What is integers (positive and negative numbers)?

Why it matters

Integers are the first time most kids work with numbers smaller than zero — temperatures below freezing, bank balances in the red, elevations below sea level, football yardage lost. They also set up every later algebra move involving negatives, so getting the signs right here pays off for years.

Worked example

A thermometer reads −4°F at 6 a.m. By noon it has risen 11 degrees. What is the temperature at noon?

1. 1

   Set up the calculation: starting temperature plus the change. −4 + 11.

   Rising means adding a positive amount. Falling would mean adding a negative.

2. 2

   Picture a number line. Start at −4 and move 11 spots to the RIGHT (because we’re adding a positive number).

   On a number line, adding a positive number moves right. Adding a negative number moves left.

3. 3

   Moving 4 spots right gets you to 0. You’ve used 4 of your 11 moves.

   Always pass through zero on the way up from a negative.

4. 4

   You have 11 − 4 = 7 more moves left. From 0, move 7 right: you land on 7.

5. 5

   So −4 + 11 = 7. The temperature at noon is 7°F.

Common mistakes

• •Treating subtraction of a negative as subtraction: writing 5 − (−3) = 2 instead of 5 − (−3) = 8. (Subtracting a negative is the same as adding a positive.)
• •Ignoring the sign on the larger number when adding numbers with different signs — e.g. writing −9 + 4 = 5 instead of −5.
• •Saying −2 is bigger than −1 because "2 is bigger than 1." On the number line, −1 is to the right of −2, so −1 is actually larger.
• •Forgetting that the negative sign attaches to a number — writing 6 − 4 instead of 6 + (−4) when both should give the same answer (2), then losing track on harder problems.

How Briveli teaches integers (positive and negative numbers)

Briveli introduces integers in Grade 6 on a horizontal and vertical number line first (thermometers, elevations, bank balances) before moving to the symbolic rules, so kids have a picture to fall back on when signs get confusing.