Open Question #1

Stand in one of the squares on a floor number path. You want to walk forward and backwards several times and end up on the same square. How many steps forward would you go and how many steps backwards? Sample answers: I would go 1 step forward and 1 step back and then 2 steps forward and 2 steps back. OR I would go 2 steps forward and 3 steps back and 2 steps forward and 1 step back.

Open Question #2

Create a pattern that involves spoons.

Sample answers:

OR

Open Question #3

☐35 and 6☐7 are about the same distance apart as 5☐4 and ☐☐2. What might the missing digits be? Sample answer: 935 and 617 are about the same distance apart as 544 and 862.

Open Question #4

What numbers might go in the blanks to make a pattern? Why? 4, __, 10, __, __, __, 22, … Sample answer: The pattern could be 4, 7, 10, 13, 16, 19, 22, … if it’s an increasing pattern that goes up by 3 each time. OR The pattern could be 4, 4, 10, 10, 16, 16, 22, … if it starts with 4, then the previous term value is repeated, then 6 is added, then the previous term value is repeated, then 6 is added, then the previous term value is repeated, then 6 is added, and so on. OR The pattern could be 4, 8, 10, 14, 16, 20, 22, … if the rule is to start at 4, then add 4 to get the next term value, then add 2 to get the next term value, then add 4 to get the next term value, then add 2 to get the next term value, and those additions keep repeating.

Open Question #5

• Choose a number between 1000 and 5000, and write it in scientific notation.
• Now write 5 times that number in scientific notation.
• If your exponent for 10 changed, choose a different number so that it will not change when you multiply your number by 5. If your exponent did not change, choose a different number so that it will change.

Sample answer: I chose 4500 and wrote it as 4.5 × 10³. 5 times as much is 22 500, which I would write as 2.25 × 10⁴. The exponent changed, so I have to pick a smaller number. I chose 1200, which I would write as 1.2 × 10³. Then 5 times as much is 6000, which I would write as 6 × 10³.

Open Question #6

In a certain linear increasing pattern, one term is 100 times as big as another. What could the pattern be? What is the pattern rule? Are there any other terms that are 100 times as big as other terms in the pattern?

Sample answers:
The pattern could be 2, 4, 6, 8, 10, … .
The pattern rule is start at 2 and go up by 2 each time.
The number 200 is in the pattern, and it is 100 times as big as 2.
400 is also there, and it is 100 times as big as 4.

OR The pattern could be 4, 7, 10, 13, … 400 … .
The pattern rule is 3n + 1.
The number 400 is the 133rd number in the pattern, and it is 100 times as big as 4.
I wondered if 700 is also in the pattern.
700 = 699 + 1, which is 3 × 233 + 1, so 700 is also in the pattern as the 233rd number.