Adding integers
The purpose of this activity is to support students to understand addition as it applies to integers.
About this resource
New Zealand Curriculum: Level 4
Learning Progression Frameworks: Measurement sense, Signpost 7-8
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.
Adding integers
Achievement objectives
NA4-2: Understand addition and subtraction of fractions, decimals, and integers.
Required materials
See Materials that come with this resource to download:
- Adding integers CM (.pdf)
1.
Use the integer cards to generalise the effect of adding positive and negative integers.
Hone says that addition always makes the number bigger. He uses 3 + 5 = 8 as an example. 8 is bigger than 3.
Arohia says that Hone is right for some examples. She thinks that addition does not always make the number bigger.
- Who do you think is right?
2.
Let students discuss the claims of Hone and Arohia.
After a while, invite them to share their ideas.
Students might mention that the addition of zero leaves the number unchanged.
3.
Use the integer cards to explicitly act out the addition of zero.
For example, make a positive four or a negative five and act by combining those collections with a set of no cards. What is the result? Generalise that adding zero results in the sum being the same as the other addend.
Record the equations:
- +4 + 0 = +4
- -5 + 0 = -5
Students might also think of examples where a negative amount is combined with a positive amount, for example, +3 + -5 = -2, as shown by the arrows below.
4.
Create further examples of equations where the sum is greater than the first addend, equal to the first addend, and less than the first addend. Examples might be:
5.
Invite students to generalise the situations in which the addition of a number makes the sum greater, less, or equal to the first addend. It is important that students focus on the effect of the operation rather than the starting addend.
- Does it matter whether, or not, the first number, addend, is positive or negative?
- What happens if the first addend is zero?
6.
Use a number line to represent the generalisation.
7.
Apply the direction model with examples, such as:
- +3 + -6 = -3
- -2 + 7 = +5
1.
Progress to balance situations where an integer is added. For example, begin with a balance of +2.
2.
Explore what happens to the balance as integer amounts are added.
- +2 + +3 = +5
- +2 + -3 = -1
3.
Explore adding three or more integers, such as +5 + -3 + -4.
4.
Explore whether, or not, the order of the addend affects the sum. For example:
Is this true? +4 + -3 = -3 + +4.
5.
Apply the addition of integers to contexts such as height above sea level, temperature, and finance.
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