Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Browse grades and teaching videos01 · Read and understand
What you will learn
- Identify common factors.
- Find the greatest feasible group count.
- Distinguish grouping from repeated-event timing.
Before you start
Know multiplication facts through twelve and recognize division with no remainder.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A teacher has 24 pencils and 36 erasers. What is the greatest number of identical kits that can use every item, with a whole number of each item per kit?
Why this math matters
Equal grouping turns a practical packing problem into a divisibility question. The kit count must divide both collections. Choosing the greatest common factor maximizes the number of kits while preserving identical contents.
Set up the model
A useful answer starts with clear assumptions:
- Every item must be used exactly once.
- All kits have identical contents and contain whole pencils and erasers.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Make the greatest number of identical kits
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A teacher has 24 pencils and 36 erasers. What is the greatest number of identical kits that can use every item, with a whole number of each item per kit?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
List the feasible divisors
24: 1, 2, 3, 4, 6, 8, 12, 24
Each divisor could split the pencils evenly. A valid kit count must also split the erasers evenly.
Compare with the second collection
36: 1, 2, 3, 4, 6, 9, 12, 18, 36; GCF = 12
The shared divisors are 1, 2, 3, 4, 6, and 12. Twelve is the greatest of these, not merely one possible count.
Describe and verify a kit
24/12 = 2 pencils; 36/12 = 3 erasers
Twelve copies of this kit use 24 pencils and 36 erasers exactly. The interpretation checks both collections, not only one.
The result
Make 12 identical kits containing 2 pencils and 3 erasers each.
The greatest kit count gives the smallest identical kit under these rules. Asking for the greatest number of items per kit would be a different objective and could lead to one large kit.
Common mistakes to catch
- A number that divides only one collection cannot produce identical complete kits.
- Least common multiple solves a different problem, such as when repeating schedules coincide.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Split 30 stickers and 45 cards into the greatest number of identical kits.
Show a hint
Find the greatest common factor of 30 and 45.
Reveal answer and explanation
15 kits: 2 stickers and 3 cards each
The GCF is 15. Dividing each total by 15 gives the contents and leaves no remainder.
Practice 2
Two lights flash together now, then every 6 and 8 seconds. When do they next flash together?
Show a hint
This asks for a common multiple, not a factor.
Reveal answer and explanation
24 seconds later
The first positive shared multiple of 6 and 8 is 24: four six-second intervals equal three eight-second intervals.
Take the idea with you
Ask whether you are dividing a collection into equal groups or waiting for repeated cycles to meet. That decides between factors and multiples.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Turn a map measurement into a real distance
Completion is your own study record, not a test score. It stays in this browser, does not sync to another device, and can be removed by clearing browser data.