Number Bonds to Five

The pairs that build five.

A whole and two parts

A number bond shows one number split into two parts. The whole sits in the top circle, and the two parts sit in the circles below it. The two parts together make the whole.

Split 5 into 4 and 1. Nothing was added and nothing was taken away, so the two parts put back together make 5 again: 5 is 4 + 1. Count on from 4 to check: the next number is five, and that one step is the other part.

541

The whole, 5, is at the top. Its two parts, 4 and 1, are below it.

More than one way to split five

Five can be split another way: into 3 and 2. Hold up 3 fingers, then 2 more, and together they make 5. So 5 is also 3 + 2.

Here is every way to split 5 into two parts: 5 and 0, 4 and 1, 3 and 2, 2 and 3, 1 and 4, 0 and 5. The last three are the first three with the parts swapped, and swapping the parts gives the same whole.

532

The same whole, 5, split into 3 and 2.

Finding the missing part

When you know the whole and one part, you can find the other part. For 3 + ? = 5, take the part you know away from the whole: 5 − 3 = 2. The missing part is 2.

Or count up from the part you know until you reach the whole: after 3 comes four, five. That is 2 counts, so the missing part is 2.

The two parts do not have to be the same size, but together they must make exactly the whole. If 3 is one part of 5, the other part is 2, not 3: 3 and 3 make 6, which is more than 5.

53?

The whole is 5 and one part is 3. The question mark is the missing part.

514

5 − 1 = 4, which is what 1 needs to make 5

Find what 3 needs to make 5.

The same 5 squares at every split, from 0 + 5 to 5 + 0. With 3 squares in the left part, the other 2 are in the right part: 5 − 3 = 2.

5 squares in all: 3 are the part you know, and the 2 gold squares are the missing part.

Worked example: Five Fingers, Some Up and Some Down

Question Eva has 5 fingers on one hand. (a) She holds 2 fingers up. How many fingers are down? (b) Now she holds 4 fingers up. How many fingers are down?

  1. 1.Draw a five frame. It has 5 cells, one for each finger.

    up5??
    up5??
    The five frame has 5 cells, one for each finger.
  2. 2.Put in 2 counters for the 2 fingers that are up.

    up52?
    up52?
    There are 2 counters for the 2 fingers that are up.
  3. 3.(a) Count the empty cells: 1, 2, 3. So 2 + 3 = 5, and 3 fingers are down.

    up1235232 + 3 = 5, so 3 are down
    up1235232 + 3 = 5, so 3 are down
    (a) Count the empty cells: 1, 2, 3. 2 + 3 = 5, so 3 fingers are down.
  4. 4.(b) Put in 4 counters for the 4 fingers that are up. There is 1 empty cell. So 4 + 1 = 5, and 1 finger is down.

    up15414 + 1 = 5, so 1 is down
    up15414 + 1 = 5, so 1 is down
    (b) Now there are 4 counters for the 4 fingers that are up. 1 cell is empty. 4 + 1 = 5, so 1 finger is down.

Answer: (a) 3 fingers; (b) 1 finger

Common mistakes

  • Saying 2 fingers are down because 2 fingers are up. The two parts do not have to be the same. They have to make 5 together.
  • Putting the numbers together in part (b) to get 4 + 5 = 9. The 4 fingers are part of the 5 fingers, so count the empty cells.

More counting and comparing problems, worked step by step →

Practice Number Bonds to Five in the app