Solved Exercises on Representing Numbers with Base-Ten Blocks in Grade 1

Master place value: visualizing numbers with base-ten blocks, understanding tens and ones, and number composition through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Representing numbers with base-ten blocks
Exercise 1
Show these numbers using base-ten blocks:
24, 37, 51
Definition:

Base-ten blocks: Visual tools where long sticks represent tens and small squares represent ones

Base-ten representation method:
  1. Identify the tens and ones in the number
  2. Draw the appropriate number of ten sticks
  3. Draw the appropriate number of one units
  4. Verify that the total equals the original number
Number Tens Ones Blocks Needed Visual Representation
24 2 4 2 sticks + 4 units
10
10
1
1
1
1
37 3 7 3 sticks + 7 units
10
10
10
1
1
1
1
1
1
1
51 5 1 5 sticks + 1 unit
10
10
10
10
10
1
Step 1: Identify tens and ones in 24

24 = 2 tens and 4 ones

Step 2: Draw base-ten blocks

Draw 2 long sticks (each representing 10) and 4 small squares (each representing 1)

Step 3: Verify total

(2 × 10) + (4 × 1) = 20 + 4 = 24 ✓

24 = 2 tens + 4 ones
10
10
1
1
1
1
24: 2 tens + 4 ones
37: 3 tens + 7 ones
51: 5 tens + 1 one
Final answer:

24: 2 ten sticks + 4 one units, 37: 3 ten sticks + 7 one units, 51: 5 ten sticks + 1 one unit

Applied rules:

• Base-10 representation: Each stick = 10, each unit = 1

• Place value: Tens digit tells how many ten sticks needed

• Verification: Total blocks should equal original number

2 Identifying numbers from base-ten blocks
Exercise 2
What number do these base-ten blocks represent?
4 ten sticks + 6 one units, 7 ten sticks + 3 one units
Definition:

Block identification: Counting base-ten blocks to determine the represented number

10
10
10
10
1
1
1
1
1
1
4 tens + 6 ones = 46
Blocks Tens Ones Calculation Number
4 sticks + 6 units 4 6 (4 × 10) + (6 × 1) 46
7 sticks + 3 units 7 3 (7 × 10) + (3 × 1) 73
Step 1: Count the ten sticks

4 ten sticks = 4 tens = 40

Step 2: Count the one units

6 one units = 6 ones = 6

Step 3: Add the values

40 + 6 = 46

4 tens + 6 ones = 46
7 tens + 3 ones = 73
Final answer:

4 ten sticks + 6 one units = 46, 7 ten sticks + 3 one units = 73

Applied rules:

• Block counting: Count each type of block separately

• Value calculation: Sticks × 10, units × 1

• Summation: Add tens value and ones value together

3 Numbers with zero in ones place
Exercise 3
Show these numbers using base-ten blocks:
40, 70, 90
Definition:

Zero in ones place: Numbers that have no individual units, only tens

Number Tens Ones Blocks Needed Visual Representation
40 4 0 4 sticks + 0 units
10
10
10
10
70 7 0 7 sticks + 0 units
10
10
10
10
10
10
10
90 9 0 9 sticks + 0 units
10
10
10
10
10
10
10
10
10
10
10
10
10
40 = 4 tens + 0 ones
Step 1: Identify tens and ones in 40

40 = 4 tens and 0 ones

Step 2: Draw base-ten blocks

Draw 4 long sticks (each representing 10) and 0 small squares

Step 3: Verify total

(4 × 10) + (0 × 1) = 40 + 0 = 40 ✓

40: 4 tens + 0 ones
70: 7 tens + 0 ones
90: 9 tens + 0 ones
Final answer:

40: 4 ten sticks + 0 one units, 70: 7 ten sticks + 0 one units, 90: 9 ten sticks + 0 one units

Applied rules:

• Zero representation: No individual units needed

• Round numbers: Only tens blocks required

• Place value: Zero still holds the ones place

Base-Ten Block System and Place Value
Number = (Tens × 10) + (Ones × 1)
Base-Ten Block Formula
Ten Stick
= 10
Represents 10 ones
One Unit
= 1
Represents 1 one
Base-10
Groups of 10
Our number system
Key definitions:

