New Zealand

Number

• Number structures and operations

  • Knowledge

    • Non-repeating, infinite decimals are irrational numbers; some of them are represented by special symbols, such as √2 and π.

      • Classify numbers (10-A.1)

    • The terms index, power, and exponent are used interchangeably.

    • For the number aⁿ, a represents the base, and n represents the exponent.

      • Powers with integer bases (10-S.1)
      • Powers with decimal and fractional bases (10-S.2)

    • Exponent rules govern how operations involving exponents work and include:

      • a^m × aⁿ = a^m+n (the product-of-exponents rule).

        • Multiplication with exponents (10-S.4)

      • ^am/_aⁿ = a^m–n (the quotient-of-exponents rule).

        • Division with exponents (10-S.5)

      • (a^m)ⁿ = a^m×n (the exponent-of-exponents rule).

        • Power rule (10-S.7)

      • a^–m = ¹/_a^m, (a ≠ 0) (the negative exponent rule).

        • Negative exponents (10-S.3)

      • a⁰ = 1 (a ≠ 0) (the zero exponent rule).

        • Powers with integer bases (10-S.1)

    • Only like roots can be added and subtracted; multiples of a root are represented with coefficients.

      • Add and subtract radical expressions (10-CC.5)

    • There are rules for working with roots, including not leaving roots in a denominator: √a × √a = a; √a × √b = √ab; √a ÷ √a = 1; √a ÷ √b = √(^a/_b) = ^√a/_√b × ^√b/_√b = ^√ab/_b.

      • Simplify radical expressions involving fractions (10-CC.3)
      • Multiply radical expressions (10-CC.4)

    • The rules for identifying significant figures are:

      • all non-zero digits are significant.

      • zeros appearing anywhere between two non-zero digits are significant.

      • leading zeros are not significant.

      • trailing zeros are significant if there is a decimal point present, and are not significant otherwise.

      • exact numbers have an unlimited number of significant figures.

    • For numbers written in scientific notation as a × 10^k, the number of significant figures is determined by applying the rules to the value of a.

    • The order of operations is important when evaluating or forming expressions. Operations are done as follows: grouped operations; exponents or powers; multiplication and division, from left to right; addition and subtraction, from left to right.

      • Evaluate numerical expressions involving integers (10-A.10)
      • Evaluate numerical expressions involving rational numbers (10-A.13)

    • A mnemonic, such as GEMA — Grouped, Exponents, Multiplicative (× and ÷), Additive (+ and −) — can be used to remember the order of operations.

      • Evaluate numerical expressions involving integers (10-A.10)
      • Evaluate numerical expressions involving rational numbers (10-A.13)

    • Every non-zero number has a multiplicative inverse (reciprocal), and their product is 1.

      • Reciprocals and multiplicative inverses (10-A.5)

    • Percentages are a way of expressing a fraction of 100.

      • Convert between percents, fractions and decimals (10-E.1)

    • Percentages can be used to proportionally increase or decrease a quantity by multiplication and can be presented as decimal multipliers.

      • A percentage increase can be described by the additional percentage or the percentage of the final amount compared to the original amount.

        • Percent of change (10-E.4)
        • Percent of change: word problems (10-E.5)

      • A percentage decrease can be described by the percentage lost or the percentage of the final amount compared to the original amount.

        • Percent of change (10-E.4)
        • Percent of change: word problems (10-E.5)

    • Ratios show part-to-part or part-to-whole comparisons of two or more quantities.

      • Understanding ratios (10-D.1)

    • Ratios can be scaled up or down or simplified.

      • Identify equivalent ratios (10-D.2)
      • Write an equivalent ratio (10-D.3)

    • A rate proportionally compares two quantities that have different units of measure; when working with rates, 'per' means 'for every' in day-to-day contexts.

      • Unit rates (10-D.4)
      • Unit prices (10-D.5)

  • Practices

    • Identifying, reading, writing, representing, comparing, ordering, and converting between fractions, decimals, and percentages.

      • Compare and order rational numbers (10-A.2)
      • Convert between decimals and fractions (10-A.4)
      • Convert between percents, fractions and decimals (10-E.1)

    • Recording, comparing, ordering, and calculating with numbers in scientific notation.

      • Convert between ordinary numbers and standard form (10-U.1)
      • Compare numbers written in standard form (10-U.2)
      • Add and subtract numbers written in scientific notation (10-U.3)
      • Multiply numbers written in standard form (10-U.4)
      • Divide numbers written in standard form (10-U.5)

    • Identifying irrational numbers.

