Solved Exercises on Expanded Form in Grade 1

Master expanded form: place value, number decomposition, standard to expanded conversion through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Converting Standard to Expanded Form
Exercise 1
Write the number 58 in expanded form.
Show how many tens and ones are in the number.
Definition:

Expanded form: A way to write numbers showing the value of each digit. It breaks a number into the sum of each digit's value based on its place.

Conversion method:
  1. Identify the place value of each digit (tens, ones)
  2. Determine how many tens and how many ones
  3. Write the value of each digit separately
  4. Combine with addition symbol (+)
TENS PLACE
5
ONES PLACE
8
5 tens = 50
+
8 ones = 8
Step 1: Identify each digit's position

In 58: 5 is in the tens place, 8 is in the ones place

Step 2: Determine the value of each digit

5 in tens place = 5 tens = 5 × 10 = 50

8 in ones place = 8 ones = 8 × 1 = 8

Step 3: Write in expanded form

58 = 50 + 8

58 = 50 + 8
Final answer:

58 in expanded form is 50 + 8 (5 tens and 8 ones)

Applied rules:

• Place value: Each position has a specific value (tens, ones)

• Expanded form: Express a number as the sum of the values of its digits

• Decomposition: Break the number into parts based on place value

2 Converting Expanded to Standard Form
Exercise 2
Convert the expanded form 70 + 4 to standard form.
Explain how you combined the tens and ones.
Definition:

Standard form: The normal way we write numbers using digits (like 74). It's the opposite of expanded form.

70 (7 tens)
+
4 (4 ones)
70 + 4 = 74
Step 1: Identify the tens and ones

70 represents 7 tens (7 × 10), 4 represents 4 ones (4 × 1)

Step 2: Add the tens and ones together

70 + 4 = 74

Step 3: Write the standard form

The tens digit (7) goes in the tens place, the ones digit (4) goes in the ones place

Final answer:

70 + 4 in standard form is 74

Applied rules:

• Combination: Add the value of tens and ones to get the total number

• Place value: Tens digit goes in tens place, ones digit goes in ones place

• Recomposition: Put the parts back together to form the whole number

3 Identifying Place Values
Exercise 3
For the number 93, identify how many tens and ones.
Then write the expanded form and verify by converting back to standard form.
Definition:

Place value identification: Determining how many tens and how many ones make up a number.

DIGIT
9
PLACE
TENS
VALUE
90
DIGIT
3
PLACE
ONES
VALUE
3
93 = 90 + 3
Step 1: Identify each digit's position in 93

9 is in tens place, 3 is in ones place

Step 2: Calculate the value of each digit

9 tens = 9 × 10 = 90, 3 ones = 3 × 1 = 3

Step 3: Write expanded form

93 = 90 + 3

Step 4: Verify by converting back

90 + 3 = 93 ✓

Final answer:

93 has 9 tens (90) and 3 ones (3). Expanded form: 90 + 3. Verification: 90 + 3 = 93

Applied rules:

• Verification: Always check by converting back to standard form

• Place value: Digit position determines its value

• Decomposition: Break apart to understand the number's structure

Expanded Form Rules and Methods
47 = 40 + 7
Expanded Form
Standard to Expanded
58 → 50 + 8
Break apart by place value
Expanded to Standard
60 + 3 → 63
Combine tens and ones
Place Value
Tens + Ones
Position determines value
Key Rule: Expanded form shows the value of each digit based on its position.
Verification: Adding the parts of expanded form should equal the original number.
Tip 1: Remember that the tens digit represents groups of 10.
Tip 2: Use visual aids like base-10 blocks to understand the concept.
Tip 3: Always check your work by adding the expanded parts together.
Key Rules to Remember:

• Place value: In 2-digit numbers, left digit = tens, right digit = ones

• Expanded form: Sum of each digit's place value (57 = 50 + 7)

• Conversion: Tens value = digit × 10, Ones value = digit × 1

• Verification: Expanded parts should sum to original number

AB = A×10 + B×1
General Formula
Standard Form Tens Ones Expanded Form 23 20 3 20 + 3 45 40 5 40 + 5 67 60 7 60 + 7 89 80 9 80 + 9
Additional Practice
4 Mixed Practice
Exercise 4
Complete the following conversions:
a) 64 = ___ + ___
b) 30 + 7 = ___
c) 89 = ___ tens + ___ ones
Definition:

Mixed practice: Combining different types of expanded form problems to strengthen understanding.

Part a: 64 = ___ + ___

6 is in tens place (6 × 10 = 60), 4 is in ones place (4 × 1 = 4)

64 = 60 + 4

Part b: 30 + 7 = ___

30 represents 3 tens, 7 represents 7 ones

30 + 7 = 37

Part c: 89 = ___ tens + ___ ones

8 is in tens place (8 tens), 9 is in ones place (9 ones)

89 = 8 tens + 9 ones

Final answers:

a) 64 = 60 + 4

b) 30 + 7 = 37

c) 89 = 8 tens + 9 ones

Applied rules:

• Consistency: Apply the same method to all parts of the problem

• Place value: Position determines the value of each digit

• Verification: Check each answer by recomposing the number

5 Problem Solving
Exercise 5
Sarah has 4 tens blocks and 6 ones blocks. Write the number she has in standard form and expanded form.
Definition:

Problem solving: Applying expanded form concepts to real-world scenarios with visual representations.

