Concept 3 of 5
Combine-the-Groups Sums
Today's big idea
Add every group for a total, or subtract one from another to compare them.
Read whether the question wants a total or a difference before adding.
How it works
👀 What's going on?
Three shops, three classes, three baskets. Questions like these hand you a pile of separate numbers. Everything then depends on whether you are asked to put them together or set them against each other.
💡 Here's the trick
Look at the groups above. Adding every group gives a total, which answers how many altogether. Taking one group from another gives a difference, which answers how many more. Same numbers, and the question word decides which sum you do.
🪄 How to do it
- 1.List each group from the table above with its number.
- 2.Decide whether the question wants everything together or two of them compared.
- 3.Add for a total, or subtract for a difference.
✍️ Try it
Three shops sold 128, 96 and 205 items, so how many altogether? Then: Class A has 32 children and Class B has 28, so how many more are in A?
The shops give 128 plus 96 plus 205, which is 429 items. The classes are being compared rather than combined, so 32 take away 28 gives 4 more children.
⚠️ Watch out
You might be thinking more groups always means adding. It does not. The phrase how many more asks for a difference, however many groups are listed. Adding there gives an answer far too big to be sensible.
🌟 Why this matters
Totalling a shopping list, or working out which of two teams scored more, is the same pair of moves. Knowing which one the words are asking for is the whole skill.
Exam tip: Circle the words altogether or more before touching the numbers.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Three shops sold 145, 178 and 92 ice creams. How many in all?”
- 1
Take one group at a time
145, then 178, then 92.
- 2
Add all the groups
145 + 178 + 92 = 415
- 3
Answer ✓
Total = 415
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Find each group first, then add for a total or subtract to compare.
GROUPS · ROUND 1 OF 3
Box A 27, Box B 46
How many balls in all?
Quick check
✅ VERIFICATION
Three groups hold 200 in total. Two of them hold 75 and 60. What does the third hold?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Number Detective
Fix one digit first, then fill the rest.