Visual Model 1
Question: Study the labeled expression diagram below: What is the coefficient in Term 3?
- A. \(2\)
- B. \(7\)
- C. \(y\)
- D. \(4\)
Why it works: Term 3 is \(2y\), so the coefficient is \(2\).
Answer: \(2\)
CH03-03 lesson
Terms, Factors, and Coefficients Learning Activity
A focused Grade 6 learning session for Terms, Factors, and Coefficients using visual models, worked examples, strategy guidance, and a short mastery check.
- 15
- minutes
- 6
- lesson parts
- 11
- practice items
Students will build Grade 6 mastery of terms, factors, and coefficients using models, equations, and test-style reasoning.
Student goal: I can solve problems involving terms, factors, and coefficients.
Helpful first:
Translating Words into Expressions
Learn the Idea
Terms, Factors, and Coefficients means choosing a model, naming what each number means, and explaining the strategy.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
See the Math
Follow a Worked Example
Example 1
Question: In the expression shown, what is the sum of all coefficients?
- A. \(4\)
- B. \(12\)
- C. \(0\)
- D. \(-4\)
- Sum: \(6 + 2 + (-4) = 4\).
- Note: when including negative coefficients, add them with their signs.
Answer: \(4\)
Example 2
Question: Complete the table by identifying the number of terms in each expression: What is the total of the two missing numbers?
| Expression | Number of Terms |
|---|---|
| \(7a\) | \(1\) |
| \(4x + 2y\) | ? |
| \(5m + 3n + 2p + 1\) | ? |
- A. \(5\)
- B. \(7\)
- C. \(4\)
- D. \(6\)
- \(4x + 2y\) has 2 terms. \(5m + 3n + 2p + 1\) has 4 terms.
- Total: \(2 + 4 = 6\).
Answer: \(6\)
Connect It to a Real Situation
Problem 1
Question: A garden is \(8\) meters long and \(w\) meters wide. The area is \(8w\) square meters. In the expression \(8w\), what are the factors?
- A. \(8\) and \(w\)
- B. The area and the width
- C. \(8\) only
- D. \(w\) only
Why it works: In a product, factors are the numbers or variables being multiplied. Here, \(8 \times w = 8w\), so the factors are \(8\) and \(w\).
Answer: \(8\) and \(w\)
Avoid Mistakes and Choose a Strategy
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Remember the Key Idea
Terms, Factors, and Coefficients becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
Solve before opening the answer
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
warmup
2 questionsIn the expression \(5x+3y+8\), what is the coefficient of \(y\)?
- A \(5\)
- B \(3\)
- C \(8\)
- D \(y\)
Check answer and explanation
Answer B: \(3\)
The coefficient is the number multiplied by the variable. The term \(3y\) has coefficient \(3\).
Which expression has exactly 4 terms?
- A \(2a+5\)
- B \(3x+2y+4z+1\)
- C \(6m\)
- D \(7p+3q\)
Check answer and explanation
Answer B: \(3x+2y+4z+1\)
Counting each separated term: \(3x\), \(2y\), \(4z\), and \(1\) gives 4 terms.
guided
1 questionWhat is the coefficient of \(x\) in the expression \(-4x+9+2y\)?
- A \(4\)
- B \(2\)
- C \(9\)
- D \(-4\)
Check answer and explanation
Answer D: \(-4\)
The coefficient includes the sign. Since the term is \(-4x\), the coefficient is \(-4\), not \(4\).
practice
5 questionsIn the expression \(6a+3b+7\), which is the constant term?
- A \(6a\)
- B \(3b\)
- C \(7\)
- D \(ab\)
Check answer and explanation
Answer C: \(7\)
A constant term is a number with no variable attached. Here, \(7\) is the only constant.
What is the coefficient of \(m\) in the expression \(m+5n+2\)?
- A \(0\)
- B \(1\)
- C \(5\)
- D \(2\)
Check answer and explanation
Answer B: \(1\)
When a variable appears with no visible number, the coefficient is \(1\). So \(m = 1m\).
Study the labeled expression diagram below: What is the coefficient in Term 3?
- A \(2\)
- B \(7\)
- C \(y\)
- D \(4\)
Check answer and explanation
Answer A: \(2\)
Term 3 is \(2y\), so the coefficient is \(2\).
Which pair are like terms?
- A \(3x\) and \(3y\)
- B \(5a\) and \(5b\)
- C \(4x\) and \(x^2\)
- D \(2m\) and \(2m\)
Check answer and explanation
Answer D: \(2m\) and \(2m\)
Like terms have the same variable raised to the same power. Both \(2m\) and \(2m\) are identical terms.
Which pair are unlike terms?
- A \(6x\) and \(2x\)
- B \(7y\) and \(-3y\)
- C \(4a\) and \(4b\)
- D \(5n\) and \(n\)
Check answer and explanation
Answer C: \(4a\) and \(4b\)
\(4a\) and \(4b\) have different variables (\(a\) vs.\ \(b\)), so they are unlike terms.
exit
3 questionsUse the table to match each term to its coefficient: What is the coefficient of the third term (a constant with no variable)?
- A The constant has no coefficient
- B \(1\)
- C \(12\)
- D \(0\)
Check answer and explanation
Answer A: The constant has no coefficient
A constant term like \(12\) is a number with no variable. Constants do not have coefficients; coefficients are numbers that multiply variables.
A garden is \(8\) meters long and \(w\) meters wide. The area is \(8w\) square meters. In the expression \(8w\), what are the factors?
- A \(8\) and \(w\)
- B The area and the width
- C \(8\) only
- D \(w\) only
Check answer and explanation
Answer A: \(8\) and \(w\)
In a product, factors are the numbers or variables being multiplied. Here, \(8 \times w = 8w\), so the factors are \(8\) and \(w\).
How many terms does the expression \(9a+4b+3c+2\) have?
- A \(2\)
- B \(3\)
- C \(4\)
- D \(5\)
Check answer and explanation
Answer C: \(4\)
Each term separated by \(+\) or \(-\) counts as one term. Here: \(9a\), \(4b\), \(3c\), \(2\).
