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Year 7 Essential Skills

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Place value and calculation
Value of a digit in a decimal
\[ \text{Value of 7 in } 3.472 \]
Use place value: what is the digit worth?
Multiply and divide by 10, 100, 1000
\[ 3.6 \times 100 \]
Move the digits, do not just add zeros.
Order decimals
\[ 0.4, 0.35, 0.405 \]
Fill with zeros so every number has the same length.
Round whole numbers to 1 s.f.
\[ 4\,682 \to 5\,000 \]
Round the first digit, then fill with zeros.
Round decimals to 1 s.f.
\[ 0.0482 \to 0.05 \]
Start from the first digit that is not zero.
Multiply or divide a decimal by a whole number
\[ 0.7 \times 6 = 4.2 \]
Work in tenths or hundredths, then convert back.
Order of operations
\[ 3 + 4 \times 2 \]
Brackets, indices, then × and ÷, then + and −.
Directed number
Order directed numbers
\[ -7, -3, 0, 4 \]
The further below zero, the smaller the number.
Add, crossing zero
\[ (-5) + 8 = 3 \]
Count up to zero, then past it.
Subtract to get a negative
\[ 3 – 9 = -6 \]
Count down to zero, then below it.
Add two negatives
\[ (-4) + (-6) \]
Adding a negative moves you further left.
Subtract a negative
\[ 5 – (-3) = 8 \]
Subtracting a negative is the same as adding.
Multiply and divide negatives
\[ (-6) \times (-4) \]
Same signs give a positive, different signs a negative.
Factors, multiples and powers
Squares, cubes and roots
\[ 4^3 = 64 \]
Squared: × itself. Cubed: × itself three times.
Count the factors
\[ \text{Factors of 36: } 9 \]
Find the factors in pairs, and count each once.
Identify a prime number
\[ \text{Prime: } 51, 53, 57? \]
Exactly two factors. 1 is not prime.
Highest common factor
\[ \text{HCF of } 18, 24 \]
The biggest number that divides into both.
Lowest common multiple
\[ \text{LCM of } 6, 8 \]
The smallest number in both times tables.
Fractions, decimals and percentages
Equivalent fractions
\[ \frac{3}{4} = \frac{\square}{20} \]
Multiply or divide the top and bottom by the same number.
Fraction to decimal
\[ \frac{3}{8} = 0.375 \]
Make the bottom 10, 100 or 1000.
Decimal to percentage
\[ 0.035 = 3.5\% \]
Multiply by 100.
Percentage to fraction
\[ 35\% = \frac{7}{20} \]
Write it over 100, then simplify.
Unit fraction of an amount
\[ \frac{1}{5} \text{ of } 40 \]
Divide by the bottom number.
Non-unit fraction of an amount
\[ \frac{3}{5} \text{ of } 40 \]
Divide by the bottom, multiply by the top.
Find 10% of an amount
\[ 10\% \text{ of } 340 \]
10% is one tenth: divide by 10.
Find a multiple of 10%
\[ 30\% \text{ of } 80 \]
Find 10%, then multiply.
Find 5% or 25%
\[ 25\% \text{ of } 64 \]
5% is half of 10%. 25% is a quarter.
Adding and subtracting fractions
Add fractions: same denominator
\[ \frac{2}{7} + \frac{3}{7} \]
Add the tops. The bottom stays the same.
Subtract fractions: same denominator
\[ \frac{7}{9} – \frac{2}{9} \]
Subtract the tops. The bottom stays the same.
Add and subtract: one denominator a multiple
\[ \frac{1}{3} + \frac{2}{9} \]
Change one fraction so the bottoms match.
Add and subtract: both denominators change
\[ \frac{2}{3} + \frac{1}{4} \]
Find a common denominator for both.
Sequences and algebra
Continue a linear sequence
\[ 23, 19, 15, \ldots \]
Find the difference, then keep going.
Term-to-term rule
\[ 17, 13, 9 \to -4 \]
How do you get from one term to the next?
Find a term further on
\[ 10\text{th term of } 5, 8, 11 \]
From the 1st to the 10th term is 9 jumps.
Function machines
\[ 5 \to \boxed{\times 3} \to \boxed{-4} \]
Forwards: in order. Backwards: inverses, in reverse.
Write an expression
\[ \text{5 less than } x \]
Turn the words into algebra, in the right order.
Substitute into an expression
\[ 3a + 2,\ a = 4 \]
Swap each letter for its value, then calculate.
Collect like terms
\[ 5x + 3y – 2x \]
Only terms with exactly the same letters combine.
Simplify products and powers
\[ a \times a \times a = a^3 \]
Multiply the numbers; repeated letters become powers.
Expand a single bracket
\[ 3(2x – 5) \]
Multiply every term inside by the number outside.
One-step equations: + or −
\[ x – 4 = 9 \]
Do the inverse to both sides.
One-step equations: × or ÷
\[ \frac{x}{3} = 5 \]
Do the inverse to both sides.
Two-step equations
\[ 3x + 5 = 20 \]
Undo the + or − first, then the × or ÷.
Geometry and measures
Angles on a straight line
\[ x + 65^\circ = 180^\circ \]
Angles on a straight line add up to 180°.
Angles at a point
\[ x + 250^\circ = 360^\circ \]
Angles around a point add up to 360°.
Vertically opposite angles
\[ \text{Opposite angles: equal} \]
Where two lines cross, opposite angles are equal.
Angles in a triangle
\[ x + 50^\circ + 70^\circ = 180^\circ \]
The three angles add up to 180°.
Angles in a quadrilateral
\[ \text{Four angles: } 360^\circ \]
The four angles add up to 360°.
Perimeter of a rectangle
\[ 8 + 5 + 8 + 5 \]
Add all four sides.
Area of a rectangle
\[ 8 \times 5 = 40\text{cm}^2 \]
Length times width, in square units.
Area of a triangle
\[ \frac{1}{2} \times 10 \times 4 \]
Half of base times perpendicular height.
Area of a parallelogram
\[ 10 \times 4 = 40\text{cm}^2 \]
Base times perpendicular height.
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