Learning platform · Mathematics · Stage 1 (Years 1–2)
Number and algebra / Addition and subtraction
Adds two-digit numbers with and without regrouping
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Lesson outline
In this level
I can add one- and two-digit numbers by partitioning tens and ones when the ones total is less than 10 and the total stays below 100.
Learning objectives:
- I can split a two-digit number into its tens and its ones.
- I can add the tens, add the ones, and put the two results back together.
- I can show an addition with base-ten blocks and read the answer off the blocks.
- I can add a whole ten to a two-digit number without changing the ones digit.
- I can check that my answer is sensible by estimating before I start.
Tutor session plan
Lesson plan Lesson activities: 60 minutes · After the lesson: 35 minutes
Use this sequence for independent study or a tutor session. Further practice follows the lesson and is timed separately.
- 1 Readiness and lesson goal5 min · Guided learning
- 2 Concepts and visual model12 min · Guided learning
- 3 Worked model and guided application13 min · Guided learning · 2 questions
- 4 Independent application18 min · Independent practice · 4 questions
- 5 Short check and error review12 min · Independent practice
- 6 Separate follow-up practice and retrieval35 min · Further practice · 8 questions
Introduction
34 + 25 can be represented by joining tens rods and unit cubes. Add matching place values, then combine the results.
Prerequisite review
- Reads, writes and partitions two-digit numbers into tens and ones — Use the checks below to review this prerequisite. Revisit the linked explanation if needed, and return to the lesson when the method is clear.
- Recalls addition facts to 20 — Use the checks below to review this prerequisite. Revisit the linked explanation if needed, and return to the lesson when the method is clear.
Readiness check
Adds two-digit numbers with and without regrouping
Adding ones to a two-digit number
For 34 + 5, partition 34 as 30 + 4. Add 4 + 5 = 9, then 30 + 9 = 39. The tens remain unchanged in this example because the ones total is below 10. If the ones total reaches 10, regrouping is needed.
Adding whole tens
For 43 + 20, add 40 + 20 = 60 and retain the 3 ones, giving 63. Adding a multiple of ten leaves the ones digit unchanged; larger totals may also change the hundreds digit.
Adding two two-digit numbers
For 34 + 25, add the matching parts: tens 30 + 20 = 50; ones 4 + 5 = 9. Recombine 50 + 9 = 59. This is partitioning, also called the split strategy.
Use blocks, sketches or the labelled place-value table to distinguish tens from ones. Record the value of each part before adding.
Estimate before you calculate
Round 34 and 25 to the nearest ten to estimate 30 + 30 = 60. The exact total 59 is close to 60. Estimation checks the size of an answer; it does not prove exact correctness. Check the place-value calculation as well.
The tens or ones may be added first because the same quantities are combined. Both orders must preserve every part of each addend.
Explanation step 1 of 4.
Worked examples
Work out 52 + 36 by splitting, and check the answer against an estimate.
First an estimate: 52 is about 50 and 36 is about 40, so the answer should be near 90.
Now split both numbers. 52 is 50 and 2. 36 is 30 and 6.
Add the tens: 50 + 30 = 80. This is the fact 5 + 3 = 8, scaled to tens.
Add the ones: 2 + 6 = 8.
Rejoin: 80 + 8 = 88. So 52 + 36 = 88.
Check against the estimate: 88 is close to 90, so the answer is in the right neighbourhood. If I had written 8 or 818, the estimate would have caught it immediately.
52 + 36 = 88. Split: 50 + 30 = 80 and 2 + 6 = 8, then 80 + 8 = 88. The estimate of about 90 is consistent with it.
The Year 1 class collected 43 bottle tops and the Year 2 class collected 20. How many bottle tops altogether?
Are the amounts being joined? (Yes, so this is an addition: 43 + 20.)
Which part of 43 is going to change? (Only the tens, because 20 is a whole two tens with no ones.)
Add the tens. (40 + 20 = 60.)
What happens to the 3 ones? (Nothing - they stay as they are.)
So what is the total? (63 bottle tops.)
43 + 20 = 63, so the two classes collected 63 bottle tops. The tens go from 4 to 6 and the ones digit stays as 3.
work out 41 + 37 by splitting, and estimate first.
Write an estimate in one line.
Split both numbers into tens and ones.
Add the tens, then add the ones.
Rejoin the two results and compare with your estimate.
Estimate: 41 is about 40 and 37 is about 40, so the answer should be near 80. Split: 41 is 40 and 1; 37 is 30 and 7. Tens: 40 + 30 = 70. Ones: 1 + 7 = 8. Rejoin: 70 + 8 = 78. So 41 + 37 = 78, which is 2 below the estimate of 80; rounding 41 down by 1 and 37 up by 3 increased the total by 2.
