Dice Rollin': Associative Property at its Most Fun!

CCSS Context:

At this point in the year, students have had many opportunities to add 2 addends together, but this is the first unit where they are asked to add 3. Many students will take to this immediately in that they will understand to make 3 groups and count all of them. However, mathematically proficient students will apply MP8, Look for and express regularity in repeated reasoning. These students will understand that there are more efficient ways to add 3 numbers. In this lesson, students are repeatedly providing the associative property-the idea that you can add 3 numbers together by combining any 2 addends first. This is a rigorous mathematical principle!

Review what we have learned:

We have been working on lots of different kinds of word problems. Today we are going to think about what happens when we add 3 numbers. 

Connect to Real Life:

It is important that we learn how to add lots of groups together because we are going to need to be able to do this in real life! Sometimes we have 3 groups we have to put together and figure out how many in all.

Objective:

Today we are going to play a fun game to help us practice adding the three numbers. Your thinking job while you play today is: What strategies can I use to make it easier to add 3 numbers?

During this lesson, we are going to start with playing the game, then come together after to share how we solved the problem. The reason we are starting with the game is because I want to see what strategies students create on their own to make it easier to add 3 numbers. This is aligned to the CCSS shift towards less scaffolded problem solving. Students do the heavy lifting; I just facilitate the process!

This game is called Magic 3. In this game, you are adding 3 numbers together. But the goal is to be able to add them up quickly.

 Magic 3 Rules:

1. Partner 1 rolls 3 dice.
2. Partner 2 writes down the number sentence on the recording sheet.
3. Partner 1 figures out how many in all.
4. Partner 2: How do you know?
5. Partner 2: Records the answer
6. Switch.

The recording sheet I'll use is attached! I'll have a chart paper version of it to model with students. 

We will practice a few rounds together on the rug. Then I'll send kids to play with a partner. Students will play 5-7 minutes and then we will come back together. They won't be ready to stop playing, but you can always remind them that they will get to play again in a few minutes.

• To help differentiate this game, think about what kind of dice you give different students. Give high students numbers only, give lower students dots only, give the middle kids a mixture to encourage counting on.

As students play, I'll be looking for different strategies that they use. See the Student Share section for the strategies I plan on sharing.

Stop the game! Bring students together to have this strategy discussion!

When you were playing this game, I saw a few different people solve the same kind of problem in very different ways. We are going to share some of the ways we added the numbers together so all of us can get some different ideas of what strategies we can use to solve these number sentences easily.

I'll show 3 different strategy levels : Low, middle, high with the same numbers. I'll use 3, 3 and 1.

Strategy 1: Count All

One strategy I saw was to count all the dots. Let’s do that together. How many in all? What’s the number sentence? Show power fingers if you used that strategy sometimes today.

Strategy 2: Count On

This friend started at 3, and then counted the rest. Let’s do that together. What was the answer? It was the same as the other one! Which one was a tiny bit faster? Why was it a little easier?

Strategy 3: Make a Bunny

The other strategy I saw was to put two of the addends together. Addend is a math word for the numbers we are adding together. We are adding 3 numbers together in this number sentence, so there are 3 addends.

Show a silent hand if you see a number sentence inside this number sentence that you already know the answer to. What number sentence do you see?

• So in this strategy, we started with 3 groups but we put 2 of the groups together first. We did 3+3 (move the two towers together) and then 1 more (move the 1 on top of it)

See Make a Bunny.tiff for how I represent this with kids:

• Let me show you how I would represent what we did. I would make a bunny. We said that 3 + 3 is 6. So I am going to draw 2 ears-one from the 3 and the other from the 3. In the bunny’s head, I am going to write what 3+3 equals, 6! That way you know I did 3+3 first and then added 1 more.

Students continue to play the game at their desks. Students continue to play with differentiated dice, as mentioned above. 

While students play, I will monitor and record which students are already combining numbers to make easier number sentences. This early assessment will help inform my planning over the next couple of days with students! I keep track on my clipboard next to student names.

The student recording sheet is attached!

I'll end the lesson whole group by presenting students with just a number sentence that has 3 addends. I want students to be able to apply what they did in the game to this ending activity! Students can then discuss in partners how they would solve.