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Telling time to the minute (age 9+)
Measurement
Solve problems involving converting between units of time (hours↔minutes, minutes↔seconds, years↔months, weeks↔days)
Tenths (age 9+)
Fractions
Recognise and use thousandths; relate them to tenths, hundredths, and their decimal equivalents (e.g. 1/1000 = 0.001, 35/1000 = 0.035)
Transformations on a Grid
Geometry
Identify, describe, and represent the position of a shape following a reflection or translation using appropriate language; know that the shape has not changed
Understanding angles (age 9+)
Geometry
Use the properties of rectangles to deduce related facts and find missing lengths and angles
Understanding fractions
Multiplication & Division
Solve problems involving scaling by simple fractions and problems involving simple rates
Understanding fractions (age 9+)
Fractions
Understand a fraction a/b with a > 1 as a sum of fractions 1/b (e.g. 3/5 = 1/5 + 1/5 + 1/5)
Understanding fractions (age 9+)
Mathematical Thinking
Construct and present logical mathematical arguments involving multiple steps; critique others' reasoning about fractions, angles, or calculations and clearly explain errors or alternative methods
Understanding Percentages
Fractions
Understand the per cent symbol (%); know that per cent means ‘number of parts per hundred’; write percentages as a fraction with denominator 100 and as a decimal
What Is an Angle?
Geometry
Understand that an angle is a geometric shape formed by two rays sharing a common endpoint (vertex); recognise angles in real-life contexts and 2-D shapes
Working with Large Numbers
Number Representation & Place Value
Solve number and practical problems involving reading, writing, ordering, comparing, and rounding whole numbers up to 1,000,000
2-D shapes (age 10+)
Geometry
Draw 2-D shapes using given dimensions and angles, using a ruler and protractor accurately
3-D shapes (age 10+)
Geometry
Recognise, describe, and build simple 3-D shapes, including making nets
Adding and subtracting (age 10+)
Addition & Subtraction
Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why, with numbers up to 10,000,000 and decimals
Adding Fractions (Unlike Denominators)
Fractions
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator
Addition and subtraction strategies (age 10+)
Addition & Subtraction
Add and subtract decimals to hundredths using strategies based on place value, properties of operations, and the relationship between addition and subtraction; relate strategies to written methods and explain reasoning
Advanced Maths Vocabulary
Mathematical Thinking
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
Advanced Multi-Step Problems
Mathematical Thinking
Make sense of complex multi-step problems involving ratio, proportion, algebra, negative numbers, and all four operations with fractions and decimals by analysing given and unknown quantities, planning solution strategies, and evaluating reasonableness using estimation and inverse operations
Angles in triangles (age 10+)
Geometry
Find unknown angles in triangles, quadrilaterals, and regular polygons using angle sum properties
Area of Triangles & Parallelograms
Measurement
Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles)
Area with Fractions
Fractions
Find the area of a rectangle with fractional side lengths by tiling with unit-fraction squares; show that the area equals the product of the side lengths
Brackets in Expressions
Multiplication & Division
Use parentheses, brackets, or braces in numerical expressions and evaluate expressions containing these grouping symbols
Calculating Percentages
Ratio & Proportion
Solve problems involving the calculation of percentages of amounts (e.g. 15% of 360) and the use of percentages for comparison
Calculating Simple Probability
Probability
Calculate the probability of a simple event with equally likely outcomes using the formula: probability = number of favourable outcomes ÷ total number of possible outcomes; express the result as a fraction in its simplest form; apply to rolling dice, drawing from bags, and other simple chance situations
Calculating the Mean
Data & Statistics
Calculate and interpret the mean as an average of a data set