##
* *Reflection: Developing a Conceptual Understanding
Where On The Line? - Section 1: Creating Number lines

The Common Core standards suggest the use of number lines as a strategy for solving math problems. Second graders should leave second grade with a variety of strategies for solving math problems. They should feel confident using and explaining those strategies (MP5).

Often, commercial number lines used in classrooms are shown with the numbers 1 - 20 written on them. Students think of the number line as a strategy for low numbers. By using an open number line (no numbers on it), students can see that the number line can be a useful tool for harder problems, and it can also be easily drawn when they need a visual to help them see how the numbers they are dealing with are related. Students started today with a completely blank line. Together we did fill in the line but only counting by 10 so students then had to visualize where numbers where between these landmarks other numbers would lie.

This lesson could be done earlier in the year, but it is also a good way to end the year by reinforcing a strategy that students have used, but have not extended to the larger numbers they are now dealing with.

*Number Line Strategy*

*Developing a Conceptual Understanding: Number Line Strategy*

# Where On The Line?

Lesson 7 of 16

## Objective: SWBAT estimate where a number would fall on an open (blank) number line, and use the line to solve math equations.

## Big Idea: Do you know where a number would be? Can you use a number line as a tool to solve problems?

*55 minutes*

#### Creating Number lines

*15 min*

I hand each student a blank number line. I use sentence strips on the single line side for this. I ask students to use a ruler and to mark the line off in 1 inch segments. We discuss the term segment, or line segment that we have used before.

Once everyone has marked the line, I ask students to write the number 336 on the first marking. Now I ask them what would come next if we are adding 10 to the number? (346). Ok, now I want you to number the line counting by 10s. I want students to be able to model with mathematics as they think about how a number line would be laid out. (MP4) Being able to add and subtract ten and one hundred from numbers to 1000 is a Common Core goal for second grade and one that most of my students have demonstrated mastery of in the past, but this review will give me another chance to make sure this is true. This is an essential skill for adding and subtracting using place value strategies.

Now that the line is numbered, I give each student a second sentence strip. I tell them that we will be playing a game on with number lines.

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#### Where On The Line Game

*15 min*

Students will practice guessing where a number might be on the number line by working with a partner. The first person will choose a number on the number line they just created (from 336 to about 500 depending on how accurately the students marked their line (MP6) and notice where it is, then he or she will cover the line with the blank sentence strip and say the number to the partner. The partner must place a chip where he/she thinks the number might be. The chip must be placed on the desk next to the line so that when the asker removes the cover, the chip remains where it was placed. Because I want students to begin to form a mental image of the line, the chip gives a close approximation of where a number might be. Students know the first and last number on the number line before they try to estimate where the number might be. They write these numbers on the 2 ends of the blank paper.

I chose the range above 300 because I want students to realize that they can use number lines for larger numbers and I want them to have a chance to cross centuries as they form a mental image and reason more abstractly about where the number might be. (MP2)

It helps to have the placer keep his/her finger on the chip as the asker removes the cover. If the child is close (in the right ball park or within 3 number marks of the correct place,) he/she gets a point.

Players switch roles and play repeats.

The idea is for students to be able to use a blank number line and to understand how it is laid out. They will use a blank number line for their independent work today.

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#### Independent Work

*15 min*

I give students a practice page asking them to add and subtract on an open number line and count by 2s, 5s or 10s to find the answers. This is a skill that students have used in the past, but they still find it necessary to number every mark by 1 and try to count singly. I have given specific directions for what to count by to help develop the use of a more informal number line to solve harder math problems.

I hope that students will gain a better understanding of the changing over decades as they use their informal number line to complete the problems. A number line shows the relationships between numbers. It is still possible for students to use an open number line to add the ones and then the tens on the same line. If the problem is 13 + 26, a child might count by ones to solve 3 + 6 = 9, and then count by tens to say 10 + 20 = 30.

I give students about 20 minutes to complete the paper. I ask them to make up their own word problems using number lines if they finish early. See: counting on a blank line.

At the end of 20 minutes, or sooner if everyone is done, I bring students together on the rug to go over the number line problems.

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#### Closing

*10 min*

Students are gathered at the rug with the papers they just completed. I begin by asking if anyone has any questions, or observations about using the blank number line to solve harder problems.

Now I ask for a volunteer to come up and show us how they solved one problem using a blank number line that I have drawn on the easel. I encourage students to ask questions about the solution and we discuss how the number line strategy works.

We continue to solve problems together as students check their own work.

*expand content*

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- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work

- LESSON 1: My Special Strategies
- LESSON 2: Division Strategies
- LESSON 3: Estimation as a Strategy for Checking Work
- LESSON 4: Using Math at Work
- LESSON 5: Measurement Strategies
- LESSON 6: Double-Digit Subtraction - We Can Do It
- LESSON 7: Where On The Line?
- LESSON 8: Stop, Look and Check
- LESSON 9: Stop, Look and Check (Part 2)
- LESSON 10: Attributes of Groups
- LESSON 11: Relative Size
- LESSON 12: Counting Coins Again
- LESSON 13: Another Visit to Double-Digit Work
- LESSON 14: Visiting the Olympics
- LESSON 15: Creating Math Games
- LESSON 16: Playing Our Own Games