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Ministry of Education New Zealand
Te whenu
Te whenu - Maths

Whenu: He Uri Whakaheke#

Mokopuna are learning Pāngarau in 4 different learning strands called ‘whenu’.

Find out more about whenu.

Pāngarau whenu

Kaupapa: Tau (number)#

By the end of Tau 7 at kura, mokopuna will be learning to explore scenarios where positive and negative numbers are used, such as temperature changes or financial transactions.

Mokopuna will explore increasingly complex ideas about number structure including:

  • using exponents (such as 1,000 = 10³)
  • square numbers and square roots
  • integers (negative and positive numbers)
  • calculate costs, and change for any amount of money
  • calculate the percentage discounts to whole-dollar amounts
  • identify, read, write, and represent fractions, decimals to 3 places, and percentages.

Ideas for whānau activities#

Write down birth years of whānau members and use them to practise addition, subtraction, and division, by: 

  • finding age differences
  • adding birth years together, or dividing by the number of people
  • converting ages into different forms (for example, months, weeks and days).

Prices

Talk about sales in town, such as, 25% off, 30%, 10% or half price. Look for the best value and make a game of calculating the savings on items mokopuna are interested in.

Or, plan for a whānau event. What is the cheapest option for kai – cooking at home or getting takeaways?

Ngā tini mata o te reo o te tau – the language of number

  • wāwāhinga moni – change
  • mati ā-ira – decimal places
  • whakahekenga ōrau – percentage discount
  • huri – convert
  • whakaāwhiwhi – round number.

Whenu: He Ākonga#

Kaupapa: Taurangi (algebra)#

By the end Tau 7 at kura, mokopuna will be learning to understand number line relationships (on a number line fractions and decimals are located between integers, while negative numbers are positioned to the left of 0).

Mokopuna will solve equations using variables (letters in place of a missing number) and investigate patterns and write the rule as an equation.

Ideas for whānau activities#

Costs

Work out costs for family events, such as: "Movie tickets are $15.50 per person, and we have 6 people, plus 2 popcorns at $11 each."

Mystery number

Create a mystery number challenge like: "I'm thinking of a number that, when multiplied by 5 and increased by 3, equals 28. What's my number?"

Sports

Pick a favourite sports player and analyse their stats. For example, if a player scores 3 points per game, write a formula for their total points after 'n' games. Points = 3n. Predict how many points they’ll score after 20 games!

Ngā tini mata o te reo o te taurangi – the language of algebra

  • taurangi – algebra
  • whārite – equation
  • huinga takirua raupapa – set of ordered pairs
  • kauwhata rārangi – line graph
  • tūtohi – chart
  • tuaka pae – x-axis (horizontal axis)
  • tuaka pou – y-axis (vertical axis)
  • whakamāori – interpret
  • whakahou – revise.

Whenu: He Ākonga#

Kaupapa: Ine (measurement)#

By the end of Tau 7 at kura, mokopuna will be learning to coordinate systems and maps to express position, direction, and pathways.

Mokopuna will read, interpret, and use timetables and charts to plan journeys, and work out how long they would take. They will:

  • investigate perimeter, area and volume, including finding missing lengths, in practical situations
  • estimate and then measure length, area, volume, capacity, mass (weight), temperature, data storage, time, and angle
  • select the appropriate tool and unit for the task, convert between metric units of length, mass (weight) and capacity, and use whole numbers and decimals to express parts of a unit (for example, 724 g = 0.724 kg).

Ideas for whānau activities#

Timetables

Plan a journey using a bus or train timetable. Find out how long it will take to get to 3 different destinations.

Clocks

Practice reading analogue and digital clocks. Convert between 12-hour and 24-hour time. Challenge: If a hāngī is put down at 10.30am and takes 4 hours to cook, what time is it ready?

Ngā tini mata o te reo o te ine – the language of measurement

  • inenga pāpātanga – rate units (for example, km/hr, price/kg)
  • paenga – perimeter
  • horahanga – area
  • mita (m) – metre (m)
  • mitarau (cm) – centimetre (cm)
  • manokaramu (kg) – kilogram (kg)
  • ritamano (ml) – millilitre (ml).

Whenu: He Uri Whakaheke#

Kaupapa: Āhuahanga (geometry)#

By the end of Tau 7 at kura, mokopuna will be learning to describe position, direction and pathways using te ao tūroa, (as in Māori systems of knowledge), or using scale, compass points, and environmental features. They will:

  • visualise, construct, and draw plan views for front, back, left, right and top views for 3D shapes
  • classify shapes based on their properties, including identifying different classes of shapes
  • use toi Māori shapes to create transformational patterns.

