Exercises on Determining Numbers from Base Ten Blocks in Grade 1

Master base ten blocks identification: place value, visual representation, counting strategies, and number recognition through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Simple Tens and Ones
Exercise 1
What number is represented by the base ten blocks shown below?
1 ten rod and 5 one cubes
Definition:

Base Ten Blocks: Visual tools where rods represent tens (worth 10) and small cubes represent ones (worth 1).

Base Ten Block Identification Method:
  1. Count the number of ten rods
  2. Count the number of one cubes
  3. Multiply tens by 10 (each rod = 10)
  4. Add the tens value and ones value together
10
1
1
1
1
1
1 ten and 5 ones
Step 1: Count the ten rods

There is 1 ten rod, each worth 10

Step 2: Calculate tens value

1 ten = 1 × 10 = 10

Step 3: Count the one cubes

There are 5 one cubes, each worth 1

Step 4: Calculate ones value

5 ones = 5 × 1 = 5

Step 5: Add tens and ones

10 + 5 = 15

1 ten + 5 ones = 10 + 5 = 15
Final answer:

The number represented is 15

2 Multiple Tens
Exercise 2
What number is represented by the base ten blocks shown below?
3 ten rods and 2 one cubes
Definition:

Multiple Tens: When there are several ten rods, each still represents 10.

10
10
10
1
1
3 tens and 2 ones
Step 1: Count the ten rods

There are 3 ten rods

Step 2: Calculate tens value

3 tens = 3 × 10 = 30

Step 3: Count the one cubes

There are 2 one cubes

Step 4: Calculate ones value

2 ones = 2 × 1 = 2

Step 5: Add tens and ones

30 + 2 = 32

3 tens + 2 ones = 30 + 2 = 32
Final answer:

The number represented is 32

3 Zero Ones
Exercise 3
What number is represented by the base ten blocks shown below?
4 ten rods and 0 one cubes
Definition:

Zero Ones: When there are no one cubes, the ones value is 0.

10
10
10
10
4 tens and 0 ones
Step 1: Count the ten rods

There are 4 ten rods

Step 2: Calculate tens value

4 tens = 4 × 10 = 40

Step 3: Count the one cubes

There are 0 one cubes

Step 4: Calculate ones value

0 ones = 0 × 1 = 0

Step 5: Add tens and ones

40 + 0 = 40

4 tens + 0 ones = 40 + 0 = 40
Final answer:

The number represented is 40

Base Ten Block Identification Guide
(Tens × 10) + (Ones × 1) = Number
Base Ten Formula
Ten Rod
1 rod = 10
Worth 10 ones
One Cube
1 cube = 1
Single unit
Value Calculation
Tens × 10 + Ones × 1
Total number
Key definitions:

Base Ten Blocks: Physical or visual tools representing place value (rods = tens, cubes = ones)

Ten Rod: Long rectangular block representing 10 units

One Cube: Small square block representing 1 unit

Place Value: Value determined by position in number

Complete identification methodology:
  1. Identify blocks: Separate ten rods from one cubes
  2. Count each type: How many tens? How many ones?
  3. Calculate values: Tens × 10, Ones × 1
  4. Combine values: Add tens and ones together
  5. Verify result: Check if answer makes sense
Tip 1: Always count tens first, then ones to stay organized.
Tip 2: If there are no ones, the number ends in 0.
Tip 3: Count by tens for the tens: 10, 20, 30, etc.
Tip 4: Draw lines connecting blocks to numbers to visualize the process.

Common errors: Counting tens as ones, forgetting to multiply by 10.
Memory aid: "Long rods are tens, small cubes are ones."
Essential Rules:

• Value Rule: 1 ten rod = 10, 1 one cube = 1

• Multiplication Rule: Tens × 10

• Addition Rule: Tens + ones = total number

• Verification Rule: Always check your answer

Block Identification Tips

This is what 1 ten rod represents (10 ones)
Solution: Exercises 4 to 5
4 Reverse Process
Exercise 4
Draw the base ten blocks that represent the number 27.
Show 27 using tens and ones.
Definition:

Reverse Process: Starting with a number and showing it with base ten blocks.

10
10
1
1
1
1
1
1
1
2 tens and 7 ones = 27
Step 1: Identify place values in 27

2 is in tens place, 7 is in ones place

Step 2: Draw tens

Draw 2 ten rods (each worth 10)

Step 3: Draw ones

Draw 7 one cubes (each worth 1)

Step 4: Verify the representation

2 tens = 20, 7 ones = 7, 20 + 7 = 27 ✓

2 tens + 7 ones = 27
Final answer:

27 is represented by 2 tens and 7 ones

5 Mixed Practice
Exercise 5
What number is represented by the base ten blocks shown below?
2 ten rods and 8 one cubes
Then draw the blocks for 43.
Definition:

Mixed Practice: Problems that involve both reading and creating base ten block representations.