Base-ten blocks: Manipulative tools that visually represent place value

Ten stick: A long rectangular block representing 10 units

One unit: A small cube representing 1 unit

Place value: The value of a digit based on its position

Visual representation: Using physical or drawn blocks to show numbers

Base-ten block methodology:
  1. Identify the number: Determine what number needs representation
  2. Separate tens and ones: Break down the number into place values
  3. Select appropriate blocks: Choose the right number of sticks and units
  4. Verify accuracy: Ensure total blocks equal original number
Tip 1: Remember: 1 ten stick equals 10 individual units in value.
Tip 2: Always count tens first, then ones when reading blocks.
Tip 3: Zero in ones place means no individual units needed.
Tip 4: Practice drawing blocks to reinforce the concept.
Base-10 system: We use 10 as our base for grouping numbers.
Visual learning: Blocks make abstract concepts concrete.
Base-ten block rules to remember:

• Ten stick = 10 individual units

• One unit = 1 individual unit

• Tens digit = number of ten sticks needed

• Ones digit = number of one units needed

• Total value = (sticks × 10) + (units × 1)

Base-Ten Block Guide
📊
Ten Stick
Long block representing 10 units
24: 2 ten sticks = 20
One Unit
Small cube representing 1 unit
24: 4 one units = 4
Place Value
Tens and ones represented separately
24: 2 tens + 4 ones
Total Value
Sum of all block values
20 + 4 = 24
Solution: Exercises 4 to 5
4 Converting between forms
Exercise 4
Convert between number form and base-ten block form:
63 → base-ten blocks, base-ten blocks (5 sticks + 8 units) → number
Definition:

Form conversion: Changing between numerical and visual representations

Conversion Tens Ones Blocks Calculation Result
63 → blocks 6 3 6 sticks + 3 units (6 × 10) + (3 × 1) 63
blocks → number 5 8 5 sticks + 8 units (5 × 10) + (8 × 1) 58
10
10
10
10
10
10
1
1
1
63 = 6 tens + 3 ones
Step 1: For 63 → blocks

63 has 6 tens and 3 ones

Step 2: Draw corresponding blocks

6 ten sticks and 3 one units

Step 3: For blocks → number

5 sticks + 8 units = (5 × 10) + (8 × 1) = 50 + 8 = 58

63 → 6 ten sticks + 3 one units
5 sticks + 8 units → 58
Final answer:

63 → 6 ten sticks + 3 one units, 5 sticks + 8 units → 58

Applied rules:

• Direct correlation: Tens digit = number of ten sticks

• Ones correlation: Ones digit = number of one units

• Reverse calculation: Multiply and add to find total

5 Problem solving with base-ten blocks
Exercise 5
Tom has 3 ten sticks and 5 one units. How many total does he have? Draw the blocks and write the number.
Definition:

Problem solving: Applying base-ten block knowledge to solve real-world scenarios

Description Tens Ones Blocks Calculation Result
Tom's tens 3 - 3 sticks 3 × 10 = 30 30
Tom's ones - 5 5 units 5 × 1 = 5 5
Total 3 5 3 sticks + 5 units 30 + 5 = 35 35
10
10
10
1
1
1
1
1
3 tens + 5 ones = 35
Step 1: Identify given blocks

Tom has 3 ten sticks and 5 one units

Step 2: Calculate value of tens

3 ten sticks = 3 × 10 = 30

Step 3: Calculate value of ones

5 one units = 5 × 1 = 5

Step 4: Find total value

30 + 5 = 35

Tom has 35 total
Final answer:

Tom has 35 total (3 ten sticks + 5 one units)

Applied rules:

• Problem translation: Convert words to block counts

• Value calculation: Multiply blocks by their values

• Summation: Add all values to get total

Comprehensive Summary: Representing Numbers with Base-Ten Blocks
N = (T × 10) + (O × 1)
Base-Ten Block Formula
Key definitions:

Base-ten blocks: Manipulative tools that visually represent place value using sticks for tens and units for ones

Ten stick: A long rectangular block representing 10 individual units

One unit: A small cube representing 1 individual unit

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

Visual representation: Using physical or drawn blocks to model numbers concretely