      • Classify numbers (10-A.1)

    • Generalising about whether square and cube roots of whole numbers are rational or irrational.

      • Square roots (10-A.6)
      • Cube roots (10-A.7)

    • Calculating using integer exponents.

      • Powers with integer bases (10-S.1)
      • Powers with decimal and fractional bases (10-S.2)
      • Multiplication with exponents (10-S.4)
      • Division with exponents (10-S.5)
      • Multiplication and division with exponents (10-S.6)
      • Power rule (10-S.7)
      • Evaluate expressions using properties of exponents (10-S.8)
      • Identify equivalent expressions involving exponents (10-S.9)

    • Calculating exactly using fractions, roots, and multiples of π.

      • Simplify radical expressions (10-CC.1)
      • Simplify radical expressions with variables (10-CC.2)
      • Simplify radical expressions involving fractions (10-CC.3)
      • Multiply radical expressions (10-CC.4)
      • Add and subtract radical expressions (10-CC.5)

    • Using rounding, including to specified significant figures, and estimation to predict results and to check the reasonableness of calculations.

      • Estimate population size using proportions (10-D.12)

    • Rounding to the degree of precision required for the context.

      • Word problems with money (10-A.14)
      • Rate of travel: word problems (10-D.7)
      • Weighted averages: word problems (10-FF.9)

    • Adding, subtracting, multiplying, and dividing positive and negative numbers, including fractions and decimals.

      • Add and subtract rational numbers (10-A.11)
      • Multiply and divide rational numbers (10-A.12)

    • Evaluating positive integer exponents for positive and negative numbers.

      • Powers with integer bases (10-S.1)
      • Powers with decimal and fractional bases (10-S.2)

    • Finding a fraction or percentage of a number.

      • Percent word problems (10-E.3)

    • Finding the whole amount, given a fraction or percentage.

      • Percent of change: word problems (10-E.5)

    • Expressing a number as a fraction or percentage of another number.

      • Solve percent equations (10-E.2)
      • Percent word problems (10-E.3)

    • Applying a proportional increase or decrease to a number.

      • Scale drawings: word problems (10-D.13)
      • Percent of change (10-E.4)
      • Percent of change: word problems (10-E.5)

    • Calculating the percentage increase or decrease between two numbers.

      • Percent of change (10-E.4)
      • Percent of change: word problems (10-E.5)

    • Comparing and using ratios and rate.

      • Unit rates (10-D.4)
      • Unit prices (10-D.5)
      • Compare ratios: word problems (10-D.6)
      • Solve proportions (10-D.10)
      • Solve proportions: word problems (10-D.11)
      • Scale drawings: word problems (10-D.13)

• Financial mathematics

  • Knowledge

    • Percentages, ratios, rates, and proportions are often applied in financial situations.

      • Unit rates (10-D.4)
      • Unit prices (10-D.5)
      • Percent of a number: GST, discount and more (10-E.8)
      • Find the percent: discount and mark-up (10-E.9)
      • Multi-step problems with percents (10-E.10)

  • Practices

    • Converting New Zealand dollars into other currencies, and vice versa.

    • Finding proportions of costs.

      • Unit prices (10-D.5)

    • Calculating compound interest on dollar amounts, by calculating simple interest month by month for short time periods.

      • Simple interest (10-E.6)
      • Compound interest (10-E.7)

Algebra

• Equations and relationships

  • Knowledge

    • The properties of operations (commutative, distributive, associative, inverse, and identity) and the order of operations apply to numbers and variables.

      • Properties of addition and multiplication (10-B.4)
      • Distributive property (10-B.5)
      • Simplify variable expressions using properties (10-B.6)

    • When operating on or writing equations with fractions, fractions of magnitude greater than 1 are usually written as improper fractions.

    • Multiplying or dividing by a negative number reverses an inequality.

      • Solve one-step linear inequalities: multiplication and division (10-J.5)

    • The constant rate of change of a linear graph is the vertical change (how far it goes up or down) divided by the horizontal change (how far it moves sideways).

      • Find the gradient of a graph (10-M.1)

    • Finding square roots of numbers and solving quadratic equations are related but have some differences.

      • Any positive real number has two square roots: one positive (the principal square root) and one negative.

