Excess & Shortage
Two plans for the same supply — one leaves extras, one comes up short, or both, or the speeds change. Every disguise hides the same bridge: the gap between the plans equals the per-group amount times the gap in groups. Try each problem first, then watch the trick.
1 Explore — try these first
Try before you watch. Pick a level below and give the problem an honest try on paper first — wrong turns and all. Then open the video to see the trick. Every level rides one habit: The gap between two plans for the same supply is fixed — it equals the per-group amount times the gap in groups, no matter what extra story (leftover, shortage, swing, mismatched groups, or speed and time) is wrapped around it.
L0 · Leftover-Over-Gap
A volunteer is packing care kits for new families. If she packs 2 kits, 6 juice boxes are left over. If she packs 5 kits, the juice boxes fit exactly. How many juice boxes go in each kit?
L1 · Shortage-Over-Gap
A volunteer is packing welcome boxes for new families. If she packs 8 boxes, she still needs 10 more soap bars. If she packs 6 boxes, the soap bars fit exactly. How many soap bars go in each box?
L2 · Swing = Excess + Shortage
A volunteer at an animal shelter is packing pet-food bags for rescued animals. If she fills 5 bags, 7 food packs are left over. If she fills 7 bags, she needs 3 more food packs. How many food packs are there altogether?
L3 · Difference of Leftovers
A volunteer at a community centre is preparing book bundles for newcomer families. If she makes 5 bundles, 16 books are left over. If she makes 7 bundles, 2 books are left over. How many books are there altogether?
L4 · Match Groups First, Then Bridge
A volunteer is arranging flowers into vases for seniors at a care home. If she uses 3 vases, 18 flowers are left over. If she uses 5 vases with 2 more flowers in each vase than before, they fit exactly. How many flowers are there altogether?
L5 · Time-Saved = Speed Bridge
Mia walks to an animal rescue centre to help with evening care. If she walks at 40 metres per minute, she arrives 7 minutes late. If she walks at 50 metres per minute, she arrives 2 minutes late. How far is the rescue centre from her home?
2 Learn — watch the solutions
Gave each one a real try? Now watch the trick. (Stuck is fine — that's the point.)
L0 · The Leftover Trick
Peek the trick — The Leftover Trick
When two plans share the same supply, the leftover from the smaller plan must fill the extra groups in the larger plan. Divide the leftover by the gap in groups and you have the per-group amount.
L1 · The Shortage Trick
Peek the trick — The Shortage Trick
Same family as the Leftover Trick, just flipped. When two plans share the same supply, the shortage from the larger plan equals the gap in groups times the per-group amount, so the per-group amount is the shortage divided by the gap.
L2 · The Swing Trick
Peek the trick — The Swing Trick
When one plan leaves a leftover and the other comes up short, the total swing between them is leftover plus shortage. That swing equals the gap in groups times the per-group amount, so divide the swing by the gap.
L3 · The Difference Trick
Peek the trick — The Difference Trick
When both plans leave a leftover, subtract the smaller pile from the bigger pile. The difference is what filled the extra groups in the larger plan, so per-group equals the difference of the leftovers divided by the gap in groups.
L4 · The Adjustment Trick
Peek the trick — The Adjustment Trick
When the two plans use different per-group amounts, first absorb the offset so both plans use the SAME per-group amount, then the usual bridge works — leftover minus the absorbed offset, divided by the gap, gives the per-group amount.
L5 · The Schedule Trick
Peek the trick — The Schedule Trick
When two travel plans cover the same distance at different speeds and different arrival times, the time saved by the faster plan, multiplied by both speeds and divided by the speed gap, equals the distance — the same plans-and-gap bridge wearing speed and time.
3 Master — practice on your own
Print the practice sheet and solve without the videos. Check your answers at the back — if one is wrong, the answer key names the trick so you know exactly which video to rewatch.
Download fresh practice problems PDF
