Solved Exercises on Expanded Form in Grade 1

Master expanded form: place value, tens and ones, number decomposition, base-10 blocks, visual representations through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Understanding Tens and Ones
Exercise 1
Write 24 in expanded form using tens and ones.
Show with base-10 blocks.
Definition:

Expanded form: Writing a number as the sum of its place values (tens + ones)

Place value method:
  1. Identify the tens digit and ones digit
  2. Write the tens as tens (multiply by 10)
  3. Write the ones as ones (multiply by 1)
  4. Add them together
Number
24
Expanded
20 + 4
Step 1: Identify place values

In 24, the tens digit is 2 and the ones digit is 4

Step 2: Convert tens to value

2 tens = 2 × 10 = 20

Step 3: Keep ones as value

4 ones = 4 × 1 = 4

Step 4: Combine with addition

20 + 4 = 24

24 = 20 + 4
Final answer:

24 = 20 + 4 (two tens and four ones)

Applied rules:

• Place value: Each digit has a value based on its position

• Tens rule: Tens digit × 10

• Ones rule: Ones digit × 1

2 Decomposing Numbers
Exercise 2
Write 37 in expanded form.
Draw the base-10 blocks.
Definition:

Number decomposition: Breaking apart a number into its tens and ones components

Number
37
Expanded
30 + 7
Visual
3 rods + 7 cubes
Step 1: Separate digits

37 has 3 tens and 7 ones

Step 2: Calculate tens value

3 × 10 = 30

Step 3: Calculate ones value

7 × 1 = 7

Step 4: Add together

30 + 7 = 37

37 = 30 + 7
Final answer:

37 = 30 + 7 (three tens and seven ones)

Applied rules:

• Decomposition: Every number can be broken into tens and ones

• Base-10 system: Uses groups of 10

• Visual representation: Helps understand place value

3 Place Value Understanding
Exercise 3
Write 56 in expanded form.
Show how many tens and ones.
Definition:

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

Number
56
Place Value
5 tens + 6 ones
Expanded
50 + 6
Step 1: Identify positions

In 56, 5 is in the tens place and 6 is in the ones place

Step 2: Convert tens place

5 in tens place = 5 × 10 = 50

Step 3: Convert ones place

6 in ones place = 6 × 1 = 6

Step 4: Add to get original

50 + 6 = 56

56 = 50 + 6
Final answer:

56 = 50 + 6 (five tens and six ones)

Applied rules:

• Position matters: Left digit is tens, right digit is ones

• Value calculation: Digit × Place value

• Verification: Sum of parts equals original number

Rules and methods, laws,...
24 = 20 + 4
Expanded Form
Rule 1
Tens = digit × 10
Calculate tens value
Rule 2
Ones = digit × 1
Keep ones value
Rule 3
Expanded = tens + ones
Combine with addition
Key definitions:

Expanded form: Writing a number as the sum of its place values

Place value: Value of a digit based on its position

Base-10 blocks: Visual tools showing tens and ones

Complete methodology:
  1. Identify digits: Separate tens and ones digits
  2. Convert tens: Multiply tens digit by 10
  3. Keep ones: Ones digit stays as is
  4. Add together: Sum gives expanded form
Tip 1: Count tens by 10s (10, 20, 30, 40...)
Tip 2: Use base-10 blocks to visualize the number.
Tip 3: Always check: expanded form should equal original number.
Tip 4: Practice with numbers up to 99.
Common errors: Confusing tens and ones positions, forgetting to multiply by 10.
Key concepts: Place value, base-10 system, number decomposition.
Formulas to know by heart:

• Tens value = Tens digit × 10

• Ones value = Ones digit × 1

• Expanded form = Tens value + Ones value

• Original number = Expanded form

Solution: Exercises 4 to 5
4 Mixed Practice
Exercise 4
Write 48 in expanded form.
Show with base-10 blocks and words.
Definition:

Base-10 blocks: Rods represent tens, cubes represent ones

Number
48
Expanded
40 + 8
Words
4 tens + 8 ones
Step 1: Identify digits

48 has 4 tens and 8 ones

Step 2: Calculate tens

4 × 10 = 40

Step 3: Calculate ones

8 × 1 = 8

Step 4: Combine

40 + 8 = 48

48 = 40 + 8
Final answer:

