Problem Analysis:
The image presents a "Timester Challenge" focusing on
Collecting Like Terms. The tasks are divided into three levels:
Bronze,
Silver, and
Gold. Each level involves simplifying algebraic expressions or solving related problems.
---
Bronze Level: Simplify
#### Task 1: Simplify \( a + a + a + a - a + a \)
- Combine all the \( a \) terms:
\[
a + a + a + a - a + a = (1 + 1 + 1 + 1 - 1 + 1)a = 5a
\]
-
Answer: \( 5a \)
#### Task 2: Simplify \( 3a + 7b + 5a + 2b \)
- Combine the \( a \)-terms and \( b \)-terms separately:
\[
3a + 5a = 8a \quad \text{and} \quad 7b + 2b = 9b
\]
-
Answer: \( 8a + 9b \)
---
Silver Level: Simplify
#### Task 1: Simplify \( a^2 + a^2 + a^2 \)
- Combine the \( a^2 \)-terms:
\[
a^2 + a^2 + a^2 = 3a^2
\]
-
Answer: \( 3a^2 \)
#### Task 2: Simplify \( 8a + 6 - 9 - 4a \)
- Combine the \( a \)-terms and constant terms separately:
\[
8a - 4a = 4a \quad \text{and} \quad 6 - 9 = -3
\]
-
Answer: \( 4a - 3 \)
---
Gold Level: Fill in the Blocks
#### Task: To fill in a block, the sum of the two blocks directly below it makes the block.
- Given blocks:
\[
\begin{array}{ccc}
& ? & \\
7a & & -2a + b \\
4a & & ?
\end{array}
\]
1.
Top-left block: Sum of \( 7a \) and \( 4a \):
\[
7a + 4a = 11a
\]
2.
Top-right block: Sum of \( -2a + b \) and the unknown block below it (let's call it \( x \)):
- We know the top-right block is \( 7a \), so:
\[
-2a + b + x = 7a
\]
Solving for \( x \):
\[
x = 7a - (-2a + b) = 7a + 2a - b = 9a - b
\]
-
Completed grid:
\[
\begin{array}{ccc}
& 11a & \\
7a & & -2a + b \\
4a & & 9a - b
\end{array}
\]
---
Gold Level: Mel's Statement
#### Task: Mel says that \( 5a - (2a + 6) = 3a + 6 \). Is Mel correct? Give a reason for your answer.
- Simplify the left-hand side:
\[
5a - (2a + 6) = 5a - 2a - 6 = 3a - 6
\]
- Compare with the right-hand side:
\[
3a - 6 \neq 3a + 6
\]
-
Conclusion: Mel is incorrect because the simplified expression is \( 3a - 6 \), not \( 3a + 6 \).
---
Final Answers:
1.
Bronze Level:
- Task 1: \( \boxed{5a} \)
- Task 2: \( \boxed{8a + 9b} \)
2.
Silver Level:
- Task 1: \( \boxed{3a^2} \)
- Task 2: \( \boxed{4a - 3} \)
3.
Gold Level:
- Filled Blocks:
\[
\begin{array}{ccc}
& 11a & \\
7a & & -2a + b \\
4a & & 9a - b
\end{array}
\]
- Mel's Statement: Incorrect. Reason: \( 5a - (2a + 6) = 3a - 6 \), not \( 3a + 6 \).
Parent Tip: Review the logic above to help your child master the concept of collecting like terms worksheet.