        • Square roots (10-A.6)

      • The square root operation √ refers specifically to the principal square root.

        • Square roots (10-A.6)

      • There are 0, 1, or 2 real-number solutions to x² = a, where a is a number.

        • Solve a quadratic equation using square roots (10-AA.1)

    • The zero product property states that if two expressions multiply to be zero, then at least one expression must be zero.

      • Solve a quadratic equation using the zero product property (10-AA.2)

    • There are specific factorising relationships that are useful to recognise:

      • x(x + a) = x² + ax.

        • Factorise out a monomial (10-Y.2)

      • difference of two squares: (x + a)(x – a) = x² – a².

        • Factorise quadratics: special cases (10-Y.6)

      • square of a sum: (x + a)² = x² + 2ax + a².

        • Factorise quadratics: special cases (10-Y.6)

      • square of a difference: (x – a)² = x² – 2ax + a².

        • Factorise quadratics: special cases (10-Y.6)

    • The solution to a linear inequality is a set of values which may be represented with a number line.

      • Graph inequalities (10-J.1)
      • Write inequalities from graphs (10-J.2)

    • For a specific straight line, the gradient, m, and y-intercept, c, are fixed, and x varies with y according to the rule y = mx + c.

      • Find the gradient and y-intercept of a linear equation (10-M.4)

    • The y-intercept touches the y-axis and has coordinates (0,c).

      • Find the gradient and y-intercept of a linear equation (10-M.4)

    • The gradient m of a straight line can be determined with the formula m = ^rise/_run = ^∆y/_∆x.

      • Find the gradient of a graph (10-M.1)
      • Find the gradient from two points (10-M.2)

    • A vertical line has an infinite gradient. This cannot be expressed in the formula m = ^rise/_run as it becomes m = ^rise/₀, which cannot be evaluated.

      • Graph a horizontal or vertical line (10-N.12)

    • The equation of a vertical line is x = b, where the x-intercept is (b,0).

      • Equations of horizontal and vertical lines (10-N.11)

  • Practices

    • Simplifying and manipulating algebraic expressions involving sums, products, differences, and positive integer powers, by:

      • collecting like terms.

        • Simplify variable expressions involving like terms and the distributive property (10-B.7)
        • Add and subtract polynomials (10-X.9)

      • factorising using common factors.

        • HCF of monomials (10-Y.1)
        • Factorise out a monomial (10-Y.2)

      • factorising quadratic expressions with a leading coefficient of 1.

        • Factorise quadratics with leading coefficient 1 (10-Y.4)

      • expanding products, including multiplying a single term by a bracketed term, and multiplying two expressions each of the form ax + b, where a and b are integers.

        • Multiply a polynomial by a monomial (10-X.11)
        • Multiply two binomials (10-X.13)
        • Multiply two binomials: special cases (10-X.14)

      • factorising by grouping.

        • Factorise by grouping (10-Y.7)

    • Forming and solving linear equations and linear inequalities with rational number coefficients, giving exact or rounded solutions, and representing the solution on a number line.

      • Solve equations using order of operations (10-B.9)
      • Write variable equations (10-C.1)
      • Does x satisfy the equation? (10-C.2)
      • Model and solve equations using algebra tiles (10-C.5)
      • Write and solve equations that represent diagrams (10-C.6)
      • Solve one-step linear equations (10-C.7)
      • Solve two-step linear equations (10-C.8)
      • Solve advanced linear equations (10-C.9)
      • Solve equations with variables on both sides (10-C.10)
      • Solve equations: complete the solution (10-C.11)
      • Solve linear equations: word problems (10-C.15)
      • Solve linear equations: mixed review (10-C.16)
      • Graph inequalities (10-J.1)
      • Write inequalities from graphs (10-J.2)
      • Identify solutions to inequalities (10-J.3)
      • Solve one-step linear inequalities: addition and subtraction (10-J.4)
      • Solve one-step linear inequalities: multiplication and division (10-J.5)
      • Solve one-step linear inequalities (10-J.6)
      • Graph solutions to one-step linear inequalities (10-J.7)
      • Solve two-step linear inequalities (10-J.8)
      • Graph solutions to two-step linear inequalities (10-J.9)
      • Solve advanced linear inequalities (10-J.10)
      • Graph solutions to advanced linear inequalities (10-J.11)

    • Solving quadratic equations that are factorised or of the form x² + c = 0 (where c is an integer), and connecting the solutions to the x-intercepts of the related graph.

