Warm-up: Notice and Wonder: Toy Boxes (10 minutes)
The purpose of this warm-up is to elicit the idea that filling the wagon with with cubic cardboard boxes is different than filling the wagon with people. While students may notice and wonder many things about this image, the size of the boxes is an important discussion point.
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
- 1 minute: partner discussion
- Share and record responses.
- Focus question:
- “How is filling the wagon with boxes different than filling the wagon with people?”
Activity 1: Sand Wagon (15 minutes)
The purpose of this activity is for students to apply what they know about multiplication and division to solve problems involving the volume of the Radio Flyer. Students estimated the dimensions and volume of the wagon in the previous lesson and now they learn the actual dimensions and solve problems with those dimensions. The context in this activity is filling the wagon with sand. Students will use multiplication and division to find how many bags of sand it will take to fill the wagon and then they find the cost and weight of all of that sand (MP2). The activity synthesis focuses on a strategic way to calculate the number of bags of sand it takes to fill the Radio Flyer.
To add movement to this activity, students could create a poster for the problems and do a gallery walk to look for similarities and differences in the strategies used to multiply and divide.
- Groups of 2
27 feet long
13 feet wide
2 feet deep
- “These are the approximate dimensions of the actual Radio Flyer. How do they compare to the estimates you made in the previous lesson?” (We were close for the length and depth but the actual wagon is wider than what we guessed.)
- “Imagine the wagon was being filled with sand. Would you want to buy large bags of sand or small bags of sand? Why?” (I would want large bags because it would take fewer of them.)
- 2–3 minutes: quiet think time
- 7-8 minutes: partner work time
- A 150-pound bag of sand will fill about 9 cubic feet. How many bags of sand will it take to fill the wagon with sand?
- A 150-pound bag of sand costs about \$12. About how much will it cost to fill the wagon with sand? Explain or show your reasoning.
- How many pounds of sand does the Radio Flyer hold when it is full? Explain or show your reasoning.
- Invite students to share their responses for the number of bags of sand it takes to fill the Radio Flyer.
- Display expression: \((27 \times 13 \times 2) \div 9\)
- “How does this expression represent the number of bags of sand it takes to fill the Radio Flyer?”(The product is the number of cubic fee the wagon holds and then each bag of sand fills 9 cubic feet so dividing by 9 gives the number of bags of sand you need to fill the wagon.)
- “Jada says that she can find the value of the expression quickly by first finding the value of \(27 \div 9\). Will her strategy work? How do you know?” (Rather than finding the product of all 3 numbers and then dividing by 9, Jada notices that she can just divide 27 by 9 and that’s 3. Then she just needs to multiply 3 by 13 and 2 which is easier since they are smaller numbers.)
Activity 2: More Boxes (15 minutes)
The purpose of this activity is for students to solve another problem about the Radio Flyer using multiplication and division. Instead of filling the wagon with sand, they consider filling the wagon with boxes and determine how many boxes will fill the wagon. Unlike with the sand, the boxes do not fill the wagon completely and the number of boxes that do fit is not a divisor of the total number of boxes. Accounting for these considerations will be the focus of the synthesis. When students account for these constraints of the situation, they persevere in solving the problem (MP1).
Advances: Reading, Representing
Supports accessibility for: Memory, Attention.
- Groups of 2
- 2–3 minutes: independent work time
- 7-8 minutes: partner work
- Monitor for students who use partial quotients to find the quotient and interpret the leftover boxes.
The Radio Flyer wagon is 27 feet long 13 feet wide and 2 feet deep.
The wagon is being used to deliver 4,000 boxes that each have the side lengths 2 feet by 2 feet by 2 feet. How many trips will the wagon have to make? Explain or show your reasoning.
- Invite students to share their responses for the number of trips.
- “How did you find how many boxes will fit in the wagon?” (I counted how many rows of boxes I could fit and how many were in each row.”
- “Did the boxes fill the wagon?” (No. The length and width of the wagon are odd and the boxes are all 2 feet wide and long so there is 1 foot of empty space left on both sides.)
- “Do you think you could fit more boxes and make fewer trips?” (Yes. I could definitely fit those extra 22 boxes along the side where it is not full in all of those other trips. I would just need to be careful so they don't fall over the side.)
“What strategies for multiplication and division did you find most helpful today? Why were they helpful?” (I used the standard algorithm to multiply because some of the numbers were large and I could not see a mental strategy that would work. I used partial quotients for division. It took time but it helped me keep track of my calculations.)