4 tens = 40
+
6 ones = 6
Step 1: Count the tens blocks

Sarah has 4 tens blocks = 4 × 10 = 40

Step 2: Count the ones blocks

Sarah has 6 ones blocks = 6 × 1 = 6

Step 3: Combine to find the total

Total = 40 + 6 = 46

Final answer:

Standard form: 46, Expanded form: 40 + 6

Applied rules:

• Visual representation: Blocks help understand the concept concretely

• Combination: Add tens value and ones value to get the total

• Application: Connect abstract math to physical objects

Comprehensive Summary: Expanded Form
AB = A×10 + B×1
Expanded Form Formula
Key Definitions:

Expanded form: A way to write numbers showing the value of each digit based on its position. It breaks a number into the sum of each digit's value.

Standard form: The normal way we write numbers using digits (like 58).

Place value: The value of a digit based on its position in a number (tens, ones).

Tens: Groups of 10 (1 ten = 10, 2 tens = 20, etc.).

Ones: Single units (1 one = 1, 2 ones = 2, etc.).

Complete Methodology:
  1. Identify place value: Recognize tens and ones positions
  2. Determine digit value: Calculate how many tens and ones
  3. Convert to expanded form: Write the sum of each digit's value
  4. Convert to standard form: Add tens and ones together
  5. Verify accuracy: Check that conversions are correct
Tip 1: Remember that 1 ten equals 10 ones (10 = 1 ten).
Tip 2: Always verify by adding expanded parts to see if you get the original number.
Tip 3: Use visual aids like base-10 blocks to understand the concept better.
Tip 4: The tens digit tells you how many groups of 10, ones digit tells you extra units.
Common errors: Confusing tens and ones, forgetting to multiply by 10 for tens place, misplacing the addition sign.
Key insights: Expanded form reveals the structure of numbers and builds foundation for higher math concepts.
Core Rules and Principles:

• Place value principle: In 2-digit numbers, left digit = tens, right digit = ones

• Expanded form rule: Each digit's value = digit × its place value (tens × 10, ones × 1)

• Verification principle: Expanded parts should sum to original number

• Decomposition method: Break numbers into parts based on place value

• Recomposition method: Combine parts to form the whole number

Examples: 23=20+3, 56=50+6, 89=80+9
Concrete Examples
Memory aid: "Expanded" means stretched out - the number is stretched into its parts.
Success check: If 45 = 40 + 5, then 40 + 5 should equal 45. ✓

Questions & Answers

Question: Why do we need to learn expanded form? Isn't it easier to just write the number normally?

Answer: Great question! Expanded form is very important for several reasons:

  • Understanding place value: It helps you see that the "4" in 45 actually represents 40, not just 4
  • Building math skills: It prepares you for addition, subtraction, and larger numbers
  • Problem solving: It makes complex calculations easier by breaking numbers into smaller parts
  • Foundation for future math: You'll use these concepts in higher grades

Think of it like taking apart a toy to see how it works - expanded form shows you how numbers are built!

Example: 73 = 70 + 3 shows you that 73 is made of 7 tens and 3 ones, which helps you understand the number better.

Question: My child is getting confused between the digit and its value. How can I help them understand that the "3" in 37 means 30?

Answer: This is a very common challenge! Here are effective strategies:

  • Use manipulatives: Base-10 blocks where a rod of 10 represents tens and small cubes represent ones
  • Visual grouping: Draw circles around groups of 10 objects to show what "tens" means
  • Language connection: Say "3 tens" instead of just "the 3 in the tens place"
  • Real examples: Use money (dimes for tens, pennies for ones) to make it concrete

Activities to try:

  • Build numbers with blocks and say "37 has 3 tens and 7 ones"
  • Count by tens: 10, 20, 30, then add the ones: 31, 32, 33, 34, 35, 36, 37
  • Practice saying numbers in expanded form: "37 is 30 plus 7"

The key is connecting the abstract concept to concrete, visual representations.

Question: How do I quickly convert from expanded form back to standard form? Like changing 60 + 8 back to a regular number.

Answer: Converting from expanded to standard form is quite straightforward:

Simple Addition Method:

  • Just add the expanded parts together
  • 60 + 8 = 68
  • 40 + 5 = 45
  • 90 + 3 = 93

Place Value Method:

  • The tens part tells you what goes in the tens place
  • The ones part tells you what goes in the ones place
  • 60 + 8 → 6 goes in tens place, 8 goes in ones place → 68

Quick tip: Look at the expanded form and ask yourself "How many tens?" and "How many ones?" Then put those digits together!

Example: 70 + 2 means 7 tens and 2 ones, so the number is 72.