      • Solve a quadratic equation using square roots (10-AA.1)
      • Solve a quadratic equation using the zero product property (10-AA.2)
      • Solve a quadratic equation with leading coefficient 1 by factorising (10-AA.3)

    • Substituting into, rearranging, and simplifying expressions or formulae that involve squares or square roots.

      • Rearrange multi-variable equations (10-B.10)

    • Interpreting and graphing linear equations in the form y = mx + c, using the gradient and y-intercept.

      • Graph an equation in y=mx+c form (10-N.2)
      • Write an equation in y=mx+c form from a graph (10-N.3)
      • Evaluate a linear function from its graph: word problems (10-P.4)

    • Calculating the gradient and y-intercept of a line, using a graph.

      • Find the gradient of a graph (10-M.1)
      • Write an equation in y=mx+c form from a graph (10-N.3)

    • Comparing the relative magnitude of m in two or more linear graphs, using the concept of steepness and relating it to the magnitude of m.

      • Compare linear functions: graphs, tables and equations (10-P.5)

    • Finding the equation of a line, given two points or the gradient and a single point.

      • Write an equation in y=mx+c form (10-N.4)

    • Determining the effect on graphs in the coordinate plane of changing the coefficient of x² and the fixed value c, for a range of quadratic equations of the form y = ax² or y = x² + c, where a is a positive integer and c is an integer.

      • Transformations of quadratic functions (10-Z.4)
      • Graph quadratic functions (10-Z.5)

Measurement

• Measuring

  • Knowledge

    • A solution to a calculation cannot be more precise than the least precise number used in that calculation.

      • Precision (10-F.2)
      • Greatest possible error (10-F.3)

    • The number of significant figures in a measurement is the number of digits that contribute to the degree of accuracy of the measurement, given as the number of digits known with certainty plus one uncertain digit.

    • When calculating, it is best to use at least one more significant figure than is required in the final solution, and round at the end of the whole calculation.

    • Conversions between different-sized metric units may be needed to give the appropriate units for a measurement or calculation.

      • Convert rates and measurements (10-F.1)

    • The metric prefixes kilo-, mega-, giga-, and tera- signify a unit that is one thousand, one million, one billion, and one trillion times larger than the base unit.

      • Convert rates and measurements (10-F.1)

    • The metric prefixes centi-, milli-, micro-, and nano- signify a unit one hundredth, one thousandth, one millionth, and one billionth the size of the base unit.

      • Convert rates and measurements (10-F.1)

    • Derived units reflect a relationship — a product or quotient — between two different measurements.

      • Area (10-G.2)
      • Volume of prisms and cylinders (10-G.9)

    • The area of a circle is given by A = πr².

    • The surface area of a solid object is a measure of the total area that the surface of the object occupies.

      • Surface area of prisms and cylinders (10-G.12)
      • Surface area of pyramids (10-G.13)

    • The general formula for the volume of a prism is V = Al, where A is the consistent cross-sectional area and l is perpendicular to the plane of the cross-sectional area.

      • Volume of prisms and cylinders (10-G.9)

    • Resizing (enlarging or reducing) a shape changes its perimeter, area, or volume proportionally according to the dimensions of the units; linear metric conversions must be squared to convert area and cubed to convert volume.

      • Dilations and scale factors (10-H.7)
      • Perimeter, area and volume: changes in scale (10-H.16)

    • For right-angled triangles, Pythagoras' theorem states that the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.

      • Converse of Pythagoras' theorem: is it a right triangle? (10-I.4)

    • If (a,b,c) is a Pythagorean triple, then so is (ka,kb,kc), where k is a positive integer.

    • There is a fixed relationship between speed, distance, and time: speed = ^distance/_time.

      • Rate of travel: word problems (10-D.7)

    • In position-time graphs, the gradient represents speed.

    • Decimal measures are used for very small durations; the rest of time measurement uses a different system, based principally on 12 and 60.

  • Practices

    • Estimating, calculating, converting, and accurately representing measurements using significant figures.

      • Convert rates and measurements (10-F.1)
      • Greatest possible error (10-F.3)
      • Minimum and maximum area and volume (10-F.4)
      • Percent error (10-F.5)
      • Percent error: area and volume (10-F.6)

    • Converting between metric units, and using the appropriate prefixes in the metric system.

      • Convert rates and measurements (10-F.1)

    • Finding:

      • the area of circles and composite shapes that include circles or semicircles.

