##
* *Reflection: Staircase of Complexity
10 More and 10 Less - Section 2: Develop the Concept

I begin this lesson talking simply about how the students can use the model of a hundred chart to understand the patterns in counting, in this case counting on by tens. However, the goal of the lesson is to move from using the model, to thinking about how the digits change as the number gets greater by tens or less by tens. The biggest idea of this lesson is to have the students understand that there is specific language of math. My students typically do very well when I ask them what ten more than a specific number is. However, when I change the language some students have a difficult time understanding.

*The Language of Math*

*Staircase of Complexity: The Language of Math*

# 10 More and 10 Less

Lesson 4 of 6

## Objective: Students will be able to identify and write the numbers that are 10 more and 10 less.

#### Activator

*10 min*

I begin this lesson by having the students take our their hundred chart. I have the students turn and talk about what they know about the way a hundred chart is set up. I give them a hint - look for patterns.

I am listening for the students to be talking about how if they move to the left the numbers become less by one, if they move to the right the numbers get greater by one, if they move up the numbers get less by 10, if they move down the numbers get greater by 10. I have some students share their thinking.

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#### Develop the Concept

*20 min*

I begin by writing 10 more than 24 is _____ on the board. Students are told to put a chip on 24 on the hundred chart.

I tell the students that I know how to do this! I'll solve this problem. I then slowly move my chip to the right, counting on by one. The goal is for my students to realize that this is not the most efficient way to add ten on a hundred chart.

I ask if they have ideas on what to do if they want to add ten more using their hundred chart. (MP 4 & 7) We've been using the hundred chart for awhile, and my students should (and do) recognize that we move down one row on the hundred chart. I ask more questions, to make sure students attend to precision when using this tool (MP 5 & 6).

*Can I move sideways when adding ten? How do I move when I'm subtracting ten?*

*What happens if I'm not being careful, and my counter sort of drifts over a row when I'm adding ten? *

*Does the "ones" change when I add ten?*

We establish that to add ten, we move straight down to the next row.

We practice several more of these examples. Even though we are using a hundred chart, the objective is to move them away from using it so I am assisting students to recognize that when we look at 10 less, the digit in the tens place goes up one number; when we look at 10 less, the digit in the tens place goes down one number (MP8)

In order to ensure the students are really understanding the concept, I write the following problem on the board:

**65 is 10 less than _____**

I ask the students to turn and talk about how they could figure the answer to this problem. Several students may answer 75 and others may say 55.

*Who thought about this problem as a comparison problem?*

I tell them to remove the 10 from the sentence and try one of their numbers (in this case 55). The sentence now says: *65 is less than 55*. I ask the students, "Does this make sense? Is 65 less than 55?" They should say no.

We try the other number students came up with: *65 is less than 75*. I ask, *"Does this make sense? Is 65 less than 75?" Yes! *

So then I place the 10 back in the sentence, and ask if the number sentence still makes sense.: *65 is 10 less than 75*. Does that make sense? I would practice several more of these examples to get the students used to the language, because that (rather than the concept of 10 less) was what was tripping them up.

This is a difficult idea because sometimes this language can be confusing. It is important to practice both ways (10 more than 24 is____ and 24 is 10 more than ____) because this develops their understanding and use of mathematical language (MP 2 & 6).

#### Resources

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#### Practice the Concept

*20 min*

In this section I have the students play the game, Race to 100. Each student will need a Race to 100 Game Board, and a transparent colored Bingo chip. The students play the game in partners, and each pair will need a 10 more 10 less spinner. The students take turns spinning the spinner. They follow the directions of the spinner (1 more, 1 less, 10 more, 10 less, lose a turn). At the beginning of the game the students might have difficulty moving because they could land on 1 less or 10 less. When they are in the top spaces or the top row they can not move, and unfortunately lose their turn.

The students play the game and try to be the first person to get on or past 100 on the hundred chart/game board.

While students are playing, I circulate, taking particular care to check in frequently on those students who had more trouble with the start of the lesson. My objective is not to stop students from "making mistakes" but to be there as a sounding board, helping them to discover information, strategies, and errors.

What do you notice about...? (MP1)

What is the same and what is different about...? (MP2)

Is there a tool that you can use to help you? (MP5)

How could you test this to check your answer? (MP7)

Is this always true, sometimes true ? How would we prove that...? (MP8)

What is happening here _____? What would happen if_____? (MP8)

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#### Summarizer

*10 min*

After the students have had the chance to play the game once or twice, I have the students come back together as a class, either at their seats or in our rug area. I write the number 67 on the board and ask the students to turn and talk with a partner about what they know about that number. There are many responses that are correct:

- It has 6 tens and 7 ones
- It is ten less than 77
- It is ten more than 57
- It is one more than 66
- It is one less than 68
- It is a two-digit number

I am looking for the students to be able to recall as much as they can about numbers. Could they draw a model for the number? What about tally marks? I really like to finish my lessons with a wrap-up that connects much of the things I have taught thus far. It helps the students see lessons as a cohesive unit, not just concepts in isolation.

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This is also a great review for any 3rd graders who may need some extra practice w/their place value skills! Thanks!

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