masters 4-28 and 7-4 could be useful to help students with the conversions and to practise other conversions (available at
www.nzmaths.co.nz/node/1594).

Answers to Activity

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