Adding and subtracting with tens and ones
Adding within 100 using place value, finding ten more or ten less mentally, and subtracting multiples of ten
About four lessons of 40 to 45 minutes
Add the tens, add the ones, then put them back together
48 + 27 looks big, but it breaks into two much smaller sums. Add the tens: 40 + 20 = 60. Add the ones: 8 + 7 = 15. Now combine them: 60 + 15 = 75. Every two-digit addition works this way once you know your tens and ones.
You will also learn two fast mental tricks: finding ten more or ten less than a number instantly, without counting, and subtracting a multiple of ten from another, like 80 - 30, by working only with the tens.
- 34 + 23, split into tens and ones30 + 20 = 50, and 4 + 3 = 7, so 50 + 7 = 57
- 10 more than 47, instantly47 becomes 57, only the tens digit changes
- 80 - 30, working only with tens8 tens minus 3 tens is 5 tens, so 80 - 30 = 50
- 48 + 27, where the ones make a new ten8 + 7 = 15, so a new ten gets carried into the tens
What students will be able to do
Students will add a two-digit number to a one- or two-digit number by adding tens to tens and ones to ones, mentally find ten more or ten less than a two-digit number, and subtract a multiple of ten from another multiple of ten between 10 and 90.
- I can add a two-digit number to another number by adding the tens and the ones separately.
- I can find ten more or ten less than a two-digit number without counting.
- I can subtract multiples of ten, such as 80 - 30, using place value.
Standards this unit teaches
- 1.NBT.C.4Common Core (US)Add within 100
Add a two digit number to a one or two digit number using place value and properties of operations.
- 1.NBT.C.5Common Core (US)Ten more and ten less
Mentally find ten more or ten less than a two digit number without counting.
- 1.NBT.C.6Common Core (US)Subtract multiples of ten
Subtract multiples of ten from larger multiples of ten in the range 10 to 90 using place value.
- AC9M1N02Australian Curriculum v9 (ACARA)Place value and the role of zero (Year 1)
Partition, regroup and rename two- and three-digit numbers in different ways, including understanding the job a zero does.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Tens digit
- the left digit of a two-digit number, showing how many bundles of ten
- Ones digit
- the right digit of a two-digit number, showing how many loose ones
- Regroup
- trade ten ones for one ten when the ones add up to ten or more
- Multiple of ten
- a number made of whole tens with no leftover ones, such as 30, 60, or 80
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Adding tens to tens and ones to ones
PictorialTo add 34 + 23, split each number into its tens and ones. 34 is 3 tens and 4 ones. 23 is 2 tens and 3 ones. Add the tens together: 3 tens and 2 tens make 5 tens, which is 50. Add the ones together: 4 and 3 make 7. Combine the two results: 50 + 7 = 57.
This place-value method works because a two-digit number is just tens and ones added together in the first place, so adding two of them is really adding tens to tens and ones to ones, then recombining.
Add 52 + 36 using tens and ones.
- Split into tens and ones: 52 is 5 tens and 2 ones, 36 is 3 tens and 6 ones.
- Add the tens: 5 tens + 3 tens = 8 tens, which is 80.
- Add the ones: 2 + 6 = 8.
- Combine: 80 + 8 = 88.
Answer: 52 + 36 = 88.
- Split 41 and 27 into tens and ones before adding.
- Why does adding tens to tens and ones to ones give the correct total?
2. When the ones add up to a new ten
PictorialSometimes the ones add up to 10 or more, and that extra amount is really a new ten. Add 48 + 27: the tens give 40 + 20 = 60, and the ones give 8 + 7 = 15. Fifteen is itself a ten and 5 ones, so combine carefully: 60 + 15 = 75.
The important habit is to add the ones first and check whether they reach 10 or more before combining with the tens. Skipping that check is the single most common slip in this unit.
Add 39 + 16.
- Split into tens and ones: 39 is 3 tens and 9 ones, 16 is 1 ten and 6 ones.
- Add the ones first: 9 + 6 = 15.
- Add the tens: 3 tens + 1 ten = 4 tens, which is 40.
- Combine: 40 + 15 = 55.
Answer: 39 + 16 = 55.
- In 48 + 27, why do the ones need extra care when they add up to 15?
- Add 27 + 15. Do the ones make a new ten?
3. Ten more or ten less, instantly
AbstractTen more than a two-digit number is found without counting at all: just add 1 to the tens digit and leave the ones digit exactly as it is. Ten more than 47 is 57, because the 4 tens becomes 5 tens while the 7 ones stays a 7. Ten less works the same way in reverse: subtract 1 from the tens digit and keep the ones the same.
This works because adding or subtracting exactly ten only ever changes the tens digit; it never touches the ones digit, since ten is a whole bundle of ten ones with no loose ones of its own.
Find ten more and ten less than 56.
- Ten more: keep the ones digit 6 the same, and add 1 to the tens digit 5, making 6 tens.
- Ten more than 56 is 66.
- Ten less: keep the ones digit 6 the same, and subtract 1 from the tens digit 5, making 4 tens.
- Ten less than 56 is 46.
Answer: Ten more than 56 is 66, and ten less than 56 is 46.
- What is ten more than 73?
- What is ten less than 73?
4. Subtracting multiples of ten
AbstractA multiple of ten, like 80, is made entirely of tens with no loose ones. Subtracting one multiple of ten from another, such as 80 - 30, can be done by working only with the tens: 8 tens minus 3 tens is 5 tens, so 80 - 30 = 50. There is no need to think about ones at all, because there are none in either number.
This connects directly to basic subtraction facts you already know: if 8 - 3 = 5, then 80 - 30 = 50, because you are subtracting the same number of tens instead of the same number of ones.
