Adding Subtracting Decimals
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 decimals
Grade 5 · Math for Young Minds Total time: ~22 minutes Common Core: 5.NBT.B.7 Today's idea: When you add or subtract decimals, line up the decimal points — just like at the cash register.
What students will be able to do
By the end of this session, the student can:
- Add and subtract decimals by lining up the decimal points.
- Add zeros at the end as placeholders when needed.
- Apply this to real money problems.
Materials
- Worksheet (one per student)
- Pencil
- Scrap paper
Substitution: If you don't have the worksheet printed, write the four problems on the board. Any scrap paper works for the column setup.
New words
| Word | Meaning we use in class |
|---|---|
| align | Line up by place value — decimal points stacked. |
Heads-up — common confusions
- Some students will line up the right edge instead of the decimal point. Watch for this on problem 1.
- Forgetting placeholder zeros:
0.4 + 0.27needs to become0.40 + 0.27so the columns match. - Misplacing the decimal in the answer — remind them: the decimal in the answer drops straight down from the lined-up decimals above.
Plan
1 · Hello & today's idea — 2 min
"Today we're doing math that grown-ups actually use every single day — adding up money. Think about a receipt at the grocery store. Every line has dollars and cents. To total them, there's one trick that has to happen first."
Write on the board: align the decimal points.
"That's it. That's the whole move. Line up the dots. Everything else is just adding."
2 · Hands-on explore — 6 min
Write on the board:
3.4
+ 2.75
Ask: "What looks weird here?"
Let them notice that one number has two decimal places and one has only one.
"If I just smash them together on the right, my places don't match. The 4 is tenths. The 5 is hundredths. They're not the same thing."
Now rewrite, lining up the decimal points:
3.40
+ 2.75
------
"I added a zero at the end of 3.4 to make it 3.40. Same number, just dressed up. Now the tenths line up with tenths, and hundredths line up with hundredths. That's what align means."
Solve together, right to left:
3.40
+ 2.75
------
6.15
Point at the decimal point in the answer.
"The decimal drops straight down from the ones above. Don't move it."
3 · Connect to the math — 3 min
Name the steps out loud. Write them on the board as a short list:
- Stack the numbers with decimal points lined up.
- Add zeros at the end if you need to fill in places.
- Add or subtract like normal, right to left.
- Drop the decimal point straight down into the answer.
"Same four steps, every time. Addition, subtraction, doesn't matter. Money, measurements, doesn't matter."
4 · Practice with support — 9 min
Pass out the worksheet.
Problem 2 (solo): 7.83 − 4.5
"Set this one up on scrap paper. What do you need to do to 4.5 before you subtract?"
Listen for: "Add a zero — make it 4.50." Answer: 3.33
Problem 3 (solo): A snack costs $2.45. You give the cashier $5. How much change?
"What operation? Why?"
Listen for: subtraction. Set it up as 5.00 − 2.45. Two placeholder zeros this time. Answer: $2.55
Problem 4 (stretch): Add $12.40 + $3.99 + $0.50. Show your work.
Three numbers stacked. Decimals all line up. Answer: $16.89
If a student is stuck, ask: "Are your decimal points stacked straight down?" That fixes most mistakes.
5 · What we did + Try at home — 2 min
"Today you learned the one trick for adding and subtracting decimals: align the decimal points, add zeros if you need to, then add or subtract like normal."
Hand out the take-home note:
"Tonight, find a receipt at home — grocery, restaurant, gas, online order, anything. Pick two prices and add them up. Or take one off the total to see what's left. Show me tomorrow."
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 | Lines up the right edge instead of the decimal. Forgets placeholder zeros. May misplace the decimal in the answer. |
| Using | Stacks decimals correctly, adds zeros when needed, drops the decimal straight down, gets the right answer on problems 2 and 3. |
| Extending | Sets up problem 4 cleanly with three numbers stacked. Catches their own placeholder-zero mistakes without prompting. |
No fail state. "Developing" today is "using" next week.
What's next (Session 3)
Building on this, Session 3 — Multi-digit multiplication & division (fluency) is where we get faster at multi-digit operations — the foundations for everything else this year.
✏️ Worksheet (for students)
Math for Young Minds · Grade 5
Session 2 — Adding & subtracting decimals
[ Hello ] → [ Explore ] → [ Connect ] → [ Practice ← we are here ] → [ Try at home ]
Today's big idea
To add or subtract decimals, line up the decimal points. Then add zeros at the end so every number has the same length.
This is called align — stack the decimal points right on top of each other.
Example we did together
A receipt says: $4.30 for a sandwich, $1.5 for juice. Total?
$ 4 . 3 0
+ 1 . 5 0 ← we added a zero so it lines up
──────────
$ 5 . 8 0
The decimal points are stacked. The answer's decimal goes right below them.
Problem 1 — together
Add 3.4 + 2.75. Align the decimals. Add a zero where you need one.
┌─────────────────────────────────────────────────────────┐
│ │
│ . │ │
│ + . │ │
│ ─────┴──── │
│ . │ │
│ │
│ │
│ │
└─────────────────────────────────────────────────────────┘
Answer: ______
Problem 2 — on your own
Subtract 7.83 − 4.5. Line up the decimal points first.
┌─────────────────────────────────────────────────────────┐
│ │
│ │
│ │
│ │
│ │
│ │
│ │
│ │
└─────────────────────────────────────────────────────────┘
Answer: ______
Problem 3 — on your own
A snack costs $2.45. You give the cashier $5.
How much change do you get back?
Hint: $5 is the same as $5.00. Now the decimals can align.
