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.
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.
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.
The whole is 5 and one part is 3. The question mark is the missing part.
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.Draw a five frame. It has 5 cells, one for each finger.
The five frame has 5 cells, one for each finger. 2.Put in 2 counters for the 2 fingers that are up.
There are 2 counters for the 2 fingers that are up. 3.(a) Count the empty cells: 1, 2, 3. So 2 + 3 = 5, and 3 fingers are down.
(a) Count the empty cells: 1, 2, 3. 2 + 3 = 5, so 3 fingers are down. 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.
(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.