Reward Tickets - Free Printable
Educational worksheet: Reward Tickets. Download and print for classroom or home learning activities.
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Step-by-step solution for: Reward Tickets
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Show Answer Key & Explanations
Step-by-step solution for: Reward Tickets
It looks like you've uploaded an image showing a set of point cards used in a classroom or game setting. Each card has a star and indicates a certain number of points: 1, 2, 5, or 10 points.
Here's what I can see:
- There are 15 cards arranged in a grid.
- The distribution of point values is:
- 1 POINT: 3 cards
- 2 POINTS: 3 cards
- 5 POINTS: 4 cards
- 10 POINTS: 5 cards
---
Since you mentioned "a task" but didn't specify the exact question, here are a few common types of problems that might be associated with such an image:
#### 🔹 Possible Task 1: Calculate the Total Points
Problem: What is the total number of points across all cards?
Solution:
We multiply the number of cards by their point value:
- 1-point cards: $ 3 \times 1 = 3 $
- 2-point cards: $ 3 \times 2 = 6 $
- 5-point cards: $ 4 \times 5 = 20 $
- 10-point cards: $ 5 \times 10 = 50 $
Now add them up:
$$
3 + 6 + 20 + 50 = 79
$$
✔ Answer: 79 points total
---
#### 🔹 Possible Task 2: How many ways can you make 10 points?
Problem: How many different combinations of cards sum to exactly 10 points?
Solution:
We need to find combinations of the available cards (1, 2, 5, 10) that add to 10, considering the limits on how many of each we have.
Available:
- 1s: 3
- 2s: 3
- 5s: 4
- 10s: 5
Let’s list valid combinations (order doesn’t matter):
1. One 10-point card → ✔
2. Two 5-point cards → ✔ (we have 4 fives)
3. One 5 + two 2s + one 1 → $5 + 2+2+1 = 10$ → ✔
4. One 5 + one 2 + three 1s → $5 + 2 + 1+1+1 = 10$ → ✘ (only 3 ones, so this uses 3 ones — okay, but only one 2 needed)
- Wait: $5 + 2 + 1+1+1 = 10$ → yes, possible
5. Five 2-point cards → $5×2=10$, but we only have 3 twos → ✘
6. Ten 1-point cards → only 3 available → ✘
7. One 5 + five 1s → too many 1s → ✘
8. Four 2s + two 1s → $4×2 + 2×1 = 10$, but only 3 twos → ✘
9. Three 2s + four 1s → $6 + 4 = 10$, but only 3 ones → ✘
10. One 5 + one 2 + three 1s → already listed above → ✔
11. Two 5s → already listed → ✔
12. One 10 → already listed → ✔
13. One 5 + one 2 + three 1s → same as #3
14. One 5 + five 1s → not possible
15. Two 2s + six 1s → no
So valid combinations:
- [10]
- [5,5]
- [5,2,2,1] → $5+2+2+1=10$
- [5,2,1,1,1] → $5+2+1+1+1=10$
Wait — check if these use more than available:
- [5,2,2,1]: needs 1 five, 2 twos, 1 one → all within limits → ✔
- [5,2,1,1,1]: needs 1 five, 1 two, 3 ones → all available → ✔
Are there others?
- [2,2,2,1,1,1,1] → $6 + 4 = 10$ → needs 3 twos and 4 ones → only 3 ones → ✘
- [2,2,1,1,1,1,1] → $4 + 5 = 9$ → not enough
- [2,1,1,1,1,1,1] → $2+6=8$ → no
- [1,1,...] → too many
What about [2,2,2,2,2]? 5 twos → only 3 → ✘
So only four distinct combinations:
1. [10]
2. [5,5]
3. [5,2,2,1]
4. [5,2,1,1,1]
✔ So 4 combinations that sum to 10 points.
---
#### 🔹 Possible Task 3: Which point value appears most frequently?
- 10-point cards: 5 → most frequent
- Answer: 10 points
---
> ✔ The total number of points is 79.
