Solved Exercises on Comparing Lengths in Grade 1 (Year 3)

Master comparing lengths: measuring with standard units, comparing using centimeters and meters, solving length problems with addition and subtraction through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Unit conversion
Exercise 1
A table is 1 meter long. A chair is 80 centimeters long. Which is longer?
Definition:

Standard units: Centimeter (cm) and Meter (m) are standard measurement units

Conversion: 1 meter = 100 centimeters

Conversion method:
  1. Convert all measurements to the same unit (centimeters)
  2. Compare the numbers
  3. Express the answer using the original units
1 meter = 100 centimeters

So the table is 100 cm long

Table (1m)
100cm
Chair
80cm
Step 1: Convert to same units

Table: 1 meter = 100 centimeters, Chair: 80 centimeters

Step 2: Compare the numbers

100 > 80

Step 3: Express the answer

The table is longer than the chair

Table (100cm) > Chair (80cm)
Final answer:

The table is longer because 1 meter (100cm) is greater than 80 centimeters

Applied rules:

• Unit conversion: Always convert to the same unit before comparing

• Relationship: 1 meter = 100 centimeters

• Comparison: Larger number represents longer length

2 Addition of lengths
Exercise 2
Sam's rope is 45cm long. He ties another piece that is 32cm long. How long is the total rope? Is it longer than 70cm?
Definition:

Total length: Adding lengths together when objects are joined

Addition: 45cm + 32cm = total length

First Piece
45cm
Second Piece
32cm
Step 1: Add the lengths

45cm + 32cm = 77cm

Step 2: Compare with 70cm

77 > 70

Step 3: State the answer

The total rope is 77cm, which is longer than 70cm

Total = 45cm + 32cm = 77cm > 70cm
Final answer:

The total rope is 77cm long, which is longer than 70cm

Applied rules:

• Addition: When joining objects, add their lengths

• Comparison: Compare final result with given value

• Units: Keep the same unit throughout the calculation

3 Subtraction of lengths
Exercise 3
A ribbon was 95cm long. After cutting off 28cm, how long is the remaining ribbon? Is it longer than 60cm?
Definition:

Remaining length: Original length minus the cut portion

Subtraction: 95cm - 28cm = remaining length

Original Ribbon
95cm
Cut Portion
28cm
Step 1: Subtract to find remaining

95cm - 28cm = 67cm

Step 2: Compare with 60cm

67 > 60

Step 3: State the answer

The remaining ribbon is 67cm, which is longer than 60cm

Remaining = 95cm - 28cm = 67cm > 60cm
Final answer:

The remaining ribbon is 67cm long, which is longer than 60cm

Applied rules:

• Subtraction: When removing part of an object, subtract the lengths

• Comparison: Compare result with the given value

• Verification: Check that the remaining part is less than original

Rules and methods, laws,...
1 \text{ meter} = 100 \text{ centimeters}
Unit Conversion
Key definitions:

Centimeter (cm): A small unit of length, about the width of your pinky finger

Meter (m): A larger unit of length, about the height of a doorknob

Standard unit: A consistent way to measure length

Total length: Combined length when objects are added together

Complete methodology:
  1. Identify units: Check if all measurements are in the same unit
  2. Convert if needed: Change all measurements to the same unit
  3. Perform operation: Add or subtract as required
  4. Compare results: Use appropriate comparison symbols
Tip 1: Always convert to the same unit before comparing lengths.
Tip 2: Remember: 1 meter = 100 centimeters.
Tip 3: When adding lengths, make sure units match before calculating.
Tip 4: Check your answer makes sense by estimating the result.
Common errors: Forgetting to convert units, mixing up addition and subtraction operations.
Key concepts: Standard units, conversion, addition/subtraction of lengths, comparison.
Important rules to remember:

• Always convert to the same unit before comparing

• 1 meter = 100 centimeters

• When joining objects, add their lengths

• When removing part, subtract from original length

• Always check your answer is reasonable

Solution: Exercises 4 to 5
4 Multi-step comparison
Exercise 4
A bookshelf is 120cm tall. A desk is 75cm tall. A chair is 45cm tall. Is the bookshelf taller than the desk and chair combined?
Definition:

Combined height: Adding multiple heights together

Multi-step comparison: Comparing one object to a combination of others

Bookshelf
120cm
Desk + Chair
75cm + 45cm = 120cm
Step 1: Add desk and chair heights

75cm + 45cm = 120cm

Step 2: Compare bookshelf to combined height

120cm vs 120cm

Step 3: Determine relationship

120cm = 120cm

Bookshelf (120cm) = Desk + Chair (120cm)
Final answer:

The bookshelf is not taller than the desk and chair combined - they are equal in height (both 120cm)

Applied rules:

• Multi-step process: First combine, then compare

• Addition: Add the smaller objects' heights

• Comparison: Compare single object to combined total

5 Complex ordering
Exercise 5
Order these from shortest to tallest: 1m 15cm, 98cm, 1m 5cm, 102cm
Definition:

Complex measurement: Measurements with both meters and centimeters

Conversion: Convert mixed units to a single unit for comparison

1 meter = 100 centimeters

Converting all to centimeters:

