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Year 7 Essential Skills
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Sequences
Continue a linear sequence
\[ 3, 7, 11, 15, \ldots \]
Find the next three terms of a linear sequence.
Find the term-to-term rule
\[ 5, 8, 11, 14, \ldots \]
State the term-to-term rule for a given linear sequence.
Find a specific term
\[ \text{10th term of } 2, 5, 8, \ldots \]
Calculate a specific term in a linear sequence.
Algebraic notation
Write expressions
\[ 3n + 5 \]
Convert a word description into an algebraic expression.
Simplify by collecting like terms
\[ 3a + 2b + a \]
Collect like terms to simplify an algebraic expression.
Substitute into expressions
\[ 2x + 3 \text{ when } x = 4 \]
Substitute a value for a variable and evaluate the expression.
Simplify with indices
\[ a^3 \times a^2 \]
Simplify expressions involving powers of variables.
Expand single brackets
\[ 3(x + 4) \]
Expand an expression with a single bracket.
Equations
Solve one-step (+ or −)
\[ x + 5 = 12 \]
Solve an equation requiring one addition or subtraction step.
Solve one-step (× or ÷)
\[ 3x = 18 \]
Solve an equation requiring one multiplication or division step.
Solve two-step equations
\[ 2x + 3 = 11 \]
Solve an equation requiring two inverse operations.
Place value
Value of a digit in a decimal
\[ \text{Value of 7 in } 3.472 \]
State the value of a specific digit in a decimal number.
Order decimals
\[ 0.35, 0.4, 0.29 \]
Arrange a set of decimal numbers in ascending order.
Round integers to 1 s.f.
\[ 3{,}847 \approx \text{?} \]
Round an integer to one significant figure.
Round decimals to 1 s.f.
\[ 0.0456 \approx \text{?} \]
Round a decimal to one significant figure.
FDP equivalence
Fraction to decimal
\[ \frac{3}{4} = \text{?} \]
Convert a fraction to its decimal equivalent.
Decimal to percentage
\[ 0.35 = \text{?}\% \]
Convert a decimal to its percentage equivalent.
Percentage to fraction
\[ 40\% = \text{?} \]
Convert a percentage to a fraction in simplest form.
Equivalent fractions
\[ \frac{2}{3} = \frac{\square}{12} \]
Find a missing numerator or denominator in equivalent fractions.
Fractions of amounts
Unit fraction of an amount
\[ \frac{1}{4} \text{ of } 24 \]
Calculate a unit fraction of a given quantity.
Non-unit fraction of an amount
\[ \frac{3}{5} \text{ of } 40 \]
Calculate a non-unit fraction of a given quantity.
Percentages of amounts
Find 10% of an amount
\[ 10\% \text{ of } 80 \]
Calculate 10% of a given quantity.
Find a multiple of 10%
\[ 30\% \text{ of } 60 \]
Calculate a percentage (multiple of 10) of a given quantity.
Find 5% or 25%
\[ 25\% \text{ of } 48 \]
Calculate 5% or 25% of a given quantity.
Directed number
Order directed numbers
\[ -5, 2, -8, 0, 3 \]
Arrange a set of integers including negatives in ascending order.
Add integers crossing zero
\[ -7 + 12 \]
Add two integers where the calculation crosses zero.
Subtract to get negative
\[ 5 – 12 \]
Subtract integers where the result is negative.
Add two negatives
\[ 5 + (-3) \]
Add a negative integer to another integer.
Subtract a negative
\[ 3 – (-5) \]
Subtract a negative integer from another integer.
Multiply with negatives
\[ (-4) \times 6 \]
Multiply two integers where one or both are negative.
Fraction operations
Add fractions (same denom)
\[ \frac{2}{7} + \frac{3}{7} = \square \]
Add two fractions that share a common denominator.
Subtract fractions (same denom)
\[ \frac{5}{8} – \frac{2}{8} = \square \]
Subtract two fractions that share a common denominator.
Add fractions (related denom)
\[ \frac{1}{2} + \frac{1}{4} = \square \]
Add two fractions where one denominator is a multiple of the other.
Angles
Missing angle on straight line
\[ x + 65° = 180° \]
Calculate the missing angle when angles sum to 180°.
Missing angle at a point
\[ 120° + 90° + x = 360° \]
Calculate the missing angle when angles sum to 360°.
Vertically opposite angles
\[ \text{Opposite} = 45° \]
Identify that vertically opposite angles are equal.
Factors and multiples
Count the factors
\[ \text{Factors of } 24 \]
Count how many factors a given integer has.
Find the HCF
\[ \text{HCF}(12, 18) \]
Calculate the highest common factor of two integers.
Find the LCM
\[ \text{LCM}(4, 6) \]
Calculate the lowest common multiple of two integers.
Primes
Identify prime numbers
\[ 21, 23, 27, 29, 33 \]
Identify which numbers from a list are prime.
Perimeter and area
Perimeter of a rectangle
\[ 2(l + w) \]
Calculate the perimeter of a rectangle given its length and width.
Area of a rectangle
\[ l \times w \]
Calculate the area of a rectangle given its length and width.
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