This is a level 4 number link activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
add and subtract integers
Games One and Two
Both games are similar to Integer Zap but also give practice with adding integers and working with three or more digits to achieve a set sum of 12 or -12. The students will need to have developed some understanding of and confidence in adding small integers to cope with the calculations required. They need to be able to
• positive + positive (for example, 5 + 3 = 8)
• negative + positive (for example, -3 + 5 = 2)
• positive + negative (for example, 5 + -3 = 2)
• negative + negative (for example, -5 + -3 = -8)
Students may benefit from some practice at solving problems such as those listed above. Challenge them to think out the answers in their head. Discuss and share responses to the question “Can you tell the class the answer and how you got it?”
Some students may need to model the problems using a two-coloured counter set. For example,
for -3 + 5 = :
Each positive and negative matching pair of counters cancel out because together they equal zero, which leaves two positive counters.
You could ask the students to explore related addition and subtraction facts using integers on a number line. The number line below shows that 6 + -4 = 2.
From this, the students can derive the rest of the family of facts.
6 + -4 = 2 2 – -4 = 6
-4 + 6 = 2 2 – 6 = -4
The students should also be able to solve these problems on a calculator once they are reasonably proficient at mental imaging. They can use calculators to check their thinking about adding and subtracting integers.
For example, to add -3 + 6 on the calculator, enter 3 +/- + 6 = . (On a DAL calculator, enter +/ 3 + 6 + = .) The +/- key will change the calculator from positive to negative. Check that the students press this key after they have entered the number. They can press the operation key in the usual way straight afterwards without overriding the negative integer sign.
While the students are playing either of the games on this page, you can watch to see who is able to carry out integer addition mentally and who needs further assistance. Game Two is an extension of Game One. It may be extended further by allowing both addition and subtraction to be used or, alternatively, by allowing bonus points to be scored for other combinations that can be found to give 12 or -12 in the same hand. One student may be assigned the job of verifying answers on the calculator. As players get better, you could set a time limit for each turn.
Answers to Activity
Two games using integers