How to teach adding and subtracting integers

Why this matters

A student who can subtract 2 from 9 can still write 1 for the change from -4° to 3°, by combining the two numbers instead of counting across zero. On a worksheet, that 1 stays wrong until it's graded, and the teacher has to wait for quiz day to find out.

Adding and subtracting integers

Integers are the whole numbers and their opposites, such as -4, 0 and 3. On a number line, adding a positive number moves right and adding a negative number moves left. Subtracting a number is the same as adding its opposite, so 3 - (-4) = 3 + 4 = 7. The distance between two numbers on the number line is the absolute value of their difference, which is why a temperature that goes from -4° to 3° changes by 7 degrees (Common Core 7.NS.A.1).

In the Flint activity, each student fills in how much the temperature changed each day for a week, and Sparky, Flint's AI tutor, sets the story in the student's own winter interest. A student who writes 1 for -4° to 3° gets a hint about that answer: how far it is from -4 to 0, and then from 0 to 3. The hint arrives while the student is still on that day, which a worksheet graded later can't do. After each right answer, the student writes the subtraction, like 3 - (-4) = 7, and gets a harder day: a cold front, then decimals.

Leo's week at the ski resort

Leo is a middle schooler who snowboards and has a resort trip coming up in December. He adds and subtracts positive numbers without trouble and knows -5° is colder than -2°. He hasn't worked out yet what happens when the temperature crosses zero.

Every student in the class gets the same five days of temperatures and the same task: fill in how much the temperature changed from 6 a.m. to 3 p.m. Sparky sets the story in each student's interest, and its next message depends on what that student just answered.

Sparky uses Leo's interestSparky answers what Leo just said

L

Leo

Interest: SnowboardingStarting point: Fine with positive numbers

Sparky

Before we dive into some math, what do you like to do in the winter or cold weather? Skiing, snowboarding, hockey, sledding, something else?

Leo

snowboarding! im going to a resort in december

Sparky

Imagine you're a snowboarder checking the week's forecast before your big trip. Your job is to fill in the Change column: how much did the temperature change from 6 a.m. to 3 p.m. each day? Let's start with Monday: 2°F at 6 a.m. and 9°F at 3 p.m.

Leo

7

Sparky

That's right! Now write it as a subtraction expression: 3 p.m. minus 6 a.m.

Leo

9 - 2 = 7

Sparky

Tuesday's in! Two down, three to go. Now Wednesday: it was -4°F at 6 a.m. and 3°F at 3 p.m. How many degrees did the temperature change?

Leo

1

Sparky

Not quite! Think about it this way: how many degrees does it take to go from -4 to 0? And then from 0 to 3?

Leo

4 to get to 0 and then 3 more. so 7

Sparky

Yes! That's exactly the right thinking. Now write it as a subtraction expression: 3 - (-4) = ?

Leo

3 - (-4) = 7

Sparky

Wednesday is locked in. Heads up, a cold front is rolling in for Thursday! It was 3°F at 6 a.m. and -6°F at 3 p.m. How many degrees did the temperature change?

Leo

-9 because it got colder

Sparky

The temperature log is complete! You crushed it, all five days done.

Understanding check

Can you explain in your own words why subtracting a negative number gives the same answer as adding a positive number?

Leo

subtracting a negative is like taking away cold, so it gets warmer. thats why its the same as adding

Sparky

I love that explanation. When you did 3 - (-4), what did that equal? And what does 3 + 4 equal?

Wrong on Wednesday, right after one hint, then the cold front

Leo is an example student, and his chat is shortened. The spreadsheet shows all five days, including the ones left out of the chat.

What Flint did for Leo

• Sparky set the whole week in Leo's December snowboarding trip after his first answer.
• Sparky made the temperature log as a spreadsheet beside the chat and wrote in each change once Leo got it right.
• When Leo wrote 1 for -4° to 3°, Sparky asked how far it is from -4 to 0 and from 0 to 3, and didn't give the answer.
• After each right answer, Sparky asked for the subtraction, like 3 - (-4) = 7, then gave Leo a harder day: a cold front, then decimals.
• Sparky flagged Leo's Wednesday mistake for the teacher in Needs attention.

A teacher can't do this by hand for 30 students at once. Sparky does it in every student's chat.

The activity page shows who got stuck on which day

While students work, Needs attention lists each student who is stuck and the message that showed it. Once three or more students submit, activity analytics sums up what the class understood and what to practice next.

Set up the activity for free

The temperature log is in Flint's public library, with the five days, Sparky's guidelines and the greeting already written. Open it, duplicate it into a free Flint account, and assign it to a class. Every student gets their own chat with Sparky, and the activity page fills in as they work.

For more math activities, see Flint for math.