Today your thinking job is: How can I make the two sides of this equation equal?
Hook: Present New Tool!
To start the lesson, I am going to introduce students to a new mathematical tool: the balance. I am going to use a virtual tool instead of a physical balance for 2 reasons.
You can find the online balance tool here. Just select the "Bucket Balance" from the dropdown menu, and you're on your way!
I'll explain the balance like this: "A balance compares 2 weights. When two amounts are equal, it will be straight. The heavier side, which has the greatest amount, always falls to the bottom, while the lighter amount, which has fewer, rises to the top". I'll model a few-students will think this is super cool!
Let's show this equation and see if it is equal: 5 + 5 + 2=5 + 4 + 3
Now I have an equation that is not equal yet. We have to balance it: 13 = 10 + ____
Partner talk: How many have to be on both sides to make it equal?
I'll give students whiteboards to solve and prove their answers!
Hear one student explain how he knew in the Why 3 More? video! You'll also see the expectations around listening to one student speak. All eyes are on the speaker, and everyone has to agree/disagree with their thinking. This comes from a lot of practice, and is aligned to the Speaking and Listening emphasis within the CCSS.
We will model figuring this out using the balance. We will put 13 on one side, and 10 on the other.
Let's show one more equation we need to balance: 12 = _____ - 1
I recorded student thinking on a Class Chart. See attached example!
*Number cards and equation cards should be printed on different colors so students can differentiate between the two!*
Game Rules: This game can be played in partners or can be played by individual students!
1. Pull a number card. Pull an equation card.
2. Think: How can I make the equation card match the number card?
3. Model your answer. Students should use cubes, base ten models, number lines, etc to model how they figured out this answer. This emphasizes that students are always expected to represent their thinking using mathematical tools appropriately, MP5.
I'll model playing the game a few times with students. I'll particularly make sure to model a few that have the whole unknown in the equation. These are the most tricky because they are the hardest to act out. Have students retell the story based on the number sentence: First there were some, then we took away 3, now there will be 10. They might need to be reminded of strategies we have used across the whole unit-this is a great time to refer them to anchor charts from the week!
Every time we do a new equation, I'll also model it using the balance. I'll particularly model expectations for what they should do for Step 3, Model your answer, and show students how to use the recording sheet.
Students will play the game with a partner. The game is differentiated based on number size. Most students will use numbers under 20. As an extension, students can play the game with number sentences equaling less than 100.
Watch a video of 2 students playing with extension cards here: Extension Group
Make it Equal!.docx is attached! It includes all of the number cards needed.
Make it Equal Recording Sheet.docx is also attached for students to use to record their thinking!
One of the most difficult part of teaching missing part problems is that students often immediately add the numbers. To help students see what each part of the number sentence means, students need to explain it out loud to someone. I have one little girl who has struggled on and off with this concept throughout the year. You can watch this video to see how I question her to make sure she has a deep conceptual understanding, and isn't just copying someone else's thinking. Having a deep conceptual understanding is a key component of the Common Core.
I'll present a number sentence outside of the context of the game. This is to make sure students can apply the strategies they just used to help them figure out the missing part. I'll have students do this number sentence as an exit ticket.
The number sentence I'll give kids is 12 = 7 + ___.