If your actual task was something else (like probability, average, or grouping), please clarify! But based on typical uses of such images, total points is the most likely intended task.
Here's what I can see:
- There are 15 cards arranged in a grid.
- The distribution of point values is:
- 1 POINT: 3 cards
- 2 POINTS: 3 cards
- 5 POINTS: 4 cards
- 10 POINTS: 5 cards
---
Task Interpretation:
Since you mentioned "a task" but didn't specify the exact question, here are a few common types of problems that might be associated with such an image:
#### 🔹 Possible Task 1: Calculate the Total Points
Problem: What is the total number of points across all cards?
Solution:
We multiply the number of cards by their point value:
- 1-point cards: $ 3 \times 1 = 3 $
- 2-point cards: $ 3 \times 2 = 6 $
- 5-point cards: $ 4 \times 5 = 20 $
- 10-point cards: $ 5 \times 10 = 50 $
Now add them up:
$$
3 + 6 + 20 + 50 = 79
$$
✔ Answer: 79 points total
---
#### 🔹 Possible Task 2: How many ways can you make 10 points?
Problem: How many different combinations of cards sum to exactly 10 points?
Solution:
We need to find combinations of the available cards (1, 2, 5, 10) that add to 10, considering the limits on how many of each we have.
Available:
- 1s: 3
- 2s: 3
- 5s: 4
- 10s: 5
Let’s list valid combinations (order doesn’t matter):
1. One 10-point card → ✔
2. Two 5-point cards → ✔ (we have 4 fives)
3. One 5 + two 2s + one 1 → $5 + 2+2+1 = 10$ → ✔
4. One 5 + one 2 + three 1s → $5 + 2 + 1+1+1 = 10$ → ✘ (only 3 ones, so this uses 3 ones — okay, but only one 2 needed)
- Wait: $5 + 2 + 1+1+1 = 10$ → yes, possible
5. Five 2-point cards → $5×2=10$, but we only have 3 twos → ✘
6. Ten 1-point cards → only 3 available → ✘
7. One 5 + five 1s → too many 1s → ✘
8. Four 2s + two 1s → $4×2 + 2×1 = 10$, but only 3 twos → ✘
9. Three 2s + four 1s → $6 + 4 = 10$, but only 3 ones → ✘
10. One 5 + one 2 + three 1s → already listed above → ✔
11. Two 5s → already listed → ✔
12. One 10 → already listed → ✔
13. One 5 + one 2 + three 1s → same as #3
14. One 5 + five 1s → not possible
15. Two 2s + six 1s → no
So valid combinations:
- [10]
- [5,5]
- [5,2,2,1] → $5+2+2+1=10$
- [5,2,1,1,1] → $5+2+1+1+1=10$
Wait — check if these use more than available:
- [5,2,2,1]: needs 1 five, 2 twos, 1 one → all within limits → ✔
- [5,2,1,1,1]: needs 1 five, 1 two, 3 ones → all available → ✔
Are there others?
- [2,2,2,1,1,1,1] → $6 + 4 = 10$ → needs 3 twos and 4 ones → only 3 ones → ✘
- [2,2,1,1,1,1,1] → $4 + 5 = 9$ → not enough
- [2,1,1,1,1,1,1] → $2+6=8$ → no
- [1,1,...] → too many
What about [2,2,2,2,2]? 5 twos → only 3 → ✘
So only four distinct combinations:
1. [10]
2. [5,5]
3. [5,2,2,1]
4. [5,2,1,1,1]
✔ So 4 combinations that sum to 10 points.
---
#### 🔹 Possible Task 3: Which point value appears most frequently?
- 10-point cards: 5 → most frequent
- Answer: 10 points
---
Final Answer (if task was total points):
> ✔ The total number of points is 79.
If your actual task was something else (like probability, average, or grouping), please clarify! But based on typical uses of such images, total points is the most likely intended task.
Parent Tip: Review the logic above to help your child master the concept of printable reward tickets.