10
10
1
1
1
1
1
1
1
1
2 tens and 8 ones = 28
Step 1: Read 2 tens and 8 ones

2 tens = 2 × 10 = 20, 8 ones = 8 × 1 = 8

Step 2: Calculate total

20 + 8 = 28

Step 3: Draw blocks for 43

43 = 4 tens and 3 ones

Step 4: Verify both answers

2 tens + 8 ones = 28 ✓, 4 tens + 3 ones = 43 ✓

2 tens + 8 ones = 28, 43 = 4 tens + 3 ones
Final answers:

2 tens and 8 ones = 28; 43 = 4 tens and 3 ones

Complete Summary: Base Ten Block Identification
(Tens × 10) + (Ones × 1) = Number
Base Ten Formula
Key definitions:

Base Ten Blocks: Visual tools that help understand place value (rods = tens, cubes = ones)

Ten Rod: Long block representing 10 units (worth 10 ones)

One Cube: Small block representing 1 unit

Place Value: The value of a digit based on its position in the number

Complete identification methodology:
  1. Identify blocks: Distinguish between ten rods and one cubes
  2. Count accurately: Carefully count each type of block
  3. Apply values: Multiply tens by 10, ones by 1
  4. Combine totals: Add tens value and ones value
  5. Verify answer: Check that the sum makes sense
Tip 1: Use your fingers to touch each block as you count to avoid missing any.
Tip 2: Say the number out loud as you count: "10, 20, 30" for tens.
Tip 3: Draw a circle around each group of 10 ones to see if you can make a ten.
Tip 4: Practice with real or virtual base ten blocks to build understanding.

Foundation Skill: Understanding base ten blocks is essential for all future math.
Real-world use: Helps with money counting, measuring, and organizing.
Essential Rules:

• Value Rule: 1 ten rod = 10, 1 one cube = 1

• Multiplication Rule: Number of tens × 10

• Addition Rule: Tens value + ones value = total

• Verification Rule: Always check that parts equal the whole

• Organization Rule: Keep tens and ones separate when counting

Base Ten Block Examples

Blocks Shown Tens Ones Calculation Number
1 ten, 5 ones 1 5 (1×10) + (5×1) 15
3 tens, 2 ones 3 2 (3×10) + (2×1) 32
4 tens, 0 ones 4 0 (4×10) + (0×1) 40
2 tens, 8 ones 2 8 (2×10) + (8×1) 28

Questions & Answers

Question: My child keeps confusing the ten rods and one cubes. How can I help them remember which is which?

Answer: Use these memory aids:

  • Size clue: "Big blocks (long rods) are tens, small blocks (cubes) are ones"
  • Name clue: "Tens are longer, so they're worth more"
  • Counting clue: "Ten rods are made up of 10 little ones put together"

Practice with real objects: show them that 10 individual cubes can be lined up to match the length of 1 ten rod. This visual connection helps cement the relationship. Also, have them say "ten rod" and "one cube" out loud when counting to reinforce the names.

Question: Some students are counting each individual cube in a ten rod. How can I teach them to count by tens?

Answer: Build the concept gradually:

  1. Show the relationship: Count 10 individual cubes, then show how they form 1 ten rod
  2. Practice skip counting: Count by tens (10, 20, 30...) while pointing to each rod
  3. Use visual cues: Draw circles around groups of 10 ones to show they make a ten
  4. Connect to real life: Compare to bundles of 10 pencils or packs of 10 crayons
  5. Reinforce regularly: Daily practice with counting by tens

Emphasize that the ten rod is a "shortcut" for counting 10 ones quickly. Once they understand this concept, they'll naturally count rods as "10, 20, 30" rather than "1, 2, 3..."

Question: How can I help students who struggle with the concept that 1 ten rod equals 10 ones?

Answer: Use concrete, hands-on experiences:

  • Build it yourself: Have students line up 10 individual cubes next to a ten rod to see they're equal
  • Exchange activity: Let them trade 10 ones for 1 ten rod and vice versa
  • Grouping exercise: Give them 20 individual cubes and have them group into sets of 10
  • Visual comparison: Show side-by-side that 10 small cubes = 1 long rod

Make it a game: "How many ones do you need to get 1 ten rod?" or "If I have 1 ten rod, how many ones could I trade for?" This hands-on exploration helps build the conceptual understanding that's crucial for place value mastery.