##
* *Reflection: Complex Tasks
Division Strategies - Section 2: Playing a Game

It might see obvious to an adult that if you have 13 chips and you need to divide them into 4 even piles, you will have 1 left over, but for second graders that is not the case. The task is more complex than it sounds because they are not used to the concept of left over. In the past they have added and used all the chips, subtracted and used all the chips, but now I am telling them that they may or may not be able to use all the chips. This is a new concept.

Students may want to divide a number like 11 into 4 piles and put 2 in each pile and a third in 3 of the piles. The idea that those 3 can be left over confuses them. There are almost enough to have equal amounts in every pile so why not just leave it like that.

I worked with the groups helping students to make sure that each pile had an equal number of chips and that they took the extras for themselves. The modeling with the chips (MP4) helped to strengthen students grasp of the new concept of equal piles and left overs.

*Left Overs*

*Complex Tasks: Left Overs*

# Division Strategies

Lesson 2 of 16

## Objective: SWBAT use the concepts of odd and even, and arrays to divide things into equal groups.

## Big Idea: It is time to add a new strategy - division of objects into equal groups - to the student's repertoire.

*55 minutes*

#### Array Review

*15 min*

Today we will review the concept of arrays before introducing division of objects into equal sets. I hand each student a piece of graph paper. I tell them that today we will start by making arrays. I bring out the gigantic dice and ask one student to roll the first one. I ask all the students to make a row of whatever number comes up on the die. Now I ask a second student to roll the other die. Whatever number comes up, I ask students to make that number of rows. I ask students if anyone can write a math sentence to describe the array we just made. They may use addition or multiplication.

We repeat the process 2 more times.

I ask students if anyone can tell me how addition and multiplication are related? I introduce the idea that multiplication and addition are relatives - like cousins. (Multiplication is the same as repeated addition).

I tell students that today we are going to look as subtraction's relative or cousin. Can anyone guess who it might be? (Division). I am not sure if students are familiar enough with division to know that it is related to subtraction but as this is an introductory lesson, that does not make a difference at this point.

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#### Playing a Game

*15 min*

I invite students to come to the rug. I have dice and colored chips set up for groups of 2 students. I begin by demonstrating the game.

I say that the first student may take no more than 20 chips and spread them out in a line.

The second student rolls the die and rearranges the chips into as many piles as the number on the die. They put one chip in each pile and then repeat the process until there are not enough piles left to put one in each. I make sure to really stress that they need to stop putting one chip in each pile when there are not enough for every pile. I stress that the piles must all contain the same amount of chips. If there are any chips left over, the student keeps them in his/her pile. At the end of the game students count how many chips they collected. This is their final score. For example: If the first partner takes 16 chips and the second partner rolls a 5 on the die, then he/she must divide the 16 chips into 5 even piles. The one that is left over is kept by the person who rolled the die. Students are modeling division with the chips (MP4).

You can decide if the highest or lowest number of chips should win the game. I tend to vary which will win just to keep students interested, and also to prevent "cheating".

I partner students up and let them play for 10 minutes. I circulate around to check in with different groups and see if they are able to understand how to divide up the chips.

#### Resources

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I tell students that we will create a garden divided into rows. I pass out 4 types of seeds, a plate of glue for each group and a large green sheet of paper. I ask students to divide their garden into 4 even rectangles by folding the paper in half lengthwise and in half again widthwise.

Now I ask them to use a crayon to trace along the folds. They will be able to "plant" 4 different sections in their garden. I tell them that I will tell them how may seeds can be put in each garden section.

*For the first section you must have 12 seeds divided into 3 even rows. *I let students take the seeds and try to arrange them. Then I ask, *How many seed can you put in each row?* (4). Students glue on their seeds. I ask if anyone can give me a math sentence for this. I write the math sentence on the board. I am hoping a student will suggest 4 + 4 + 4 or 3 + 3 + 3 + 3. If they suggest 6 + 6, I say, that is true but does it match our picture? We can use 6 + 6 to solve the problem when we add 2 rows together 3 + 3,and two more rows together 3 + 3.

*In the next section part of your garden you can plant 18 seeds.* *You need to put the seed in 6 even rows.* I let students take the seeds and try to arrange them. Then I ask,* How many seeds can you put in each row?* (3) Again I ask for a volunteer to tell us a number sentence for the garden and I write it on the board.

*In the next section of the garden you can plant 20 seeds in 4 even rows.* I let students take the seeds and try to arrange them. Then I ask, *How many seeds can you put in each row?* (5) We write a number sentence. In all of these it would also be possible for a student to say 20 - 5-5-5-5 to show that they started with twenty and took away 5 each time they built a row. If this does not come up, I demonstrate this for students at the end of the garden planting.

*In the last section of your garden you can plant an even number of seeds in even rows.* *You can't have more than 24 seeds in this garden plot.* I let students create their own division array in the last section of the garden.

I end out gardening by telling students they can have 5 minutes to decorate each garden plot so they remember what they planted.

#### Resources

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#### Closing

*5 min*

Students created a Strategies Booklet in a previous lesson. I ask them to take out their booklet and to copy the 12 seeds of their garden plot on the empty page just as it looks on their paper, at the end of the booklet so they remember that division into equal rows or groups is another way to solve math problems. I ask them to copy the math sentence that goes with the 12 into their booklet as well.

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- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work

- LESSON 1: My Special Strategies
- LESSON 2: Division Strategies
- LESSON 3: Estimation as a Strategy for Checking Work
- LESSON 4: Using Math at Work
- LESSON 5: Measurement Strategies
- LESSON 6: Double-Digit Subtraction - We Can Do It
- LESSON 7: Where On The Line?
- LESSON 8: Stop, Look and Check
- LESSON 9: Stop, Look and Check (Part 2)
- LESSON 10: Attributes of Groups
- LESSON 11: Relative Size
- LESSON 12: Counting Coins Again
- LESSON 13: Another Visit to Double-Digit Work
- LESSON 14: Visiting the Olympics
- LESSON 15: Creating Math Games
- LESSON 16: Playing Our Own Games