From toothpaste to take-off: Practical ideas for maths teaching and learning

A classroom display filled with whānau-sourced carbon emissions data. A challenge to estimate Aotearoa’s toothpaste use. Subtraction songs echoing from the mat. These are just some of the engaging activities in a new resource full of practical ideas to help ākonga thrive in maths.

A new book, Teaching and learning mathematics and statistics: Karawhiua!, has recently been released to support kaiako and ākonga with the maths curriculum.

The authors aimed to help teachers better support ākonga to see the relevance of mathematical ideas for themselves and others.

This article explores some of the classroom examples drawn directly from the book – practical stories that may be useful in each school setting.

Working with decimals to explore carbon emissions

Understanding climate change and environmental sustainability is important. To help ākonga understand how mathematics and statistics are powerful tools to make a positive difference for their environment, this kaiako used carbon emission values as a context for developing fluency with decimals.

First, they shared with ākonga and their whānau that they would be investigating carbon emissions over the next few weeks. The kaiako asked them to prepare by finding out what carbon emissions are and exploring and identifying examples of carbon emissions from transportation.

To support the investigation, the kaiako provided examples sourced online, such as driving for one kilometre creates about 0.12 kilogrammes of carbon dioxide, using one litre of petrol creates about 2.3 kilogrammes of carbon dioxide, and a passenger jet creates around 0.115 kilogrammes of carbon dioxide per passenger for each kilometre.

A display area was set up in the classroom where ākonga could add what they and their whānau found out.

The learning purpose was shared clearly: to use decimals and addition, subtraction, division and multiplication to explore carbon emissions and how to reduce them.

Examples from the display were used to develop questions such as:

• How many kilogrammes of carbon dioxide would be made from all students driving from home to school and back?

• From using a whole tank of petrol?

• From a 10-minute ride in a helicopter?

By the end of the topic, ākonga were creating and solving more complex problems, such as calculating the carbon emissions for their whānau if they flew to Auckland or Wellington and comparing this with other types of transport. Involving whānau from the start proved valuable, as ākonga were able to share their learning at home throughout the topic.

How much toothpaste was used this morning?

The following examples come from the chapter on ”Inspiring mathematics teaching.”

In the authors’ experience, ākonga are most inspired to learn mathematics when:

• their teacher knows the content, enjoys their subject, is open, positive, encouraging, interested in and receptive to ākonga and cares about ākonga learning

• the teaching strategies are varied, engaging, have challenge and enable ākonga to work with others and alone

• the learning activities have purpose and are interesting, accessible and varied.

The following example activity includes an accessible starting idea (toothpaste use), mathematics accessible to many learners (estimation, addition, multiplication, division), a specific challenge (working out how much toothpaste has been used across Aotearoa), autonomy and collaborative learning, and discussion and negotiation to form a shared response.

The challenge is to estimate how much toothpaste was used this morning across Aotearoa.

Ākonga are asked to provide a detailed rationale for their estimate, including calculations, and be prepared to present this. Working collaboratively is encouraged so multiple perspectives can be considered.

Final estimates are collected on the board, then compared and discussed as a class to arrive at a shared estimate.

The mathematics involved can lead into further learning around estimation, measurement, very large and very small numbers, and variation.

The question is an example of a Fermi problem – an open-ended problem that requires making and justifying assumptions, estimates and educated guesses to work out a way to solve a problem. Fermi problems are named after Enrico Fermi (1901–1954).

Singing with numbers

Other ways to inspire ākonga mathematically include exploring mathematics in interesting and ‘multi-modal’ ways in activities they enjoy doing together.

This activity uses patterns in well-known and made-up songs and rhymes to investigate subtraction, using fingers as representations, recording number patterns, and predicting the next number.

In this classroom, singing is used regularly to support maths concepts. One focus is subtraction, where ākonga benefit from additional support.

For subtraction and skip counting, variations of the “10 Green Bottles” song are used: “10 green bottles hanging on the wall …”

As each verse is sung, students use their fingers to represent the bottles, putting one down each time one ‘falls.’

Numbers are written on the board (10, 9, 8, 7, 6 …), and the class discusses how each verse represents subtracting one. Predictions are made for how many bottles will remain after the next verse, followed by subtraction questions.

Another song used is “10 fat sausages sizzling in a pan …”

This decreases by two each time. The songs are adapted to explore other subtraction patterns, such as 20 red apples skip-counted by 2s, or 17 toy teddies decreasing by 3s.

Ākonga enjoy creating new variations, using materials to represent objects, recording the patterns, predicting next numbers, and building toward algebra and further pattern work.

Final reflections

Having a clear purpose of learning is crucial for inspiring ākonga in mathematics.

Intentional, reflective practice supports thoughtful planning and review.

Throughout Teaching and Learning Mathematics and Statistics: Karawhiua!, more examples like these can be found, including chapters on:

• fostering fluency, retention and enjoyment

• addressing misconceptions and common errors

• developing language and literacy

• planning for diverse learning needs.

This pukapuka is grounded in the Aotearoa context, ready for classroom use, and driven by a shared vision: helping all learners thrive in maths.

Read more at nzcer.org.nz