Adding several two-digit numbers, and jumping by tens and hundreds
Adding up to four two-digit numbers with place value, and mentally adding or subtracting ten or a hundred
About three lessons of 40 to 45 minutes
Four numbers are just one more round of tens and ones
Adding two two-digit numbers uses tens and ones. Adding three or four is exactly the same idea, just with more numbers to combine: add every ones digit together first, then every tens digit together, then combine the two totals.
You will also practise a fast mental trick from Grade 1, stretched further: adding or subtracting exactly ten, or exactly a hundred, from a bigger number between 100 and 900, changing only one digit each time.
- 23 + 16 + 34 + 17, four two-digit numbersadd all the ones together, then all the tens, then combine
- 10 more than 456only the tens digit changes: 456 becomes 466
- 100 more than 456only the hundreds digit changes: 456 becomes 556
- 100 less than 528only the hundreds digit changes: 528 becomes 428
What students will be able to do
Students will add up to four two-digit numbers using place value strategies, and mentally add or subtract ten or a hundred from a number between 100 and 900.
- I can add up to four two-digit numbers by adding all the ones, then all the tens, then combining.
- I can mentally find ten more or ten less than a number between 100 and 900.
- I can mentally find a hundred more or a hundred less than a number between 100 and 900.
Standards this unit teaches
- 2.NBT.B.6Common Core (US)Add up to four two digit numbers
Add up to four two digit numbers using place value strategies and properties of operations.
- 2.NBT.B.8Common Core (US)Add and subtract tens and hundreds
Mentally add or subtract ten or a hundred from a number between 100 and 900.
- AC9M2N01Australian Curriculum v9 (ACARA)Partition into tens and ones (Year 2)
Break one- and two-digit numbers apart in different ways using materials, including splitting two-digit numbers into tens and ones.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Ones total
- the sum of every ones digit across all the numbers being added
- Tens total
- the sum of every tens digit across all the numbers being added
- Hundreds digit
- the leftmost digit of a three-digit number, showing how many hundreds
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 three or four two-digit numbers
PictorialTo add several two-digit numbers, add all the ones digits together first, keeping a running total, then add all the tens digits together, then combine the two results. For 15 + 27 + 38: the ones are 5, 7, and 8, totalling 20. The tens are 10, 20, and 30, totalling 60. Combine: 60 + 20 = 80.
Adding every ones digit before touching the tens keeps the method identical no matter how many numbers you are adding, two, three, or four. It also isolates any regrouping to one clean step: check the ones total once, then move on.
Add 23 + 16 + 34 + 17.
- Add the ones digits: 3 + 6 + 4 + 7 = 20.
- Add the tens digits: 20 + 10 + 30 + 10 = 70.
- Combine: 70 + 20 = 90.
Answer: 23 + 16 + 34 + 17 = 90.
- Add the ones digits of 12, 19, and 27 before adding the tens.
- Why does adding all the ones digits first work no matter how many numbers you are adding?
2. Mentally adding or subtracting ten or a hundred
AbstractFor a number between 100 and 900, adding or subtracting ten changes only the tens digit, exactly like in Grade 1, just now with a hundreds digit sitting untouched on the left. Adding or subtracting a hundred changes only the hundreds digit, leaving the tens and ones digits exactly as they are.
456 + 10 = 466: the ones digit 6 and the hundreds digit 4 do not move, only the tens digit changes from 5 to 6. 456 + 100 = 556: the tens digit 5 and ones digit 6 do not move, only the hundreds digit changes from 4 to 5.
Find ten more, ten less, a hundred more, and a hundred less than 372.
- Ten more: only the tens digit changes, 7 becomes 8, giving 382.
- Ten less: only the tens digit changes, 7 becomes 6, giving 362.
- A hundred more: only the hundreds digit changes, 3 becomes 4, giving 472.
- A hundred less: only the hundreds digit changes, 3 becomes 2, giving 272.
Answer: Ten more: 382. Ten less: 362. A hundred more: 472. A hundred less: 272.
- What is a hundred more than 528?
- What is ten less than 640?
Common misconceptions and how to address them
MisconceptionWhen adding several two-digit numbers, the child adds the numbers two at a time and loses track partway through, accidentally skipping one of the three or four addends.
Why it happens: Holding a running total across four separate numbers is harder to track than adding just two, and it is easy to lose count of which addends have already been included.
How to address it: Write every number's ones digit in a column and every tens digit in a separate column before adding, so each addend is visibly accounted for exactly once.
MisconceptionWhen the ones digits add up to a multiple of ten with nothing left over, such as 3 + 6 + 4 + 7 = 20, the child forgets that this contributes 2 full tens with zero ones, rather than a single ten.
