# Year 4: Mathematics

A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 71 concepts ready. In the app: https://ai.page/roadmap/nz-moe-year-4

Part of: [New Zealand Curriculum: Mathematics](https://ai.page/roadmap/nz-moe.md)

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

## 1. Number · Number structures

- [Place value of each digit](https://ai.page/c/place-value-of-each-digit/index.md): Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
- [Numbers to 10,000](https://ai.page/c/numbers-to-10-000/index.md): Identify, represent, and estimate numbers up to 10,000 using different representations
- [Estimating by rounding](https://ai.page/c/estimating-by-rounding/index.md): Estimate the answer to a calculation and use inverse operations to check answers; apply to increasingly large numbers using rounding and inverse reasoning
- [Rounding to 10, 100, 1000](https://ai.page/c/rounding-to-10-100-1000/index.md): Round any number to the nearest 10, 100, or 1000
- [Square and cube numbers](https://ai.page/c/square-and-cube-numbers/index.md): Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
- [Negative Numbers](https://ai.page/c/negative-numbers/index.md): Count backwards through zero to include negative numbers
- [Fractions of a whole](https://ai.page/c/fractions-of-a-whole/index.md): 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
- [Reading and writing numbers (age 9+)](https://ai.page/c/reading-and-writing-numbers-age-9/index.md): 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](https://ai.page/c/counting-forwards-and-backwards/index.md): Count forwards and backwards in steps of 3 from 0
- [Tenths](https://ai.page/c/tenths/index.md): 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
- [Tenths (age 8+)](https://ai.page/c/tenths-age-8/index.md): Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10
- [Factor Pairs & Commutativity](https://ai.page/c/factor-pairs-and-commutativity/index.md): Recognise and use factor pairs and commutativity in mental calculations

## 2. Number · Operations

- [Order of operations](https://ai.page/c/order-of-operations/index.md): Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations
- [Mental multiplication and division](https://ai.page/c/mental-multiplication-and-division/index.md): 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
- [Adding numbers](https://ai.page/c/adding-numbers/index.md): Add up to four two-digit numbers using strategies based on place value and properties of operations
- [Division with remainders (age 10+)](https://ai.page/c/division-with-remainders-age-10/index.md): 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

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

## 4. Number · Percentages

- [Percentage and decimal equivalents](https://ai.page/c/percentage-and-decimal-equivalents/index.md): 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

- [Decimal & Percent Notation](https://ai.page/c/decimal-and-percent-notation/index.md): 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
- [Adding money and giving change](https://ai.page/c/adding-money-and-giving-change/index.md): Find different combinations of coins that equal the same amount of money
- [Giving Change](https://ai.page/c/giving-change/index.md): Add and subtract amounts of money to give change, using both £ and p in practical contexts

## 6. Algebra · Equations and relationships

- [Comparing Large Numbers](https://ai.page/c/comparing-large-numbers/index.md): Order and compare numbers beyond 1000
- [What the equals sign means](https://ai.page/c/what-the-equals-sign-means/index.md): Understand the meaning of the equal sign as 'is the same as' and determine if equations are true or false

## 7. Algebra · Growing patterns

- [Shape patterns](https://ai.page/c/shape-patterns-maths/index.md): 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
- [Extending Table Patterns](https://ai.page/c/extending-table-patterns/index.md): 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

- [Numbers on a number line](https://ai.page/c/numbers-on-a-number-line-2/index.md): 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

- [Measuring with different units](https://ai.page/c/measuring-with-different-units/index.md): Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen
- [Choosing measurement units](https://ai.page/c/choosing-measurement-units/index.md): 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
- [Calculating with measurements](https://ai.page/c/calculating-with-measurements/index.md): 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

- [Measuring length (age 10+)](https://ai.page/c/measuring-length-age-10/index.md): 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
- [Area (age 8+)](https://ai.page/c/area-age-8/index.md): Measure areas by counting unit squares (square cm, square m, square in, square ft)
- [Area by Tiling](https://ai.page/c/area-by-tiling/index.md): Find the area of a rectangle by tiling it with unit squares and show that the result equals the product of the side lengths
- [Understanding angles (age 8+)](https://ai.page/c/understanding-angles-age-8-maths/index.md): Multiply side lengths to find areas of rectangles and represent whole-number products as rectangular areas
- [Volume as additive](https://ai.page/c/volume-as-additive/index.md): Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms
- [Measuring Perimeters](https://ai.page/c/measuring-perimeters/index.md): Measure the perimeter of simple 2-D shapes
- [Perimeters of polygons](https://ai.page/c/perimeters-of-polygons/index.md): 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)
- [Counting Unit Cubes](https://ai.page/c/counting-unit-cubes/index.md): Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units

## 11. Measurement · Angles

- [Degrees and turns](https://ai.page/c/degrees-and-turns/index.md): 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
- [Angle Sum Rules](https://ai.page/c/angle-sum-rules/index.md): 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
- [Right Angles & Turns](https://ai.page/c/right-angles-and-turns/index.md): Identify right angles; recognise that two right angles make a half-turn, three make three-quarters, and four make a complete turn
- [Estimating Angles](https://ai.page/c/estimating-angles/index.md): Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size

## 12. Measurement · Time

- [Telling Time: Minutes](https://ai.page/c/telling-time-minutes/index.md): Tell and write the time to five minutes, including quarter past and quarter to, and draw clock hands to show these times
- [Telling time to the minute](https://ai.page/c/telling-time-to-the-minute/index.md): Measure and begin to record time in hours, minutes, and seconds
- [Telling time to the minute (age 8+)](https://ai.page/c/telling-time-to-the-minute-age-8/index.md): Tell and write time to the nearest minute using analogue and digital clocks
- [Converting measurement units](https://ai.page/c/converting-measurement-units/index.md): Convert between different units of measure (e.g. kilometre to metre, hour to minute, minute to second, year to month, week to day)
- [Comparing Time Durations](https://ai.page/c/comparing-time-durations/index.md): Compare durations of events and calculate the time taken by particular events or tasks
- [Numbers on a number line](https://ai.page/c/numbers-on-a-number-line-4/index.md): Solve word problems involving elapsed time by adding and subtracting time intervals in minutes, including using a number line

