🧱

Base Ten Blocks & Decimals

Practice Problems

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Section 1

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:

Mat (Flat)
= 1.00
one whole
Strip
= 0.1
one tenth
Unit (Small Square)
= 0.01
one hundredth

🔟 The Trading Rule

Remember This!

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!

Section 2

Blocks → Decimals 📝

Look at the blocks and write the decimal!

✏️ What decimal is shown?

2 mats
3 strips
5 units
1 2 mats + 3 strips + 5 units = ?
Answer:
2.35

✏️ What decimal is shown?

1 mat
0 strips
7 units
2 1 mat + 0 strips + 7 units = ?
Answer:
1.07
Think About It

If there are 0 strips, what number belongs in the tenths place?

✏️ What decimal is shown?

none
0 mats
4 strips
2 units
3 0 mats + 4 strips + 2 units = ?
Answer:
0.42

✏️ What decimal is shown?

3 mats
9 strips
none
0 units
4 3 mats + 9 strips + 0 units = ?
Answer:
3.9 or 3.90

⚡ Quick Practice Round!

Write the decimal for each

A. 5 mats, 2 strips, 8 units

5.28

B. 0 mats, 0 strips, 4 units

0.04

C. 1 mat, 6 strips, 0 units

1.60 or 1.6

D. 4 mats, 0 strips, 1 unit

4.01
Section 3

Decimals → Blocks 🧱

Now let's go the other way! I give you the decimal, you figure out the blocks.

🏗️ Build This Decimal!

1.56

How many of each piece do you need?

1
mat
5
strips
6
units

🏗️ Build This Decimal!

0.08

How many of each piece do you need?

0
mats
0
strips
8
units
Think About It

What does the 0 in the tenths place tell us about strips?

🏗️ Build This Decimal!

2.40

How many of each piece do you need?

2
mats
4
strips
0
units
Partner Talk

Do we need any units? Is 2.40 the same as 2.4? Discuss!

🤝 Partner Practice

Take Turns!

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!

Try These Together

0.99

1.11

3.05

Section 4

Minimal Collection 🎯

Use the FEWEST pieces possible by regrouping!

🔄 Regroup to Minimal Collection

1 I have 12 strips. What's the minimal collection?
Think About It

Can we trade 10 strips for something? What do 10 strips equal?

1
mat
2
strips
0
units
=
1.2

🔄 Regroup to Minimal Collection

2 I have 15 units. What's the minimal collection?
Think About It

10 units = 1 strip. So 15 units = ?

0
mats
1
strip
5
units
=
0.15

🔄 Big Regrouping Challenge!

Challenge Problem

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

Section 5

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

or

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

Partner Talk

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

Section 6

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!

Challenge 1

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!

Challenge 2

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!