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How to learn Year 4: Mathematics

The New Zealand Curriculum (Ministry of Education): Mathematics, Year 4

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1. Number · Number structures

  1. Place value of each digit: Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
  2. Numbers to 10,000: Identify, represent, and estimate numbers up to 10,000 using different representations
  3. Estimating by rounding: Estimate the answer to a calculation and use inverse operations to check answers; apply to increasingly large numbers using rounding and inverse reasoning
  4. Rounding to 10, 100, 1000: Round any number to the nearest 10, 100, or 1000
  5. Square and cube numbers: Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
  6. Negative Numbers: Count backwards through zero to include negative numbers
  7. Fractions of a whole: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b
  8. 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
  9. Counting forwards and backwards: Count forwards and backwards in steps of 3 from 0
  10. Tenths: Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and from dividing one-digit numbers or quantities by 10
  11. Tenths (age 8+): Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10
  12. Factor Pairs & Commutativity: Recognise and use factor pairs and commutativity in mental calculations

2. Number · Operations

  1. Order of operations: Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations
  2. Mental multiplication and division: Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1, dividing by 1, and multiplying together three numbers
  3. Adding numbers: Add up to four two-digit numbers using strategies based on place value and properties of operations
  4. 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

  1. Decimal equivalents of tenths and hundredths: Recognise and write decimal equivalents of any number of tenths or hundredths (e.g. 3/10 = 0.3, 27/100 = 0.27)
  2. 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)
  3. Mixed numbers and improper fractions: Recognise mixed numbers and improper fractions; convert from one form to the other (e.g. 2/5 + 4/5 = 6/5 = 1 1/5)
  4. Equivalent fractions: Recognise and show, using diagrams, equivalent fractions with small denominators
  5. Simple Fraction Sums: Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)
  6. Adding and subtracting mixed numbers: Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations
  7. Comparing Decimals: Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <

4. Number · Percentages

  1. Percentage and decimal equivalents: Solve problems requiring knowledge of percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and fractions with denominators that are multiples of 10 or 25

5. Number · Financial mathematics

  1. Decimal & Percent Notation: Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value
  2. Adding money and giving change: Find different combinations of coins that equal the same amount of money
  3. Giving Change: Add and subtract amounts of money to give change, using both £ and p in practical contexts

6. Algebra · Equations and relationships

  1. Comparing Large Numbers: Order and compare numbers beyond 1000
  2. What the equals sign means: Understand the meaning of the equal sign as 'is the same as' and determine if equations are true or false

7. Algebra · Growing patterns

  1. 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
  2. Extending Table Patterns: Recognise and use repeated reasoning to generalise: extend multiplication table patterns, derive unknown facts from known ones, and describe rules for sequences

8. Algebra · Coordinate plane

  1. Numbers on a number line: Understand a coordinate system defined by two perpendicular number lines (axes) with an origin at (0,0); know that an ordered pair (x, y) specifies a unique point where the first number gives horizontal distance and the second gives vertical distance from the origin

9. Measurement · Measuring

  1. 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
  2. Choosing measurement units: Choose and use appropriate standard units to measure length (m/cm), mass (kg/g), temperature (°C), and capacity (litres/ml) to the nearest appropriate unit
  3. Calculating with measurements: Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units

10. Measurement · Area and Volume

  1. Measuring length (age 10+): Recognise volume as an attribute of solid figures; understand that a unit cube (side length 1 unit) has 'one cubic unit' of volume and can be used to measure volume; a solid packed with n unit cubes has volume n cubic units
  2. Area (age 8+): Measure areas by counting unit squares (square cm, square m, square in, square ft)
  3. Area by Tiling: Find the area of a rectangle by tiling it with unit squares and show that the result equals the product of the side lengths
  4. Understanding angles (age 8+): Multiply side lengths to find areas of rectangles and represent whole-number products as rectangular areas
  5. Volume as additive: Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms
  6. Measuring Perimeters: Measure the perimeter of simple 2-D shapes
  7. Perimeters of polygons: Solve problems involving perimeters of polygons: find perimeter from side lengths, find an unknown side length, and explore rectangles with same perimeter but different areas (or vice versa)
  8. Counting Unit Cubes: Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units

11. Measurement · Angles

  1. 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
  2. Angle Sum Rules: 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
  3. Right Angles & Turns: Identify right angles; recognise that two right angles make a half-turn, three make three-quarters, and four make a complete turn
  4. Estimating Angles: Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size

12. Measurement · Time

  1. Telling Time: Minutes: Tell and write the time to five minutes, including quarter past and quarter to, and draw clock hands to show these times
  2. Telling time to the minute: Measure and begin to record time in hours, minutes, and seconds
  3. Telling time to the minute (age 8+): Tell and write time to the nearest minute using analogue and digital clocks
  4. 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)
  5. Comparing Time Durations: Compare durations of events and calculate the time taken by particular events or tasks
  6. Numbers on a number line: Solve word problems involving elapsed time by adding and subtracting time intervals in minutes, including using a number line

13. Geometry · Shapes

  1. Regular and irregular polygons: Distinguish between regular and irregular polygons based on reasoning about equal sides and equal angles
  2. Parallel and perpendicular lines: Identify horizontal and vertical lines and pairs of perpendicular and parallel lines
  3. 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
  4. Understanding angles: Recognise angles as a property of shape or a description of a turn
  5. Lines, Rays & Angles: Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures

14. Geometry · Spatial reasoning

  1. 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
  2. Transformations on a Grid: Identify, describe, and represent the position of a shape following a reflection or translation using appropriate language; know that the shape has not changed

15. Statistics · Developing knowledge

  1. Estimating answers (age 7+): Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, and hours
  2. Calculating the Mean: Calculate and interpret the mean as an average of a data set

16. Statistics · Visualisation of data

  1. Bar graphs: Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs
  2. Pictograms and tally charts: Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables

17. Statistics · Interpretation of data

  1. Statistical Analysis Vocabulary: Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describes

18. Probability · Experimental probability

  1. Likelihood Language: Use probability language to describe and compare the likelihood of everyday events using words such as certain, likely, even chance, unlikely, impossible
  2. 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
  3. 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
  4. 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
  5. Equally Likely Outcomes: Understand that 'equally likely' means every outcome has exactly the same chance of occurring; identify whether a given situation has equally likely outcomes (a fair coin, a fair die, a spinner with equal sections) or unequally likely outcomes (a bag with more of one colour, a spinner with unequal sections)
  6. Probabilities Sum to One: Understand that when all possible outcomes of a trial are listed, their probabilities must add up to 1; use this to find the probability of an event NOT happening: P(not A) = 1 − P(A); apply this shortcut to avoid counting all unfavourable outcomes directly