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How to learn Year 9: Mathematics

The New Zealand Curriculum (Ministry of Education): Mathematics, Year 9

0 of 32 concepts ready to learn · Markdown, for your AI

1. Number · Number structures and operations

  1. Square and cube numbers: Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations
  2. Powers of Ten Notation: Interpret and compare numbers in standard form A × 10ⁿ where 1 ≤ A < 10 and n is an integer; convert between ordinary numbers and standard form
  3. Positive and Negative Numbers: Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances
  4. Sign Rules for Multiplication: Multiply and divide with positive and negative integers and rational numbers, understanding the rules for the sign of the product or quotient
  5. Estimating by rounding: Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b; understand upper and lower bounds of rounded values
  6. Substituting into Formulae: Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations
  7. Percentages as Fractions: Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%
  8. Mixed & Improper Fractions: Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

2. Number · Number structures

  1. Ratio Notation: Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations
  2. Dividing Quantities by Ratio: Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division as a fraction of the whole

3. Number · Financial mathematics

  1. Percentages (age 12+): Solve problems involving percentage increase, percentage decrease, finding the original value after a percentage change, and calculating simple interest

4. Algebra · Equations and relationships

  1. Algebraic Transformations: Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations
  2. Numbers on a number line: Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations
  3. Collecting Like Terms: Simplify algebraic expressions by collecting like terms — combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence

5. Algebra · Quadratic equations and factorising

  1. Quadratic Graphs: Recognise that quadratic functions produce curved (parabolic) graphs, distinguish them from linear graphs, and use plotted quadratic graphs to estimate values and find approximate solutions

6. Algebra · Linear equations and graphs

  1. Linear Function Graphs: Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context
  2. Plotting Linear Graphs: Plot linear graphs by generating a table of values, reduce a two-variable linear equation to the form y = mx + c, and calculate gradients from two points on a line

7. Algebra · Linear patterns

  1. Solving Linear Equations: Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients

8. Measurement · Metric units

  1. Compound Units: Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units

9. Measurement · Area and volume

  1. Angles in triangles (age 11+): Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning
  2. Circles: Circumference & Area: Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts

10. Measurement · Scaling

  1. Unit Conversions: Convert freely between related standard units of measurement (time, length, area, volume/capacity, mass) using decimal notation to up to three decimal places where appropriate

11. Measurement · Pythagoras' theorem

  1. Types of angles (age 13+): Apply Pythagoras’ Theorem (a² + b² = c²) to calculate unknown side lengths in right-angled triangles, including in real-world and coordinate-geometry contexts

12. Geometry · Shapes

  1. Angles with parallel lines: Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles
  2. Parts of a circle: Illustrate and name parts of circles, including radius, diameter, and circumference; know that the diameter is twice the radius

13. Geometry · Spatial reasoning

  1. Coordinate Transformations: Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original
  2. 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

14. Statistics · Relationship investigations

  1. Scatter Graphs & Correlation: Describe simple mathematical relationships between two variables using scatter graphs, identify positive, negative, or no correlation, and use a line of best fit to make predictions

15. Statistics · Interpretation of data

  1. Comparing measurements: Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers

16. Probability · Experimental and theoretical probability

  1. Experimental vs Theoretical: Run repeated probability experiments and compare experimental (relative frequency) results with theoretical predictions; understand and demonstrate that as the number of trials increases, the experimental probability tends towards the theoretical probability — and that short runs can give very different results
  2. 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
  3. Tree diagrams: Generate theoretical sample spaces for single and combined events using listing, tables, and tree diagrams, and calculate theoretical probabilities as the number of favourable outcomes divided by the total number of equally likely outcomes