CCSS.Math.Content.1.NBT.C.6 states that students will "relate the strategy to a written method and explain the reasoning used". Students have been writing in math all year, but in this lesson I am pushing them on using high quality answers. Before I have them write though, I have them talk! Oral language develops before the written, so this gives students the practice they need to explain their thinking.
We have been working on solving story problems with BIG numbers. We have used base ten blocks, hundreds charts, number lines, cubes and counting strategies. Today we are going to practice explaining how we solved.
Great thinkers make sure they can explain their own thinking and explain other people's thinking. This helps you learn from each other!
Your thinking job today is: What do I need to include in my thinking so other people can explain what I did?
We are going to use a method called Criteria for Success; a Criteria for Success tells students exactly what the expectations are!
Criteria for Success:
When you explain your thinking today, you are going to include a few important things. These things will help your listener figure out what you did.
You need to include:
1. Your tool: What did you use to solve?
2. What did you do first, next, and last?
3. How did you count?
This writing activity is aligned to a couple of math practice standards. MP5, which asks students to "use appropriate tools strategically" aligns here because students are being expected to choose a tool that will best help them solve the problem. MP6 is also coming into play, because students need to be able to explain what tool they used and express WHY they used it, an expectation that will require them to communicate precisely about their mathematical thinking.
I make sure to tell students that they are going to practice this with their strategy today. I say: First, you will solve a problem. Then you will explain how you solved it to lots of partners!
Present Problem: I have 50 friends at my house for dinner. After dinner, 20 friends leave. How many friends are at my house now?
I'll give students 7-9 minutes to solve.
After students finish solving the problem, I'll bring all of them together and show the Criteria for Success checklist. I'll do an exemplar, and then 2 nonexamples. After each presentation I do, I'll have students "rate" me on the checklist.
I used base 10 blocks because I wanted to show the numbers in tens. First I made 50 using 5 tens. Then I took away 3 of my tens. Last I counted the left over tens. I counted by tens. I said, "10, 20."
Nonexamples: I'll give my students a copy of the checklist and have them rate me as I talk. We are pushing accountable talk, which includes good listening. See Students Working on Checklists video for what this looked like in action!
Each nonexample has a few of the elements from the Criteria for Success, but they are all missing at least one key piece. They are also very common responses from kids! This gives students a chance to practice evaluating a response before they evaluate a partner's.
1. I used a number line. I got to 20.
This response tells us the tool and the answer, but it doesn't say what they did first, next and last on the number line.
2. I used cubes. First I had 50 cubes. I took away 30 of my cubes. Last I had 20.
This responds tells us the tool and what they did first, next and last. It doesn't tell us how they counted though!
After each nonexample, I'll have students rate me on the checklist and then discuss with a partner why they gave me checks for some of the parts, and what I was missing.
Students work in an inner circle/outer circle, which is why the lesson is called "Speed Date." For more, see Inner/Outer Circle Visual video and see what this looks like in action!
Each student gets multiple checklists. They will travel with that checklist throughout the activity. See the Great Explanations List.pdf
Students take turns explaining their thinking to a partner. Each partner gets to "rate" each other. After the first round, I'll model what I would do if I didn't get a check for one of the things on the list. This helps kids learn how to understand and incorporate feedback. See Student Checklist Example for a picture of one student's checklist.
This is a really important part of MP3, "Construct viable arguments and critique the reasoning of others." Students need to be able to tell each other what they need to do to make their explanations better, and then students need to know what to do with that feedback!
I'll float and check in with kids to see how they are explaining their thinking. See Student Speed Date Discussion to hear 2 students sharing!
I'll have students work on an independent problem and write what they did. I'll make sure they self assess to see if they included all of the components.
The work will be differentiated based on what strategy students used for the initial problem.
Group A: Intervention; Students used individual cubes
These students will get numbers under 50, on the decade. The push for these students is to group those cubes into tens.
Group B: Right on Track; Students used base ten blocks consistently
These students will get numbers under 100, on the decade. The push for these students is to try counting backwards as they use their base ten blocks. This will help them bridge to a counting strategy.
Group C: Extension; Students used counting strategies to figure out 50-30
I'll push these students to the 2nd grade level of this concept: numbers off the decade. For example, they will solve 52-31.
See attached documents for independent practice!
We will end the lesson by self-assessing our writing using the rubric!