Solved Exercises on Comparing Lengths in Grade 1

Master comparing lengths: measuring with non-standard units, ordering objects by length, comparing lengths using mathematical language through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Ordering by length
Exercise 1
Order these objects from shortest to longest: pencil (12cm), ruler (30cm), eraser (5cm)
Definition:

Length: How long something is from one end to the other

Shortest to Longest: Arranging objects starting with the smallest length

Comparison method:
  1. Look at the measurements of each object
  2. Compare the numbers (5, 12, 30)
  3. Arrange from smallest to largest number
  4. Match each number to its object
Eraser
5cm
Pencil
12cm
Ruler
30cm
Step 1: Identify the measurements

Eraser = 5cm, Pencil = 12cm, Ruler = 30cm

Step 2: Compare the numbers

5 is smaller than 12, and 12 is smaller than 30

Step 3: Arrange from shortest to longest

Eraser (5cm), then Pencil (12cm), then Ruler (30cm)

Eraser < Pencil < Ruler
Final answer:

From shortest to longest: Eraser (5cm), Pencil (12cm), Ruler (30cm)

Applied rules:

• Comparison: Smaller numbers represent shorter lengths

• Ordering: Start with the smallest number and go to largest

• Visual aid: Draw lines to compare lengths visually

2 Comparing lengths
Exercise 2
Sarah's rope is 8 meters long. Tom's rope is 5 meters long. Which rope is longer?
Definition:

Longer: Having a greater length than another object

Shorter: Having a smaller length than another object

Sarah's Rope
8m
Tom's Rope
5m
Step 1: Identify the lengths

Sarah's rope = 8 meters, Tom's rope = 5 meters

Step 2: Compare the numbers

8 is greater than 5 (8 > 5)

Step 3: Determine which is longer

Since 8 > 5, Sarah's rope is longer

Sarah's rope (8m) > Tom's rope (5m)
Final answer:

Sarah's rope is longer because 8 meters is greater than 5 meters

Applied rules:

• Greater than: When comparing numbers, the larger number represents the longer length

• Symbol: Use > for "greater than" and < for "less than"

• Language: Longer means bigger length, shorter means smaller length

3 Ordering multiple objects
Exercise 3
Order these pencils from longest to shortest: Blue (15cm), Red (10cm), Green (20cm), Yellow (7cm)
Definition:

Ordering: Arranging objects based on their length measurements

Longest to Shortest: Starting with the largest length and ending with the smallest

Green Pencil
20cm
Blue Pencil
15cm
Red Pencil
10cm
Yellow Pencil
7cm
Step 1: List all measurements

Blue = 15cm, Red = 10cm, Green = 20cm, Yellow = 7cm

Step 2: Compare and order from largest to smallest

20, 15, 10, 7

Step 3: Match numbers to colors

Green (20cm), Blue (15cm), Red (10cm), Yellow (7cm)

Green > Blue > Red > Yellow
Final answer:

From longest to shortest: Green (20cm), Blue (15cm), Red (10cm), Yellow (7cm)

Applied rules:

• Descending order: Largest number first, smallest last

• Comparison: Compare all numbers at once to find the sequence

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

Rules and methods, laws,...
\(\text{Length}_1 > \text{Length}_2\) when \(\text{Length}_1\) is longer
Length Comparison
Key definitions:

Length: How long something is from one end to the other

Longer: Greater in length than another object

Shorter: Less in length than another object

Equal: Same length as another object

Complete methodology:
  1. Identify lengths: Look at the measurements given
  2. Compare numbers: Look at the numerical values
  3. Order if needed: Arrange from smallest to largest or vice versa
  4. Express answer: Use correct mathematical language
Tip 1: Draw lines to represent lengths and compare visually.
Tip 2: Remember: bigger numbers mean longer lengths.
Tip 3: Use symbols > (greater than) and < (less than) to show comparisons.
Tip 4: Always match the number back to the correct object.
Common errors: Mixing up greater than and less than symbols, forgetting to match numbers to objects.
Key concepts: Length, longer, shorter, equal, comparison, ordering.
Important rules to remember:

• Longer = bigger number, Shorter = smaller number

• Use > for "is longer than", < for "is shorter than"

• When ordering: ascending (smallest to largest) or descending (largest to smallest)

• Always check your answer makes sense with the original problem

Solution: Exercises 4 to 5
4 Equal lengths
Exercise 4
Lisa has a ribbon that is 12cm long. Maya has a ribbon that is also 12cm long. Are their ribbons the same length?
Definition:

