This is a level 3 number activity from the Figure It Out theme series.
add and subtract with integers
Sports scores in a game such as golf provide an excellent context for working with positive and negative numbers (integers). This context also helps students to recognise the different representations of zero. For example, a golfer might score +2, –1, and –1 over three holes. The overall result for those three holes is par (or 0), which is often referred to as “all square”.
In this activity, students are performing simple additions of integers by calculating scores in relation to par. Consider a golfer who scores +3 for her first hole and –2 for her second hole. Her current score could be shown using a number line:
As an equation, this can be expressed as +3 + –2 = +1, so her overall score for the first two holes is +1 (or one over par). Reversing the scores to get –2 for the first hole and +3 for the second hole can be expressed as:
As an equation, this is –2 + +3 = +1, so her overall score is still +1. These examples show that the order of the numbers being added does not affect their sum, which is also the case with counting numbers.
The students may wish to keep track of each golfer’s score from questions 2 and 3 using a counter sliding across an integer number line. For an under-par hole, the students would slide the counter to the left, and for an over-par score hole, they would move it to the right.
Golf scores can also be used for students to investigate adding and subtracting negative numbers. Removing a negative score has the same result as adding a positive score, and removing a positive score has the same result as adding a negative score. The students can check their ideas about adding and subtracting integers using a calculator. For example, +3 + –2 = can be calculated by pushing 3, +, 2, +/– ,= . The key +/– changes the sign of a number from positive to negative
or vice versa. For example, to calculate the example above, –1 – –2 = +1, on a calculator, the students would press 1, +/–, – , 2, +/–, = .
Answers to Activity
1. a. A positive score, such as +2, shows how many shots more than the par for the hole the player had. A negative score, such as -1, shows how many shots less than par the player had.
b. The usual notation is 0 (neither over nor under par).
Both players are equal after five holes (25 shots each).
b. Both players are 4 shots over par (+4).
Susan is winning by one shot.
4. a. What hole each par is on will vary. The total par for these nine holes is 36.
b. Scorecards will vary, but the second nine should add up to 45 for Adam and 43 for Susan. A possible scorecard is:
c. Adam is +15 and Susan is +12. Susan has won the game.
5. a. Discussion will vary, but their scores would be likely to be under par because they would probably not have the high scores on some holes that Adam and Susan had.
b. Practical activity