Approximate placement of numbers to 10 on the number line

General

Students learn to approximate the positions of numbers to 10 on the number line, when only the numbers 0 and 10 are given.

Common core standard(s)

K.CC.A.1
K.CC.A.2

Relevance

Discuss with students the importance of knowing approximately what the correct place for a number on the number line is. If you know approximately where it should be, you will be able to determine which numbers are bigger and smaller because you know where the number belongs.

Introduction

Start with a game using the number line to 10. If students don't know what a number line is, tell them it is a line with numbers placed in their correct position. They are in counting order.
Put the number cards 0 and 10 on the ground with space for the numbers between them. Give a few students cards from 1-9 and ask them to go, one by one, to stand on the number line. Show that the students with the number cards have made a number line to 10. Ask students to determine which numbers are missing from the number line. How do they figure this out? (counting, close to 0, 5, or 10, counting forward or counting backwards).

Development

Show the students the two number lines on the interactive whiteboard, one with lines, the other without. Ask students what the difference is between the two. Discuss that on the first number line you can see exactly where every number belongs and that you can't see that on the second number line. Introduce the term "approximate" and say that it means you don't know exactly but you have a rough idea. Tell students that if you place numbers on an empty number line, that they first have to find the middle. The number in the middle of 0 and 10 is 5, so that is the middle. Place a number on the number line by first determining the middle and then by looking to see if the number comes before or after the middle, and then approximating where it belongs. The first number that you'll place together is under 5. The next one is above 5. Show this step by step by moving the covers on the interactive whiteboard. Practice together with the students by placing the numbers 3 and 5 on the number line and by asking students which number they start with. Students should start with 5 because that is the middle. Check that the numbers are correctly placed by checking it against the number line below. Next practice if students can recognize a number on an empty number line. Have them start with finding the middle of the line and then by counting forward or back to find the closest number. Check if their answer is correct by comparing it to the number line below. If this is unclear for students, you can write the lines and numbers on the blank number line to show the process.

Check that students are able to approximate placement of numbers to 10 on the number line by asking the following questions:
- Which number do you first look for on a number line from 0 to 10?
- How can you figure out which number a given number is close to on a blank number line?

Guided Practice

Students first practice placing numbers on an empty number line, where the middle point of 5 has already been given and they select from given answers. Next students get the same exercise, but with fill in the blank. Finally they must determine numbers on an empty number line.

Closing

Discuss again that approximating placement of numbers to 10 on the number line will help you in the future to determine which numbers are bigger or smaller. Check that students know how to place numbers on an empty number line- by finding the middle- and then looking to see if the number is bigger or smaller than that point. Ask students to draw a number line with 0 and 10 and then to fill in the rest of the numbers. Check to see if they start at 5. Finish with a game with number cards. Set the number cards 0 to 10 on the ground. Give 9 students a number card from 1 to9. Have them walk to their approximate place on the number line, and have them explain how they know this is their place on the number line.

Teaching Tip

For students who have difficulty with working with empty number lines, have them use number lines with lines for every number. They can be completed from 0 to 10 or just have the lines as support.