Grade 5 · Session 04

Multiplying Decimals

Part of the Math for Young Minds curriculum — designed for neurodivergent students, grounded in real-world examples.

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📋 Session plan (for teachers)

Session 4 — Multiplying decimals

Grade 5 · Math for Young Minds Total time: ~22 minutes Common Core: 5.NBT.B.7 Today's idea: When you multiply decimals, count the decimal places in the factors — that's how many you'll have in the answer.

What students will be able to do

By the end of this session, the student can:

Multiply a decimal by a whole number.
Multiply two decimals together.
Count the decimal places in the factors to place the decimal in the answer.

Materials

Graph paper
Worksheet (one per student)
Pencil

Substitution: If you don't have graph paper, plain paper works — just ask students to line up digits carefully in columns.

New words

Word	Meaning we use in class
decimal places	The digits after the decimal point — they count!

Heads-up — common confusions

The biggest trap: misplacing the decimal in the answer. Slow down and count.
0.3 × 0.4 is 0.12 — not 0.012 and not 1.2. We'll prove this one together.
Some students will multiply like whole numbers and forget to put the decimal back. The rule: count places in the factors, then count that many in the answer.

Plan

1 · Hello & today's idea — 2 min

"Today we're doing math grown-ups actually use — figuring out the cost of stuff at the store. If gas is $3.45 a gallon and you get 4 gallons, how much do you pay? That's decimal multiplication."

Write on the board: $3.45 × 4 = ?

"By the end of today, you'll have a rule that always works. It's about counting the decimal places."

2 · Hands-on explore — 6 min

Hand out graph paper.

Prompt: "Draw a rectangle that is 3 squares by 4 squares. How many small squares inside?"

Wait. They'll say 12.

"Easy — 3 × 4 = 12. Now here's the twist."

Write on the board: 0.3 × 0.4

"Same digits — a 3 and a 4. But now they're tenths. What do you think the answer is?"

Take guesses. You'll hear 1.2, 0.12, maybe 0.012. Don't correct yet.

On graph paper, draw a 1-by-1 square. Split it into 10 columns and 10 rows. Shade a strip 3 columns wide and 4 rows tall.

"How many little squares did we shade? Out of how many total?"

Count it together: 12 out of 100. That's 12/100, which is 0.12.

"Tenths times tenths gave us hundredths. Hold onto that."

3 · Connect to the math — 4 min

Now name the rule.

Write on the board:

   0.3   ×   0.4   =   0.12
   ↑          ↑         ↑
 1 place   1 place   2 places

"Step 1: multiply like they're whole numbers. 3 × 4 = 12." "Step 2: count the decimal places in the factors. One here, one here — that's two." "Step 3: put two decimal places in the answer. 0.12."

Do problem 1 together:

"Compute 0.4 × 6."

Multiply: 4 × 6 = 24.
Count decimal places in the factors: 1 (just the 0.4).
Answer has 1 decimal place: 2.4.

"Check: 0.4 is a little less than half. Half of 6 is 3. So 2.4 makes sense."

4 · Practice with support — 8 min

Pass out the worksheet. Students work problems 2, 3, and 4. Circulate.

Problem 2 (solo): 0.3 × 0.4 → 0.12 Watch for students writing 1.2. Point back to the shaded square.

Problem 3 (solo): A gallon of gas costs $3.45. You buy 4 gallons. How much total?

345 × 4 = 1380
2 decimal places in $3.45, 0 in 4, so 2 places in the answer.
$13.80

"Quick check: 4 gallons at about $3.50 each is about $14. ✓"

Problem 4 (stretch): A rectangle is 2.5 m by 1.4 m. What is its area?

25 × 14 = 350
1 decimal place + 1 decimal place = 2 decimal places.
3.50 m² → 3.5 m²

If a student is stuck, ask: "What's 2 × 1? About 2. So your answer should be near 2 or 3 — does it match?"

5 · What we did + Try at home — 2 min

"Today you learned the rule: multiply like whole numbers, then count the decimal places in the factors. That's how many go in the answer."

Hand out the take-home:

"Tonight, find a decimal price — maybe a snack or a drink. Multiply it by 3, 5, or 10. What would that many cost? Try 3 lattes at $4.75, or 10 candy bars at $0.99, or 4 gallons of gas."

