Add and subtract with tens

Count groups of ten

Put ten objects into a group. Make another group of ten. Count the groups: ten, twenty. Six groups of ten are sixty. Ten groups of ten are one hundred.

A ten and an one are different units. In 34, the 3 means three tens and the 4 means four ones. Three tens and four ones make thirty-four. In 40, the zero tells us there are no extra ones.

You can draw a long stick for a ten and a small dot for an one. Each stick must mean ten dots. Drawing the stick longer does not change its value.

Add tens to tens and ones to ones

For 23 + 14, put two tens and three ones beside one ten and four ones.

• Two tens and one ten make three tens.
• Three ones and four ones make seven ones.

The answer is three tens and seven ones: 37. Written in columns, the ones go under ones and the tens go under tens. The columns keep the units together.

Check your understanding 1 Keep the units together

Find 32 + 25. How many tens and how many ones are in your answer?

Tens in the answer

Ones in the answer

Thirty-two plus twenty-five

Check answer

Show answer

Five tens and seven ones make 57. The digit 5 names five tens, not five ones.

When the ones make another ten

Find 28 + 17. Two tens and one ten make three tens. Eight ones and seven ones make fifteen ones.

Fifteen ones can be shown as one ten and five ones. Add the new ten to the three tens you already have. Now you have four tens and five ones: 45.

Here is the same written working. Start with ones. “Sent on” means one unit of the next larger place: ten ones become one ten.

The tens total includes the ten sent from the ones. The answer digits, read from tens to ones, give 45. If the last column sends one more unit on, keep it at the front: 45 + 55 = 100, with a new hundred and zero tens and ones.

In a written addition, the small 1 carried into the tens column means one ten. It does not mean one extra one. Check with a different way: 28 + 10 + 7 = 38 + 7 = 45.

You can make ten when adding three small numbers too. For 6 + 4 + 3, combine six and four first: 10 + 3 = 13. You may regroup the addends because you still include each amount once.

Exchange a ten before subtracting

Find 43-18. Start with four tens and three ones. You need to take away one ten and eight ones. Three ones are not enough to take away eight ones.

Exchange one of the four tens for ten ones. Now 43 is shown as three tens and thirteen ones. The amount has stayed the same.

Try the model. You can change your answer or look at the worked model. This activity has no score.

Check the amounts and how they fit together. Moving a counter inside a box does not change its value. You can also draw on paper and compare with the public answer.

Show solution

The same quantity: 43 counters. Reference whole: 1 counters. Bars use the same scale.

1010101111111111111

In the written columns, “available” means the units you can now take away from. A 1 in the last column records taking one higher unit and making ten units here.

The three tens already account for the ten passed to the ones. Do not take it away a second time.

Now take away eight ones: thirteen ones minus eight ones leaves five ones. Take away one ten: three tens minus one ten leaves two tens. The answer is 25.

Check by adding the part back: 25 + 18 = 43. Two tens plus one ten, and five ones plus eight ones, give three tens and thirteen ones. Exchanging ten of those ones gives four tens and three ones again.

If you take three from eight just because eight is the larger digit, you change the subtraction. Keep the whole 43 in view and exchange its units first.

Check your understanding 2 Show the exchange

Find 52-27. Say how 52 can be shown so you can take away seven ones. Then check your result with addition.

Your exchange and addition check

Ones after exchanging

Tens after giving one ten to the ones

Fifty-two minus twenty-seven

Check answer

Show answer

52 is four tens and twelve ones. Taking away two tens and seven ones leaves two tens and five ones: 25. Check: 25 + 27 = 52. The number check compares the regrouping and final answer. Compare your written subtraction and addition check with this model too.

For 100-36, one hundred can become ten tens. Exchange one ten for ten ones, leaving nine tens and ten ones. Take away three tens and six ones: six tens and four ones remain, so the answer is 64. The hundreds column now has zero; you do not need a zero at the front of 64.

Before you move on

Explain why one ten and ten ones can replace each other. Then choose your own two-digit addition or subtraction. Use a drawing if it helps, write the calculation and check with the related operation.