Year 7 in England
6th grade algebra
20 6th grade algebra skills, each with a worked example, free practice that checks every answer, and a printable worksheet. Start with a mixed review, or jump to the skill you need.
Mixed review
Ten questions drawn from every skill below.
Write algebraic expressions
CCSS 6.EE.A.2.ACCSS 6.EE.A.2.BCCSS 6.EE.B.6England: Y6 AlgebraEngland: KS3 Algebra
Example
Which expression means "n subtracted from 2"?
- 2 − n
Answer: 2 − n
Evaluate expressions
CCSS 6.EE.A.2.CEngland: Y6 AlgebraEngland: KS3 Algebra
Example
Find the value of 8x + 6 when x = 2.
- 8 × 2 + 6
- = 16 + 6 = 22
Answer: 22
Simplify expressions: like terms
CCSS 6.EE.A.3CCSS 6.EE.A.4CCSS 7.EE.A.1England: KS3 AlgebraEngland: GCSE Foundation Algebra
Example
Simplify 5x + 4x.
- 5 + 4 = 9
- 9x
Answer: 9x
One-step equations
CCSS 6.EE.B.5CCSS 6.EE.B.7England: Y6 AlgebraEngland: KS3 Algebra
Example
Solve: x/9 = 11
- x/9 = 11
- x = 11 × 9
- x = 99
Answer: x = 99
Inequalities: meaning and solutions
CCSS 6.EE.B.5CCSS 6.EE.B.8England: KS3 AlgebraEngland: GCSE Foundation Algebra
Example
Which inequality matches? "You must be at least 12 years old to ride." (x is the amount)
- x ≥ 12
Answer: x ≥ 12
Dependent and independent variables
CCSS 6.EE.C.9England: KS3 Algebra
Example
Felix earns 5 for each hour of dog walking: e = 5h. How much does Felix earn for 7 hours?
- 5 × 7 = 35
Answer: 35
Order of operations with exponents
CCSS 6.EE.A.1England: KS3 Number
Example
Work out 11 + 5 × 6².
- 6² = 36
- 5 × 36 = 180
- 11 + 180 = 191
Answer: 191
Multi-step calculations with brackets, powers and division
CCSS 6.EE.A.1CCSS 6.EE.A.2.CEngland: KS3 Number
Example
Work out (4 + 11)² ÷ 5 − 18.
- 15² = 225
- 225 ÷ 5 = 45
- 45 − 18 = 27
Answer: 27
Builds on: Order of operations with exponents
Name the parts of an expression: terms, coefficients and constants
CCSS 6.EE.A.2.BEngland: KS3 Algebra
Example
In 10x + 11y + 10, what is the coefficient of y?
- The y-term is 11y, so the coefficient is 11.
Answer: 11
Builds on: Write algebraic expressions
Turn word descriptions into two-step expressions
CCSS 6.EE.A.2.ACCSS 6.EE.B.6England: KS3 Algebra
Example
Write an expression for: the difference of n and 4, multiplied by 9.
- 9(n − 4)
Answer: 9(n-4)
Builds on: Write algebraic expressions
Evaluate expressions with powers and two variables
CCSS 6.EE.A.2.CEngland: KS3 Algebra
Example
Evaluate 5x² + 20 when x = 9.
- 9² = 81
- 5 × 81 = 405
- 405 + 20 = 425
Answer: 425
Substitute into everyday formulas
CCSS 6.EE.A.2.CEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Example
The perimeter of a rectangle is P = 2(l + w). Find P when l = 15 cm and w = 3 cm.
- P = 2(15 + 3) = 2 × 18 = 36 cm
Answer: 36
Builds on: Evaluate expressions
Recognise equivalent expressions
CCSS 6.EE.A.3CCSS 6.EE.A.4England: KS3 Algebra
Example
Which expression is equivalent to 7(x + 3)?
- 7(x + 3) = 7x + 21
Answer: 7x + 21
Builds on: Simplify expressions: like terms
Leads to: Expand brackets with positive terms
Expand brackets with positive terms
CCSS 6.EE.A.3England: KS3 Algebra
Example
Expand 3(x + 12).
- 3 × x = 3x
- 3 × 12 = 36
- 3x + 36
Answer: 3x+36
Builds on: Recognise equivalent expressions
Solve x + a = b and x − a = b, including decimals and fractions
CCSS 6.EE.B.7England: KS3 Algebra
Example
Solve: y + 4.9 = 9.7
- y = 9.7 − 4.9
- y = 4.8
Answer: y = 4.8
Builds on: One-step equations
Leads to: Write and solve one-step equations from real situations
Solve ax = b and x ÷ a = b, including fraction coefficients
CCSS 6.EE.B.7England: KS3 Algebra
Example
Solve: x ÷ 9 = 15
- x = 15 × 9
- x = 135
Answer: x = 135
Builds on: One-step equations
Leads to: Write and solve one-step equations from real situations
Write and solve one-step equations from real situations
CCSS 6.EE.B.7England: KS3 Algebra
Example
Priya buys 7 identical phone cases and pays $63 in total. Solve 7p = 63 to find the price p of one case.
- p = 63 ÷ 7
- p = 9
Answer: p = 9
Write inequalities for real-life limits
CCSS 6.EE.B.8England: KS3 Algebra
Example
Write an inequality: The speed limit is 88 km/h (s = speed). (Type ≤ as <= and ≥ as >= if you need to.)
- s ≤ 88
Answer: s ≤ 88
Builds on: Inequalities: meaning and solutions
Match inequalities and number-line graphs
CCSS 6.EE.B.8England: KS3 Algebra
Example
Which graph shows x ≥ −5?
- Closed circle at −5, arrow right
Answer: Closed circle at −5, arrow right
Builds on: Write inequalities for real-life limits
Find the equation linking two variables in a table
CCSS 6.EE.C.9England: KS3 Algebra
Example
x: 4, 6, 7, 10. y: 44, 66, 77, 110. Write an equation for y in terms of x. Type the right-hand side only.
- 44 ÷ 4 = 11
- y = 11x
Answer: 11x
Builds on: Dependent and independent variables
Keep exploring
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