Add and Subtract Decimals
I can add and subtract decimals by lining up the place values and the decimal points.
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🎯 Content Objective / Objetivo de contenido
I can add and subtract decimals by lining up the place values and the decimal points.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
The fuel tank reads 128.75 liters, a shuttle delivers 46.8 liters, and docking thrusters used 19.35 liters. Why must you line up the decimal points before adding or subtracting these amounts?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Space Station Fuel Monitor
The space station's main fuel tank reads 128.75 liters. A resupply shuttle delivers 46.8 liters of fuel, but the thrusters used 19.35 liters during docking. What is the fuel level after both events?
Concept Launch
💡 How do you add and subtract decimals?
A decimal is a number with a point that shows parts smaller than one whole. To add or subtract decimals, you line up the decimal points so the same place values match.
Line up the decimal points, annex zeros if needed, then add or subtract one column at a time.
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 |
|---|---|---|---|
| Decimal Decimal |
A number with a dot that shows a part between whole numbers. Un número con un punto que muestra una parte entre números enteros. |
3.75 means 3 ones + 7 tenths + 5 hundredths — it is between 3 and 4 | |
| 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 4.38: the 4 = 4 ones, the 3 = 3 tenths (0.3), the 8 = 8 hundredths (0.08) | |
| Tenths Décimas |
The first spot after the decimal point. It shows parts out of 10. El primer lugar después del punto decimal. Muestra partes de 10. |
0.7 = 7/10 — like 7 slices of a pizza cut into 10 equal slices | |
| Hundredths Centésimas |
The second spot after the decimal point. It shows parts out of 100. El segundo lugar después del punto decimal. Muestra partes de 100. |
0.05 = 5/100 — like 5 pennies out of a dollar (100 pennies) | |
| Annex zeros Agregar ceros |
Adding zeros at the end of a decimal so numbers line up evenly. Agregar ceros al final de un decimal para que los números se alineen. |
15.7 becomes 15.70 so you can subtract 15.70 − 8.36 with aligned place values |
Which Word Fits?
A number that uses a point to show a value less than one whole is a ___.
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 fuel tank reads 128.75 liters, a shuttle delivers 46.8 liters, and docking thrusters used 19.35 liters. Why must you line up the decimal points before adding or subtracting these amounts?
👂 Listen For
Students explain that aligning decimal points lines up matching place values (tenths under tenths, hundredths under hundredths) so the addition and subtraction are correct.
Extend: Estimate the final fuel level by rounding each number, then explain how that estimate checks your exact answer of 128.75 + 46.8 − 19.35.
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
Plot each decimal on the number line, then find the sum or difference as indicated.
✍️ Explore Discourse
How does a number line help you see what happens when you add or subtract decimals?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
When you added 128.75 and 46.8, how did you handle 46.8 having fewer decimal places, and when did you need to regroup?
👂 Listen For
Students annex a zero to write 46.80, aligning hundredths, and explain regrouping happens when a column sum is 10 or more (or borrowing is needed when subtracting).
Extend: Why does annexing a zero to make 46.8 into 46.80 not change its value? Justify with place value.
Practice Check A
A student buys items costing $4.59, $12.75, and $3.80. What is the total cost?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
What is 14.6 + 3.85?
✍️ 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
Estimate each sum or difference by rounding to the nearest whole number, then sort: is the result greater than 10 or less than 10?
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: "Line up the decimal points, annex zeros if needed, then add or subtract one column at a time." — and it works because ___.
Because Decimal means ___, but a tricky part is ___, so I have to ___.
A common mistake with Decimal is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Place value to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Line up the decimal points, annex zeros if needed, then add or subtract one column at a time. because ___
Line up the decimal points, annex zeros if needed, then add or subtract one column at a time. but ___
Line up the decimal points, annex zeros if needed, then add or subtract one column at a time. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Plot each decimal on the number line, then find the sum or difference as indicated.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
What is 14.6 + 3.85?
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 runner's times for three laps are 2.45 minutes, 2.6 minutes, and 2.38 minutes. She wants to find her total time to see if she beat her personal record of 7.5 minutes.
✍️ Connection Reasoning
How do you add decimals with different numbers of decimal places to find her total time?
The runner's total time is ___ minutes because 2.45 + 2.60 + 2.38 = ___.
Turn & Talk — Connect
A runner's three laps are 2.45, 2.6, and 2.38 minutes. How do you add decimals with different numbers of places to find her total time?
👂 Listen For
Students annex zeros (2.60), align the decimal points, and add 2.45 + 2.60 + 2.38 = 7.43 minutes.
Extend: Her personal record is 7.5 minutes. Did she beat it? Compare 7.43 and 7.5 using place value and justify.
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
What is 32.6 − 14.85?
Bonus Exit Check
What is 20.3 − 7.48?
✍️ 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 explain that aligning decimal points lines up matching place values (tenths under tenths, hundredths under hundredths) so the addition and subtraction are correct.
• Students annex a zero to write 46.80, aligning hundredths, and explain regrouping happens when a column sum is 10 or more (or borrowing is needed when subtracting).
• Students annex zeros (2.60), align the decimal points, and add 2.45 + 2.60 + 2.38 = 7.43 minutes.
• Students explain that decimals can have different numbers of places, so lining up the decimal point (not the right edge) is what keeps tenths with tenths and hundredths with hundredths.
Common mistake: A common mistake in Add and Subtract Decimals is skipping the key idea: "Line up the decimal points, annex zeros if needed, then add or subtract one column at a time." — 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: $21.14 — 4.59 + 12.75 + 3.80 = 21.14. Line up decimal points and add column by column.
✓ Practice 2: 18.45 — Line up decimals: 14.60 + 3.85. Hundredths: 0 + 5 = 5. Tenths: 6 + 8 = 14, write 4 carry 1. Ones: 4 + 3 + 1 = 8. Tens: 1. Answer: 18.45.
✓ Practice 3: 12.82 — Rewrite as 20.30 − 7.48. Annex a zero so both have two decimal places. Work carefully with borrowing: 20.30 − 7.48 = 12.82.
✓ Practice 4: 13.75 — Line up decimals: 9.05 + 4.70. Hundredths: 5 + 0 = 5. Tenths: 0 + 7 = 7. Ones: 9 + 4 = 13. Answer: 13.75.
✓ Exit ticket: 17.75 — Rewrite as 32.60 − 14.85. Hundredths: 0 − 5 → borrow → 10 − 5 = 5. Tenths: 5 − 8 → borrow → 15 − 8 = 7. Ones: 1 − 4 → borrow → 11 − 4 = 7. Tens: 2 − 1 = 1. Answer: 17.75.