Practice set
Lesson workbook
The same practice, printed, with space to write.
Answer a question, then check it. Hints open one at a time.
34 + 5 = ?
Enter a number without units. Use a slash for a fraction (for example, 2/7) and a space for a mixed number (for example, 3 2/7).
62 + 7 = ?
Enter a number without units. Use a slash for a fraction (for example, 2/7) and a space for a mixed number (for example, 3 2/7).
43 + 20 = ?
Enter a number without units. Use a slash for a fraction (for example, 2/7) and a space for a mixed number (for example, 3 2/7).
25 + 30 = ?
Enter a number without units. Use a slash for a fraction (for example, 2/7) and a space for a mixed number (for example, 3 2/7).
34 + 25 = ?
Enter a number without units. Use a slash for a fraction (for example, 2/7) and a space for a mixed number (for example, 3 2/7).
52 + 36 = ?
Enter a number without units. Use a slash for a fraction (for example, 2/7) and a space for a mixed number (for example, 3 2/7).
41 + 17 = ?
Enter a number without units. Use a slash for a fraction (for example, 2/7) and a space for a mixed number (for example, 3 2/7).
Fill each gap.
Two collections contain 4 tens rods and 3 unit cubes beside 2 tens rods and 5 unit cubes. Write the addition and give the total: + =
Fill each gap.
Set out 63 + 24 as a split, showing the tens line and the ones line separately. Tens: 60 + 20 = Ones: 3 + 4 = Rejoin:
At the school fete, the cake stall took $32 and the plant stall took $25. How much did the two stalls take altogether? Enter the amount in dollars, without the dollar sign.
Enter a number without units. Use a slash for a fraction (for example, 2/7) and a space for a mixed number (for example, 3 2/7).
Fill each gap.
Find the missing number: 34 + = 54
Fill each gap.
Round each addend to the nearest ten, then calculate 47 + 31 exactly. Estimate: Exact sum: Amount by which the estimate exceeds the exact sum:
Rhea works out 43 + 20 and writes 65. Which of these is her mistake?
Work out 42 + 36 twice: once by adding the tens first and once by adding the ones first. Explain why both give the same answer.
Guided review: this task involves explanation, construction or more than one valid response. It is not automatically marked.
Submit a response to each practice question to open the worked solutions. Hints remain available as you work.
Lesson check
6 questions. The required score is 80%.
On the platform the lesson check is a separate page and the platform marks it, so its answers are not shown here. Reading, hints and practice responses do not count towards it.
Work out 56 + 3. Enter the numerical value.
Work out 27 + 40. Enter the numerical value.
Work out 35 + 24. Enter the numerical value.
Work out 64 + 23. Enter the numerical value.
Find the missing number: 51 + □ = 71. Enter the numerical value.
Round each addend to the nearest ten, then add to estimate 38 + 41. Enter the numerical value.
Common errors
Changing the ones digit when only tens were added: 43 + 20 answered as 65 or 45. Diagnostic pattern: the untouched digit drifting, usually toward the digits of the number being added.
Say which column the added number lives in before adding. Twenty is two rods and no cubes, so the cubes cannot change. Compare the block model with the written calculation and revisit the distinction during later practice.
Adding the digits as if they were all ones: treating 34 + 25 as 3 + 4 + 2 + 5. Diagnostic pattern: single-digit or low-teens answers to two-digit questions.
Write the split out in full - 30 + 4 and 20 + 5 - before adding anything. Writing 30 makes the tens value explicit.
Adding a ten to a one: lining up 34 and 5 so that the 5 joins the 3. Diagnostic pattern: 34 + 5 answered as 84.
Keep the columns labelled. Ones join ones and tens join tens - a cube can only be added to the cube pile. When written in columns, the ones digits must sit directly under one another.
Skipping the estimate, so a place-value error survives to the final answer. Diagnostic pattern: wildly wrong answers written down with total confidence.
Require an estimate on its own line before any calculating. It is a prediction, and its whole value is that it was made before the answer was known.
Assuming the split strategy works the same way when the ones make more than nine, and writing 27 + 15 as '3 tens and 12 ones' read off as 312. Diagnostic pattern: three-digit answers to two-digit questions.
Use the Developing explanation of exchanging ten ones for one ten when the ones total reaches 10.
Extension
ExtensionBuilding without trading. (a) Write three different additions of two two-digit numbers that give 68, where neither number ends in zero and the ones do not add to more than nine. (b) What has to be true about the two ones digits for a question like this to need no trading? (c) Is 39 + 24 one of the no-trading kind? Explain without working out the answer. (d) How many two-digit numbers could be added to 43 without needing a trade from the ones column, even if a hundreds trade is needed, if the other number must also be a two-digit number?
Optional extension task. It does not change lesson access.
Section 1 of 9: In this level
