There are 169 Underpinning Topics
Below are 169 topics which are a good starting point for everyone (GCSE Grades 1-2)
You need to be able to do the first 3 sections containing 778 topics to pass at Foundation Level!
These are the 169 GCSE building blocks at Key Stage 2. This is not a complete Key Stage 2 course.
Number
- STEP 01
- Round positive whole numbers to the nearest 10, 100 or 1000
- Add, subtract multiply and divide integers - positive and negative
- Use standard column procedures to add and subtract whole numbers
- Know by heart multiplication facts up to 10 × 10
- Use halving
- Use doubling
- Partition to multiply mentally TU × U
- Find a difference by counting up through the next multiple of 10
- Add three or more multiples of 10
- Recognise multiples up to 10 × 10
- Apply simple tests of divisibility (2, 9, 10, 5)
- Know square numbers, 10 × 10, 1 × 1 to 5 × 5
- Order positive and negative integers
- Use diagrams to compare two or more simple fractions
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- STEP 02
- Apply four operations in correct order to integers and proper fractions
- Extend written methods to HTU × U
- Understand addition and subtraction as they apply to whole numbers and decimals
- Multiply and divide integers by 10 and 100, and explain the effect
- Understand that halving is the reverse of doubling
- Apply simple tests of divisibility (3, 6, 4, 25)
- Know square numbers 6 × 6 to 9 × 9
- Put digits in the correct place in a calculation
- Know what each digit represents in numbers with up to two decimal places
- Be able to use > or < correctly between two positive decimals. Decimals should be to 4 or 5 significant figures
- Be able to order positive decimals with the largest on the left. Decimals should be to 4 or 5 significant figures
- Be able to order positive decimals as a list with the smallest on the left. Decimals should be to 4 or 5 significant figures
-
- STEP 03
- Round decimals to the nearest whole number
- Multiply and divide decimals by 10, 100, 1000, and explain the effect
- Multiply by 0
- Understand multiplication as it applies to whole numbers and decimals
- Understand division as it applies to whole numbers and decimals
- Extend written methods to HTU ÷ U
- Use standard column procedures to add and subtract decimals with up to two places
- Extend written methods to TU × TU
- Know and use the order of operations
- Quickly derive associated division facts
- Check a result by working it backwards
- Round numbers to decimal places
- Recognise and use multiples and factors (divisors) and use simple tests of divisibility
- Identify numbers with exactly 2 factors (primes)
- Understand the difference between factor, multiple and prime numbers
- Find all the factor pairs for any whole number without any support
- Able to determine factors and multiples of numbers by listing
- Understand the vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples.
- Recognise that every number can be written as a product of two factors
- Convert terminating decimals to fractions, e.g. 0.23 = 23/100
- Recall known facts including fraction to decimal conversions
- Extend mental methods of calculation to include percentages
- Calculate simple percentages
- Recognise the first few triangular numbers
- Know square numbers beyond 10 × 10
- Find roots of square numbers upto 100 (i.e. roots upto 10)
- Compare decimals in different contexts
- Understand and use decimal notation and place value
- Approximate before carrying out an addition or subtraction
The MatheMagician
"Number is about 22-28% of the Foundation exam and 12-18% of the Higher exam."
Algebra
- STEP 01
- Topic does not start until Step 03
-
- STEP 02
- Topic does not start until Step 03
-
- STEP 03
- Find outputs of more complex functions expressed in words (e.g. add 6 then multiply by 3)
- Find the inputs of simple functions expressed in words by using the output and inverse operations
- Use function machines to find coordinates
- Discuss and interpret line graphs and graphs of functions from a range of sources
- Read values from straight-line graphs for real-life situations
- Draw, straight-line graphs for real-life situations
- Use conventions and notation for 2-D co-ordinates in all four quadrants.
- Draw, label and scale axes
- Use the correct notation to show inclusive and exclusive inequalities
- Describe simple functions in words (e.g. add 3, multiply by 6, subtract 4)
- Generate terms of a simple sequence using term to term rules like +3, -2
- Find the next term in a sequence, including negative values
- Generate and describe simple integer sequences – square and triangle numbers
- Generate terms of a simple sequence arising from practical contexts
- Generate terms of a more complex sequence arising from practical contexts
- Use notation and symbols correctly
The MatheMagician
"Algebra is about 17-23% of the Foundation exam and 27-33% of the Higher exam."
Geometry &
Measures
- STEP 01
- Explain why some shapes tessellate and why other shapes do not
- Tessellate combinations of polygons
- Know the sum of angles on a straight line
- Find the perimeter of a square/rectangle by counting
- Know the terms face, edge and vertex
- Identify and name common solids: cube, cuboid, cylinder, prism, pyramid, sphere and cone
- Identify complex arrangements of a net of an open cube
- Identify more complex arrangement of a net of a closed cube
- Work out time intervals
- Read and interpret scales on a range of measuring instruments
- Record readings from scales to a suitable degree of accuracy
- Suggest suitable units to estimate or measure length, mass and capacity
- Identify all the symmetries of 2-D shapes
- Recognise properties of rectangles
- Recognise properties of squares
- Draw sketches of shapes
- Scale a shape on a grid (without a centre specified)
- Understand and use the language associated with reflections
- Understand and use the language associated with translations
- Recognise where a shape will be after reflection
-
- STEP 02
- Use a protractor to measure acute angles to the nearest degree
- Measure lines to the nearest millimetre
- Know the sum of angles round a point
- Identify parallel lines
- Find the perimeter of a square/rectangle
- Construct diagrams of everyday 2-D situations involving rectangles, triangles, perpendicular and parallel lines
- Know and use geometric properties of cuboids
- Choose suitable metric units to estimate length and area.
