Base Ten Blocks & Decimals
Practice Problems
Quick Review 🔄
Let's remember what each base ten piece is worth when the mat equals 1 whole.
🧱 Base Ten Pieces = Decimals
When the mat = 1 whole, here's what each piece is worth:
🔟 The Trading Rule
10 of these = 1 of those (to the left)
10
units
=
1
strip
10
strips
=
1
mat
100
units
=
1
mat
This is just like: 10 hundredths = 1 tenth, and 10 tenths = 1 whole!
Blocks → Decimals 📝
Look at the blocks and write the decimal!
✏️ What decimal is shown?
✏️ What decimal is shown?
If there are 0 strips, what number belongs in the tenths place?
✏️ What decimal is shown?
✏️ What decimal is shown?
⚡ Quick Practice Round!
A. 5 mats, 2 strips, 8 units
B. 0 mats, 0 strips, 4 units
C. 1 mat, 6 strips, 0 units
D. 4 mats, 0 strips, 1 unit
Decimals → Blocks 🧱
Now let's go the other way! I give you the decimal, you figure out the blocks.
🏗️ Build This Decimal!
How many of each piece do you need?
🏗️ Build This Decimal!
How many of each piece do you need?
What does the 0 in the tenths place tell us about strips?
🏗️ Build This Decimal!
How many of each piece do you need?
Do we need any units? Is 2.40 the same as 2.4? Discuss!
🤝 Partner Practice
Partner A: Say a decimal between 0 and 5 (example: 3.27)
Partner B: Tell how many mats, strips, and units to build it
Then switch roles!
0.99
1.11
3.05
Minimal Collection 🎯
Use the FEWEST pieces possible by regrouping!
🔄 Regroup to Minimal Collection
Can we trade 10 strips for something? What do 10 strips equal?
🔄 Regroup to Minimal Collection
10 units = 1 strip. So 15 units = ?
🔄 Big Regrouping Challenge!
I have: 2 mats, 14 strips, and 23 units
Regroup to a minimal collection and write the decimal!
Step 1: 23 units → 2 strips + 3 units
Step 2: 14 strips + 2 more strips = 16 strips
Step 3: 16 strips → 1 mat + 6 strips
Step 4: 2 mats + 1 more mat = 3 mats
= 3 mats, 6 strips, 3 units = 3.63
Comparison Problems ⚖️
Use blocks to help compare decimals!
⚖️ Equal or Not Equal?
1 mat + 5 strips
1 mat + 50 units
They're EQUAL! Both = 1.5
5 strips = 50 units (because 5 tenths = 50 hundredths)
1.5 = 1.50
⚖️ Which is Greater?
0.6
6 strips
0.42
4 strips + 2 units
0.6 is GREATER!
0.6 = 6 tenths = 60 hundredths
0.42 = 42 hundredths
60 hundredths > 42 hundredths
📊 Put in Order: Least to Greatest
1.2
1.09
1.15
Think about it with blocks! How many strips and units for each?
1.09 = 1 mat, 0 strips, 9 units
1.15 = 1 mat, 1 strip, 5 units
1.2 = 1 mat, 2 strips, 0 units
1.09 < 1.15 < 1.2
Mixed Practice 🌟
Put it all together with these challenge problems!
📖 Word Problem
Maria is building a decimal with base ten blocks. She uses:
- 2 mats
- 4 strips
- 12 units
What decimal did Maria build?
Write it as a minimal collection too!
First: 12 units = 1 strip + 2 units
Then: 4 strips + 1 strip = 5 strips
Final: 2 mats, 5 strips, 2 units
= 2.52
⭐ Challenge Round!
I'm thinking of a decimal.
It has 2 more strips than mats.
It has 3 fewer units than strips.
The total is 1.52.
How many of each piece?
1.52 = 1 mat, 5 strips, 2 units
Check: 5 strips is 4 more than 1 mat ❌
Hmm... let's think differently!
If mats = 1, strips = 3, units = 0... that's 1.30 ❌
If mats = 1, strips = 3, units = 0... no wait:
1 mat, 3 strips, 0 units... but that's 1.30!
Trick question! The clues don't perfectly match 1.52 in minimal form. 🤔
⭐ Final Challenge!
Without regrouping, what's the LARGEST decimal you can make with:
- No more than 3 mats
- No more than 9 strips
- No more than 9 units
Use the maximum of each!
3 mats + 9 strips + 9 units
= 3.99
Fantastic Work!
You're becoming a base ten blocks expert! Remember: the mat is 1 whole, strips are tenths, and units are hundredths. Keep practicing and these connections will become automatic!