Adding Subtracting Within 100
Part of the Math for Young Minds curriculum — designed for neurodivergent students, grounded in real-world examples.
📋 Session plan (for teachers)
Session 2 — Adding & subtracting within 100
Grade 2 · Math for Young Minds Total time: ~20 minutes Common Core: 2.NBT.B.5 Today's idea: When ones pile up to 10 or more, we regroup — trade 10 ones for 1 ten.
What students will be able to do
By the end of this session, the student can:
- Add two 2-digit numbers, with and without regrouping.
- Subtract a 2-digit number from another 2-digit number.
- Use base-10 blocks to show why regrouping works.
Materials
- Base-10 blocks per pair (tens rods and ones cubes)
- Place-value mat (one per pair)
- Worksheet (one per student)
- Pencil
Substitution: If you don't have base-10 blocks, use bundles of 10 popsicle sticks for tens and single sticks for ones. Or draw tens as long sticks and ones as dots on the board.
New words
| Word | Meaning we use in class |
|---|---|
| regroup | Trade 10 ones for 1 ten (when adding). Or trade 1 ten for 10 ones (when subtracting). |
Heads-up — common confusions
- Kids often forget to regroup when the ones add up to more than 9. Watch for answers where the ones digit is 10 or bigger written in one column.
- Some will mix up the add column and the subtract column. Point at the sign before starting each problem.
- In subtraction, kids may take the smaller digit from the bigger digit instead of regrouping. Slow down and show the trade with the blocks.
Plan
1 · Hello & today's idea — 2 min
"Today we're going to add and subtract bigger numbers — all the way up to 100. And we have a special move called regrouping that helps when things get crowded."
Hold up a tens rod and a ones cube.
"This long one is 1 ten. This little one is 1 one. If I have 10 little ones, I can trade them for 1 long ten. That trade is called regrouping."
2 · Hands-on explore — 6 min
Hand each pair a place-value mat and base-10 blocks.
Problem 1 — together: 34 + 22.
"Build 34 on your mat. 3 tens and 4 ones. Now add 22 more — 2 tens and 2 ones."
Wait while they build.
"Count your tens. Count your ones. What did you get?"
Listen for 5 tens and 6 ones — that's 56. Write 34 + 22 = 56 on the board.
"Did we need to trade? No — the ones stayed under 10. Easy day."
Now set up the next idea:
"Build 47 on your mat. Now add 35 more."
Let them build. When they see 12 ones piled up, pause everyone.
"You have more than 9 ones. That's the moment we regroup. Trade 10 ones for 1 ten. Show me."
3 · Connect to the math — 4 min
Write on the board:
47
+ 35
----
"Start with the ones. 7 + 5 = 12. That's 1 ten and 2 ones. We write the 2 down here, and the new ten goes up with the other tens."
Show it:
1
47
+ 35
----
82
"Now the tens: 1 + 4 + 3 = 8. Answer: 82."
"Subtraction has the same idea, but backwards. If you don't have enough ones, borrow a ten and break it into 10 ones."
Show 63 − 28 with the blocks: 3 ones isn't enough to take 8 away, so trade 1 ten for 10 ones. Now you have 5 tens and 13 ones. 13 − 8 = 5. 5 − 2 = 3. Answer: 35.
4 · Practice with support — 6 min
Pass out the worksheet. Problems are already on it:
- (together, done) 34 + 22 = 56
- (solo) 47 + 35 — regroup the ones.
- (solo) 63 − 28 — regroup a ten.
- (stretch) A book costs 56 cents. You pay 75 cents. How much change?
Let students work with their partner and blocks. Circulate. Look for:
- Did they line up tens with tens, ones with ones?
- Did they trade when the ones piled up?
- For problem 4, did they see it as 75 − 56?
If a student is stuck on the stretch, ask: "What are you starting with? What are you taking away?" Answer: 19 cents.
5 · What we did + Try at home — 2 min
"Today you learned that when ones pile up past 9, we regroup — trade 10 ones for 1 ten. And when we don't have enough ones to subtract, we trade a ten back into 10 ones."
Hand out the take-home note:
"Tonight, make up your own 2-digit problem from something at home. Maybe pages in two books added together. Maybe minutes until dinner. Maybe coins you've saved. Maybe family ages added up. Solve it with a grown-up."