- Understand that area is measured in square centimetres
- Draw parallel lines
- Mark parallel lines on a diagram
- Identify quadrilaterals from everyday usage
- Know the sum of angles in a triangle is 180°
- Use correct notation for labelling lines
- Recognise reflection symmetry
- Understand and use the language associated with rotations
- Recognise where a shape will be after translation
- Translate a shape on a square/coordinate grid
- Recognise and visualise the reflection in a mirror line of a 2-D shape
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- STEP 03
- Use correct notation for labelling angles
- Distinguish between acute and obtuse angles
- Distinguish between acute, obtuse and reflex angles
- Identify perpendicular lines
- Use the formula for the area of a rectangle/square
- Calculate the surface area of cubes with a net
- Use nets to calculate the surface area of simple cuboids
- Calculate perimeter and area of compound shapes made from triangles, rectangles and other shapes
- Identify different nets of a cuboid
- Know and use geometric properties of shapes made from cuboids
- Record estimates to a suitable degree of accuracy
- Use units of measurement to estimate and solve problems in everyday contexts involving length, area, volume, mass, time and angle
- Know that measurements using real numbers depend upon the choice of unit
- Use correct notation for labelling triangles
- Mark perpendicular lines on a diagram
- Recognise and visualise the symmetry of a 2-D shape: line symmetry
- Calculate angles in a triangle
- Identify simple angle, side and symmetry properties of triangles
- Identify angle, side and symmetry properties of simple quadrilaterals
- Recognise and visualise – rotation about a given point (rotation point must be outside the shape)
- Begin to estimate the size of angles
- Use a protractor to measure obtuse angles to the nearest degree
- Use a protractor to draw acute angles to the nearest degree
- Use a protractor to measure reflex angles to the nearest degree
- Measure shapes to find (perimeters and) areas
The MatheMagician
"Geometry is about 12-18% of the Foundation exam and 17-23% of the Higher exam."
Ratio, proportion &
rates of change
- STEP 01
- Convert a percentage to a number of hundredths or tenths.
- This is the only topic at Step 01
-
- STEP 02
- Read and construct scale drawings
- This is the only topic at Step 02
-
- STEP 03
- Use fraction notation to describe parts of shapes
- Recognise the equivalence of percentages, fractions and decimals
- Define percentages as number of parts per hundred
- Draw lines and shapes to scale
- Use and interpret maps and scale drawings, using a variety of scales and units
- Estimate length using a scale diagram
- These are the only topics at Step 03
The MatheMagician
"Ratio, Proportion & Rates of Change is about 22-28% of the Foundation exam and 17-23% of the Higher exam."
Probability
- STEP 01
- Topic does not start until Step 03
-
- STEP 02
- Topic does not start until Step 03
-
- STEP 03
- Use a probability scale with words
- Mark events and/or probabilities on a probability scale of 0 to 1
- These are the only topics at Step 03
The MatheMagician
"Statistics & Probability is about 12-18% of the Foundation exam and 12-18% of the Higher exam."
Statistics
- STEP 01
- Find range from a set of ordered data
- This is the only topic at Step 01
-
- STEP 02
- Find the range of a small set of data.
- This is the only topic at Step 02
-
- STEP 03
- Choose and justify appropriate diagrams, graphs and charts, using ICT as appropriate, to illustrate a short report of a statistical enquiry
- Draw conclusions based on the shape of line graphs
- Represent data in a table
- Extract data and interpret discrete bar charts
- Find mode from a discrete data bar chart
- Extract data and interpret line graphs
- Find mode group from a discrete data grouped bar chart
- Construct on paper, and using ICT simple bar graphs to represent discrete data
- Answer simple questions about 'most likely' from a simple bar chart
- Find the mode from any bar chart
- Construct on paper, and using ICT, bar – line graphs to represent data
- Produce bar charts including dual bar charts
- Produce pictograms
- Find the mode and range for a small set of discrete data
- Calculate the median of a set of data
- Find the modal class for a small set of grouped discrete data
- Compare two simple distributions using the range and the mode
- Draw conclusions from simple statistics for a single distribution
- Find the modal class of a set of continuous data
- Calculate the mean, median, mode and range for discrete data
- Find the mode and range from a bar chart
- Interpret simple pie charts using simple fractions and percentages and multiples of 10% sections
The MatheMagician
"Statistics & Probability is about 12-18% of the Foundation exam and 12-18% of the Higher exam."
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