Interactive open number line

What an open number line is

An open number line is a line with no numbers printed on it. You mark only the numbers you need: where you start, where each jump lands, and where you finish. Children use it to show how they added or subtracted in their heads, one jump at a time, so their thinking is visible on the page.

On this page you choose Add or Subtract and set the start number with the buttons from −100 to +100. Each Jump button adds an arc of 1, 10 or 100 to the right, or to the left when subtracting. Bigger jumps draw longer arcs, but the line is not to scale, just like one drawn by hand. The readout gives the whole equation, how many jumps of each size you made, and the answer. Give me a problem sets a sum and keeps track of how much you have added or taken away so far.

Why jumps help

Jumping in tens and ones is place value in action. To add 47 + 27, a child jumps 10 to 57, 10 to 67, then 7 ones to 74. Later they combine the ones into one jump of 7, or jump 3 to reach 50 first. The line keeps track while the child decides the jumps, so the strategy belongs to them.

Common mix-ups

• Counting the start number as the first jump. The arcs make clear that a jump starts at 47 and lands on 48.
• Jumping 10 by counting 10 ones. Ask the child to say where a jump of 10 lands before pressing the button.
• Losing track of how much has been added. The readout totals the jumps, such as 2 jumps of 10 and 7 jumps of 1.
• Going the wrong way when subtracting. On this line subtraction always jumps left, toward smaller numbers.

A 10-minute jumping routine

• Start at 35. Ask the child to add 10 three times, saying each landing number before the jump.
• Add 24 to 38 together: two jumps of 10, then four jumps of 1. Read the equation aloud.
• Press Undo until you are back at 38 and ask for a way to add 24 with the 1s first.
• Switch to Subtract. Start at 71 and take away 26 in tens and ones.
• Press Give me a problem and let the child solve it alone, then explain the jumps.

Where it fits by grade

• Grade 1: find 10 more or 10 less than a two-digit number without counting (1.NBT.C.5) and add within 100 using tens and ones (1.NBT.C.4).
• Grade 2: add and subtract within 100 fluently using place value strategies (2.NBT.B.5), and within 1,000 with jumps of 100 (2.NBT.B.7). In England, Year 2 adds and subtracts two-digit numbers and Year 3 adds and subtracts ones, tens and hundreds mentally.
• Grade 3: fluently add and subtract within 1,000 (3.NBT.A.2). The open number line stays useful for checking written methods.

Learning more

Addition and subtraction with regrouping are skills on Eurekami's skill map, and Daily Practice brings them back when they start to fade. Lessons draw diagrams live from the numbers in each question, and the AI tutor checks each line of a child's working and points to the first line that goes wrong.