Write & Read Algebraic Expressions · MCAP 6.EE.A.2

Learning Goal: Translate words into algebraic expressions and identify their parts, such as terms and coefficients.

Vocabulary

variableA letter that stands for an unknown number, like x or n.

termA single part of an expression separated by + or − signs. In 3x + 5, the terms are 3x and 5.

coefficientThe number multiplied by a variable. In 7y, the coefficient is 7.

constantA term that is just a number with no variable, like the 5 in 3x + 5.

expressionA math phrase with numbers, variables, and operations but no equal sign.

What You Need to Know

'Sum' means add, 'difference' means subtract, 'product' means multiply, 'quotient' means divide.
'More than' and 'increased by' mean add; 'less than' and 'decreased by' mean subtract.
Watch the order: '5 less than x' is x − 5, NOT 5 − x.
A coefficient sits in front of a variable; 'x' alone has a coefficient of 1.
Terms are separated by + or − signs; count them to know how many terms there are.
'Twice a number' means 2 × the number, written 2n.

Worked Example I Do — watch how it works

Write an expression for 'the cost of t tickets at $9 each, plus a $4 service fee,' then name the coefficient and constant.

Step 1. Cost of tickets is $9 times the number of tickets: 9t.
Step 2. Add the flat $4 service fee: 9t + 4.
Step 3. The coefficient is 9 (multiplies t) and the constant is 4.

Answer: 9t + 4; coefficient 9, constant 4

Guided Practice We Do — try it together

1. Write 'a number n decreased by 7' as an expression.
💡 Hint: 'Decreased by' means subtract, in the order given.
2. How many terms are in 4x + 2y + 9, and what is the coefficient of y?
💡 Hint: Count parts separated by + signs; the coefficient is the number in front of y.
3. Write 'the product of 6 and a number x' as an expression.
💡 Hint: 'Product' means multiply.

Independent Practice You Do — show your work

1. Write '8 more than a number m' as an expression.
2. Write '3 less than twice a number p' as an expression.
3. Identify the coefficient and constant in 10g + 15.
4. Write 'the quotient of a number y and 5' as an expression.
5. How many terms are in the expression 5a + 7 − b?

MCAP-Style Practice

Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.EE.A.2.

Item 1Selected Response6.EE.A.2

Which expression represents '5 less than a number n'?

Select the correct answer.

○ A. 5 − n○ B. n − 5○ C. 5n○ D. n + 5

Item 2Selected Response6.EE.A.2

In the expression 7x + 12, which statement is true?

Select the correct answer.

○ A. 7 is the constant○ B. 12 is the coefficient○ C. 7 is the coefficient and 12 is the constant○ D. x is the constant

Item 3Constructed Response6.EE.A.2

A taxi charges a $3 base fee plus $2 for each mile m. Write an expression for the total cost.

Enter your answer in the space provided. Show your work.

Enter your answer:

Teacher Answer Key (click to show)

Independent 1	m + 8
Independent 2	2p − 3
Independent 3	Coefficient 10, constant 15
Independent 4	y ÷ 5 (or y/5)
Independent 5	3 terms
Item 1 · 6.EE.A.2	B — '5 less than n' starts with n and subtracts 5, giving n − 5.
Item 2 · 6.EE.A.2	C — 7 multiplies the variable x (coefficient) and 12 stands alone (constant).
Item 3 · 6.EE.A.2	2m + 3 — $2 per mile gives 2m, plus the $3 base fee, so 2m + 3.

Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.EE.A.2