┌─────────────────────────────────────────────────────────┐
│ │
│ │
│ │
│ │
│ │
│ │
│ │
│ │
└─────────────────────────────────────────────────────────┘
Change: $ ______
Problem 4 — stretch
You buy three things: $12.40, $3.99, and $0.50.
Add them all up. Show your work — stack them with decimals aligned.
┌─────────────────────────────────────────────────────────┐
│ │
│ $ . │ │
│ $ . │ │
│ + $ . │ │
│ ───────────┴── │
│ $ . │ │
│ │
│ │
└─────────────────────────────────────────────────────────┘
Total: $ ______
Did the decimal points stay in a straight line all the way down? Check it.
Today's words
| Word | What it means |
|---|---|
| align | Line up by place value — decimal points stacked right on top of each other |
Try at home tonight (1 minute)
Find a receipt somewhere at home. Pick two prices. Add them up — or subtract one from the total to see what the rest cost.
Receipts to hunt for:
- A grocery receipt
- A restaurant bill
- An online order confirmation
- A gas receipt
- A snack or coffee receipt in a pocket or bag
Write your two numbers, stack them with the decimals aligned, and solve:
$ ___ . ___ ___
+ ___ . ___ ___
─────────────────
$ ___ . ___ ___
Show a grown-up tomorrow. Next time: we get faster at multi-digit multiplying and dividing — the foundation for everything else this year.
🏠 Family guide (for parents)
Math for Young Minds · Grade 5 · Session 2
A note for grown-ups: today we added and subtracted decimals
What your child did today
In class today, we worked with decimals — the kind you see on every receipt.
The big idea: when you add or subtract decimals, you line up the decimal points first. Once the decimals are stacked, the rest works just like regular addition and subtraction.
We practiced with money: totaling prices, figuring out change from a $5 bill, and adding up a small shopping list. Your child also learned a small trick — adding a zero at the end of a number (like writing 0.4 as 0.40) so the columns line up neatly.
Why this matters
This is one of those grown-up math skills your child will actually use — checking a bill, splitting a total, knowing if their change is right. We're slowing down on the lining up part because that's where most mistakes happen. Get the setup right, and the answer follows. No timed tests, no rush. Understanding the setup now means fewer "wait, where does the decimal go?" moments later.
🏠 Try this tonight (1 minute)
Grab a receipt from anywhere — grocery, restaurant, gas station, an online order email. Pick two prices and ask your child one of these:
- "Can you add these two together?"
- "If we only bought this one thing, how much less would the total be?"
Receipts that work well:
| Receipt | What to try |
|---|---|
| Grocery receipt | Add two items |
| Restaurant bill | Subtract the drink from the total |
| Online order confirmation | Add two line items |
| Gas receipt | Add tax to the fuel amount |
Have them write it on scrap paper with the decimal points stacked. If one number is shorter, they can add a zero at the end to make the columns match.
Words your child is learning
- Align — line up by place value, with the decimal points stacked on top of each other
If your child says…
"This is easy." Good. Hand them a receipt and ask for the total of three items instead of two. Or ask what the total would have been without one item. Real receipts have messy numbers — that's the point.
"This is hard." Also good. Slow down and just focus on lining up the decimal points on scrap paper. Draw a vertical line through the decimals if it helps. Add a zero at the end of the shorter number so the columns match. The math itself is the easy part — the setup is what we're practicing.
"I don't want to." Fair. Keep it to one quick question at the kitchen table, not a worksheet. "What's this plus this?" is enough. One minute, then done. The receipt goes back in the drawer.
What's next
Next session, we move into multi-digit multiplication and division. We'll work on getting faster and more fluent — these are the foundations for almost everything else this year. Understanding first, speed second.
Thanks for taking a minute tonight. Receipts are real math, and your kitchen counter is a great classroom.
— Math for Young Minds
🔑 Cheat sheet (visual)
💵 Line up the dots!
The big idea
To add or subtract decimals → ALIGN the decimal points.
▲
│
stack them straight up & down
Picture 1 — Together: 3.4 + 2.75
3.4 ← needs a placeholder zero
+ 2.75
──────
STEP 1: align dots STEP 2: add a 0 STEP 3: add
3.4 3.40 3.40
+ 2.75 + 2.75 + 2.75
────── ────── ──────
6.15 ✨
▲
dots stacked
Answer: 6.15
Picture 2 — Subtract: 7.83 − 4.5
7.83 7.83
− 4.5 → add a 0 → − 4.50
────── ──────
3.33
▲
dots stacked
Answer: 3.33
How to read the setup
┌──── decimal points stacked
│
2 . 4 5
+ 0 . 5 0 ← zero added as a placeholder
─────────
2 . 9 5
│
└──── decimal drops straight down into the answer
When does the zero trick fit?
| ✅ Add a zero when... | ❌ You don't need one when... |
|---|---|
0.4 + 0.27 → 0.40 + 0.27 |
0.45 + 0.27 already match |
7.83 − 4.5 → 7.83 − 4.50 |
7.83 − 4.50 already match |
If the columns don't reach → add a 0 at the end.
Picture 3 — Money: $5.00 − $2.45
You pay: $5.00 ← add the zeros!
Snack: − $2.45
──────
Change: $2.55 🪙
Answer: $2.55
Stretch — Receipt time 🧾
$12.40
+ $3.99
+ $0.50
────────
$16.89
$12.40
+ $3.99
────────
$16.39
+ $0.50
────────
$16.89 ✨
Try this in your head
🥤 $1.20 + 🍌 $0.80 = $ ____
➤ Line up the dots…
Answer:
$1.20 + $0.80 = $2.00