Gift Stacks
Use the information to work out how many gifts there are in each
pile.
Age
7 to 11
Challenge level
Problem
Image
|
There are twenty gifts stacked up into four
piles. The first pile has 3 less than the second pile. The second pile has two more than the third pile. The fourth pile has twice as many as the second pile. How many gifts are in each pile? |
Getting Started
How many gifts could there be in the first pile? So how many does this mean there are in the second? And third? Does this fit all the information?
If not, what could you try next?
You might find it helpful to use some counters as the presents, or draw some pictures.
Student Solutions
From Josh of Alameda School, Ampthill, Beds:
There are 5 presents in the second pile, 2 presents in the first pile, 3 presents in the third pile and 10 in the fourth pile.
I worked it out by saying the second pile equalled x. The first pile would then be x-3, the third pile x-2 and the fourth pile was 2x.
Simplified this gave me 5x-5 = 20. So 5x = 20+5. 5x = 25. And so x, the number of presents in the second pile, is 5.
Teachers' Resources
Why do this problem?
This problem encourages learners to apply their knowledge of
number operations using trial and improvement. It could also be
used to introduce algebraic notation to older children.
Key questions
What could you try to start with?
Have you checked it fits all the information?
What could we try next?
Possible support
Using blocks or counters to represent gifts will help pupils
to try out their ideas.