Modeling Decimals
Subtraction Strategies & Exploring Thousandths
📋 Learning Targets
What we'll accomplish today
5.NBT.1 — Recognize that a digit represents 10× what it represents to its right and ⅟₁₀ what it represents to its left.
5.NBT.3a — Read decimals to thousandths using base-ten numerals.
5.NBT.7 — Subtract decimals to hundredths using models and strategies based on place value.
- Subtract decimals using place value strategies
- Explain the ×10 and ÷10 relationship between places
- Model and read thousandths and ten-thousandths
- Use structure to solve problems efficiently
💊 The Pharmacy Problem
Why thousandths matter in real life
A pharmacist measures medicine in milligrams.
The prescription calls for 0.125 grams of medication.
0.125What if she accidentally gives 1.25 grams instead?
That's 10 TIMES too much! ⚠️
Understanding place value can literally save lives!
🔄 Place Value Review
The foundation of our decimal system
3.45 = 3 ones + 4 tenths + 5 hundredths
💡 The ×10 and ÷10 Pattern
The key relationship between place values
Move LEFT
×10
Value gets BIGGER
Move RIGHT
÷10
Value gets SMALLER
0.1 × 10 = 1
0.01 × 10 = 0.1
0.001 × 10 = 0.01
💬 Turn & Talk
Discuss with your partner
0.003 (three thousandths!)
👁️ Subtraction Problem String
Watch how I solve this — Problem 1
This is our anchor problem — we know 5 − 3 = 2. Now let's see how this helps us with decimals!
👁️ Subtraction Problem String
Using what we know — Problem 2
💡 5 tenths − 3 tenths = 2 tenths
Same structure as 5 − 3 = 2!
👁️ Subtraction Problem String
Extending the pattern — Problem 3
💡 5 hundredths − 3 hundredths = 2 hundredths
The pattern continues!
🔍 What Do You Notice?
Looking for structure in our problem string
Problem 1
5 − 3 = 2
Problem 2
0.5 − 0.3 = 0.2
Problem 3
0.05 − 0.03 = 0.02
✨ Introducing Thousandths
One step smaller than hundredths
If we divide one hundredth into 10 equal parts...
0.01 ÷ 10 = 0.001
Each part is one thousandth
Answer: 0.005 − 0.003 = 0.002
📊 Modeling Thousandths
Visualizing tiny decimal places
Imagine splitting that tiny square into 10 pieces!
🔬
📖 Reading Thousandths
How to say these numbers
🔬 Ten-Thousandths
Going even smaller!
What if we divide one thousandth into 10 equal parts?
0.001 ÷ 10 = 0.0001
Each part is one ten-thousandth
Scientists use ten-thousandths (and even smaller!) when measuring things like atoms, blood cells, and chemical reactions.
📊 Extended Place Value Chart
From ones all the way to ten-thousandths
2.5047
Two and five thousand forty-seven ten-thousandths
💬 Turn & Talk
Check your understanding
The 2 is in the thousandths place.
Its value is 0.002 (two thousandths)
✍️ Guided Practice
Let's solve together — Problem 1
8 tenths − 5 tenths = 3 tenths
✍️ Guided Practice
Let's solve together — Problem 2
74 hundredths − 31 hundredths = 43 hundredths
✍️ Guided Practice
Let's solve together — Problem 3
625 thousandths − 418 thousandths = 207 thousandths
✍️ Guided Practice
Let's solve together — Problem 4
Think: 1.50 − 0.75 = 0.75
✍️ Guided Practice
Let's solve together — Problem 5
The 7 is in the hundredths place = 7 hundredths
📝 Your Turn!
Independent Practice — Problem 1
0.5
📝 Your Turn!
Independent Practice — Problem 2
0.34
📝 Your Turn!
Independent Practice — Problem 3
0.250 or 0.25
📝 Your Turn!
Independent Practice — Problem 4
0.06
6 hundredths
✅ Quick Check
Show what you know!
Which number shows five thousandths?
🏠 Modeling Decimals Home Connection
Tonight's assignment
- Complete the Modeling Decimals Home Connection worksheet
- Practice reading decimals to thousandths out loud
- Find 3 examples of decimals at home (prices, measurements, etc.)
- Write each decimal in word form
Look at nutrition labels, gas prices, or sports statistics — decimals are everywhere!
📌 What We Learned
Key takeaways from today
- ✅ Subtracted decimals using place value strategies
- ✅ Explained the ×10 and ÷10 relationship
- ✅ Modeled and read thousandths and ten-thousandths
- ✅ Used structure (5 − 3 = 2) to solve related problems
🔑 Big Idea: Moving right in the place value chart divides by 10. Thousandths are 10× smaller than hundredths!
🎫 Exit Ticket
Show your understanding
- Solve: 0.72 − 0.45 = ____
- Solve: 0.008 − 0.003 = ____
- Write in word form: 0.047
- What is the value of 5 in 3.2567?
Turn in your exit ticket before you leave! 📤