Observation rubric — what to notice in this session
Use this during the session, not as a test. One observation per student is plenty.
| Where the student is | What you'd see |
|---|---|
| Developing | Needs reminders to line up tens and ones. May forget to trade when ones go past 9. Counts blocks one by one. |
| Using | Adds and subtracts 2-digit numbers correctly. Regroups when needed. Can explain the trade using the blocks. |
| Extending | Solves the stretch problem without prompting. Notices that subtraction regrouping is just addition regrouping in reverse. Invents their own 2-digit problem. |
No fail state. "Developing" today is "using" next week.
What's next (Session 3)
Building on this, Session 3 — Mental math strategies takes the same adding and subtracting and finds faster ways to do it in our head — without paper or blocks.
✏️ Worksheet (for students)
Math for Young Minds · Grade 2
Session 2 — Adding & subtracting within 100
[ Hello ] → [ Explore ] → [ Connect ] → [ Practice ← we are here ] → [ Try at home ]
Today's big idea
When the ones add up to 10 or more, we regroup: trade 10 ones for 1 ten. When we can't subtract the ones, we trade 1 ten for 10 ones.
Stack the tens under tens. Stack the ones under ones.
Example we did together
Tens │ Ones
──────┼──────
2 │ 5 25
+ 1 │ 3 + 13
──────┼────── ────
3 │ 8 38
Ones first: 5 + 3 = 8. Then tens: 2 + 1 = 3. No regrouping needed.
Problem 1 — together
Add 34 + 22. Use your base-10 blocks. Check the ones first.
Tens │ Ones
──────┼──────
│ 34
│ + 22
──────┼────── ────
│
Draw the tens (sticks) and ones (dots) for each number:
┌─────────────────────────────────────────────────────────┐
│ 34: │
│ │
│ │
│ │
│ 22: │
│ │
│ │
│ │
└─────────────────────────────────────────────────────────┘
34 + 22 = ____
Problem 2 — on your own
Add 47 + 35. You'll need to regroup the ones.
Tens │ Ones
──────┼──────
│ 47
│ + 35
──────┼────── ────
│
Draw the blocks. Circle 10 ones and trade them for 1 ten:
┌─────────────────────────────────────────────────────────┐
│ 47: │
│ │
│ │
│ │
│ 35: │
│ │
│ │
│ │
└─────────────────────────────────────────────────────────┘
47 + 35 = ____
Problem 3 — on your own
Subtract 63 − 28. You'll need to regroup.
You can't take 8 ones from 3 ones. Trade 1 ten for 10 ones.
Tens │ Ones
──────┼──────
│ 63
│ − 28
──────┼────── ────
│
Draw 63 in blocks. Cross out 28. Show the trade:
┌─────────────────────────────────────────────────────────┐
│ 63: │
│ │
│ │
│ │
│ After trading 1 ten for 10 ones: │
│ │
│ │
│ │
└─────────────────────────────────────────────────────────┘
63 − 28 = ____
Problem 4 — stretch
A book costs 56 cents. You pay 75 cents.
How much change do you get back?
You paid: 75 cents
Book cost: 56 cents
────────
Change: ?? cents
- Is this add or subtract? ____________
- Do you need to regroup? ____
- Set it up here:
┌─────────────────────────────────────────────────────────┐
│ Tens │ Ones │
│ ──────┼────── │
│ │ │
│ │ │
│ ──────┼────── │
│ │ │
│ │
│ Your change is ____ cents. │
└─────────────────────────────────────────────────────────┘
Hint: 75 − 56. Can you take 6 ones from 5 ones? Trade first!
Today's words
| Word | What it means |
|---|---|
| regroup | Trade 10 ones for 1 ten (when adding), or 1 ten for 10 ones (when subtracting) |
Try at home tonight (1 minute)
Make up your own 2-digit add or subtract problem from something at home. Solve it with a grown-up. Ideas:
- Page numbers — add the pages of two books
- Minutes — how many minutes until dinner?
- Coins — count up your savings
- Ages — add the ages of two family members
- Steps — count steps from your room to the kitchen, then to the door
Write your problem here:
______ ___ ______ = ______
Show a grown-up. Next time: mental math — adding and subtracting in your head, no paper!
🏠 Family guide (for parents)
Math for Young Minds · Grade 2 · Session 2
A note for grown-ups: today we added and subtracted with two-digit numbers
What your child did today
In class today, we worked on adding and subtracting numbers up to 100.
