You already know that when you want to combine equal groups you multiply and we have discovered a relationship between multiplication and division. Today you will be learning that when you want to share equally you can divide. Name some things you share with your friends (toys, pencils, stickers). How do you decide how to share equally?
Now, I need your help with this problem I have. Four of my friends picked 20 apples.
I place 20 counters out in front of 4 students.
They want to share them equally, you know, so nobody gets upset about how many the other person has. How many apples should each person get?
Give students a chance to work in pairs, using counters or other manipulatives (MP5). I focus here on the common core standards that require students to understand division as the number of objects in equal shares. I invite students to share their work and solutions. The Mathematical Practice that I emphasize in this section is students making sense of, and persevering in solving, problems (MP1). In 3rd grade, students are still developing the language of thinking, and so I think it is important to provide meaningful experiences for students to explain themselves and the meaning of a problem.
The end goal of this lesson, and this progression of lessons, is for students to develop fluency in solving multiplication and division problems. When students understand the relationship of related facts they are able to solve problems more fluently.
When you share things equally, you separate or divide them into equal groups. Division is an operation you can use to find how many groups and how many are in each group when you divide things up.
Write on the board: 20 apples shared by 2 friends; 20 apples shared by 5 friends.
Work with your partner. For each problem, draw a picture and write a division sentence to find how many apples each person will get. Remember that we want to share equally between people!
Here I allow students about 5 minutes to do their work. I do not rush them if they are all engaged, using accountable talk and explaining their reasoning to their partner.
I saw some really good examples of sharing equally from each group! In what ways did you guys discover that can you divide 20 apples into equal groups? (1 group of 20; 10 groups of 2; 20 groups of 1).
When students share their work I focus on their ability to make sense of the problem, how they determined which strategy to use to solve, and what model and tools they used. Students are often able to teach one another about their own thinking when you focus on having them explain their reasoning.
I think you’re ready for more practice. I want you to be thinking about dividing equally as you solve problems and make sure you draw a picture or model so I can see just how you solved each problem. (MP6)
At each table I place word problem cards that require division, with divisors up to 10. The problems use student names and real world situations so that students have a meaningful context for their work. Each table also has a large piece of paper with 10 circles drawn on it for those students who need something tangible to put their objects in as they divide. I model using only 2 of the circles if my problem calls for dividing 2 ways.
Standard 3.OA.3 states that students solve word problems, using drawings an equations. So it is important my students have practice making sense of word problems.
Who would like to share one of the problems they solved and teach us all about the strategy they used in solving it?
As the student shares, I encourage other students to ask questions. Students must be able to explain their reasoning and defend their answers. It is in doing this that I am ensuring the students think quantitatively - that that they are making meaning of their actions (MP2) in dividing objects into equal shares (MP4), by explaining their thinking or questioning the thinking of others (MP3).
Why does your model represent division? Why is it important that you share equally? How did you know you were going to divide?