Work out 70 - 40.
- Both numbers are multiples of ten, so work only with the tens: 7 tens and 4 tens.
- 7 - 4 = 3, so 7 tens minus 4 tens is 3 tens.
- 3 tens is 30.
Answer: 70 - 40 = 30.
- Work out 90 - 60 using tens.
- Why can 80 - 30 be solved using the basic fact 8 - 3?
Common misconceptions and how to address them
MisconceptionAdding 48 + 27, the child adds the tens and the ones separately but writes them side by side without recombining, such as writing '615' instead of 75.
Why it happens: The two separate results, 60 and 15, are correct on their own, but the child has not yet learned to actually add them together into one final number.
How to address it: Always finish with an explicit combining step: say 60 plus 15 equals 75, out loud, and write only the final combined total as the answer.
MisconceptionWhen adding the ones reaches 10 or more, such as 8 + 7 = 15 in 48 + 27, the child ignores the extra ten hidden inside 15 and simply writes both digits of 15 next to the tens result.
Why it happens: Regrouping (recognising that 15 ones is really 1 ten and 5 ones) is a genuinely new idea at this stage and easy to skip under time pressure.
How to address it: After adding the ones, ask: is this ones total 10 or more? If so, say it as a ten and some ones (15 is 1 ten and 5 ones) before combining with the tens total.
MisconceptionFinding ten more or ten less, the child changes the ones digit instead of the tens digit, for example thinking ten more than 47 is 48.
Why it happens: Adding any small number usually changes the ones digit, so that habit is applied here even though ten specifically only changes the tens digit.
How to address it: Say the rule every time: adding ten changes only the tens digit, the ones digit stays exactly the same. Check with a bundle model: one more bundle of ten added, the loose ones are untouched.
MisconceptionSubtracting multiples of ten, such as 80 - 30, the child treats the zeros as ordinary digits to subtract on their own, getting confused and producing an incorrect answer like 500 or 5.
Why it happens: The zero in a multiple of ten is a placeholder, not a digit to subtract independently, and that distinction is not yet automatic.
How to address it: Cover the zero and subtract only the tens digits (8 - 3 = 5), then reattach the zero to show the answer is a multiple of ten: 50, not 5 or 500.
Guided practice (with answers)
1. Add 25 + 34 using tens and ones.
Answer: 59. Tens: 20 + 30 = 50. Ones: 5 + 4 = 9. Combine: 50 + 9 = 59.
2. Add 39 + 16 using tens and ones.
Answer: 55. Tens: 30 + 10 = 40. Ones: 9 + 6 = 15. Combine: 40 + 15 = 55.
3. What is ten more than 56?
Answer: 66. Only the tens digit changes, from 5 to 6.
4. What is ten less than 56?
Answer: 46. Only the tens digit changes, from 5 to 4.
5. Work out 90 - 40.
Answer: 50. 9 tens minus 4 tens is 5 tens, which is 50.
6. Add 43 + 28 using tens and ones.
Answer: 71. Tens: 40 + 20 = 60. Ones: 3 + 8 = 11. Combine: 60 + 11 = 71.
Independent practice worksheets
Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Start without regrouping to secure the tens-and-ones method, then move to regrouping once that is solid.
Differentiation
- Practise ten more and ten less with a physical hundred chart, moving down or up one row.
- Keep to sums with no regrouping (ones totalling under 10) until the tens-and-ones method is secure, before adding regrouping.
- Use bundles of ten straws or base-ten blocks so the tens and ones stay physically visible while adding.
- For subtracting multiples of ten, always say the basic fact first (8 - 3 = 5) before attaching the zero (80 - 30 = 50).
- Add two two-digit numbers where both the tens and the ones need regrouping thinking, such as 68 + 57.
- Find ten more and ten less than a number several times in a row, such as 34, 44, 54, watching the pattern.
- Subtract a multiple of ten from a number that is not itself a multiple of ten, such as 73 - 30, as a bridge toward Grade 2.
- Explain in words why adding ten only ever changes the tens digit and never the ones digit.
Assessment: exit ticket
A three-question exit ticket for the last five minutes, sampling place-value addition, ten more or less, and subtracting multiples of ten.
1. Add 26 + 43 using tens and ones.
Answer: 69. Tens: 20 + 40 = 60. Ones: 6 + 3 = 9. Combine: 60 + 9 = 69.
2. What is ten less than 82?
Answer: 72. Only the tens digit changes, from 8 to 7.
3. Work out 60 - 20.
Answer: 40. 6 tens minus 2 tens is 4 tens, which is 40.
Teacher notes and timings
- Rough timing across four lessons: Lesson 1 adding tens and ones with no regrouping (section 1), Lesson 2 adding when the ones make a new ten (section 2), Lesson 3 ten more and ten less (section 3), Lesson 4 subtracting multiples of ten (section 4) plus the exit ticket.
- These three standards cluster naturally because they are all place-value reasoning strategies for two-digit numbers, building directly on the Grade 1 tens-and-ones place-value unit rather than introducing a new written algorithm.
- Language to keep saying: add the tens, add the ones, then combine, and adding ten only moves the tens digit. These phrases pre-empt the misconceptions above.
- Curriculum note: US Grade 1 states adding within 100 (1.NBT.C.4), ten more/ten less (1.NBT.C.5) and subtracting multiples of ten (1.NBT.C.6) as three standards. ACARA Year 1 folds all of this place-value reasoning, including the role of zero as a placeholder, into one broad Number descriptor (AC9M1N02).
- Present mode and print both work: use the Print button for a student worksheet, or project the page and build the bar models together with real base-ten blocks or bundled straws.