These 10 problems practice writing, evaluating, and rewriting algebraic expressions from Common Core 6.EE.A.2, 6.EE.A.3, and 6.EE.A.4. Early problems name the parts of an expression and translate phrases; later problems use exponents, formulas, the distributive property, and like terms.
Problems 8 through 10 are word problems about pay, area, and a gift box. Write each step of your substitution so that the work is easy to check.
Problem 1: Parts of an Expression
Use the expression \(7x + 4y + 9\) to answer each question.
- How many terms does it have?
- What is the coefficient of \(x\)?
- What is the coefficient of \(y\)?
- Which term is the constant?
Problem 2: Writing Simple Expressions
Write an algebraic expression for each phrase.
- 8 more than \(n\)
- 6 less than \(y\)
- the product of 5 and \(m\)
- \(k\) divided by 4
Problem 3: Writing Longer Expressions
Write an algebraic expression for each phrase.
- twice the sum of \(x\) and 7
- 3 times \(a\), decreased by 2
- the quotient of 20 and \(p\)
- 9 less than the product of 4 and \(t\)
Problem 4: Evaluating Expressions
Evaluate each expression when \(x = 6\).
- \(x + 9\)
- \(4x\)
- \(\frac{30}{x}\)
- \(3x – 5\)
Problem 5: Exponents and Formulas
Evaluate each expression or formula.
- \(n^2\) when \(n = 7\)
- \(5x^2 – 10\) when \(x = 4\)
- \(V = s^3\) when \(s = 5\text{ ft}\)
- \(A = 6s^2\) when \(s = \frac{1}{2}\text{ in}\)
Problem 6: Distributive Property
Apply the distributive property to write an equivalent expression.
- \(3(x + 5)\)
- \(4(2y + 1)\)
- \(6x + 9\) as a product of 3 and a sum
- \(10 + 15m\) as a product of 5 and a sum
Problem 7: Combining Like Terms
Simplify each expression by combining like terms.
- \(7a + 3a\)
- \(9b – 4b\)
- \(2x + 5 + 6x + 1\)
- \(3y + 4 + y + 2y\)
Problem 8: Dog Walking Pay
Ethan earns $12 for each hour he walks dogs and gets a $5 tip. Write an expression for his total pay for \(h\) hours, then evaluate it when \(h = 6\).
Problem 9: Flower Bed Area
A rectangular flower bed is \(4\text{ ft}\) wide and \((x + 6)\text{ ft}\) long. Write two equivalent expressions for its area, then show that they have the same value when \(x = 3\).
Problem 10: Gift Box
Sofia wraps a cube-shaped gift box with edges of \(8\text{ in}\). Wrapping paper costs $0.02 per square inch.
- Find the volume of the box using \(V = s^3\).
- Find the surface area using \(A = 6s^2\).
- Find the cost of the paper needed to cover the whole box.
See every chapter on the Grade 6 math page.