Exercises on Identifying Numbers Represented by Base 10 Blocks in Grade 1

Master base 10 blocks: 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 shown by these blocks?
2 tens and 3 ones
Definition:

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

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

There are 2 tens rods, each worth 10

Step 2: Calculate tens value

2 tens = 2 × 10 = 20

Step 3: Count the ones

There are 3 ones cubes, each worth 1

Step 4: Calculate ones value

3 ones = 3 × 1 = 3

Step 5: Add tens and ones

20 + 3 = 23

2 tens + 3 ones = 20 + 3 = 23
Final answer:

The number represented is 23

Applied rules:

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

• Multiplication Rule: Tens × 10

• Addition Rule: Tens value + ones value

2 Multiple Tens
Exercise 2
What number is shown by these blocks?
4 tens and 7 ones
Definition:

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

10
10
10
10
1
1
1
1
1
1
1
4 tens and 7 ones
Step 1: Count the tens

There are 4 tens rods

Step 2: Calculate tens value

4 tens = 4 × 10 = 40

Step 3: Count the ones

There are 7 ones cubes

Step 4: Calculate ones value

7 ones = 7 × 1 = 7

Step 5: Add tens and ones

40 + 7 = 47

4 tens + 7 ones = 40 + 7 = 47
Final answer:

The number represented is 47

Applied rules:

• Multiplication Rule: Number of tens × 10

• Addition Rule: Total = tens + ones

• Verification Rule: Check that parts add to whole

3 Zero Ones
Exercise 3
What number is shown by these blocks?
5 tens and 0 ones
Definition:

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

10
10
10
10
10
5 tens and 0 ones
Step 1: Count the tens

There are 5 tens rods

Step 2: Calculate tens value

5 tens = 5 × 10 = 50

Step 3: Count the ones

There are 0 ones cubes

Step 4: Calculate ones value

0 ones = 0 × 1 = 0

Step 5: Add tens and ones

50 + 0 = 50

5 tens + 0 ones = 50 + 0 = 50
Final answer:

The number represented is 50

Applied rules:

• Zero Rule: Adding zero doesn't change the value

• Place Value Rule: Tens digit in tens place, zeros in ones place

• Multiplication Rule: Any number × 0 = 0

Base 10 Blocks Concept Guide
(Tens × 10) + (Ones × 1) = Number
Base 10 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 10 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 methodology:
  1. Identify blocks: Separate tens rods from ones 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

Base 10 Block Values

This is what 1 ten rod represents (10 ones)
Solution: Exercises 4 to 5
4 Reverse Process
Exercise 4
Draw the base 10 blocks for the number 34.
Show 34 using tens and ones.
Definition:

Reverse Process: Starting with a number and showing it with base 10 blocks.

10
10
10
1
1
1
1
3 tens and 4 ones = 34
Step 1: Identify place values in 34

3 is in tens place, 4 is in ones place

Step 2: Draw tens

Draw 3 tens rods (each worth 10)

Step 3: Draw ones

Draw 4 ones cubes (each worth 1)

Step 4: Verify the representation

3 tens = 30, 4 ones = 4, 30 + 4 = 34 ✓

3 tens + 4 ones = 34
Final answer:

34 is represented by 3 tens and 4 ones

Applied rules:

• Place Value Rule: Tens digit = number of tens

• Representation Rule: Draw corresponding blocks

• Verification Rule: Check that blocks equal original number

5 Mixed Practice
Exercise 5
What number is shown by these blocks?
1 ten and 9 ones
Then draw the blocks for 26.
Definition:

Mixed Practice: Problems that involve both reading and creating base 10 block representations.

10
1
1
1
1
1
1
1
1
1
1 ten and 9 ones = 19
Step 1: Read 1 ten and 9 ones

1 ten = 1 × 10 = 10, 9 ones = 9 × 1 = 9

Step 2: Calculate total

10 + 9 = 19

Step 3: Draw blocks for 26

26 = 2 tens and 6 ones

Step 4: Verify both answers

1 ten + 9 ones = 19 ✓, 2 tens + 6 ones = 26 ✓

1 ten + 9 ones = 19, 26 = 2 tens + 6 ones
Final answers:

1 ten and 9 ones = 19; 26 = 2 tens and 6 ones

Applied rules:

• Reading Rule: Count and multiply blocks

• Creating Rule: Use place values to determine blocks

• Verification Rule: Always check both directions

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

Base 10 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 methodology:
  1. Identify blocks: Distinguish between tens rods and ones 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 10 blocks to build understanding.
Foundation Skill: Understanding base 10 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 10 Block Examples

Blocks Shown Tens Ones Calculation Number
2 tens, 3 ones 2 3 (2×10) + (3×1) 23
4 tens, 7 ones 4 7 (4×10) + (7×1) 47
5 tens, 0 ones 5 0 (5×10) + (0×1) 50
1 ten, 9 ones 1 9 (1×10) + (9×1) 19

Questions & Answers

Question: My child keeps confusing the tens and ones blocks. 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 blocks 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.