Open Questions

These open questions focus on number and data and suit students from Kindergarten to Grade 8.

Grades K–2

Grades 3–5

Grades 6–8

Grades k–2

Grades 3–5

Grades 6–8

Grades K–2

Open Question #1

Choose a number between 1 and 100.
When would that number be a lot?
When would it not be a lot?

Sample answer:
I think 50 would be a lot of kids in a class, but it would not be a lot of fans at a professional hockey game.

Open Question #2

What might this tally graph be about? Why does that make sense?

Sample answers:
I can see there are 34 tallies in total, and I know there are 34 kids in both Grade 2 classes in our school, so I think it’s something about Grade 2 kids. I also see that there are hardly any tallies in one group, a whole lot in another, and a medium amount in the third group. I know that a lot of Grade 2 kids played soccer last year, but not as many played this year. So, I think this tally graph might be showing that 20 Grade 2 kids played soccer last year but not this year, 11 Grade 2 kids played soccer this year and last year, and 3 Grade 2 kids never played.

OR There are 34 apartments in our building. Maybe the tally graph is showing that there are 20 apartments that have families with 2 or 3 kids, 3 apartments that have families with more than 3 kids, and 11 apartments that have families with no kids. I think this tally graph is about that because I know lots of people in my building, and most of the families have 2 or 3 kids, a few have more than 3 kids, and lots have no kids.

Grades 3–5

Open Question #3

Fill in the blanks below with numbers from 1 to 9. You can use each digit only once. Then solve each equation.

× 8 = a 4 × b =

6 ÷ c = 5 ÷ d =

2 ÷ e =

Sample answers:
2 × 8 = a, so a = 16
4 × a = 3 6 , so a = 9
6 4 ÷ a = 8 , so a = 8
1 5 ÷ a = 5 , so a = 3
7 2 ÷ a = 9 , so a = 8

OR 9 × 8 = a, so a = 72
4 × a = 7 6 , so a = 19
6 8 ÷ a = 2 , so a = 34
1 5 ÷ a = 5 , so a = 3
3 2 ÷ a = 4 , so a = 8

Open Question #4

Create a bar graph or a double bar graph with a scale of 20. The total number of squares in all categories is 15, and the number in the highest or widest bar represents 140 items.

Sample answers:

Grades 6–8

Open Question #5

The product of two fractions is a lot less than their quotient.
What could the two fractions be?

Sample answers:
The two fractions could be \(\frac{5}{6}\) and \(\frac{1}{100}\) because the product is only \(\frac{5}{600}\), which is really close to 0, but the quotient is 500 ÷ 6, which is more than 80.

OR The fractions could be \(\frac{12}{13}\) and \(\frac{1}{8}\) since the product is only \(\frac{3}{26}\), but the quotient is 96 ÷ 13, which is about 7\(\frac{1}{2}\).

Open Question #6

You start with a set of data with a mean of 20. You remove one piece of data, and now the mean is 18. What could the numbers in the set of data have been at the start? What number did you remove?

Sample answer:
I started with 10, 18, 31, 13, and 28. My mean is 20. If I take away the 28, the mean becomes 18. I figured it out by knowing that if I had 5 numbers, the sum would be 5 × 20 = 100, but if I had 4 numbers, the sum would be 4 × 18 = 72. So, I needed the number that I could take away to be the difference: 100 − 72 = 28.

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Grades K–2

Open Question #1

You subtract two numbers, and the answer is a little closer to the greater number than to 0. What numbers could you have subtracted?

Sample answers:
15 − 7 = 8; 8 is closer to 15 than to 0.
OR 8 − 3 = 5; 5 is closer to 8 than to 0.

Open Question #2

An expression equivalent to 15 − 8 includes the digit 4. What could the expression be?

Sample answers:
11 − 4
OR 14 − 7
OR 24 − 17
OR 40 − 33

Grades 3–5

Open Question #3

You subtract 2 three-digit numbers, and the answer is about one-third of the smaller number.
What numbers might you have subtracted?

Sample answers:
600 − 450 = 150
OR 121 − 91 = 30

Open Question #4

You solve an equation, and the solution is 22.
What might the equation be?

Sample answers:
2x = 44
OR 23 − 1 = x
OR 45 − = 23

Grades 6–8

Open Question #5

You subtract two decimal numbers with thousandths, and the answer is about one-third of the smaller number.
What might you have subtracted?

Sample answers:
6.412 − 4.833 = 1.579
OR 37.437 − 28.123 = 9.314

Open Question #6

You solve an equation by dividing and then subtracting. What might the equation have been?

Sample answers:
4x + 32 = 212 [You might divide to get x + 8 = 53 and then subtract 8 from both sides.]
OR 3x + 9 = 27 [You might divide to get x + 3 = 9 and then subtract 3 from both sides.]