Open Question #1

About how big is a book that someone is likely to read to a baby?

Sample answers:
It is about 5 inches long and about 5 inches wide.
OR It is about half the size of a regular piece of printer paper.
OR It is a square with a side length about the same length as my pencil.

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.

Open Question #3

You multiply two numbers, and the product is almost 80. What might the two numbers be? Sample answers: 4 × 19 OR 2 × 38 OR 1 × 79

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:

OR

OR

Open Question #5

The circumference of a circle is 10 units greater than the perimeter of a right triangle. What could the measurements of each shape be?

Sample answers: I decided to use a 3–4–5 right triangle. It has a perimeter of 12 units. So, the circumference of the circle has to be 22 units. If I divide 22 by π, I get a diameter of about 7 units.

OR My right triangle has measurements of 1 unit, 1 unit, and √2 units. It has a perimeter of 3.414 units. That means the circle has a circumference of 13.414 units. The circle has a radius of 2.136 units.

Open Question #6

A set of data has 8 values. The range of the set is 55. The median is about half the mean. What could the values be?

Sample answer:
I made the smallest value 1 and the largest 56 so that my range is 55. I decided the median would be 7, so the mean would be 14. If the mean is 14 and there are 8 values, the sum of the values should be 8 × 14, which is 112.

My values so far are 1, __ , __ , 7, 7, __ , __ , 56.
112 – 56 – 7 – 7 – 1 = 41
I decided two of my remaining values would be 2 and 4, which are less than 7 but more than 1.
My last two remaining values could be 10 and 25, which are more than 7 but less than 56.
The data set has values of 1, 2, 4, 7, 7, 10, 25, 56.