Concept 3 of 8
Classification: Group by Shared Property
Today's big idea
Pick one sharp property, sort into buckets, then check the counts add back.
Seven numbers split 4 even and 3 odd, and 4 plus 3 returns the 7.
How it works
👀 What's going on?
Classification hands you a pile of items and asks you to sort them. The sorting is the easy part. Choosing what to sort by is what decides whether it works.
💡 Here's the trick
Look at the buckets above. Seven items get sorted by whether they are even, giving 4 in the even bucket and 3 in the odd one. Notice that 4 + 3 comes back to 7. That is your check: every item lands in exactly one bucket, none lost and none counted twice.
🪄 How to do it
- 1.List every item before you start, as the picture above lists all seven.
- 2.Choose one clear property to sort by, such as even or odd, or straight or curved.
- 3.Drop each item into a bucket, then check the bucket totals add back to your list size.
✍️ Try it
Sort these by has straight sides only: triangle, circle, rectangle, oval, hexagon, square. How many land in each bucket?
Straight sides only holds triangle, rectangle, hexagon and square, which is 4. Curved holds circle and oval, which is 2. Adding 4 and 2 gives 6, matching the six items you began with, so nothing went missing.
⚠️ Watch out
You might be thinking an item can sit in both buckets when it half fits. It cannot. If something seems to belong in two, your property is not sharp enough, so choose one that gives a clear yes or no.
🌟 Why this matters
Tidying a cupboard, sorting laundry, filing photos, organising a shop. Every one of them is a single property applied to a pile, and the counting check catches whatever you dropped.
Exam tip: Add the bucket counts back to the total every time, because a missing item is the usual reason these go wrong.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“How many EVEN in {3, 8, 9, 12, 15, 20}?”
- 1
Test each
Even end in 0, 2, 4, 6, 8.
- 2
List evens
8, 12, 20
- 3
Count
3
- 4
Answer ✓
3
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Think about where each animal mainly lives — land, water, or air?
GROUP SORT · ROUND 1 OF 2 · SORT ALL 6
Quick check
✅ VERIFICATION
Sort 4, 7, 8, 11, 12, 15 by 'is a multiple of 4'. How many land in that bucket?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Possible Combinations
Two independent groups → multiply.