Here are the step-by-step solutions for the three problems shown on the card.
Problem 7
The Problem: A wild dog ate 105 nuts in 5 days. Each day, he ate 8 more nuts than the day before. How many did he eat each day?
Step-by-Step Solution:
1.
Find the average: If the dog ate the same amount every day, we would divide the total nuts by the number of days: $105 \div 5 = 21$. Because the amounts go up by the same number each day, the middle day (Day 3) is exactly this average amount. So, on Day 3, he ate
21 nuts.
2.
Work backwards and forwards: We know each day is 8 more than the previous one.
*
Day 3: 21 nuts
*
Day 2: $21 - 8 = 13$ nuts
*
Day 1: $13 - 8 = 5$ nuts
*
Day 4: $21 + 8 = 29$ nuts
*
Day 5: $29 + 8 = 37$ nuts
3.
Check the work: Add them all up to make sure they equal 105.
$5 + 13 + 21 + 29 + 37 = 105$. The math is correct.
Problem 8
The Problem: A ball bounces to half the height it fell from. It starts at 24 metres. How high is the fifth bounce?
Step-by-Step Solution:
To find the answer, we just need to keep dividing by 2 for each bounce.
*
Start Height: 24 metres
*
Bounce 1: Half of 24 is
12 metres.
*
Bounce 2: Half of 12 is
6 metres.
*
Bounce 3: Half of 6 is
3 metres.
*
Bounce 4: Half of 3 is
1.5 metres.
*
Bounce 5: Half of 1.5 is
0.75 metres.
Problem 9
The Problem: Nicole has 100 biscuits. She puts a nut on every 3rd biscuit, icing on every 4th, and a cherry on every 5th. How many biscuits have all three decorations?
Step-by-Step Solution:
1. For a biscuit to have
all three decorations, its number must be divisible by 3, 4, and 5 at the same time.
2. First, let's find a number that 3, 4, and 5 all go into evenly. We can multiply them together because they don't share any common factors: $3 \times 4 \times 5 = 60$.
3. This means every
60th biscuit will have all three items.
4. Let's check the multiples of 60 within the limit of 100 biscuits:
* $60 \times 1 = 60$ (This is less than 100, so it counts).
* $60 \times 2 = 120$ (This is more than 100, so it doesn't count).
5. Only the 60th biscuit fits the rule.
Final Answer:
Problem 7: 5, 13, 21, 29, and 37 nuts.
Problem 8: 0.75 metres.
Problem 9: 1 biscuit.
Parent Tip: Review the logic above to help your child master the concept of problem solving maths worksheet.