Ideas for whānau activities#

Build shapes

Use rākau and harakeke or string to build cubes, pyramids, and other 3D shapes. Identify the edges, faces, and vertices of each shape. Compare your creations to real whare, pātaka, and waka.

Draw shapes

Find 3D shapes around the house (like jars, boxes and blocks) and draw what it looks like from each side and above. Then draw what they think it looks like from underneath. Once finished, check the underside of the real object against the drawing. As a challenge, combine objects to create a more interesting shape and then draw again.

Draw a treasure map

Create a grid map of your backyard or room and hide a 'treasure' somewhere on it. Give co-ordinate clues to find the location. Use compass directions (raki, tonga, rāwhiti, uru) and distance to describe the position.

Ngā tini mata o te reo o te āhuahanga – the language of geometry

  • taurahi – scale factor of enlargement
  • tauiti – scale factor of reduction
  • ōwehenga – ratio
  • koki whakaroto – interior angle
  • koki tauroto – co-interior angle
  • āwhata – scale
  • tirohanga (mai i) runga – top view
  • tirohanga (mai i) mua – front view
  • tirohanga (mai i te) matau – right side view
  • tirohanga (mai i te) mauī – left side view
  • panoni – transformation
  • hanga hiato – composite shape
  • tūnga – position.

Whenu: He Tangata#

Kaupapa: Tauanga (statistics)#

By the end of Tau 7 at kura, mokopuna will be learning to understand that the statistical enquiry cycle – Problem, Plan, Data, Analysis, Conclusion (PPDAC) – can be used to conduct data-based investigations about the wider community. They will:

  • ask questions that require investigation of different types of data (for example time series, comparison, relationship) and make statement about what the expected outcome might be
  • be learning about data, how to collect it, what it can be used for and how to present it
  • making predictions or assertions about expected findings.

Ideas for whānau activities#

Statistics at the marae

Ask marae committee members about their roles and responsibilities – what do they do? Use a voice recorder or a cellphone to record information.

Does the marae have a long-term strategy, a charter or constitution? Read the minutes of marae trustee or marae committee meetings. What are the aspirations of the wider whānau, hapū, iwi? Can you identify trends? Perhaps the goal is to have all whānau confidently speaking te reo Māori by a certain date. 

Start a survey

For your survey, use simple language and questions like: 

  • how many members of your whānau speak te reo?
  • at what level? (give options)
  • what are their age ranges?
  • Are they male, female, or non-binary? 

Ask for their thoughts on how to achieve the goal. People can answer anonymously. Use an online tool and deliver hard copies as well. 

Gather and sort information. What are the common answers and themes? What are some possible solutions or ways forward?

Think of a range of fun and creative ways to present your findings to whānau. Kia kaha rā!

Ngā tini mata o te reo o te tauanga – the language of statistics

  • tau toha ōrite – average
  • tau waenga – median
  • tau tānui – mode
  • inenga whānui – range
  • tuari – distribution
  • tāpaetanga kōrero – assertion
  • taunaki – evidence
  • taupori – population
  • tīpako – sample
  • matapōkere – random.

Whenu: He Tangata#

Kaupapa: Tūponotanga (probability)#

By the end of Tau 7 at kura, your mokopuna will be learning to plan to conduct probability experiments for chance-based situations, including undertaking trials using technology, by:

  • posing investigative questions
  • identifying similarities and differences between findings and those of others.

Ideas for whānau activities#

Prepare for manuhiri at the marae

Work with whānau expecting manuhiri at the marae. Ask: 

  • how many manuhiri are coming?
  • how long will they stay?
  • how much kai is needed? 

Write up a list of things to do. Help with the budget, shopping and kai preparation. Ask: 

  • what and how much is needed for each setting?
  • how will the seating, beds, and so on, be arranged?

Use a voice recorder, take photos, and make notes to record information.

Next time your whānau could be in charge of an aspect of mahi at the marae. You could make accurate estimates of what is needed logistically for everything to run smoothly, based on the data you have collected and analysed.

Ngā tini mata o te reo o te tūponotanga – the language of probability

  • taurangitanga – variability
  • tuari – distribute
  • haukume – biased
  • tōkeke – unbiased
  • putanga tātai – theoretical probability
  • tauira tātau – associated probabilities
  • putanga – outcomes
  • whakamātau tūponotanga – probability experiments
  • whakamātau – experiment.