48 = 40 + 8 (four tens and eight ones)

Applied rules:

• Place value recognition: Identify tens and ones positions

• Value conversion: Multiply tens by 10

• Verification: Check that parts sum to whole

5 Advanced Practice
Exercise 5
Write 73 in expanded form.
Draw base-10 blocks and write the equation.
Definition:

Equation: A mathematical statement showing equality between two expressions

Number
73
Expanded
70 + 3
Equation
73 = 70 + 3
Step 1: Separate digits

73 has 7 tens and 3 ones

Step 2: Calculate tens value

7 × 10 = 70

Step 3: Calculate ones value

3 × 1 = 3

Step 4: Write equation

73 = 70 + 3

Step 5: Verify

70 + 3 = 73 ✓

73 = 70 + 3
Final answer:

73 = 70 + 3 (seven tens and three ones)

Applied rules:

• Systematic approach: Always follow the same steps

• Verification: Add expanded parts to check accuracy

• Equation format: Original number = expanded form

Expanded Form Teaching Guide: Laws, Methods, Definitions, Expressions
24 = 20 + 4
Expanded Form Rule
Key definitions:

Expanded form: Writing a number as the sum of its place values (tens + ones)

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

Base-10 system: Number system using groups of ten

Complete methodology:
  1. Analyze the number: Identify tens and ones digits
  2. Convert tens: Multiply tens digit by 10
  3. Keep ones: Ones digit remains the same
  4. Combine: Add tens and ones with addition
  5. Verify: Check that expanded form equals original number
Tip 1: Use base-10 blocks (rods for tens, cubes for ones) to visualize numbers.
Tip 2: Count by tens to find the tens value quickly.
Tip 3: Always check your work by adding the expanded parts.
Tip 4: Practice with numbers up to 99 to master the concept.
Common errors: Forgetting to multiply tens by 10, confusing tens and ones positions.
Exam preparation: Master numbers up to 99, practice with visual aids.
Formulas to know by heart:

• Tens value = Tens digit × 10

• Ones value = Ones digit × 1

• Expanded form = Tens value + Ones value

• Original number = Expanded form

Questions & Answers

Question: I don't understand why we write 24 as 20 + 4 instead of just 2 + 4. Why do we make the 2 bigger?

Answer: Great question! The reason is because of place value. In the number 24:

  • The 2 is in the tens place, which means it represents 2 groups of ten (2 × 10 = 20)
  • The 4 is in the ones place, which means it represents 4 individual units (4 × 1 = 4)

So 24 really means 20 + 4, not 2 + 4. Think of it like having 2 bags of 10 apples and 4 loose apples. That's 20 + 4 = 24 apples total!

Example: In 37, the 3 means 30 (3 tens) and the 7 means 7 (7 ones), so 37 = 30 + 7.

Question: My child gets confused about which digit is tens and which is ones. How can I help them remember?

Answer: Here are some helpful strategies:

  • Left to right: The left digit is always tens, the right digit is always ones
  • Memory trick: "Tens are on the left, ones are on the right"
  • Visual aids: Use base-10 blocks - long rods for tens, small cubes for ones
  • Practice with counting: Count by tens (10, 20, 30...) to emphasize the tens value

You can also have them point to each digit and say "This is the tens place" and "This is the ones place" while practicing.

Tip: Start with numbers like 10, 20, 30 to emphasize the tens pattern before moving to mixed numbers.

Question: How can I help my students who struggle with the concept of expanded form? Some seem to forget the steps.

Answer: Here's a systematic approach for struggling students:

  1. Concrete first: Use physical base-10 blocks to build numbers
  2. Visual representations: Draw tens rods and ones cubes
  3. Step-by-step routine: Create a consistent process they can follow
  4. Frequent practice: Daily short sessions with immediate feedback

Teach them this simple chant: "Tens first, multiply by ten, ones stay the same, then add them again!"

Also provide anchor charts with the steps visible in the classroom for reference.