        • Area of compound figures (10-G.4)

      • the surface area and volume or capacity of prisms, pyramids, and cylinders.

        • Volume of prisms and cylinders (10-G.9)
        • Volume of pyramids (10-G.11)
        • Surface area of prisms and cylinders (10-G.12)
        • Surface area of pyramids (10-G.13)

    • Deriving the formulae for the area of half and quarter circles from the formula for a full circle.

    • Deriving the formulae for the surface area of cubes, rectangular prisms, and cylinders.

      • Surface area of prisms and cylinders (10-G.12)
      • Surface area of pyramids (10-G.13)

    • Calculating the area of half circles and quarter circles.

    • Calculating the surface area of cubes, rectangular prisms, triangular prisms, cylinders, and composite figures.

      • Surface area of prisms and cylinders (10-G.12)

    • Calculating the volume of cylinders and irregular prisms with a consistent cross-sectional area.

      • Volume of prisms and cylinders (10-G.9)

    • Scaling a shape by a factor, and determining the scale factor for the scaled shape's area or volume.

      • Dilations and scale factors (10-H.7)
      • Similar solids (10-H.14)
      • Volume and surface area of similar solids (10-H.15)
      • Perimeter, area and volume: changes in scale (10-H.16)

    • Using Pythagoras' theorem to:

      • find the length of an unknown side in a right-angled triangle.

        • Pythagoras' theorem (10-I.1)

      • check if a triangle has a right angle.

        • Converse of Pythagoras' theorem: is it a right triangle? (10-I.4)

      • calculate the distance between two points in the coordinate plane, yielding the distance formula d = √(x₂ – x₁)² + (y₂ – y₁)².

        • Distance between two points (10-K.4)

    • Finding speed, distance, or time, given any two of the measurements.

      • Rate of travel: word problems (10-D.7)

    • Reasoning about duration using different units of time, including decimal fractions of milliseconds where appropriate.

Geometry

• Shapes

  • Knowledge

    • In similar shapes, corresponding angles are equal and the lengths of corresponding sides are proportional.

      • Identify similar figures (10-H.8)

    • Congruent shapes are identical in shape and size.

      • Congruent figures: side lengths and angle measures (10-H.1)

  • Practices

    • Using the properties of similarity in 2D shapes, including right-angled triangles, to find unknown lengths and angles.

      • Similar figures: side lengths and angle measures (10-H.11)
      • Similar triangles and indirect measurement (10-H.12)

• Spatial reasoning

  • Knowledge

    • A set of points in a plane can be transformed by translation, reflection about a line, and rotation about a fixed point.

      • Translations: graph the image (10-H.2)
      • Reflections: graph the image (10-H.3)
      • Rotations: graph the image (10-H.4)
      • Sequences of congruence transformations: graph the image (10-H.5)

  • Practices

    • Representing and constructing 3D shapes, including cylinders, from nets.

      • Nets of three-dimensional figures (9-W.2)

    • Transforming 2D shapes, including composite shapes, by resizing them by any scale factor.

      • Dilations: graph the image (10-H.6)
      • Dilations and scale factors (10-H.7)

Statistics

• Developing knowledge from data

  • Knowledge

    • It is not always possible to get data from the entire population (as in a census). To make inferences about a population without a census, sampling is used.

    • Samples must be taken randomly from the population, otherwise there will be bias in the data, leading to inaccurate and misleading statistics. Samples are ideally chosen using simple random sampling, in which each item of the population has an equal probability of being chosen.

      • Identify biased samples (10-FF.1)

    • When sampling from a population, the distribution for a variable varies from sample to sample. To make a reliable inference about what is happening in the population, sample sizes need to be:

      • about 1,000 for categorical variables (with the sample obtained using technology).

      • at least 30 for numerical variables.

  • Practices

    • Planning and collecting multivariate data to respond to a statistical question using a sample or census.

    • Reasoning why a mean or median would be a better measure of central tendency for a given statistical question.

      • Calculate mean, median, mode and range (10-FF.2)
      • Interpret charts to find mean, median, mode and range (10-FF.3)

• Visualisation of data

  • Knowledge

    • A distribution is formed from all the possible values of a variable and their frequencies. It can be shown using data visualisations that show patterns, trends, and variations and that include dot plots, bar graphs, frequency tables, box plots, histograms, time-series graphs, scatter plots, and two-way tables.

