Section A
Section B
Section C
Various Practice
100
Han says that the value of the 7 in 735,208 is 10 times the value of the 7 in 137,342. Do you agree with Han? Explain or show your reasoning.
Han is not correct. The 7 in 735,208 represents 700,000 and that is 100 times the value of 7,000, the value of 7 in 137,342.
100
480 dancers make groups of 15. How many groups are there? Explain or show your reasoning.
32
100
There are 418 students at the school. Han estimates that they each drink about 5 glasses of water each day.
About how many glasses of water do all of the students together drink in one day?
2,000. I multiplied 400 by 5.
100
What is volume?
The number of unit cubes that fill a solid figure without gaps or overlap.
200
Find the value of each product. Explain or show your reasoning.
- 27 x 53
- 518 x 6
1,431
3,108
200
What is the value of 256 divided by 4? Explain your reasoning
I can add up 200 + 40 + 6 and that's 256. They are partial quotients and put together give 256 divided by 4
200
There are 418 students at the school. Han estimates that they each drink about 5 glasses of water each day.
About how many glasses of water do all students drink together in one week?
14,000. I multiplied 2,000 by 7
200
A large cargo ship can carry between 10,000 and 15,000 shipping containers. About how many cargo ships would be needed to carry the 210,000 containers of plastic the United States ships for recycling each year? Explain or show your reasoning.
15 to 20. Sample response: I know ten 10,000s is 100,000 so twenty-one 10,000s is 210,000. I also know that 14 x 15 = 210 so 14 x 15,000 = 210,000.
300
Find the value of 7,518 divided by 6. Explain or show your reasoning.
1,253
300
Use partial quotients to find the value of 243 divided by 9
27. 
300
There are 418 students at the school. Han estimates that they each drink about 5 glasses of water each day.
About how many glasses of water do all of the students together drink in one month?
56,000. I multiplied 14,000 by 4
300
Priya made a noodle that was 456 feet long. The noodle broke into two pieces. One piece was 5 times as long as the other. How long were the two noodles? Explain your reasoning.
76 feet and 380 feet. If I put the two noodles together, that's 6 times the length of the smaller one so the length of the smaller one is 456 divided by 6 which is 76 feet. The bigger one is 5 times the length or 380 feet
400
Use the standard algorithm to find the value of 16,452 x 6.
98,712
400
The area of a rectangular field is 8,320 square yards. The width is 65 yards. How long is the field? Explain your reasoning.
128 yards. I know that the product of the length and width is the area so the quotient of the area and the width is the length.
400
There are 418 students at the school. Han estimates that they each drink about 5 glasses of water each day.
About how long do you think it would take all of the students to drink 1,000,000 glasses of water?
Around 18 months. I multiplied 56,000 by 10 and that is 560,000 which is a little more than half of one million
400
Andre is playing Greatest Product. He says the greatest product it's possible to make in the game is 987 x 65. Do you agree with Andre? Explain or show your reasoning.
- Yes. I calculated the product 987 x 65 and got 64,155. That's more than anything I got in the game so it may be the biggest.
500
Using the digits 1, 2, 3, 4, and 5 make a product that is close to 8,000.
500
Andre made a noodle that was 102 feet long. The noodle broke into two pieces. One piece was 2 times as long as the other. How long were the two noodles? Explain your reasoning.
- 34 feet and 68 feet. If I put the two noodles together, that's 3 times the length of the smaller one so the length of the smaller one is 102 divided by 3 which is 34 feet. The bigger one is 2 times the length so 68 feet.
500
Colorado is 610 kilometers long and 450 kilometers wide.
- Recall that New Mexico is about 596 km long and 552 km wide. Do you think the area of Colorado is greater than or less than the area of New Mexico? Explain your reasoning.
- What is the area of Colorado?
- It is smaller. The length is about the same but the width is less. I can also see on the map that it is smaller.
- 274,500 square kilometers. I found 61 x 45 and then multiplied that by 100.
500
Kansas and South Dakota both have rectangular shapes. Kansas is 660 km long and 343 km wide. South Dakota is 610 km long and 340 km wide.
Is the area of Kansas greater than or less than 200,000 square kilometers? Explain or show your reasoning.
- Greater. I know 600 x 300 = 18,000 and then 60 x 40 is more than 20,000 so that's already more than 200,000.