What are the types of math questions for 7th grade second term?
Understand the Problem
The question is asking for examples and types of math questions suitable for a 7th-grade second-term curriculum, including multiple choice, fill-in-the-blank, and short answer formats.
Answer
The possible lengths for the third side are $6 \, \text{cm}$ and $2 \, \text{cm}$.
Answer for screen readers
The possible answers for the triangle's third side are $6 , \text{cm}$ and $2 , \text{cm}$.
Steps to Solve
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Multiple Choice Question Setup
Formulate a multiple-choice question based on basic algebra.
Example: "The solution to the equation $2x + 3 = 7$ is ()"
Possible answers:
A. $x = 5$
B. $x = 4$
C. $x = 3.5$
D. $x = 2^{237}$ -
Answering the Multiple Choice Question
Solve for $x$:
$$ 2x + 3 = 7 $$
Subtract 3 from both sides:
$$ 2x = 4 $$
Divide both sides by 2:
$$ x = 2 $$
Thus, there is an error in the choices; correct solution should be reflected. -
Fill-in-the-Blank Question Creation
Create a fill-in-the-blank question involving inequalities.
Example: "The sum of 6 and twice $x$ is negative. This can be expressed as the inequality ____."
The solution:
$$ 6 + 2x < 0 $$ -
Answering the Fill-in-the-Blank Question
Isolate $x$:
Subtract 6:
$$ 2x < -6 $$
Divide by 2:
$$ x < -3 $$
Therefore, the correct expression is $6 + 2x < 0$. -
Short Answer Question Structure
Create a short answer question based on triangle inequality.
Example: "If a triangle has two sides measuring 4 cm and 9 cm, which of the following can be the length of the third side?"
Evaluate with triangle inequality (sum of lengths of any two sides must be greater than the length of the third). We need to check each option. -
Evaluating Possible Third Sides
Evaluate:- For $13 , \text{cm}$: $4 + 9 = 13$ (not valid)
- For $6 , \text{cm}$: $4 + 6 = 10 > 9$ (valid)
- For $5 , \text{cm}$: $4 + 5 = 9$ (not valid)
- For $2 , \text{cm}$: $4 + 2 = 6 > 9$ (valid)
Valid answers: $6 , \text{cm}$ and $2 , \text{cm}$.
The possible answers for the triangle's third side are $6 , \text{cm}$ and $2 , \text{cm}$.
More Information
In algebra, multiple-choice questions can help test understanding of solving equations, while fill-in-the-blank questions engagingly reinforce concepts like inequalities. Short answer questions encourage critical thinking, especially using rules like the triangle inequality.
Tips
- Miscalculating answers in multiple-choice settings; ensure you always check your math.
- Infill-in-the-blank questions, remember that inequalities can flip signs under certain operations like multiplication or division by negative numbers.
- Forgetting the triangle inequality rule; always validate potential side lengths with the appropriate checks.
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