Base-10 system: Our decimal number system based on groups of 10

Complete base-ten block methodology:
  1. Identify the number: Determine what number needs to be represented
  2. Separate place values: Identify tens and ones digits
  3. Select appropriate blocks: Choose correct number of sticks and units
  4. Arrange systematically: Organize blocks in a clear, organized manner
  5. Verify accuracy: Ensure total block value equals original number
Tip 1: Remember: 1 ten stick equals 10 individual units in value.
Tip 2: Always draw or count tens first, then ones for organization.
Tip 3: Zero in ones place means no individual units are needed.
Tip 4: Practice drawing blocks to reinforce the connection between visual and numerical forms.
Base-10 foundation: Our entire number system is built on groups of 10.
Visual learning: Blocks make abstract place value concepts concrete and understandable.
Essential base-ten block rules:

• Block equivalence: 1 ten stick = 10 one units

• Digit correspondence: Tens digit = number of ten sticks

• Ones correspondence: Ones digit = number of one units

• Total calculation: (sticks × 10) + (units × 1)

• Zero handling: Zero in ones place means no individual units needed

Base-Ten Block Mastery Framework
📊
Ten Stick Value
Long block represents 10 units
57: 5 ten sticks = 50
One Unit Value
Small cube represents 1 unit
57: 7 one units = 7
Place Value
Tens and ones separated visually
57: 5 tens + 7 ones
Total Calculation
Sum of all block values
50 + 7 = 57
Key takeaways:

• Base-ten blocks provide concrete visualization of abstract place value concepts

• Understanding the relationship between tens and ones builds strong number sense

• Visual representations help bridge the gap between concrete and abstract thinking

• Practice with various numbers builds fluency in place value understanding

Questions & Answers

Question: Why do we use these long sticks for tens? Can't we just use 10 little squares?

Answer: Great question! We use long sticks for tens because:

  • Efficiency: It's much faster than counting 10 little squares
  • Organization: It's easier to see groups of 10 when they're bundled together
  • Real-world connection: It shows that 1 ten is a single group worth 10
  • Space-saving: 1 long stick takes up less space than 10 little squares

Think of it like having 1 bundle of 10 pencils instead of 10 separate pencils!

The long stick represents the idea that 10 ones can be grouped together to make 1 ten.

Question: My child gets confused when there are no ones units shown. How can I help them understand numbers like 40?

Answer: Zero in the ones place can be confusing! Here's how to clarify:

  • Emphasize the concept: "40 means 4 tens and 0 ones - no extra ones"
  • Use the blocks: Show 4 long sticks and explicitly say "and 0 small squares"
  • Count together: "40, 41, 42..." - there are no extra numbers after 40
  • Real examples: 40 dollars = 4 tens of dollars, no extra dollars

The zero holds the ones place and tells us there are no extra ones beyond the tens.

Practice with round numbers (20, 30, 40, 50) to build comfort with zero in ones place!

Question: How do I know if I have the right number of blocks? Sometimes I think I have the right amount but I'm wrong!

Answer: Here's a foolproof way to check your blocks:

  • Count the ten sticks: Count how many long sticks you have
  • Multiply by 10: Each stick equals 10, so multiply the number of sticks by 10
  • Count the one units: Count how many small squares you have
  • Add together: The result should equal your original number

Example: For 34, you should have 3 sticks (3 × 10 = 30) and 4 units (4 × 1 = 4), so 30 + 4 = 34 ✓

Always double-check by adding your calculated values!

The total of all your blocks should always equal the number you started with!

Question: How can I make base-ten blocks more accessible if I don't have physical ones?

Answer: There are many alternatives to physical blocks:

  • Draw them: Sketch long rectangles for tens and small squares for ones
  • Use household items: Straws bundled with rubber bands, paper clips grouped in 10s
  • Online tools: Virtual base-ten block websites and apps
  • Paper cutouts: Cut out rectangles and squares from paper

You can also use coins: dimes for tens and pennies for ones!

The key is having something to represent groups of 10 and individual units!

Question: How does working with base-ten blocks prepare students for higher math concepts?

Answer: Base-ten blocks lay the foundation for many advanced concepts:

  • Addition with regrouping: Understanding when 10 ones become 1 ten
  • Subtraction with borrowing: Breaking apart tens into ones
  • Multiplication: Understanding partial products using place value
  • Division: Working with place value in algorithms
  • Decimal system: All number work builds on base-10 understanding

Students who master base-ten blocks develop stronger computational fluency.

Example: Understanding that 45 = 40 + 5 helps with 45 + 23 = (40 + 20) + (5 + 3).

This visual foundation supports mathematical reasoning throughout schooling!