Using chalk or masking tape, make a number line on the floor. (The students will use this to find differences on a number line by hopping from a number toward 0.) Tell the students that they will now use the number line to compare
lengths. Ask one student to hop to 5 and another to hop to 3. Then ask, “Who hopped farther? How much farther?” Repeat with other students.
Next, draw a number line with the spaces one cracker apart, draw a red ring and place 3 fish-shaped crackers and a blue ring with 2 fish-shaped crackers inside. Ask: How many more fish-shaped crackers are in the ring with 3
fish-shaped crackers? How can we find out using the number line?
| Diagram 1: Number line with numerals the distance of one fish apart |
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| Diagram 2: Circle with red fish and circle with blue
fish |
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Encourage the students to line up the crackers from the red ring with the left end of the number line.
Then ask them to place the crackers from the blue ring in a line below the first line.
| Diagram 3: Number line with fish |
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Next show how to hop back from the end of the longer line, counting the hops aloud. Have the students record the comparison using the equation notation [3 - 2 = 1] on the Differences Activity Sheet.
It is not uncommon for the students to count the lines on the number line rather than the spaces covered by the hops. You may wish to highlight the fact that in this meaning for the operation of subtraction, spaces are counted, not points on the number line. You may demonstrate this by using a length of paper the size of a fish-shaped cracker to hop back with. After several examples, show the students that they do not need to place the crackers themselves on the number line, but can mark the length with a crayon.
To enrich the students' understanding of the number line concept, model how to use the Number Line Arithmetic Tool from the National Library of Virtual Manipulatives to compare lengths. Encourage the students to use this site during math center time, and assign students to work at the site in pairs. Those not taking their turn at the computer should complete the next activities.
Put the students into pairs and give each pair fish-shaped crackers, crayons, and one number line from the Number Lines activity sheet.
Ask each student to make two sets of crackers on a piece of
paper, and then enclose each in rings of different colors. Then have the students line up the crackers carefully and draw, in the appropriate colors, a line as long as the number of crackers in the set. Then ask them to compare the
lengths on the number line to find the difference and to record the comparison in pictures and in equation form. After allowing time for exploration, call the students together to read their equations and share their number line illustrations.
As a concluding activity, pose puzzles such as "I am thinking of two numbers on the number line that have a difference of 5. The larger number is 6. What is the other number?" (If the students are ready for a challenge, you might say only: "I am thinking of two numbers on the number line that have a difference of 5. What are the numbers?") You may wish to have the students create and share similar problems. One or more of these puzzles could be added to their learning portfolios.
