Math // Algebra

Using Simple Formulae

Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width))

Ages
10 to 11
Type
Method
Builds on
2 topics
Leads to
2 topics
Standards
1 code

Quick check

If the learner is told that the perimeter of a rectangle uses the formula perimeter = 2 × (length + width), can they plug in the measurements and work out the answer?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Substitute values into P = 2(l + w) to find the perimeter of a rectangle
  • Use the formula for area of a triangle (A = 1/2 × b × h) given base and height values
  • Interpret a formula expressed in words and use it to compute an output

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • Order of operationsRequired

    Multiplication & Division // Ages 10 to 11

    Substituting into formulae requires understanding order of operations

  • Writing Number SentencesHelpful

    Multiplication & Division // Ages 10 to 11

    Interpreting formulae connects to interpreting numerical expressions

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Using Simple Formulae

Ages 10 to 11 // Method

Leads to

2 topics

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Year 6 learners use simple formulae (in words or symbols) to calculate values, substituting given numbers and applying EVERY operation in the correct order. The signature pitfalls are ignoring the bracket in P = 2(l + w) and doubling only the length (2×l + w), omitting the ½ in the area of a triangle, confusing perimeter with area, and mismatched units (cm vs cm²). Connecting each formula to the shape it describes keeps the computation meaningful.

Common misconceptions

  • Ignores the bracket / order of operations: P = 2(l + w) computed as 2×l + w (e.g. 2×5+3 = 13 instead of 2×8 = 16).
  • Omits the ½ in a triangle's area, giving b×h (24) instead of ½×b×h (12).
  • Confuses perimeter and area formulae, or uses the wrong measurements.
  • Attaches wrong units (perimeter in cm², or no units).
  • Reads a worded formula incorrectly and mis-sequences the operations.

Useful representations

  • The shape itself with the formula overlaid (perimeter traced round the edge)
  • Triangle drawn inside its enclosing rectangle (why ½)
  • Function machine for the sequence of operations
  • Worded-formula ↔ symbol-formula matching cards

Teaching practices

  • Read the formula first and say what it computes and what each letter means before substituting.
  • Do the bracket first: for P = 2(l + w), add length and width, THEN double — not 2×l + w.
  • Apply every operation in the formula, including the ½ for a triangle; link it to the triangle being half its enclosing rectangle.
  • Distinguish perimeter (distance round, in cm) from area (space inside, in cm²) and attach the correct units.
  • Substitute carefully and check the result is sensible for the shape.

Activities to try

  1. 1

    Formula-on-a-shape: watch the bracket do its work

    Why it works: The bracket's order is not arbitrary here: adding-then-doubling walks the whole boundary and closes it, while doubling-then-adding misses one width and does not. The ½ for a triangle is the visible fact that a triangle has half the area of a rectangle with the same base and height.

    1. Set the length and width of a rectangle (for example with sliders), and evaluate P = 2(l + w) step by step: add length and width inside the bracket FIRST, then double.
    2. Trace the perimeter round the edge of the rectangle as the formula computes, and check the traced path closes back on itself.
    3. Toggle a 'double first' version that shows what 2×l + w would do — a path that traces both lengths but only one width, so it stops one side short and never closes round the shape.
    4. Flip to a triangle whose top vertex lies above its base and place it on a rectangle with the same base and height (on screen or with a paper/card cut-out). Cut or drag the leftover pieces of the rectangle to show they exactly cover the triangle (for a right-angled triangle, two identical copies make the rectangle), so the ½ in A = ½ × b × h is seen as the triangle being half that rectangle. (A paper cut-out has slight thickness and stands in for the ideal flat, zero-thickness triangle; it still shows the half-area relationship.)
    5. Optionally lay the formula out as a function machine so the sequence of operations the formula specifies is explicit.
  2. 2

    Substitute and compute with feedback

    Why it works: Substituting into a given formula and picking the right formula/units is a procedure built by doing and checking; the common slips are the bracket and the dropped ½, so each is targeted directly.

    1. Fill in the blank: P = 2(5 + 3) = __, showing the bracket step (2 × 8 = 16 cm) before the answer.
    2. Choose the area of a triangle with base 6 cm and height 4 cm from options including 12 cm² and the ½-omission result 24 cm²; explain why 24 is wrong.
    3. Match each worded formula to its symbol form (e.g. 'multiply the base by the height, then halve' ↔ A = ½ × b × h).
    4. Attach the correct units to each answer and say why perimeter is in cm but area is in cm².
    5. Work an unfamiliar simple worded formula end-to-end, naming each operation as you do it.
  3. 3

    Label the shape and reveal the steps

    Why it works: Connecting each symbol to the part of the shape it measures keeps the formula meaningful before computing.

    1. On a labelled rectangle, tap or point to the perimeter formula and reveal each step of the calculation in turn.
    2. Say what each letter in the formula stands for on the drawing before any numbers are substituted.
    3. Predict the next step before revealing it, then check your prediction against the shown calculation.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Ma6/2.5a

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