2nd Grade · 2.MD.B.6

Addition on a number line in 2nd grade

Addition on a number line means showing a sum (the answer to an addition) as jumps along a line of evenly spaced numbers. In 2nd grade, your child uses number lines to add and subtract within 100 and learns that each number is a distance from 0.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

2.MD.B.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

What it means, in plain words

A number line is a straight line with marks at equal spaces, labeled 0, 1, 2, 3 and so on. In 2nd grade, children see each number as a length: 7 is the distance from 0 to the 7 mark, which is 7 equal spaces. This ties number lines to rulers, where the length of an object is the number of spaces from 0.

To add, your child starts at the first number and jumps to the right by the second number. Big jumps make it quicker: for $34 + 12$ , jump 10 to 44, then 2 more to 46. To subtract, the jumps go to the left. The jumps are drawn as arcs above the line, often with only the numbers that matter written underneath.

Addition on a number line in 2nd grade also shows subtraction as a distance. The difference between 28 and 35 is how far apart the two numbers sit on the line: 7 spaces.

Your child should be able to:

Show a number as a length from 0 on a number line
Add within 100 by jumping right, using jumps of 10 and jumps of 1
Subtract within 100 by jumping left
Write the equation that matches jumps drawn on a number line

Example

What is $26 + 15$ ? Use a number line.

Start at 26.
15 is 10 and 5. Jump 10 to the right and land on 36.
Jump 5 more to the right and land on 41.
$26 + 15 = 41$ . The jumps land on 41.

Example

What is $74 - 26$ ? Use a number line.

Start at 74. Subtracting means jumping to the left.
26 is 10 and 10 and 6. Jump left 10 to 64, then 10 more to 54.
Jump left 6 more: 4 to reach 50, then 2 to reach 48.
$74 - 26 = 48$ . The jumps land on 48.

Where children usually get stuck

To show $26 + 4$ , your child says "1" while pointing at 26 and lands on 29.
The child counted the marks, starting with the mark the jumps begin from. A jump is the space between two marks, so the first jump lands on 27.
What helps. Hop a small toy along a tape measure and count each hop as it lands. The starting spot is not a hop.
For $54 - 6$ , your child jumps to the right and gets 60.
Most of the jumps so far were for adding, so jumping right has become a habit. On a number line, numbers get bigger to the right and smaller to the left.
What helps. Before each problem, ask whether the answer should be bigger or smaller than the starting number. Then ask which way that is on the line.
To add 30, your child makes 30 small jumps of 1, loses count and lands a few spaces off.
The child has not yet seen that a jump of 10 can be one hop. Long runs of 1s are slow and easy to miscount.
What helps. Count by tens together from a number like 17: 27, 37, 47. Then show that 3 jumps of 10 add 30.

Try four practice questions

Real 2nd grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
What number is missing on the number line?
A
10
B
20
C
30
D
40
Show the answer and how to solve it
The missing number is 20. The labels on the number line go up by 10 each time, so the tick between 10 and 30 must be 20.
1. 1Look at the labels on the number line: 0, 10, ?, 30. The labels go up by 10 each time.
2. 2The ? is between 10 and 30. Count up by 10 from 10 to land on the ?: $10 + 10 = 20$ . You can also count back by 10 from 30: 30 − 10 = 20.
3. 3The missing number is 20.
Common mistake. A common mistake is picking 10 or 30 — the labeled ticks right next to the ?. Those numbers are already shown on the line; the ? marks where a different number goes. Count by 10 from the visible labels to find it.
The idea underneath. Labels on a number line are equally spaced. To find a missing label, look at the labeled neighbors next to the ? and continue the counting pattern by the same amount.
2On level
What number does the point show on the number line below?
A
5
B
7
C
10
D
17
Show the answer and how to solve it
The point is at 7. Starting at the labeled mark 5 and counting two small ticks to the right gives 6, 7.
1. 1Look at the labeled marks on the number line: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. The point sits between the labeled marks 5 and 10.
2. 2Each small tick after 5 stands for 1. Count the small ticks from 5 to the point: 6, 7. The point is at the 2nd small tick after 5.
3. 3The point is at 7.
Common mistake. A common mistake is reading only the big labeled marks (0, 5, 10, 15, ...) and choosing the nearest one. When the point sits between two labels, look at the small ticks between them — each small tick is one whole number.
The idea underneath. Every small tick on this number line stands for 1. To find a value between two labeled marks, start at the closer labeled mark and count the small ticks one at a time.
3On level
Which number line shows the subtraction below?
$\displaystyle 30 - 10 = 20$
A
B
C
D
Show the answer and how to solve it
The correct number line shows a jump going LEFT from $30$ , labeled $-10$ , ending at $20$ .
1. 1Look at the subtraction: $30 - 10 = 20$ .
2. 2Subtraction means jumping LEFT on the number line. We need to start at $30$ and jump back by $10$ to land on $20$ .
3. 3The correct number line has a jump arrow pointing LEFT, labeled $-10$ , that starts at $30$ and ends at $20$ .
Common mistake. A common mistake is picking a number line where the jump goes FORWARD (right) instead of BACKWARD (left). For subtraction, the jump must go LEFT toward smaller numbers.
The idea underneath. Subtraction on a number line is always a jump going LEFT (toward smaller numbers). The number after the minus sign tells you how big the jump is.
4Stretch
The number line shows three jumps. What number do the jumps land on?
Show the answer and how to solve it
Answer. 33
The jumps land on $33$ , because $17 + 10 + 5 + 1 = 33$ .
1. 1Look at the number line. The first jump starts at 17 and goes 10 to the right.
2. 2Add 10 to 17 to find where the first jump lands.
3. 3The second jump starts at 27 and goes 5 to the right. Add 5 to 27.
4. 4The third jump starts at 32 and goes 1 to the right. Add 1 to 32.
5. 5The jumps land on 33.
Common mistake. A common mistake is adding only one or two jumps and missing the rest. Be sure to add all three — first add $10$ to $17$ to get $27$ , then add $5$ more to get $32$ , then add $1$ more to get $33$ .
The idea underneath. Each jump starts where the last one ended. To find the final number, add each jump in order to the starting number.