Using the State Curriculum: Mathematics, Grade 3

Index cards labeled 90-120, string, clothespins, copies of number lines in Activity 2 and 3, paper, pencils

Hanging Number Line

Give each student an index card labeled with whole numbers between 90 and120. Display string across the room and explain it will be used as a number line. Ask students to come up one by one in a random order and clip their cards to the string where they believe are the appropriate locations. The first student will set the benchmark for the other placements.

Have the class discuss the placements and make adjustments if necessary. Students should explain how they made their determinations. Help students see the importance of equal spacing between the numbers. If counting by ones, the tic marks on a number line would be equally spaced and increase by one. If counting by three, the spaces between the numbers would still be equal but may be larger if we want students to be able to visualize the numbers between those we are using to skip count.

Missing Numbers

Using the completed number line created in Activity 1, ask students to randomly remove 10 index cards. Discuss that the number line is still intact and the missing numbers are still there, but they just can't see the labels.

Fold the number line to only show numbers 105-120. Ask, "What happened to 90-104?" Explain that only a portion of a number line may be shown at times, but that the numbers not shown are still a part of the number line.

Practice making the number line starting at numbers other than 0.

Display the following number line.

Ask students to name the whole numbers one would find on the number line between 312 and 364. [The missing numbers are greater than 312 and less than 364.] Ask which number would be in the middle. Explain why it is in the middle.

[Possible Explanation: If I count up on the number line from 312 to 364, I find that the difference between the two numbers is 52. Half of 52 is 26. I know that since 312 + 26 = 338 and 364 - 26 = 338, the number in the middle between 312 and 364 is 338.]

Skip Counting Number Lines

Clear the number line string and re-distribute the index cards. This time, start with 3 and have the students count by threes and only label the numbers they call out (3, 6, 9, 12, 15, 18, 21, 24, 27, and 30). Leave clips in between to mark the whole numbers not shown. Repeat with another random starting value and ask students to count by a given value. For example, "My number is six. Skip count by fours." Mark six on the number line and each of the numbers named.

Ask what the "four" represents. [It is the number of units from 6 to 10, or the interval between marked numbers.]

Display the following number line.

Ask students to label the whole numbers represented by letters A and B. This is an example of skip counting by fives, but it does not start with zero. Students must recognize the equal distance between the labeled values is five units.

Answers:
A is 4
B is 19

Number Line Creation

Allow students an opportunity to create their own number line using pencil and paper. Ask students to create a number line based on these requirements:

1. It must show at least two whole numbers between 275 and 375.
2. It must show skip counting by some value other than 2, 5, or 10.

Have students share their number lines in pairs. Each partner should be able to tell what the interval is between the numbers and show other numbers on the number line to his/her partner.