The part of the standard 4.NBT.B.6 that this lesson focuses on is the part that students can find whole number quotient and explain/show the relationship between multiplication and division. We will use equations, writing and the bubble wrap (arrays) for our model! The whole idea is that students use the bubble wrap to physically show how to find out how many whole number divisors will divide into their specific bubble total! This is also covering mastering factor pairs through using the inverse.
I am hoping students also see the relationships between the divisors and the dividend. I hope it strengthens their understanding of divisibility rules and reinforces factor pair fluency.
Materials: Large square bubble wrap packing that is an array. You can buy this in rolls or companies like Crate and Barrel ship their items in this bubble wrap. (The small round bubble wrap is staggered.) Bubble Wrap Math Thinking Sheet (See reflection)
I divided students in teams of twos and threes based on their ability levels. This made coaching their thinking processes much easier. I differentiated by giving my above grade level achieving students a HUGE piece of bubble wrap with 200 or above. The below grade level achieving students had around 96 bubbles in their wrap. I thought that was a good number for them to manipulate. It wasn't too big and overwhelming, yet it gave them enough divisors to work with.
Before we began our exploration and problem solving, I told students they could use any strategy they have learned in problem solving to figure out how they would go about the task. I told them they would use a "Thinking Trail" to help guide them in their work.
I wrote the "Thinking Trail" on the white board.
Follow this Thinking Trail As You Solve
1. How will you figure out your total amount of bubbles? (MP 1, MP 7)
2. What whole number digits are one digit and how many will you use? (MP 2)
3. How will you go about testing these digits using the bubble wrap? (MP 3)
4. How will you list the factor pairs you find that are divisible into your total? (MP 3)
5. How can you explain what divisible means using the bubble wrap? (MP 4, MP 7)
We read the questions together and I explained that I wanted them to answer to each question and list it in their notebooks.
The Fun Begins! I set up the groups around the room with their bubble wrap and roved as I watched them talk and decide how to solve their problems. They used their "Thinking Trail" questions as they worked.
The group with the largest piece tended to use what they already knew about divisibility rules instead of showing how it was divisible. They figured out quickly how to use the array to figure out the total and then started dividing on paper, rather than using the bubble wrap as a tool. They lined up pencils through the center of the bubble wrap,thinking they would find factors like that. Solving together. I brought them over to the group with the smallest amount of bubble wrap because they had solved using the bubble wrap by rolling or folding. They would roll up the bubble wrap using the lines in each row and then count. What do we remember? So, first they would roll sections of two rows of bubbles. They could explain that if there were no bubbles left, the number was divisible by whatever amount they were rolling.How are you planning on solving this? They worked together to figure out what one digit factors would divide evenly into their piece of bubble wrap. Show me how it is divisible by 2. Which led into; How can you tell if they are odd or even?
I heard students discussing the plan of using strategies. One old strategy of "Math Mountain" where the product is on the top of an inverted V ( the mountain) and the factors are on the bottoms of each of the "legs" came up. Applying an old strategy...Math Mountains!
As students finished finding all of their factor pairs at different rates, I sent them back to their desks to work on iPad math aps of their choice. When everyone was finished, I wrapped up the lesson with questions about their understanding of divisibility.What does divisibility mean? I really wanted them to be able to explain how multiplication and division are related. The group with 98 bubbles did a really fine job of explaining how they found all of their factor pairs. They talked about rolling, checking and counting at the same time. They listed their factor pairs correctly in their notebooks, only forgetting one set of factor pairs. Bubble wrap worked very well for them.
When we were all done sharing our findings, we celebrated by having a Bubble wrap popping party. They had resisted popping the bubbles really well throughout the class and they cheered when I told them they could pop all the bubbles.