Counting From A Number
Lesson 7 of 11
Objective: SWBAT use the counting on strategy for combining two numbers.
I will gather the class in front of the SmartBoard and give them each a clipboard, pencil, and a piece of paper. I will display the dot cards 4 and 4. I will then display the dot cards 4 and 3, and then 3, 4, and 4. Each time I will ask the students to determine the total number of dots. After we have completed all three, I will ask the students if one combination helped them determine another combination.
The students will choose from the three games that were introduced in the previous lesson. All of these allow students to solve the combinations using one of three approaches: Counting All, Counting On, or Using a Known Fact. However, you want to guide kids who are still using the Counting All strategy toward the Counting On approach. You should do this through direct modeling and discussion with these kids.
For my students who have demonstrated fact fluency with up to 6+6 (two dice), I am going to offer them a chance to create a new recording sum game. I will give them three dice and a piece of graph paper, and ask them to create a game board that would work for three dice. The idea is that they will have to write the numbers 3-18. As they play, I want to make sure that they are combining two facts quickly and then counting on the third fact (unless they just know the three addend fact).
There are two videos in the resource section that document how to play the game and how a student came up with their idea for the game board.
Discussing Counting On
Before I call the students to the carpet, I want to make sure that I have identified two students who are using the counting on strategy.
I call the students to the carpet and have them face the document camera. I am using this so that students can demonstrate (to the rest of the class) how they are counting on from one number. The CCSS want students to look both for general methods and for shortcuts (CCSS.Math.Practice.MP8). By using the counting on strategy, students are using a more efficient way of solving a problem.
"During station time, I was watching how you were combining numbers. I noticed that many of you were using the counting on strategy. I am going to roll the number die (1-6) and the dot die (1-6). I would like (call student's name that you identified as using the counting on strategy) to model how they use counting on to find the combination."
I do this a few more times neil I feel most of the students are understanding this.
I want to end the session with a story problem that will give the students a chance to use the counting on strategy in a "real world situation." The CCSS want students to use addition within 20 to solve word problems involving situations of adding to, putting together, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem (CCSS.Math.Content.1.OA.A.1). Although I am pushing for students to make the developmental jump from counting all to counting on, some of the kids will not be ready for this yet and will refer back to counting all. On the other end, some students will be beyond the counting on strategy and will be using number relationships/known facts to solve problems.
I will use each piece of work to see what strategy students are using to combine numbers. I have chosen the numbers 8+7 to move to combining numbers above 10. This is a jump from previous opportunities.
As students finish the story problem, I have them play 10 Sticks. This allows students to count by tens and ones and to count on by ones from a groups of ten. There is a video in the resource section that demonstrators this game. The CCSS expect students (CCSS.Math.Content.1.NBT.B.2) to understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
- CCSS.Math.Content.1.NBT.B.2a 10 can be thought of as a bundle of ten ones — called a “ten.”
- CCSS.Math.Content.1.NBT.B.2b The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
- CCSS.Math.Content.1.NBT.B.2c The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
This game has students working on all of these expectations.