Advanced Maths Vocabulary
Communicate with mathematical precision: use correct vocabulary for ratio, proportion, algebra, volume, coordinate geometry, and circle parts; specify units including cm³, m³, and miles/km; use notation for algebraic expressions and order of operations accurately
What a learner can do afterwards
- Use 'radius', 'diameter', and 'circumference' correctly when describing a circle
- Distinguish between an expression, an equation, and a formula in mathematical writing
- Specify units correctly when presenting volume calculations (e.g. 60 cm³ not just 60)
1 · Read
This lesson names the parts of a circle so you can talk about them precisely, then stretches that same care further: naming the parts of algebra, and always writing the right unit for volume.
3x + 5 is an expression. It has no equals sign. 3x + 5 = 20 is an equation. It is true for one value of x. V = l × w × h is a formula. It is a rule that always works, whatever the lengths are.
Layla measures in centimetres and works out a box's volume: 4 cm × 3 cm × 2 cm = 24. She writes 24 cm³, not just 24. The little 3 shows it is a cubic measurement, made from three lengths multiplied together.
Whenever you multiply lengths in centimetres, your answer needs cm² for area or cm³ for volume. The number alone does not tell anyone what you measured.
Use radius, diameter, and circumference precisely, know an expression from an equation from a formula, and always write cm³ or m³ with a volume.
The rewritten readings were written for this dataset.
More to read
Three measurements of a circle
A radius joins a circle's centre to its edge. A diameter joins opposite edges through the centre and measures twice as much. Circumference measures the length around the circle. For example, a radius of 5 cm gives a diameter of 10 cm. Practise saying each name with its measurement to remember what it describes.
Changing between radius and diameter
No straight line segment inside a circle is longer than its diameter, which crosses the centre. Divide the diameter by two to find the radius. Multiply the radius by two to find the diameter. A diameter of 14 cm gives a radius of 7 cm. Check that the diameter is exactly twice the radius, not just bigger.
Calculating the distance around
A circle's perimeter is called its circumference. Calculate it using π × diameter or 2 × π × radius. If the radius measures 7 cm and you approximate π by 22/7, then 2 × 22/7 × 7 = 44 cm. This is an approximate circumference. Both formulas give the same result because a diameter equals two radii. Choose the formula for the measurement you know.
Expressions, equations and formulas
An expression, such as 3x + 5, represents a value. An equation states an equality: 3x + 5 = 20. A formula gives a relationship used across problems, such as V = lwh. Volume needs cubic units, so write 60 cubic cm instead of 60 alone. Use the correct terms when explaining your maths.
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2 · Watch
En anglaisTake it off screen
Where it sits
Learn first
Optional connections
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.