1m 15cm = 115cm

98cm = 98cm

1m 5cm = 105cm

102cm = 102cm

98cm
98cm
1m 5cm
105cm
102cm
102cm
1m 15cm
115cm
Step 1: Convert all to centimeters

1m 15cm = 115cm, 98cm = 98cm, 1m 5cm = 105cm, 102cm = 102cm

Step 2: Order numbers from smallest to largest

98, 102, 105, 115

Step 3: Match back to original measurements

98cm, 102cm, 1m 5cm, 1m 15cm

Step 4: State the ordered sequence

From shortest to tallest

98cm < 102cm < 1m 5cm < 1m 15cm
Final answer:

From shortest to tallest: 98cm, 102cm, 1m 5cm, 1m 15cm

Applied rules:

• Unit conversion: Convert mixed units to single unit for comparison

• Ordering: Arrange numbers from smallest to largest

• Verification: Check that each next item is taller than the previous

Comprehensive Summary: Comparing Lengths Year 3
Key Concepts and Definitions

Length: The measurement of how long something is from one end to the other.

Standard Units: Consistent ways to measure length that everyone understands.

Centimeter (cm): A small unit of length. About the width of your pinky finger.

Meter (m): A larger unit of length. About the height of a doorknob.

Unit Conversion: Changing measurements from one unit to another (1m = 100cm).

Comparison: Looking at two or more lengths to see which is longer, shorter, or equal.

Core Rules and Principles

Rule 1: Always convert measurements to the same unit before comparing.

Rule 2: 1 meter equals exactly 100 centimeters (1m = 100cm).

Rule 3: When joining objects, add their lengths together.

Rule 4: When removing part of an object, subtract from the original length.

Rule 5: Use comparison symbols: > (greater than), < (less than), = (equal to).

Step-by-Step Methods

Method 1 - Simple Comparison:

  1. Check if all measurements are in the same unit
  2. If not, convert all to the same unit
  3. Compare the numbers
  4. Express the answer using correct symbols

Method 2 - Addition Problems:

  1. Identify the lengths to be added
  2. Make sure all units match
  3. Add the lengths together
  4. Compare or state the total as needed

Method 3 - Subtraction Problems:

  1. Identify original length and amount being removed
  2. Ensure units match
  3. Subtract the smaller amount from the larger
  4. State the remaining length
Examples: Simple to Advanced

Simple Example: Which is longer: 15cm or 20cm? Answer: 20cm > 15cm

Moderate Example: Which is longer: 1m or 95cm? Answer: 1m = 100cm > 95cm

Advanced Example: Order these from shortest to longest: 1m 10cm, 98cm, 1m 5cm. Answer: 98cm, 1m 5cm, 1m 10cm

Tips, Tricks, and Common Pitfalls

Tips:

  • Always convert to the same unit before comparing
  • Draw a picture to visualize the problem
  • Remember: 1 meter = 100 centimeters
  • Check your answer makes sense

Common Mistakes:

  • Forgetting to convert units before comparing
  • Mixing up meters and centimeters
  • Using wrong comparison symbols
  • Adding when you should subtract, or vice versa
Key Notes for Memorization

Memory Aid: "Meters are big (1m = 100cm)" - remember that meters are larger units.

Symbol Trick: The < symbol points to the smaller number (think of an arrow pointing to the smaller).

Process Reminder: Always convert first, then compare.

Verification: After solving, check if your answer makes logical sense.

Questions & Answers

Question: I keep forgetting that 1 meter equals 100 centimeters. How can I remember this better?

Answer: Here are some helpful memory tricks:

  • Count to 100: Count slowly from 1 to 100 while taking 100 small steps - that's how many centimeters are in 1 meter!
  • Hand analogy: Hold up 10 fingers, then multiply by 10 - 10 × 10 = 100 centimeters in 1 meter
  • Picture connection: Imagine a meter stick divided into 100 tiny sections - each section is 1 centimeter

Practice converting simple examples: 2 meters = 200 centimeters, 3 meters = 300 centimeters. The pattern will help you remember!

Question: My child struggles with word problems involving length addition and subtraction. Any advice?

Answer: Word problems can be challenging! Try this approach:

  • Identify key words: "total," "altogether," "combined" usually mean addition
  • Identify key words: "left," "remaining," "cut off" usually mean subtraction
  • Draw pictures: Visualize the problem with sketches
  • Check reasonableness: Does the answer make sense in the context?

Practice with real objects at home - measure items, cut strings, join pieces together to make the concepts tangible.

Question: How do I know when to add lengths versus when to subtract them?

Answer: Great question! Think about what's happening:

  • Add when: You're putting things together, finding totals, or combining lengths
  • Subtract when: You're taking away part of something, cutting off a piece, or finding what's left

Examples:

  • "I have a 20cm string and add a 15cm string" → Add: 20 + 15 = 35cm
  • "I had a 50cm ribbon and cut off 20cm" → Subtract: 50 - 20 = 30cm

Ask yourself: "Am I getting more or less?" More = add, Less = subtract.