Equal lengths: When two objects have the same measurement

Symbol: Use = to show equality

Lisa's Ribbon
12cm
Maya's Ribbon
12cm
Step 1: Identify the lengths

Lisa's ribbon = 12cm, Maya's ribbon = 12cm

Step 2: Compare the numbers

12 is equal to 12 (12 = 12)

Step 3: Determine if they are the same

Since both measurements are identical, the ribbons are the same length

Lisa's ribbon = Maya's ribbon (12cm = 12cm)
Final answer:

Yes, their ribbons are the same length because both measure 12cm

Applied rules:

• Equality: When measurements are identical, objects are equal in length

• Symbol: Use = to show that lengths are the same

• Verification: Both measurements must be exactly the same

5 Mixed comparison
Exercise 5
A book is 25cm long, a notebook is 20cm long, and a folder is 25cm long. Which items have the same length?
Definition:

Same length: When multiple objects share identical measurements

Comparison: Looking at all measurements to find matches

Book
25cm
Notebook
20cm
Folder
25cm
Step 1: List all measurements

Book = 25cm, Notebook = 20cm, Folder = 25cm

Step 2: Compare each measurement

Book (25cm) = Folder (25cm), Notebook (20cm) is different

Step 3: Identify matching lengths

The book and folder both measure 25cm

Step 4: State the answer

Only the book and folder have the same length

Book = Folder (25cm = 25cm), Notebook ≠ others
Final answer:

The book and folder have the same length (25cm each), while the notebook is shorter (20cm)

Applied rules:

• Systematic comparison: Compare each measurement with all others

• Grouping: Items with same measurement belong together

• Clarity: Specify which items match and which don't

Key Concepts: Length Comparison Fundamentals
\(\text{Length A} > \text{Length B}\) or \(\text{Length A} < \text{Length B}\) or \(\text{Length A} = \text{Length B}\)
Three Possible Relationships
Key definitions:

Length: The distance from one end of an object to the other

Measurement: Using numbers to describe how long something is

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

Complete methodology:
  1. Observe: Look at the objects or their measurements
  2. Measure: Get the length of each object if not given
  3. Compare: Look at the numbers to see relationships
  4. Order: Arrange from shortest to longest or longest to shortest
  5. Express: Use correct mathematical language and symbols
Tip 1: Use physical objects to practice comparing lengths hands-on.
Tip 2: Draw pictures or use rulers to visualize differences in length.
Tip 3: Remember the memory trick: > opens toward the bigger number.
Tip 4: Practice saying "___ is longer than ___" and "___ is shorter than ___".
Common errors: Confusing longer/shorter vocabulary, misreading measurements, incorrect symbol usage.
Success strategies: Draw visual representations, use manipulatives, practice with everyday objects.
Essential comparison rules:

• When comparing numbers: larger number = longer length

• Use > for "is longer than" or "is greater than"

• Use < for "is shorter than" or "is less than"

• Use = for "is equal to" or "the same as"

• Always verify your answer makes logical sense

Questions & Answers

Question: I sometimes get confused between "longer" and "shorter" when comparing lengths. How can I remember which is which?

Answer: Great question! Here are some helpful memory tricks:

  • Longer: Think of the word "long" - it has more letters, just like the longer object has more length
  • Shorter: The word "short" has fewer letters, just like the shorter object has less length
  • Visual cue: Point to the actual longer object and say "This one is LONGER" - the action reinforces the concept

You can also use hand gestures: spread your arms wide for "longer" and bring them closer together for "shorter".

Practice with everyday objects like comparing the length of your shoes, books, or toys until the vocabulary becomes natural.

Question: My child struggles with the > and < symbols when comparing lengths. Any suggestions for making this clearer?

Answer: The > and < symbols can be tricky! Try these approaches:

  • Alligator mouth: The symbol looks like an alligator's mouth that wants to eat the bigger number
  • Arrow pointing: The small end points to the smaller number
  • Hands: Make the symbol with your hands - left hand makes <, right hand makes >

For length comparisons specifically, you can say: "The longer side gets the open mouth of the symbol."

Practice with many examples until the association becomes automatic. Consistency in using these memory devices helps reinforce learning.

Question: How do I know if two things are the same length when I can't measure them exactly?

Answer: Great question! Here are ways to compare lengths without exact measurements:

  • Line up: Place the objects next to each other at one end and see where they end
  • Visual comparison: Look at them carefully - sometimes it's obvious which is longer
  • Estimation: Use a reference object you know the length of
  • Measuring tool: Use non-standard units like paper clips or cubes

If the ends line up perfectly when aligned at one end, they are the same length. If one extends beyond the other, that one is longer.

With practice, you'll develop a good eye for comparing lengths even without measuring tools!