## 13. Geometry · Shapes

- [Regular and irregular polygons](https://ai.page/c/regular-and-irregular-polygons/index.md): Distinguish between regular and irregular polygons based on reasoning about equal sides and equal angles
- [Parallel and perpendicular lines](https://ai.page/c/parallel-and-perpendicular-lines/index.md): Identify horizontal and vertical lines and pairs of perpendicular and parallel lines
- [2-D shapes (age 8+)](https://ai.page/c/2-d-shapes-age-8/index.md): Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry
- [Understanding angles](https://ai.page/c/understanding-angles/index.md): Recognise angles as a property of shape or a description of a turn
- [Lines, Rays & Angles](https://ai.page/c/lines-rays-and-angles/index.md): 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

- [Transformations on a grid](https://ai.page/c/transformations-on-a-grid/index.md): 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
- [Transformations on a Grid](https://ai.page/c/transformations-on-a-grid-maths/index.md): 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

- [Estimating answers (age 7+)](https://ai.page/c/estimating-answers-age-7/index.md): Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, and hours
- [Calculating the Mean](https://ai.page/c/calculating-the-mean/index.md): Calculate and interpret the mean as an average of a data set

## 16. Statistics · Visualisation of data

- [Bar graphs](https://ai.page/c/bar-graphs/index.md): Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs
- [Pictograms and tally charts](https://ai.page/c/pictograms-and-tally-charts/index.md): Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables

## 17. Statistics · Interpretation of data

- [Statistical Analysis Vocabulary](https://ai.page/c/statistical-analysis-vocabulary/index.md): 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

- [Likelihood Language](https://ai.page/c/likelihood-language/index.md): Use probability language to describe and compare the likelihood of everyday events using words such as certain, likely, even chance, unlikely, impossible
- [Simple Chance Experiments](https://ai.page/c/simple-chance-experiments/index.md): 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
- [Experimental probability](https://ai.page/c/experimental-probability/index.md): 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](https://ai.page/c/the-0-to-1-probability-scale/index.md): 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
- [Equally Likely Outcomes](https://ai.page/c/equally-likely-outcomes/index.md): 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)
- [Probabilities Sum to One](https://ai.page/c/probabilities-sum-to-one/index.md): 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

## Health: 0 of 100

Of its 71 own concepts: 0 have an explanation, 0 have practice, 0 have a measurement question, 0 have a checked version.

Findings (each is a task for anyone's AI):

- Place value of each digit has no explanation yet
- Numbers to 10,000 has no explanation yet
- Estimating by rounding has no explanation yet
- Rounding to 10, 100, 1000 has no explanation yet
- Square and cube numbers has no explanation yet
- Negative Numbers has no explanation yet
- Fractions of a whole has no explanation yet
- Reading and writing numbers (age 9+) comes before Comparing Large Numbers, which it needs
- Reading and writing numbers (age 9+) has no explanation yet
- Counting forwards and backwards has no explanation yet
- Tenths has no explanation yet
- Tenths (age 8+) has no explanation yet
- Factor Pairs & Commutativity has no explanation yet
- Order of operations has no explanation yet
- Mental multiplication and division has no explanation yet
- Adding numbers has no explanation yet
- Division with remainders (age 10+) has no explanation yet
- Decimal equivalents of tenths and hundredths comes before Decimal & Percent Notation, which it needs
- Decimal equivalents of tenths and hundredths has no explanation yet
- Decimals for Tenths & Hundredths comes before Decimal & Percent Notation, which it needs
- Decimals for Tenths & Hundredths has no explanation yet
- Mixed numbers and improper fractions has no explanation yet
- Equivalent fractions has no explanation yet
- Simple Fraction Sums has no explanation yet
- Adding and subtracting mixed numbers has no explanation yet
- Comparing Decimals has no explanation yet
- Percentage and decimal equivalents has no explanation yet
- Decimal & Percent Notation has no explanation yet
- Adding money and giving change has no explanation yet
- Giving Change has no explanation yet
- Comparing Large Numbers has no explanation yet
- What the equals sign means has no explanation yet
- Shape patterns has no explanation yet
- Extending Table Patterns has no explanation yet
- Numbers on a number line comes before Lines, Rays & Angles, which it needs
- Numbers on a number line has no explanation yet
- Measuring with different units has no explanation yet
- Choosing measurement units has no explanation yet
- Calculating with measurements has no explanation yet
- Measuring length (age 10+) has no explanation yet
- Area (age 8+) has no explanation yet
- Area by Tiling has no explanation yet
- Understanding angles (age 8+) has no explanation yet
- Volume as additive has no explanation yet
- Measuring Perimeters has no explanation yet
- Perimeters of polygons has no explanation yet
- Counting Unit Cubes has no explanation yet
- Degrees and turns has no explanation yet
- Angle Sum Rules has no explanation yet
- Right Angles & Turns comes before Understanding angles, which it needs

Credit: The structure of The New Zealand Curriculum (Ministry of Education): Mathematics (https://nzcurriculum.tki.org.nz/the-nzc/learning-areas/mathematics-and-statistics); concepts from the Marble Skill Taxonomy (v1), © Generative Spark, Inc. (withmarble.com), text CC BY-SA 4.0, database ODbL 1.0: https://github.com/withmarbleapp/os-taxonomy, mapped to its standards by Marble.