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What Multiplication Means
Multiplication & Division
Interpret products of whole numbers (e.g. 5 × 7 as the total number of objects in 5 groups of 7)
Written Multiplication
Multiplication & Division
Multiply two-digit and three-digit numbers by a one-digit number using formal written layout
3-D shapes (age 9+)
Geometry
Identify 3-D shapes, including cubes and other cuboids, from 2-D representations
Adding and subtracting (age 9+)
Addition & Subtraction
Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
Adding and subtracting mixed numbers
Fractions
Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations
Adding fractions (different denominators)
Fractions
Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
Addition and subtraction word problems
Fractions
Solve word problems involving addition and subtraction of fractions with like denominators, using visual models and equations
Angle Sum Rules
Geometry
Know that angles at a point sum to 360° (one whole turn), angles on a straight line sum to 180°, and vertically opposite angles are equal; use these facts to find missing angles
Arrays for multiplication (age 9+)
Multiplication & Division
Divide numbers up to four digits by a one-digit number using short division (and place-value/array strategies); interpret remainders appropriately for the context
Bar Models for Ratios
Ratio & Proportion
Represent ratio and proportion problems using bar models (rectangular strips divided into equal parts labelled with quantities) and tape diagrams (segmented strips showing part-to-part and part-to-whole relationships); use these visual models to set up and solve unequal sharing, scaling, and percentage problems — drawing the diagram first, then reading off the answer
Checking Answers by Rounding
Addition & Subtraction
Use rounding to check answers to calculations and determine appropriate levels of accuracy in context
Choosing representations strategically
Mathematical Thinking
Select and use tools and representations strategically: choose between mental methods, formal written methods, protractors, fraction strips, and diagrams based on the demands of the problem
Classifying shapes by line properties
Geometry
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size; recognise right triangles as a category
Comparing Decimals
Fractions
Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
Comparing fractions (age 9+)
Fractions
Compare and order fractions with different numerators and denominators by creating common denominators/numerators or comparing to a benchmark such as 1/2; justify conclusions with visual models
Complex Multi-Step Problems
Mathematical Thinking
Make sense of complex multi-step problems involving large numbers, fractions, decimals, and percentages by analysing what is known and unknown, planning multi-step strategies, and evaluating reasonableness through estimation and inverse operations
Converting measurement units (age 9+)
Measurement
Know relative sizes of measurement units within one system (km/m/cm/mm, kg/g, l/ml, hr/min/sec); convert between different metric units and express measurements in terms of a smaller unit; record equivalents in conversion tables
Converting tenths to hundredths
Fractions
Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this to add fractions with denominators 10 and 100 (e.g. 3/10 + 4/100 = 34/100)
Counting forwards and backwards (age 9+)
Number Representation & Place Value
Count forwards and backwards in steps of powers of 10 (10, 100, 1000, 10,000, 100,000) for any given number up to 1,000,000
Decimal place value (age 9+)
Fractions
Round decimals with two decimal places to the nearest whole number and to one decimal place
Decimals for Tenths & Hundredths
Fractions
Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100)
Decimals to three places
Fractions
Solve problems involving numbers with up to three decimal places
Degrees and turns
Geometry
Know that angles are measured in degrees, where one degree is 1/360 of a full turn; understand that an angle turning through n one-degree angles has a measure of n degrees
Division with remainders
Multiplication & Division
Solve multi-step word problems using the four operations with whole numbers, including interpreting remainders in context; represent with equations using a letter for the unknown; check with estimation