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What your teen will learn in maths#

Your teen is learning to:

  • build confidence using mathematics to solve real-world problems
  • explore patterns in numbers, shapes, time, and data
  • learn to think logically and explain their reasoning clearly
  • see how maths connects to everyday life like money, health, and design
  • use data to make informed decisions and challenge misinformation
  • strengthen their communication, problem-solving, and critical thinking skills
  • discover how maths can lead to exciting future careers.

Good maths skills and a positive view of themselves as maths learners will help your teen in the future. Maths is important for solving problems and creative thinking.

Encourage your teen to use the maths vocabulary they learn in class.

Numbers#

Ideas to help at home

With your teen, you could:

  • compare petrol prices at different stations and talk about how the price has too many decimals for cents and why, or how many kilometres your car can travel on 1 tank of fuel
  • compare options for services such as monthly versus prepaid phone plans, gym memberships or broadband plans, to make informed decisions
  • check currency exchange rates online or in an airport to see how much your New Zealand currency could get you in another country.

Your teen is learning to:

  • understand the value of whole and decimal numbers and how to write them in scientific notation (also called standard form)
  • recognise irrational numbers such as pi and roots of non-square numbers
  • calculate answers to problems using positive and negative exponents
  • calculate answers using both positive and negative numbers to a positive exponent
  • use rounding, including significant figures and estimation to predict and check results
  • solve problems with positive and negative numbers, fractions and decimals, using the order of operations
  • work out what percentage an amount has been increased or decreased by
  • compare and use ratios and rates in practical situations such as speed, interest, wages, or currency conversion
  • find proportions of cost
  • calculate compound interest by working out the simple interest month-by-month for short-term periods.
Words your teen will be learning

Words include:

  • compound interest
  • principal square root
  • significant figures.

Algebra#

Ideas to help at home

With your teen, you could:

  • use a spreadsheet to plan a trip or event with options to add different numbers of people
  • create a simple substitution code (for example, A = 1, B = 2) and write secret messages for each other to decode.

Your teen is learning to:

  • simplify, expand, and factorise algebraic expressions with 1 or 2 sets of brackets
  • set up and solve equations and inequalities that include fractions and decimals
  • solve quadratic equations and understand how they connect to U-shaped graphs called parabolas, and explore how changing parts of a quadratic equation affects the shape and position of its graph
  • use and manipulate mathematical formulas involving squares or square roots
  • create and use straight line graphs and rearrange the formula to suit different situations
  • understand and use the equation y = mx + c, where m shows the steepness of the line and c shows where it starts
  • work out the slope (gradient) and starting point (y-intercept) from a graph and find the equation of a line using 2 points or the slope and 1 point.
Words your teen will be learning

Words include:

  • operator
  • quadratic equation, relationship
  • zero product property.

Measurement#

Ideas to help at home

With your teen, you could:

  • talk about distance in kilometres when in the car and use the odometer to see who can guess when you complete a kilometre
  • use maps or house plans to think about scale and work out how large something on the map is using the scale
  • discuss units of data like gigabytes, megabytes, or terabytes and how much data different devices store or games or apps use
  • work together to take the necessary measurements for projects around the house, such as calculating the amount of paint needed to cover the living room walls.

Your teen is learning to:

  • estimate, calculate, and convert measurements accurately, including using significant figures
  • find the area of circles and composite shapes that include circles or semicircles
  • find the surface area, volume and capacity of prisms, pyramids and cylinders.

They are learning to use Pythagoras’ Theorem to:

  • find missing side lengths in right-angled triangles
  • check if a triangle has a right angle
  • calculate the distance between 2 points on a coordinate plane.

Your teen is also learning to:

  • use a simple formula to calculate how fast something is moving, how far it goes, or how long it takes, depending on which 2 pieces of information they already have
  • understand and reason about time durations including using different units (for example, seconds, minutes) and fractions or decimals of time (for example, milliseconds).

They are learning to calculate how changing the size of a shape (scaling it up or down) affects:

  • length – the sides
  • area – the surface
  • volume – the space inside.
Words your teen will be learning

Words include:

  • distance formulae
  • resizing
  • scale factor
  • surface area.

Geometry#

Ideas to help at home

With your teen, you could:

  • use a mirror or an outside shadow to explore how similar triangles form, for example, by comparing the height of a tree and its shadow to a stick and its shadow
  • use scale drawings to plan the layout of a room in a house
  • use a printed or online map to plan a trip, measure distance using the scale, and give directions using compass points.

Your teen is learning to:

  • use the idea of similarity (when 2 shapes have the same shape but different sizes) to find missing side lengths or angles in 2D shapes, especially right-angled triangles
  • construct 3D shapes, including cylinders, from nets
  • enlarge or reduce 2D shapes by using a scale factor.
Words your teen will be learning

Words include:

  • centre of resizing or enlargement
  • similarity and congruence.

Statistics#

Ideas to help at home

With your teen, you could:

  • track and compare daily habits:
    • choose an activity to track for a week, for example, steps walked, water drunk, time spent reading or online
    • graph the results and compare across days or family members
    • ask “What do you notice? What might explain the differences?”.

Your teen is learning to:

  • work with multivariate data (data with more than one variable or category)
  • understand why a mean or a median would be a better measure of central tendency for given statistical questions
  • look for patterns, trends, or relationships in real-world data
  • make predictions (called conjectures) about what they expect to find
  • plan an investigation, making sure they know if it is about a group or population:
    • identify what data is needed
    • plan how to collect or check the data, ensuring it is fair, accurate, and ethical
  • collect and prepare data using random samples to avoid bias and check that the data is valid and makes sense
  • use the data to create graphs to show the data clearly and answer the original question
  • evaluate others’ investigations by asking, “Does this make sense? Is the conclusion fair? Does the graph show the whole story?”
  • spot mistakes, misleading visuals, or weak claims, and explain why.
Words your teen will be learning

Words include:

  • similarity.

Probability#

Ideas to help at home

With your teen, you could:

  • try the coin toss experiment:
    • ask, “Will heads or tails come up more?”
    • flip a coin 100 times (or use an online simulator)
    • record results in a tally chart
    • create a bar graph to show the outcomes
    • discuss why the results might not be exactly 50/50
  • try unusual objects:
    • toss a drawing pin, paperclip, or bottle cap
    • predict the outcomes (for example, “point up” or “flat”)
    • run 50+ trials and record what happens
    • talk about why it’s harder to predict than a coin or dice.

Your teen is learning to:

  • plan and run chance-based experiments (like coin tosses or dice rolls) for a large number of trials
  • systematically list all possible outcomes and predict what might happen
  • use digital tools (like apps or spreadsheets) to run lots of trials quickly
  • record and graph results to compare the actual results with what was expected
  • estimate probabilities and explain why results might differ from predictions.
Words your teen will be learning

Words include:

  • sampling
  • informal inference
  • interpolation, extrapolation
  • 75%-to-50% comparison rule.