Open number line addition and subtraction, explained for parents

An open number line is a plain line with no numbers printed on it. A child writes a starting number and makes jumps that are easy to add: to the next ten, then by tens, then the ones. 38 + 25 becomes +2, +20, +3, landing on 63.

Checked October 29, 2026 against the sources listed at the end.

What an open number line is

It's called open because there are no tick marks printed in advance. The child draws a line, writes the starting number, and draws curved jumps above it, writing the size of each jump. The numbers don't need to be spaced to scale.

The jumps are chosen to be easy: first to the next ten, then whole tens, then the ones left over. That uses what children know about place value instead of counting by ones.

Adding: 38 + 25

Start at 38, jump 2 to 40, jump 20 to 60, jump 3 to 63.

Start at 38.
Jump 2 to land on 40.
Jump 20 to land on 60.
Jump 3 to land on 63.
The jumps add up to 2 + 20 + 3 = 25, so 38 + 25 = 63.

Another: 56 + 37 goes +4 to 60, +30 to 90, +3 to 93, so the answer is 93.

Subtracting by counting up: 63 − 38

For subtraction, many classes count up from the smaller number to the bigger one and add the jumps. From 38 to 63: +2 to 40, +20 to 60, +3 to 63. The jumps add to 2 + 20 + 3 = 25, so 63 − 38 = 25.

It's the same thing as asking "what do I add to 38 to get 63?", which is what subtraction means. Some children who find borrowing confusing find counting up easier.

Why schools teach it

The Common Core asks second graders to show sums and differences within 100 on a number line diagram, and to add and subtract within 100 fluently using strategies based on place value and the relationship between addition and subtraction. The open number line is one of those strategies, and it shows the distance between numbers in a way a column of digits can't.

Helping with homework

Let your child choose the jumps. There's more than one right path, and a teacher wants to see the child's thinking.
If the jumps are tiny (+1, +1, +1), suggest "can you get to a ten first?"
Check the answer by adding the jumps: they should add up to the number being added or the difference.
Don't worry about spacing. The line is a sketch, not a ruler.
If your child's teacher uses different words or a different layout, use theirs. The point is that your child hears one way of explaining it, not two competing ones; a quick note to the teacher asking "how do you want this shown?" is always welcome.

Try it

Our on-screen number line can show the jumps on the board or a laptop, and the hundreds chart shows the same moves as steps down a row. For practice, print two-digit addition with regrouping and two-digit subtraction with regrouping worksheets.

Questions parents ask

Does the number line need to be to scale?

No. It's called open because it isn't measured; the jumps just need the right labels.

Isn't this slower than the column method?

At first it can be. It builds number sense, the feel for how far apart numbers are, which makes mental math faster later. Children learn the column method for bigger numbers in fourth grade.

Practice at your child's level

Peabody, our site for children, has free stories and learning games written at each reading level and math grade, with no sign-up. Start where your child is comfortable, not where the calendar says.

Start reading on Peabody Peabody asks your child's grade, starts the stories a little under it, and moves the level as books run easy or hard.
Reading levels and math by grade Where each grade starts, and a page for every level and math path.
The free library Stories sorted by level, to read on screen.
Decodable readers Stories built from the sounds a beginning reader has been taught.

Where this comes from

Written for parents, to use alongside your child's teacher, not instead of them. General information only, not professional, medical or legal advice. Checked on October 29, 2026. Something wrong or out of date? Write to hello@peabody.kids.