Solved Exercises on Standard Form in Grade 1

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

Solution: Exercises 1 to 3
1 Converting Expanded to Standard Form
Exercise 1
Convert the expanded form 40 + 6 to standard form.
Show how you combine the tens and ones.
Definition:

Standard form: The normal way we write numbers using digits (like 46). It's the opposite of expanded form.

Conversion method:
  1. Identify the tens and ones in the expanded form
  2. Add the tens value and ones value together
  3. Write the result as a standard number
Expanded Form
40 + 6
Standard Form
46
40 (4 tens)
+
6 (6 ones)
Step 1: Identify tens and ones

40 represents 4 tens (4 × 10 = 40)

6 represents 6 ones (6 × 1 = 6)

Step 2: Add tens and ones together

40 + 6 = 46

Step 3: Write in standard form

The tens digit (4) goes in the tens place, ones digit (6) goes in the ones place

40 + 6 = 46
Final answer:

40 + 6 in standard form is 46

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

2 Composing Numbers from Place Values
Exercise 2
If a number has 7 tens and 3 ones, what is the number in standard form?
Show how you build the number.
Definition:

Number composition: Building a number from its tens and ones components to create standard form.

TENS
7
ONES
3
7 tens = 70
+
3 ones = 3
Step 1: Calculate the value of tens

7 tens = 7 × 10 = 70

Step 2: Calculate the value of ones

3 ones = 3 × 1 = 3

Step 3: Add tens and ones together

70 + 3 = 73

Step 4: Write in standard form

Put the tens digit (7) in the tens place and ones digit (3) in the ones place: 73

7 tens + 3 ones = 70 + 3 = 73
Final answer:

A number with 7 tens and 3 ones is 73 in standard form

Applied rules:

• Composition: Combine tens and ones to form the complete number

• Place value: Tens digit goes first, ones digit goes second

• Value calculation: Tens = digit × 10, Ones = digit × 1

3 Verification of Standard Form
Exercise 3
Write the number 85 in expanded form, then convert back to standard form to verify your answer.
Explain the process.
Definition:

Verification: Converting between forms to check that your understanding is correct.

DIGIT
8
PLACE
TENS
VALUE
80
DIGIT
5
PLACE
ONES
VALUE
5
Standard Form
85
Expanded Form
80 + 5
Back to Standard
85
Step 1: Convert standard to expanded form

85 = 80 + 5 (8 tens and 5 ones)

Step 2: Convert expanded back to standard form

80 + 5 = 85

Step 3: Verify the result

Starting number (85) equals final number (85) ✓

Final answer:

85 in expanded form is 80 + 5. Converting back: 80 + 5 = 85. Verification confirms our answer is correct.

Applied rules:

• Verification: Always check by converting back to original form

• Reversibility: Converting between forms should give the same result

• Place value: Each digit's position determines its value

Standard Form Rules and Methods
47 = 40 + 7
Expanded to Standard
Expanded to Standard
50 + 8 → 58
Combine tens and ones
Standard to Expanded
63 → 60 + 3
Break apart by place value
Place Value
Tens + Ones
Position determines value
Key Rule: Standard form is the normal way we write numbers with digits.
Verification: Converting expanded to standard should match the original number.
Tip 1: Remember that standard form is how we normally write numbers (like 58).
Tip 2: Use visual aids like base-10 blocks to understand the concept.
Tip 3: Always check your work by verifying the conversion.
Key Rules to Remember:

• Standard form: Normal way of writing numbers using digits

• Composition: Add tens value and ones value to get standard form

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

• Verification: Expanded to standard should equal original number

A×10 + B×1 = AB
General Formula
Expanded Form Tens Ones Standard Form 20 + 3 20 3 23 40 + 5 40 5 45 60 + 7 60 7 67 80 + 9 80 9 89
Additional Practice
4 Mixed Practice
Exercise 4
Complete the following conversions:
a) 30 + 4 = ___
b) 7 tens + 2 ones = ___
c) 50 + 8 = ___
Definition:

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

Part a: 30 + 4 = ___

30 represents 3 tens, 4 represents 4 ones

30 + 4 = 34

Part b: 7 tens + 2 ones = ___

7 tens = 70, 2 ones = 2

70 + 2 = 72

Part c: 50 + 8 = ___

50 represents 5 tens, 8 represents 8 ones

50 + 8 = 58

Final answers:

a) 30 + 4 = 34

b) 7 tens + 2 ones = 72

c) 50 + 8 = 58

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
Tom has 5 tens blocks and 9 ones blocks. Write the number he has in standard form. Then write it in expanded form to verify.
Definition:

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

5 tens = 50
+
9 ones = 9
Step 1: Count the tens blocks

Tom has 5 tens blocks = 5 × 10 = 50

Step 2: Count the ones blocks

Tom has 9 ones blocks = 9 × 1 = 9

Step 3: Combine to find the total

Total = 50 + 9 = 59

Step 4: Verify by writing expanded form

59 = 50 + 9 ✓

Final answer:

Standard form: 59, Verification: 59 = 50 + 9

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: Standard Form
A×10 + B×1 = AB
Standard Form Formula
Key Definitions:

Standard form: The normal way we write numbers using digits (like 46). It's the conventional way of expressing numbers.

Expanded form: A way to write numbers showing the value of each digit (like 40 + 6).

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 standard form: Add tens and ones together
  4. Convert to expanded form: Write the sum of each digit's value
  5. Verify accuracy: Check that conversions are correct
Tip 1: Remember that standard form is how we normally write numbers (like 58).
Tip 2: Always verify by converting back to expanded form to check your work.
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: Misplacing digits (writing 64 instead of 46), forgetting to add tens and ones together.
Key insights: Standard form is the foundation for all number operations and builds place value understanding.
Core Rules and Principles:

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

• Standard form rule: Write digits in order of place value (tens first, then ones)

• Verification principle: Standard form should match when converted from expanded form

• Composition method: Combine tens and ones to form the whole number

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

Examples: 20+3=23, 50+6=56, 80+9=89
Concrete Examples
Memory aid: "Standard" means the usual way - how we normally write numbers.
Success check: If 40 + 6 = 46, then 46 should break down to 40 + 6. ✓

Questions & Answers

Question: Why do we need to learn standard form? Isn't it just regular numbers?

Answer: Yes, standard form IS regular numbers! But understanding it helps us:

  • Understand place value: Knowing that the "4" in 46 actually represents 40
  • Build math skills: It prepares you for addition, subtraction, and larger numbers
  • Problem solving: It makes complex calculations easier by understanding number structure
  • Foundation for future math: You'll use these concepts in higher grades

Think of it like understanding how words are spelled - knowing standard form helps you understand how numbers work!

Example: Understanding that 46 = 40 + 6 shows you that 46 is made of 4 tens and 6 ones, which helps you understand the number better.

Question: My child sometimes writes numbers backwards (like 64 instead of 46). How can I help them understand the correct order?

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

  • Emphasize place value: Teach that the left position is always tens, right position is ones
  • Use manipulatives: Base-10 blocks where tens come first, then ones
  • Visual cues: Point to the left side and say "tens place," right side "ones place"
  • Practice with expanded form: 4 tens + 6 ones = 46, not 64

Activities to try:

  • Build numbers with blocks and say "4 tens and 6 ones make 46"
  • Write numbers with arrows: "tens digit → 4, ones digit → 6, so 46"
  • Practice saying numbers aloud: "forty-six" not "sixty-four"

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

Question: How do I quickly convert from expanded form to standard form? Like changing 70 + 2 back to a regular number.

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

Simple Addition Method:

  • Just add the expanded parts together
  • 70 + 2 = 72
  • 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
  • 70 + 2 → 7 goes in tens place, 2 goes in ones place → 72

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

Example: 60 + 8 means 6 tens and 8 ones, so the number is 68.