We used base-10 blocks — little cubes for ones, and long sticks for tens — on a place-value mat. When the ones piled up past nine, we traded ten ones for one ten. That trade has a name: regrouping.
We added 34 + 22 together (no trade needed), then your child tried 47 + 35 and 63 − 28 on their own. We finished with a store problem: a 56-cent book paid for with 75 cents.
Why this matters
Regrouping is the heart of how our number system works. Once a child sees why ten ones can become one ten, the steps in addition and subtraction stop feeling like magic rules. We're not chasing speed yet — understanding first, speed comes later on its own. No timed tests, no rush.
🏠 Try this tonight (1 minute)
Make up one 2-digit add or subtract problem from something already around you. Solve it together.
| Thing at home | Problem to try |
|---|---|
| Two books | Add the page counts |
| The clock | Minutes until dinner |
| A coin jar | Count the savings |
| Family ages | Add two people's ages |
A short script:
- "Pick two numbers from something here."
- "Should we add them or subtract them?"
- "Want to draw tens and ones, or do it in your head?"
If they get stuck on the ones column, ask: "Do we have enough ones, or do we need to trade?"
Words your child is learning
- Regroup — trade 10 ones for 1 ten when adding, or trade 1 ten for 10 ones when subtracting.
If your child says…
"This is easy." Lovely. Ask them to make up a subtraction problem where they have to regroup. Let them quiz you, and "forget" to regroup on purpose so they can catch it.
"This is hard." Also fine. Slow down and grab small objects — pennies, beans, cereal pieces. Make ten little ones, then physically swap them for one bigger group. Seeing the trade with your hands is what makes it click.
"I don't want to." That's okay. Keep it to one problem, tied to something they already care about — their book, their snack, the clock. One minute. Then stop. Short and pleasant beats long and forced.
A couple of bumps to expect
- Forgetting to trade when the ones add up past nine.
- Mixing up which column is which.
- Subtracting the smaller digit from the bigger one out of habit, instead of regrouping.
These are normal stops along the way, not signs of trouble.
What's next
In our next session, we start mental math strategies — faster ways to add and subtract in your head, without paper. Your child has been building the foundation for this all along.
Thanks for taking a minute tonight. These small kitchen-table moments are where math lives.
— Math for Young Minds
🔑 Cheat sheet (visual)
🔑 Tens + Ones (regroup when full!)
Picture 1 — Base-10 blocks
1 ten = | | (a stick of 10)
1 one = • (a little cube)
34 → | | | • • • •
(3 tens) (4 ones)
Picture 2 — Easy add: 34 + 22 = 56
| | | • • • • ← 34
| | • • ← 22
─────────────────
| | | | | • • • • • •
(5 tens) (6 ones) = 56 ✨
No regrouping. Ones stayed under 10.
Picture 3 — Regroup when ones spill over: 47 + 35 = 82
| | | | • • • • • • • ← 47
| | | • • • • • ← 35
─────────────────────────
ones: 7 + 5 = 12 → too many!
📦 TRADE 10 ones → 1 ten
| | | | | | | | • •
(8 tens) (2 ones) = 82
regroup = trade 10 ones for 1 ten
Picture 4 — Subtract with regroup: 63 − 28 = 35
63 → | | | | | | • • •
Take away 8 ones? Only 3 ones here! 😬
📦 TRADE 1 ten → 10 ones
| | | | | • • • • • • • • • • • • •
(5 tens) (13 ones)
Now take away 2 tens and 8 ones:
| | | • • • • •
(3 tens) (5 ones) = 35 ✨
How to read the stack
tens │ ones
↓ │ ↓
4 │ 7
+ 3 │ 5
──────┼─────
8 │ 2 ← ones first, then tens
Add (or subtract) the ones column first. Then the tens column.
When do I regroup?
| ✅ Regroup when... | 🆗 No regroup when... |
|---|---|
Adding: ones add to 10 or more (7+5=12) |
Adding: ones stay under 10 (4+2=6) |
Subtracting: top ones are smaller than bottom ones (3 − 8) |
Subtracting: top ones are bigger (6 − 2) |
Try this in your head 🪙
Book costs 56¢. You pay 75¢. Change = ?
7 5
− 5 6
───────
? ?
Answer:
75 − 56 = 19¢(regroup 1 ten → 10 ones)