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Challenge · the ninth practice

Write your own question worksheets

“A shop's coins are 1c, 4c and 6c. Write a question of your own whose answer is exactly three coins.” Every other sheet asks a child to answer. This one asks them to ask.

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Write your own question worksheet — Challenge · the ninth practice, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

NAGC, NCSM and NCTM propose a ninth practice beyond the usual eight: solve problems in novel ways, and pose new mathematical questions worth investigating. Nothing else on this site does the second half, and paper turns out to be unusually good at it — inventing a question needs no marking software, only a way of telling whether the invention works.

Why this sheet works

That is the part an exhaustive engine can supply. The key does not print one answer; it prints the whole space. With 1c, 4c and 6c the amounts needing exactly three coins are 3, 9, 11, 13, 14, 16 and 18, so a child who wrote “how few coins make 14c?” and a child who wrote “how few make 9c?” have both done it right, and a parent can see that at a glance without having had either idea.

ArithmeticWrite your own

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Invent a question that fits, then answer it yourself.

1Think of a number between 10 and 50.Write a "how many factors?" question of your own whose answer is "8 factors".Your question

2A shop accepts only 1c, 3c, and 11c coins.Choose an amount and write a “fewest coins” question whose answer is exactly 6 coins.Your question

3Think of a number between 35 and 105.Write a "how many factors?" question of your own whose answer is "6 factors".Your question

Write your ownAnswer key

1. The numbers between 10 and 50 with exactly 8 factors are 24, 30, 40, 42. Any of these makes a valid question — there are 4 to choose from, so a child's answer need not match anyone else's.2. The amounts for which the fewest possible payment uses 6 coins are 30c, 32c, 38c, 40c. Any of these makes a valid question — there are 4 to choose from, so a child's answer need not match anyone else's.3. The numbers between 35 and 105 with exactly 6 factors are 44, 45, 50, 52, 63, 68, 75, 76, 92, 98, 99. Any of these makes a valid question — there are 11 to choose from, so a child's answer need not match anyone else's.

Write your own question worksheets

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