In this lesson
Adding on the number line
Addition is combining numbers. Start at the first number and move by the second:
- Add a positive → move right.
3 + 2lands at5. - Add a negative → move left.
3 + (−2)lands at1.
Try it
Drag the dots — the equation updates as you move them.
Drag with the mouse, or focus a dot and use ←/→.
Rewriting subtraction as addition
Once negatives are on the line, every subtraction can be rewritten as an addition. Drop the subtraction sign and flip the sign of the second number.
So 5 − 3 equals 5 + (−3), and 5 − (−3) equals 5 + 3. The
chip board below works on additions only; for any subtraction, apply
the rule above first, then lay down chips.
11 extra
Read the symbol by its job before you compute:
- in
−5, the minus sign belongs to the number; - in
8 − 3, the minus sign is an operation; - in
8 − (−3), the first minus says "subtract" and the second minus belongs to−3.
Is the answer reasonable?
Before reaching for an algorithm, ask: roughly how big should the
answer be, and on which side of zero? For 12 − 35, you start
near zero and move 35 left. The answer should land below zero,
somewhere near −20. The exact answer is −23, which fits. If a
calculation gave +23 or −47, the estimate would flag it as
wrong.
A reasonableness check is a bound on the answer, not a guess.
Worksheet
These aren't graded. Get them right, get them wrong. The goal is to feel out where the idea works.
Practice · Not graded
MA.7.NUM.2Practice the idea
01 / 09
What is −7 + 3?
Multiple choice: what is negative seven plus three?Drag the orange marker to figure out where you land.
Show common mistakes
Student says
“Addition always gives a bigger number, and subtraction always gives a smaller one.”
What it reveals
Pre-negative intuition. Once the second number can be negative, the operation symbol no longer decides direction; the sign does.
Targeted response
Number-line interactive. Try 5 + (−7). Adding gave −2, smaller than the start. Then try −3 − (−5). Subtracting gave +2, larger than the start. The sign of the second number sets the direction, not the operator.
Student says
“−6 − (−4) = −10.”
What it reveals
Read 'minus minus' as 'add the magnitudes': sign-rule confusion.
Targeted response
Chip board with the subtraction-as-addition preset. Start at problem 2, watch −6 + 4 cancel four zero pairs, leaving −2.
Student says
“−5 + 9 = −14.”
What it reveals
Treated + as 'combine magnitudes,' ignored the negative direction.
Targeted response
Number-line interactive. Start at −5, jump RIGHT by 9. End at +4, clearly positive.
Student says
“8 − (−3) = 5.”
What it reveals
Double-negative simplification error: treated −(−3) as just −3.
Targeted response
Rewrite the subtraction as an addition: 8 − (−3) = 8 + 3 = 11. The chip board never has to remove anything; it just lays down 11 positive chips.
Going further
Multiplication and division of integers come next. The sign rules
are different, but the underlying question is the same: what does
the − in front of a number mean?
The number line extends to decimals and fractions with finer divisions between integers. The moves stay the same.
When you add or subtract fractions and decimals later in this
strand, the curriculum names three processes that all reach the same
answer: standard algorithms (line up the place values for
decimals; convert to a common denominator for fractions), common
denominator as its own step for fractions specifically, and
expressing subtraction as related addition — the same a − b = a + (−b)
rewrite you used here, extended to rationals. Lessons 7 to 10 work
through those three explicitly; the integer chip board you've been
using is the simplest case of all three.