Addition & subtraction
Adding and Subtracting within 100
Year 1 · Year 2
- ✓By the end of this lesson students will be able to add a one-digit number to a two-digit number within 100.
- ✓By the end of this lesson students will be able to subtract a one-digit number from a two-digit number within 100.
- ✓By the end of this lesson students will be able to add and subtract multiples of 10 to/from a two-digit number within 100.
- ✓By the end of this lesson students will be able to use mental strategies, such as counting on or back, and partitioning, to solve addition and subtraction problems within 100.
- ✓By the end of this lesson students will be able to understand that addition can be done in any order, but subtraction cannot.
Key concepts
Every number up to 100 can be thought of as having 'tens' and 'ones'. For example, the number 34 has 3 tens and 4 ones. Understanding this helps us add and subtract.
When you add a one-digit number to a two-digit number, you usually only change the 'ones' digit. For example, in 23 + 5, you add 3 ones and 5 ones to get 8 ones, so the answer is 28. Sometimes, adding the ones makes a new ten, like in 27 + 5. Here, 7 ones + 5 ones = 12 ones (which is 1 ten and 2 ones). So, 2 tens + 1 ten = 3 tens, and 2 ones. The answer is 32.
When you subtract a one-digit number from a two-digit number, you usually only change the 'ones' digit. For example, in 38 - 6, you subtract 6 ones from 8 ones to get 2 ones, so the answer is 32. Sometimes, you need to 'exchange' a ten for ten ones if you don't have enough ones to subtract, like in 32 - 5. You can't take 5 ones from 2 ones, so you could think of 32 as 2 tens and 12 ones. Then 12 ones - 5 ones = 7 ones. So, 2 tens and 7 ones, which is 27.
When you add a multiple of 10 (like 10, 20, 30) to a two-digit number, you only change the 'tens' digit. The 'ones' digit stays the same. For example, in 45 + 20, you add 2 tens to 4 tens to get 6 tens. The 5 ones stay the same. So, the answer is 65.
When you subtract a multiple of 10 from a two-digit number, you only change the 'tens' digit. The 'ones' digit stays the same. For example, in 67 - 30, you subtract 3 tens from 6 tens to get 3 tens. The 7 ones stay the same. So, the answer is 37.
For addition, you can 'count on' from the larger number. For example, for 34 + 5, start at 34 and count on 5: 35, 36, 37, 38, 39. For subtraction, you can 'count back'. For example, for 38 - 6, start at 38 and count back 6: 37, 36, 35, 34, 33, 32. You can use a number line or your fingers to help.
Partitioning means breaking numbers into their tens and ones to make calculations easier. For example, to add 23 + 14, you can break 14 into 10 and 4. First, add the tens: 23 + 10 = 33. Then, add the ones: 33 + 4 = 37. You can also partition both numbers: 20 + 10 = 30, and 3 + 4 = 7. Then add these together: 30 + 7 = 37.
Key facts to remember
- 1Numbers are made of 'tens' and 'ones'.
- 2When adding or subtracting ones, the 'ones' digit usually changes.
- 3When adding or subtracting tens, the 'tens' digit usually changes.
- 4Counting on is a good mental strategy for addition.
- 5Counting back is a good mental strategy for subtraction.
- 6Partitioning (breaking numbers into tens and ones) helps make calculations easier.
- 7Addition can be done in any order (e.g., 3 + 5 = 5 + 3).
- 8Subtraction cannot be done in any order (e.g., 5 - 3 is not the same as 3 - 5).
Worked examples
Example 1
Calculate 42 + 6.
Answer
48
This is an example of adding ones without bridging a ten.
Example 2
Calculate 57 - 20.
Answer
37
This is an example of subtracting a multiple of ten.
Example 3
Calculate 36 + 18 using a mental strategy.
Answer
54
Another way to add 46 + 8 is to break 8 into 4 and 4. Add 46 + 4 = 50, then 50 + 4 = 54.
Common mistakes
- ✗Mixing up the 'tens' and 'ones' digits when adding or subtracting.
- ✗Forgetting to bridge a ten when adding ones (e.g., saying 27 + 5 = 212 instead of 32).
- ✗Counting incorrectly when using mental strategies like counting on or back.
- ✗Trying to subtract a larger number from a smaller number without understanding the concept (e.g., 3 - 5).
- ✗Not checking their answer to see if it makes sense.
Exam tips
- ★Always look carefully at whether you need to add (+) or subtract (-).
- ★Use a number line, your fingers, or draw pictures to help you with counting on or back.
- ★Break down bigger numbers into tens and ones to make them easier to work with.
- ★Practise your number bonds to 10 and 20 – they are super helpful for adding and subtracting bigger numbers!
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