Multiply Decimals
I can multiply decimals and place the decimal point correctly in the product.
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🎯 Content Objective / Objetivo de contenido
I can multiply decimals and place the decimal point correctly in the product.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
The station needs 4.5 meters of heat shielding at $12.60 per meter. About how much will it cost, and how did you estimate before multiplying?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Space Station Material Costs
The station needs 4.5 meters of heat shielding that costs $12.60 per meter. Commander Diaz needs to calculate the total cost before submitting the supply order. What is the total cost of the shielding?
Concept Launch
💡 How do you multiply decimals?
To multiply decimals, you multiply the numbers as if there were no decimal points. Then you count the decimal places and put the point back in the answer.
Multiply like whole numbers, then the product has the SAME total of decimal places as both factors combined.
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Product Producto |
The answer when you multiply. La respuesta cuando multiplicas. |
4 × 7 = 28, so the product is 28 | |
| Decimal point Punto decimal |
The dot that splits the whole number from the part after it. El punto que separa el número entero de la parte que sigue. |
In 3.25, the decimal point separates 3 (ones) from 25 (tenths and hundredths) | |
| Estimate Estimar |
A close answer you get by rounding first. Una respuesta cercana que obtienes al redondear primero. |
3.7 × 4.2: round to 4 × 4 = 16, so the exact answer should be near 16 | |
| Place value Valor posicional |
What a digit is worth based on where it sits in a number. Lo que vale un dígito según el lugar que ocupa en el número. |
In 0.36: the 3 is in the tenths place (0.3) and the 6 is in the hundredths place (0.06) | |
| Decimal places Cifras decimales |
How many digits come after the decimal point. Cuántos dígitos hay después del punto decimal. |
3.4 (1 place) × 2.6 (1 place) = 8.84 (2 places total) |
Which Word Fits?
The answer to a multiplication problem is the ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
The station needs 4.5 meters of heat shielding at $12.60 per meter. About how much will it cost, and how did you estimate before multiplying?
👂 Listen For
Students round to about 5 × $13 = $65 (or 4 × $13) to predict the cost is in the $50-$65 range, naming 4.5 and 12.60 as the factors.
Extend: Will the exact product be larger or smaller than your estimate of 5 × $13? Justify using how you rounded each factor.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Estimate each product by rounding, then sort: which products are GREATER than 20 and which are LESS than 20?
✍️ Explore Discourse
How did estimating by rounding help you sort the products? How do you decide where to place the decimal in the exact product?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
When you multiplied 4.5 × 12.60, how did you decide where to put the decimal point in the product?
👂 Listen For
Students count the decimal places, multiply the digits, then place the point to get $56.70, and use the estimate to confirm placement.
Extend: Use your launch estimate to argue that $56.70 (not $5.67 or $567) is where the decimal point belongs. Explain.
Practice Check A
A car travels 55.5 miles per hour for 2.4 hours. How far does it go?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
What is 3.4 × 2.6?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Ratio Table Builder
Fill the ratio table. Each row must be equivalent.
| Factor | A | B |
|---|---|---|
| ×1 | ||
| ×2 | ||
| ×3 |
✍️ Justify Your Thinking
Sort: when you multiply two decimals, is the product GREATER than both factors, or LESS than at least one factor?
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Multiply like whole numbers, then the product has the SAME total of decimal places as both factors combined." — and it works because ___.
Because Product means ___, but a tricky part is ___, so I have to ___.
A common mistake with Product is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Decimal point to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Multiply like whole numbers, then the product has the SAME total of decimal places as both factors combined. because ___
Multiply like whole numbers, then the product has the SAME total of decimal places as both factors combined. but ___
Multiply like whole numbers, then the product has the SAME total of decimal places as both factors combined. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Estimate each product by rounding, then sort: which products are GREATER than 20 and which are LESS than 20?
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
What is 3.4 × 2.6?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A family is buying 3.5 pounds of deli meat that costs $6.80 per pound at the grocery store.
✍️ Connection Reasoning
How do you multiply decimals to find the total cost? How can estimation help you check?
The total cost is $___ because 3.5 × $6.80 = $___, and I can estimate by rounding to ___ × ___ = ___.
Turn & Talk — Connect
A family buys 3.5 pounds of deli meat at $6.80 per pound. How do you multiply the decimals to find the total cost, and how can estimating check it?
👂 Listen For
Students compute 3.5 × 6.80 = 23.80, estimate about 4 × $7 = $28 to confirm, and explain counting decimal places to place the point.
Extend: Why does multiplying by a number less than 1 (like 0.5 pound) give a product SMALLER than the price per pound? Explain with this example.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
What is 4.6 × 2.3?
Bonus Exit Check
What is 0.7 × 1.5?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students round to about 5 × $13 = $65 (or 4 × $13) to predict the cost is in the $50-$65 range, naming 4.5 and 12.60 as the factors.
• Students count the decimal places, multiply the digits, then place the point to get $56.70, and use the estimate to confirm placement.
• Students compute 3.5 × 6.80 = 23.80, estimate about 4 × $7 = $28 to confirm, and explain counting decimal places to place the point.
• Students contrast multiplication (multiply digits, then count total decimal places) with addition (align decimal points first) and explain why the rules differ.
Common mistake: A common mistake in Multiply Decimals is skipping the key idea: "Multiply like whole numbers, then the product has the SAME total of decimal places as both factors combined." — always check your work against this rule before you submit.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 133.2 miles — 555 × 24 = 13,320. Total decimal places: 1 + 1 = 2. Answer: 133.20 = 133.2 miles.
✓ Practice 2: 8.84 — 34 × 26 = 884. There are 2 total decimal places (1 + 1), so place the decimal to get 8.84.
✓ Practice 3: 1.05 — 7 × 15 = 105. There are 2 total decimal places (1 + 1), so place the decimal to get 1.05.
✓ Practice 4: 21.2 — 53 × 4 = 212. There is 1 total decimal place, so place the decimal to get 21.2.
✓ Exit ticket: 10.58 — 46 × 23 = 1,058. There are 2 total decimal places (1 + 1), so the answer is 10.58.