How to learn Year 5: Mathematics

The New Zealand Curriculum (Ministry of Education): Mathematics, Year 5

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1. Number · Number structures

Numbers to 10,000: Identify, represent, and estimate numbers up to 10,000 using different representations
Factors, multiples, and primes: Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems
Rounding to 10, 100, 1000: Round any number to the nearest 10, 100, or 1000
Square and cube numbers: Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
Reading and writing numbers (age 9+): Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding
Counting forwards and backwards (age 9+): 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
Tenths (age 8+): Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10
Negative Numbers: Count backwards through zero to include negative numbers

2. Number · Operations

Adding and subtracting mixed numbers: Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations
Division with remainders (age 10+): Divide numbers up to 4 digits by a two-digit divisor using formal written long division, interpreting remainders as whole numbers, fractions, or by rounding as appropriate

3. Number · Rational numbers

Decimals for Tenths & Hundredths: 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)
Simplifying Fractions: Use common factors to simplify fractions to their simplest form; use common multiples to express fractions with a common denominator
Understanding Percentages: 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
Division with Decimals: Use written division methods in cases where the answer has up to two decimal places; divide decimals to hundredths by whole numbers
Multiplying by Tens: Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations
Comparing fractions (age 8+): Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols
Fractions on a number line: Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows
Decimal place value: Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy
Decimal place value (age 8+): Compare numbers with the same number of decimal places up to two decimal places
Comparing Decimals: Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
Comparing Large Numbers: Order and compare numbers beyond 1000
Equivalent fractions: Recognise and show, using diagrams, equivalent fractions with small denominators

4. Number · Financial mathematics

Decimal place value: Multiply one-digit numbers with up to two decimal places by whole numbers (e.g. 3.47 × 6)
Measurement Conversions: Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts

5. Algebra · Growing patterns

Patterns in Times Tables: Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations
Shape patterns: Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur

6. Algebra · Coordinate plane

Plotting points in the first quadrant: Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context

7. Measurement · Measuring

Measuring with different units: Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen
Calculating with measurements: Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units

8. Measurement · Area and Volume

Area of Triangles & Parallelograms: Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles)
Area (age 8+): Measure areas by counting unit squares (square cm, square m, square in, square ft)
Understanding angles (age 8+): Multiply side lengths to find areas of rectangles and represent whole-number products as rectangular areas
Estimating volume: Estimate volume of cuboids using 1 cm³ blocks; estimate capacity of containers using water
Counting Unit Cubes: Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units
Estimating answers (age 10+): Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³)

9. Measurement · Angles

Degrees and turns: 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
Estimating Angles: Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size
Measuring angles: Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure

10. Measurement · Time

Comparing Time Durations: Compare durations of events and calculate the time taken by particular events or tasks
Telling time to the minute (age 8+): Tell and write time to the nearest minute using analogue and digital clocks
12-hour and 24-hour time: Read, write, and convert time between analogue and digital 12-hour and 24-hour clocks
Converting measurement units: Convert between different units of measure (e.g. kilometre to metre, hour to minute, minute to second, year to month, week to day)
Telling time to the minute (age 9+): Solve problems involving converting between units of time (hours↔minutes, minutes↔seconds, years↔months, weeks↔days)

11. Geometry · Shapes

Parallel and perpendicular lines: Identify horizontal and vertical lines and pairs of perpendicular and parallel lines
What Is an Angle?: 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
3-D shapes (age 11+): Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections
2-D shapes (age 8+): Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry

12. Geometry · Spatial reasoning

Nets of 3-D Shapes: Identify, draw, and interpret nets of common 3-D shapes — cubes, cuboids, triangular prisms, and square-based pyramids — by predicting which 3-D shape a given flat arrangement of faces will fold into, checking whether a net will close completely, and sketching a net from a description or 3-D model; understand the relationship between the number of faces and the structure of the net
Transformations on a grid: Represent and carry out geometric transformations on squared paper or a coordinate grid: reflections (in horizontal, vertical, and diagonal mirror lines, including the axes), translations (described as a vector or as left/right/up/down moves), and rotations (90° or 180° about a stated centre point); describe each transformation precisely using the correct language; identify which transformation maps one shape onto its image by comparing position, orientation, and size

13. Statistics · Developing knowledge

Rounding Answers: Solve problems which require answers to be rounded to specified degrees of accuracy
Calculating the Mean: Calculate and interpret the mean as an average of a data set
Reading tables: Complete, read, and interpret information in tables, including timetables

14. Statistics · Visualisation of data

Bar graphs: Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs

15. Probability · Experimental probability

Experimental probability: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability
The 0-to-1 Probability Scale: Understand probability as a measure expressed as a number between 0 (impossible) and 1 (certain); place events on the probability scale; express probabilities as fractions, decimals, and percentages
Calculating Simple 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
Simple Chance Experiments: Conduct simple probability experiments — flipping a coin, rolling a die, pulling coloured counters from a bag — record results, and compare experimental outcomes with expected theoretical outcomes