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	Multiplies the digits correctly but misplaces the decimal. May write `1.2` for `0.3 × 0.4`. Needs a reminder to count places.
Using	Multiplies as whole numbers, counts decimal places in the factors, and places the decimal correctly in the answer.
Extending	Estimates first to check the decimal placement. Notices that tenths × tenths = hundredths, and can explain why.

No fail state. "Developing" today is "using" next week.

What's next (Session 5)

Building on this, Session 5 — Multiplying fractions takes the same idea into fraction form — and we'll discover something surprising: when you multiply two fractions, the answer is sometimes smaller than what you started with.

✏️ Worksheet (for students)

Math for Young Minds · Grade 5

Session 4 — Multiplying decimals

[ Hello ]  →  [ Explore ]  →  [ Connect ]  →  [ Practice ← we are here ]  →  [ Try at home ]

Today's big idea

To multiply decimals: multiply like whole numbers, then count the decimal places in the factors.

That count tells you where the decimal point goes in your answer.

Example we did together

   0.2   ×   0.3   =   ?

   Step 1:  multiply like whole numbers →  2 × 3 = 6
   Step 2:  count decimal places in the factors

            0.2  → 1 place
            0.3  → 1 place
            ─────────────
            total: 2 places

   Step 3:  put 2 decimal places in the answer →  0.06

We say it: "Two tenths times three tenths equals six hundredths."

Problem 1 — together

Compute 0.4 × 6.

Use the rule: multiply 4 × 6, then count 1 decimal place in the factors.

Show your work in the box:

┌─────────────────────────────────────────────────────────┐
│   4 × 6 = ____                                          │
│                                                         │
│   Decimal places in 0.4 → ____                          │
│   Decimal places in 6   → ____                          │
│   Total decimal places  → ____                          │
│                                                         │
│   Put the decimal point in the answer:                  │
│                                                         │
│   0.4  ×  6  =  ________                                │
└─────────────────────────────────────────────────────────┘

Problem 2 — on your own

Compute 0.3 × 0.4.

Careful! This one trips people up. Count the places.

Show your work in the box:

┌─────────────────────────────────────────────────────────┐
│   3 × 4 = ____                                          │
│                                                         │
│   Decimal places in 0.3 → ____                          │
│   Decimal places in 0.4 → ____                          │
│   Total decimal places  → ____                          │
│                                                         │
│                                                         │
│   0.3  ×  0.4  =  ________                              │
│                                                         │
└─────────────────────────────────────────────────────────┘

Problem 3 — on your own

A gallon of gas costs $3.45. You buy 4 gallons.

How much do you pay in total?

Show your work in the box:

┌─────────────────────────────────────────────────────────┐
│   345 × 4 = ____                                        │
│                                                         │
│   Decimal places in $3.45 → ____                        │
│   Decimal places in 4     → ____                        │
│   Total decimal places    → ____                        │
│                                                         │
│                                                         │
│   $3.45  ×  4  =  $________                             │
│                                                         │
└─────────────────────────────────────────────────────────┘

Problem 4 — stretch

A rectangle is 2.5 m by 1.4 m. What is its area?

                  2.5 m
            ┌───────────────┐
            │               │
     1.4 m  │               │
            │               │
            └───────────────┘

Hint: area = length × width. Multiply 25 × 14 first, then place the decimal.

Show your work in the box:

┌─────────────────────────────────────────────────────────┐
│   25 × 14 = ____                                        │
│                                                         │
│   Decimal places in 2.5 → ____                          │
│   Decimal places in 1.4 → ____                          │
│   Total decimal places  → ____                          │
│                                                         │
│                                                         │
│   2.5  ×  1.4  =  ________ m²                           │
│                                                         │
└─────────────────────────────────────────────────────────┘

Today's words

Word	What it means
decimal places	Digits after the decimal point — they count!

Try at home tonight (1 minute)

Find a decimal price at home or in a store. Multiply it by a small number — what would 3, 5, or 10 of that item cost?

3 lattes at $4.75 each
5 packs of gum at $1.29 each
10 candy bars at $0.99 each
4 gallons of gas (use today's price!)

Write it out:

  ________  ×  ____  =  $________
   price       how many    total

Show a grown-up tomorrow morning.

Next time (Session 5): we multiply fractions — and discover that the answer is sometimes smaller than what you started with!

🏠 Family guide (for parents)

Math for Young Minds · Grade 5 · Session 4

A note for grown-ups: today we multiplied decimals

What your child did today

In class today, we worked on multiplying decimals — the kind of math grown-ups actually use at the gas pump and the grocery store.