      • Create bar graphs and line graphs (10-EE.3)

    • A good data visualisation should allow viewers to discern the variable(s) and who the data was collected from, and then, depending on the type of visualisation, additional information such as frequency, proportions, patterns or trends, and units for numerical variables.

    • In relationship investigations:

      • sometimes one variable is thought of as predictive of the other variable; then the response or dependent variable is on the y-axis, and the 'predictive', explanatory, or independent variable is on the x-axis.

        • Identify independent and dependent variables (10-O.2)

      • an eyeballed line or curve of best fit can be added for paired numerical data.

        • Write equations for lines of best fit (10-GG.5)

  • Practices

    • Creating multiple data visualisations for an investigation.

      • Create bar graphs and line graphs (10-EE.3)

    • Selecting appropriate scales for data.

    • For relationship investigations, drawing an eyeballed line or curve of best fit to predict possible y-values (the response variable) for given x-values (the explanatory variable).

      • Interpret a scatter plot (10-GG.1)
      • Write equations for lines of best fit (10-GG.5)

• Interpretation of data

  • Knowledge

    • Elements of chance affect the certainty of results from observational studies and experiments.

    • Uncertainty should be taken into account when making claims.

    • To compare data on the same variable from two groups in the same population, the 75%-to-50% comparison rule for informal inferences is used. If the groups are called A and B, and if more than 50% of group B's data is larger than 75% of group A's data, then we can make the claim that B tends to be larger than A back in the population.

    • An interpolation involves making predictions within the range of a numerical data variable.

      • Interpret a scatter plot (10-GG.1)
      • Interpret regression lines (10-GG.7)

    • An extrapolation involves making predictions outside the range of a numerical data variable.

      • Interpret regression lines (10-GG.7)

  • Practices

    • Critically considering data visualisations, including those from contemporary media, to see if they support or misrepresent the data.

    • Communicating findings in context to answer an investigative question, using evidence and with an awareness of variability.

      • Interpret bar graphs and line graphs (10-EE.4)
      • Interpret box-and-whisker plots (10-EE.7)

    • Making an informal inference in comparative situations about what might be happening in the population, based on visual considerations and using the 75%-to-50% comparison rule.

      • Estimate population size using proportions (10-D.12)

    • Making informal predictions from scatter plots in relationship situations.

      • Interpret a scatter plot (10-GG.1)

Probability

• Experimental and theoretical probability

  • Knowledge

    • Some chance-based situations, such as tossing a non-regular 3D shape, can only be explored through probability experiments.

      • Experimental probability (10-HH.2)

    • Results from sets of repeated trials for the same experiment may vary.

    • The Law of Large Numbers states that as the number of trials in a chance experiment increases, the experimental probability will approach the experiment's theoretical probability.

    • Lists, tables, two-way tables, and tree diagrams are useful systematic methods for generating all possible outcomes.

      • Find probabilities using two-way frequency tables (10-HH.3)
      • Sample spaces for compound events (10-HH.4)

    • In joint events, events can be dependent or independent.

      • Identify independent and dependent events (10-HH.6)

    • Probabilities for joint events cannot simply be added, because doing so would double-count outcomes that are common to both events.

      • Probability of independent and dependent events (10-HH.7)

    • Mutually exclusive events cannot occur together.

    • The estimated probability of an event from an experiment is the number of times the event happens divided by the total number of trials in the experiment.

      • Experimental probability (10-HH.2)

  • Practices

    • Carrying out a chance experiment, including running simulations for a large number of trials using digital tools.

      • Theoretical probability (10-HH.1)
      • Experimental probability (10-HH.2)
      • Compound events: find the number of outcomes (10-HH.5)
      • Probability of independent and dependent events (10-HH.7)

    • Systematically listing outcomes for the sample space.

      • Sample spaces for compound events (10-HH.4)

    • Comparing experimental probability (from at least 30 trials) to theoretical probability for a chance experiment, and explaining why they differ and how increasing the number of trials reduces this difference.

    • Carrying out chance experiments of at least 100 trials and comparing the experimental probability of each individual outcome to its theoretical probability, in order to demonstrate the Law of Large Numbers.

    • Creating and describing data visualisations for the distribution of observed outcomes from a chance experiment.

    • Calculating probability estimates for different outcomes.

      • Experimental probability (10-HH.2)
      • Counting principle (10-HH.8)
      • Permutations (10-HH.9)