Combine and separate groups

Join two groups

Three birds are on the grass. Two more birds land beside them. How many birds are there now?

Start with three objects. Add two objects. Count all five. The two groups join to make a whole of five:

You can count on from three: four, five. Say one new number for each of the two new birds. Do not count the starting three as one of the two new birds.

A drawing can show the same story: draw three dots, leave a small gap, then draw two more. The gap shows the parts; it does not change the total.

Check your understanding 1 More pencils

You have four pencils. You get three more. How many pencils do you have now?

Number of pencils now

Check answer

Show answer

Seven pencils: 4 + 3 = 7. Four was the starting part, three was the added part, and seven is the whole.

Take a part away

There are nine blocks. Put four blocks in a box. Five blocks stay outside.

The whole was nine. The part taken away is four. The part left is five:

The sign - means subtract. Count the five blocks left. Do not count the blocks in the box as blocks left outside.

Check by putting the groups together again: 5 + 4 = 9. You get back the whole you started with.

Find a missing part

There are eight cups altogether. Five are on a tray. The rest are on a shelf. How many are on the shelf?

The two parts are the tray cups and the shelf cups. The whole is eight. You can find the missing part in either way:

• Take the known part from the whole: 8-5 = 3.
• Count on from five to eight: six, seven, eight. That is three more cups.

Both ways give three cups. Check: 5 + 3 = 8.

Check your understanding 2 Find the hidden group

There are ten shells altogether. Six are showing. The rest are under a cloth. How many are hidden?

Number of hidden shells

Check answer

Show answer

Four shells. 10-6 = 4, and 6 + 4 = 10 checks the answer. Adding ten and six would count the showing shells twice.

Find how many more

Mia has seven counters. Ali has four. How many more counters does Mia have?

Each dot is one counter. Match one of Mia’s counters with one of Ali’s. Four counters on each side have partners. Three of Mia’s counters have no partner.

So Mia has three more counters than Ali:

Seven is Mia’s whole collection. Four is the part that matches Ali’s collection. Three is the extra part. Joining both collections would give eleven counters, but that would not tell us how many more Mia has.

If each child has four counters, every counter has a partner. The collections are equal: the difference is zero, 4-4 = 0.

Check your understanding 3 Which collection has the extra part?

Sam has four shells. Jo has nine shells. How many more shells does Jo have? Say or show which shells can be paired and which are left without a partner.

Your answer or drawing on paper

Show answer

Jo has five more shells. Four of Jo’s shells can be paired with Sam’s four shells. Five of Jo’s shells have no partner: 9-4 = 5. The difference is the extra part of Jo’s collection.

The equals sign joins equal amounts

The sign + means add; - means subtract. The sign = means has the same value as. In 3 + 2 = 5, the three and two together have the same value as five.

The equal amounts can be on either side:

Both sentences are true. The equals sign does not mean “write the answer next”. Read each side and check that the amounts match.

For subtraction, 9-4 = 5 and 5 = 9-4 are also both true. Changing which side of = the calculation is on keeps the same subtraction. Swapping the numbers in the subtraction would change it.

Check your understanding 4 Place both signs

Fill the two blanks in 4 square 9 square 5. Use one - sign and one = sign. Make the whole number sentence true.

Your completed number sentence

Show answer

4 = 9-5.

The first blank is =; the second is -. Nine take away five is four, so the two sides have the same value. 4-9 = 5 would not describe equal amounts.

Before you move on

Make a story for 7-2 = 5. Say what the seven, two and five mean. Then change your story so the same two parts join together. Which addition fact checks your subtraction?