The big idea: multiply the digits like normal, then count the decimal places in the factors to place the decimal in the answer.

We warmed up with 0.4 × 6 = 2.4 together. Then your child tried 0.3 × 0.4 = 0.12 on their own, figured out the cost of 4 gallons of gas at $3.45 ($13.80), and stretched into finding the area of a 2.5 m by 1.4 m rectangle (3.5 m²).

Why this matters

Decimals show up every time money or measurement does. The rule itself is small, but placing the decimal correctly is where most people slip — even adults. We're slowing down on that one move so it sticks. Understanding before speed, as always.

🏠 Try this tonight (1 minute)

Find a decimal price on something in the house and ask: what would 3, 5, or 10 of these cost?

A short script:

"This costs $___. What would 3 of them cost?"
"How did you figure out where the decimal goes?"
"Does the answer make sense?"

Easy starters:

Item	Price	Try
Latte	$4.75	× 3
Pack of gum	$1.29	× 5
Candy bar	$0.99	× 10
Gallon of gas	$3.45	× 4

One problem is plenty. The "does it make sense?" check is the real win.

Words your child is learning

Decimal places — the digits after the decimal point. They count! When you multiply, add up the decimal places in both factors to know how many belong in the answer.

If your child says…

"This is easy." Great. Ask them 0.3 × 0.4. Many people guess 1.2 or 0.012. The answer is 0.12 — because the factors have 2 decimal places total, so the answer does too.

"This is hard." Also great. Slow down. Multiply the digits like whole numbers first (3 × 4 = 12). Then count the decimal places in the factors and place the decimal at the end. One step at a time.

"I don't want to." Fair. Skip the worksheet for tonight and just notice a price tag together. "If we bought 3, would it be more or less than $10?" Estimating counts as math.

What's next

In our next session, we'll start multiplying fractions — and discover something surprising: the answer is sometimes smaller than what you started with.

Thanks for taking a minute tonight. These small kitchen-table moments are where math lives.

— Math for Young Minds

🔑 Cheat sheet (visual)

💰 Multiplying decimals = count the places

Picture 1 — A decimal times a whole number

   0.4  +  0.4  +  0.4  +  0.4  +  0.4  +  0.4   =   2.4

   ▓░░░░░░░░░░ ▓░░░░░░░░░░ ▓░░░░░░░░░░ ▓░░░░░░░░░░ ▓░░░░░░░░░░ ▓░░░░░░░░░░

                 0.4  ×  6  =  2.4

   Step 1:  4 × 6 = 24
   Step 2:  count decimal places in factors
            0.4  →  1 place
              6  →  0 places
            total →  1 place
   Step 3:  put 1 place in the answer  →  2.4 ✨

Picture 2 — Two decimals as an area

            0.4
        ┌─────────┐
        │░░░░░░░░░│
   0.3  │░░░░░░░░░│        0.3  ×  0.4  =  0.12
        │░░░░░░░░░│
        └─────────┘

   3 × 4 = 12
   0.3 → 1 place
   0.4 → 1 place
   total → 2 places  →  0.12

How to read the places

       0 . 4    ×    0 . 4    =    0 . 1 2
         │              │              │ │
         └─ 1 place ────┘              └─┴─ 2 places
                                       (1 + 1 = 2)

decimal places: digits after the decimal point — they count!

Picture 3 — Gas pump 💵

   ⛽ $3.45  ⛽ $3.45  ⛽ $3.45  ⛽ $3.45

         4 gallons  ×  $3.45  =  $13.80

   345 × 4 = 1380
   $3.45 → 2 places
       4 → 0 places
   answer → 2 places  →  $13.80

Stretch — Rectangle area 📐

              2.5 m
        ┌───────────────┐
   1.4m │               │     2.5 × 1.4 = 3.5 m²
        │               │
        └───────────────┘

   25 × 14 = 350
   places: 1 + 1 = 2  →  3.50  =  3.5 m²

Check the place ✅ ❌

✅ Right	❌ Wrong
`0.3 × 0.4 = 0.12` (2 places)	`0.3 × 0.4 = 1.2`
`0.4 × 6 = 2.4` (1 place)	`0.4 × 6 = 0.24`
count places in both factors	guessing where the dot goes

Try this in your head

   🍫 🍫 🍫     (each candy bar costs $0.99)

➤ ____ × ____ = $____

Answer: 0.99 × 3 = 2.97 (2 places + 0 places → 2 places)

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