Why it happens: The more familiar case is a ones total between 10 and 19, contributing one new ten and some leftover ones, so an exact multiple of ten (with no leftover ones at all) is an easy edge case to miss.
How to address it: Say the regrouped amount out loud in full, 20 is 2 tens and 0 ones, and add both of those tens into the tens total, not just one.
MisconceptionFinding a hundred more or less, the child changes the tens digit instead of the hundreds digit, treating 'a hundred' the same as 'ten' from the Grade 1 pattern.
Why it happens: Ten-more and ten-less were practised extensively in Grade 1, so that same tens-digit habit gets misapplied when the jump size changes to a hundred.
How to address it: Say which digit is about to change before doing anything: 'a hundred changes the hundreds digit only.' Point to the specific digit before adjusting it.
MisconceptionThe child believes 10 more or 100 more than a number always makes it a bigger, longer-looking number, and gets confused when 10 less or 100 less shortens a number's digits, such as 100 less than 300 giving 200, not a shorter two-digit number.
Why it happens: Some subtraction cases genuinely do drop a digit (100 less than 100 gives 0), so it is reasonable to expect changes in the number of digits more often than they actually happen.
How to address it: Check the specific digit that changes each time using the place-value rule, rather than guessing whether the number gets shorter. Confirm with a few counter-examples, like 100 less than 528 still being a three-digit number, 428.
Guided practice (with answers)
1. Add 24 + 18 + 22 + 16.
Answer: 80. Ones: 4 + 8 + 2 + 6 = 20. Tens: 20 + 10 + 20 + 10 = 60. Combine: 60 + 20 = 80.
2. Add 12 + 19 + 27.
Answer: 58. Ones: 2 + 9 + 7 = 18. Tens: 10 + 10 + 20 = 40. Combine: 40 + 18 = 58.
3. What is 100 more than 372?
Answer: 472. Only the hundreds digit changes, from 3 to 4.
4. What is ten less than 640?
Answer: 630. Only the tens digit changes, from 4 to 3.
5. Add 21 + 34 + 15.
Answer: 70. Ones: 1 + 4 + 5 = 10. Tens: 20 + 30 + 10 = 60. Combine: 60 + 10 = 70.
6. What is 100 less than 528?
Answer: 428. Only the hundreds digit changes, from 5 to 4.
Independent practice worksheets
Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Two-digit addition worksheets build the tens-and-ones fluency this unit's several-number sums rely on.
Differentiation
- Start with adding just three numbers before moving to four.
- Write every addend's tens and ones digits in two labelled columns before adding, so nothing is skipped.
- Practise ten-more and ten-less on two-digit numbers as a warm-up before extending the same idea to three-digit numbers.
- Use a hundred chart or base-ten blocks to make the digit that changes for ten-more and hundred-more physically visible.
- Add four two-digit numbers where the ones total is 30 or more, regrouping three full tens.
- Find ten more, ten less, a hundred more, and a hundred less than the same starting number in one go, and check all four answers make sense together.
- Explain why adding several two-digit numbers by columns (ones, then tens) always works, no matter how many numbers there are.
- Explore what happens finding a hundred less than a number like 105, where the hundreds digit changes to zero.
Assessment: exit ticket
A three-question exit ticket for the last five minutes, sampling adding several numbers, ten more/less, and a hundred more/less.
1. Add 14 + 23 + 31 + 12.
Answer: 80. Ones: 4 + 3 + 1 + 2 = 10. Tens: 10 + 20 + 30 + 10 = 70. Combine: 70 + 10 = 80.
2. What is ten more than 285?
Answer: 295. Only the tens digit changes, from 8 to 9.
3. What is a hundred less than 730?
Answer: 630. Only the hundreds digit changes, from 7 to 6.
Teacher notes and timings
- Rough timing across three lessons: Lessons 1 to 2 adding three and four two-digit numbers (section 1), Lesson 3 mentally adding and subtracting ten and a hundred (section 2) plus the exit ticket.
- These two standards cluster naturally as Grade 2's extension of Grade 1 place-value addition: more addends at once, and a bigger mental jump (a hundred, not just a ten) on bigger numbers.
- Language to keep saying: add every ones digit first, then every tens digit, and which single digit is about to change. These phrases pre-empt the misconceptions above.
- Curriculum note: US Grade 2 states adding up to four two-digit numbers (2.NBT.B.6) and mentally adjusting by ten or a hundred (2.NBT.B.8) as two standards. ACARA Year 2 covers partitioning one- and two-digit numbers into tens and ones as one broad Number descriptor (AC9M2N01), the place-value reasoning both halves of this unit rely on.
- Present mode and print both work: use the Print button for a student worksheet, or project the page and build the bar model together with base-ten blocks.