Concept 4 of 7
Group Sorter: Count by Property
Today's big idea
Walk the list one item at a time, ticking each match, then count only the ticks.
Rules with two parts need both halves checked against every single item.
How it works
👀 What's going on?
A list and a rule, and the question is only how many items obey it. It sounds like the easiest thing in the chapter, and it is where careful children still drop marks.
💡 Here's the trick
Look at the list above. The rule is checked against one item at a time, with a tick for a match and nothing for a miss. Only then are the ticks counted. Going item by item is slower than scanning, and it is the reason it comes out right.
🪄 How to do it
- 1.Read the rule in the list above and say it back to yourself.
- 2.Walk the items one at a time, ticking each match.
- 3.Count only the ticks at the end.
✍️ Try it
How many of 6, 7, 9, 11, 12, 15 are multiples of 3? Then: how many of 7, 11, 14, 15, 21 are both odd and greater than 10?
Six, nine, twelve and fifteen all divide by three, giving 4. In the second list the rule has two parts, and 11, 15 and 21 pass both, giving 3. Seven is odd but too small, and 14 is big enough but even.
⚠️ Watch out
You might be thinking a rule with two parts can be checked one part at a time. It cannot. Tick every odd number in that second list and you get four. Seven slips through on being odd while failing the other half of the rule.
🌟 Why this matters
Counting how many things match a condition is what you do checking a shopping list or a register. The discipline of one item at a time is the whole skill.
Exam tip: Underline both halves of a two-part rule before you start ticking anything.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“How many of these are even? 1, 2, 3, 4, 5”
- 1
Read the property
'Even' means it can be divided by 2 with no remainder.
- 2
Tick each item
1 ✗, 2 ✓, 3 ✗, 4 ✓, 5 ✗.
- 3
Count the ticks
Ticks: 2, 4 → 2 items.
- 4
Answer ✓
= 2
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Which group does each item belong to? Sort them into the right bin!
GROUP SORT · ROUND 1 OF 2 · SORT ALL 6
Quick check
✅ VERIFICATION
A list has 8 items and you ticked 3 of them. How many did you skip?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Possible Combinations
Two independent groups → multiply.