Integer number lines
The purpose of this activity is to support students in identifying the relative position of integers on a number line.
About this resource
New Zealand Curriculum: Level 4
Learning Progression Frameworks: Measurement sense, Signpost 7 to Signpost 8
These activities are intended for students who use a range of strategies for the addition and subtraction of whole numbers. These strategies may include elements of integer thinking such as solving 52 – 28 by first solving 52 – 30, then compensating by adding two, such as 52 – 28 = 52 – 30 + 2 = 24. Students should also know their basic addition facts and the corresponding subtraction facts.
Integer number lines
Achievement objectives
NA4-6: Know the relative size and place value structure of positive and negative integers and decimals to three places.
Required materials
See Materials that come with this resource to download:
- Integers cards (.pdf)
1.
Present students with an image of a thermometer showing a temperature below zero.
- What does it mean to say the temperature is “minus 5 degrees”?
Students may know that on the Celsius scale, zero degrees (0⁰C) is the freezing temperature of fresh water. If possible, make links to a recent context in which the temperature has been below 0 degrees. Count the points on the thermometer scale to explicitly show that -5⁰C is five steps in the negative direction from zero. You might introduce relevant te reo Māori kupu within this discussion, such as paemahana (temperature) and tākiri (degree).
2.
Draw a vertical number line to represent a thermometer, and label in the middle 0 of it.
Use five negative (Integer cards) or draw 5 arrows each representing -1 to show the position of -5. Continue to locate other temperatures like +5⁰C, -3⁰C, +1⁰C, and -10⁰C on the integer number line. You might do this in conjunction with finding out about the temperature of different cities around the world.
3.
Ask students to create a horizontal integer number line using the (Integer cards).
4.
Progress towards imaging the position of numbers on the integer number line. Begin by only marking benchmark numbers like -10, 0, and 10 before locating other integers such as -2, 9, -7, and -11.
- Where is 5 on this number line? Students might jump steps from the positive one to find the location or halve the space between 0 and 10.
- Where is -5 on this number line? Students might jump steps of the negative one to find the location or halve the space between 0 and -10. They might also use symmetry and mark the position at the same distance from zero as 5, in the negative direction.
5.
Have students play a few games of Integer Squeeze in pairs. The game works as follows:
- Each player starts by drawing several number lines to use for working. Alternatively, you could use a laminated number line and whiteboard pens.
- Player A chooses an integer that is somewhere on the line.
- Player B has five chances to find the number by asking, “Is the number greater than ..." or “Is the number less than ..." questions.
6.
Discuss students’ strategies for playing the game and recording where the number might be.
- Player B: Is the number less than five (5)?
- Player A: Yes
- Player B: Is the number greater than negative five (-5)?
- Player A: Yes
1.
Pose problems where students need to locate a specific integer on the line. Clues might include:
- I am greater than -8.
- I am less than zero.
- I am at the same distance from zero as 6.
2.
Give students specific positions on integer number lines and ask them to name the number.
3.
For example, what numbers are at positions A, B, C, and D?
Look to see if students’ responses are consistent. For example, A and B have the same distance from zero. In mathematics, we say that the absolute value of A and B are the same and write |A|=|B|. Since A is half-way between 0 and -20, it must be -10, and B must be 10.
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