Virtual number bonds

What a number bond shows

A number bond is a picture of one number split into two parts. The whole sits in the top circle and the parts sit in the two circles below, joined by lines. The same picture holds four facts at once: for 10 = 7 + 3, a child can read 7 + 3 = 10, 3 + 7 = 10, 10 − 7 = 3 and 10 − 3 = 7.

On this page you choose a whole from 5 to 20. Drag a counter to the other circle, tap it to send it across, or use the Move one buttons. Hide a part covers the right circle so a child can work out the missing part, and the challenge keeps a list of the bonds a child has found.

Why moving counters helps

When a child moves one counter and watches one part go up by 1 while the other goes down by 1, the whole stays put. That is the idea behind every mental strategy for adding and subtracting: you can rearrange a number without changing how much there is. Bonds of 10 matter most, because making a ten is how children later add 8 + 5 or 47 + 6 in their heads.

Common mix-ups

• Counting 3 + 7 and 7 + 3 as different bonds. They are the same two parts turned around, so the challenge counts them once and tells the child so.
• Forgetting 0 + 10. Moving every counter to one side is still a bond.
• Counting every counter from 1 each time. Ask the child to say the size of one part first and count on from there.
• Seeing bonds only as adding. Use Hide a part to ask "10 take away 6 is what?" so subtraction comes from the same picture.

A 10-minute bonds routine

• Set the whole to 10. Move counters across one at a time while the child says each bond aloud.
• Press Find all the bonds of 10 and let the child hunt for the six bonds, adding each one to the list.
• Ask what they notice about the list. The left numbers go up by 1 as the right numbers go down by 1.
• Play a hiding game: you set the parts with Hide a part on, and the child names the hidden part before pressing Show.

Where it fits by grade

• Kindergarten: split numbers up to 10 into pairs in more than one way (K.OA.A.3) and find the number that makes 10 (K.OA.A.4). In England, Year 1 children represent and use number bonds within 20.
• Grade 1: add and subtract within 20 using strategies such as making ten (1.OA.C.6). Wholes from 11 to 20 show a ten and some more.
• Grade 2: know all sums of two one-digit numbers from memory (2.OA.B.2). In England, Year 2 children recall facts to 20 and use them for related facts to 100.

Learning more

Addition and subtraction facts 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 teachers can print worksheets with answer keys on the same skills.