Open Question #1

A 3-D shape has one face that looks like this:

What might the shape look like?

Sample answers: E.g.,

Open Question #2

In a pattern, these 3 shapes are in a row:

What might the core of the pattern be?

Sample answers: E.g., OR OR

Open Question #3

Name two attributes of a shape that could not be true at the same time.

Sample answers: E.g., A triangle could not be a right triangle and have all equal sides. OR A square could not have two sides that are different lengths. OR A hexagon could not have all equal sides and at least one angle of 150°.

Open Question #4

You extend a growing pattern, and the terms 48 and 64 are in the pattern but are not next to each other.
What might the pattern be?

Sample answers: E.g., 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, … OR 40, 48, 56, 64, 72, 80 …

Open Question #5

Complete this sentence three different ways.

A triangle could have a 60° angle if …

Sample answer: E.g., … it is equilateral. … it is obtuse with no angle more than 120°. … it is scalene, and no other angles are 60°.

Open Question #6

Choose a value for a and b, and create a pattern rule of the form an + b (where n is the term number) so that the number 154 is in the pattern between positions 10 and 20.

Sample answers:
E.g., If I started at 122 and went up by 2s, I think it would work. I would make a = 2 and b = 120.
It works because if 2n + 120 = 154, then n = 17, and 154 would be the 17th term:
122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, …
OR
If I started at 14 and went up by 10s, I think it would work. I would make a = 10 and b = 4.
If 10n + 4 = 154, then n = 15, and 154 would be the 15th term:
14, 24, 34, 44, 54, 64, 74, 84, 94, 104, 114, 124, 134, 144, 154, …