Open Question #1

Create a pattern block design where there are 10 blocks in total, but there are 3 more green blocks than yellow ones.

Sample answer:

Open Question #2

A pan balance has blue and red cubes on the left side and green and yellow cubes on the right side. You add 2 green cubes and 3 yellow cubes to the right side, and the sides balance. How many blue, red, green, and yellow cubes might there be on each side now?

Sample answers:
I actually used a balance and put 5 blue cubes and 4 red cubes on the left side and 3 green cubes and 2 yellow cubes on the right. But if I were to add 2 green and 3 yellow cubes, it would not balance. So, then I added 1 more red cube to the left side, and it worked. I ended up with 5 blue, 5 red, 5 green, and 5 yellow cubes.

OR I know that if I added 2 green cubes and 3 yellow cubes to make it balance, the side with blue and red cubes was 5 cubes ahead of where the green and yellow side started. I know that 11 is 5 ahead of 6, so I made the blue and red side have 11 cubes and the yellow and green side have 6 cubes to start. So, I started with 10 red cubes, 1 blue cube, 4 yellow cubes, and 2 green cubes. That means I have 10 red cubes, 1 blue cube, 7 yellow cubes, and 4 green cubes at the end.

Open Question #4

Create a pattern where you use one rule to make the 1st, 3rd, 5th, 7th, … terms and a different rule to make the 2nd, 4th, 6th, 8th, … terms. Tell what the 25th and 50th terms of your pattern would be. Sample answers: For the odd terms, I used this rule: Start at 10 and keep adding 5. For the even terms, I used this rule: Start at 4 and keep adding 2. So, my pattern is 10, 4, 15, 6, 20, 8, 25, 10, … Since 25 is odd, I figured out that I would have started at 10 and added 5 twelve times and that is 60, so the 25th term would be 70. Since 50 is even, I figured out that I would have started at 4 and added 2 twenty-four times, so that means my 50th term would be 4 + 48 = 52.

Open Question #5

You used US dollars to buy some foreign currency for travel. You paid $100 to buy the currency. You got a lot more than 100 units of the other currency. What currency might you have bought, and how much would you have gotten?

Sample answers:
I know that a US dollar is worth a lot of Mexican pesos. It’s almost 17 pesos for each dollar. So, if I had paid $100 Canadian, I would’ve gotten almost 1700 pesos.

OR I found out that you would get 88.29 Japanese yen for each Canadian dollar, so $100 US would get me 8829 yen. I would probably have to pay the exchange company a little. I checked out one company’s fee, and it was $13.44, so I would really be getting the amount of yen for $86.56, and that would be about 7642 yen.

Open Question #6

An equation of the form 3n – ☐ = ☐ has a solution that is 4 less than the solution to 4n + ☐ = ☐. Fill in the boxes to make that true.

Sample answer:
I started by using the equation 3n – 19 = 53. 3n = 72, so n = 24. That answer has to be 4 less than the solution to the other equation, so the other solution has to be 28. So, I decided to use 4n + 12 on the left, and that is 124 when n = 28. My two equations are 3n – 19 = 53 and 4n + 12 = 124.