Mathematical modelling: Year 6: Planning tool

Expected level of development

Australian Curriculum Mathematics V9: AC9M6N08, AC9M5N09

Numeracy Progression: Additive strategies: P9, Multiplicative strategies: P8, Understanding money: P8

At this level, students use mathematical modelling to solve practical problems involving natural and rational numbers and percentages, including in financial contexts. They formulate the problem, choose operations and efficient calculation strategies, and use digital tools where appropriate. They interpret and communicate solutions in terms of the situation, justifying the choices made.

Mathematical modelling process includes identifying and solving a problem that has a real-world context or is presented as a scenario for students to investigate the possible outcomes using knowledge and understanding of mathematics concepts, structures and relationships drawing on their mathematical thinking, reasoning and problem-solving skills.

Present contexts that enable students to apply mathematical thinking and approaches of their choosing. Resist the temptation to provide a ready-made path with the relevant mathematical operations as students’ thinking in these situations may be limited. Instead, use questioning and feedback to guide students through the process.

Use the framework for mathematical modelling that provides seven steps to solve a real-world problem or scenario.

Help students develop their computational thinking skills by breaking down a problem and working out what mathematical operations and computations they need to make. Students may employ a range of maths skills depending on the richness of the problem.

Look for opportunities to highlight the different approaches students use and encourage discussion about the range of approaches and choices behind them.

Teaching and learning summary:

Provide guidance on using a mathematical modelling process to solve real-world problems.
Generate problems for students that encourage them to choose a relevant mathematical operation and efficient calculation strategies.
Explicitly teach and provide guidance to support students to solve calculations as the opportunity arises.
Encourage students to make estimates for solutions involving rational numbers and percentages.

Students:

use familiar fractions, decimals and percentages to approximate solutions to problems
use appropriate estimation strategies
model practical situations and use efficient calculation strategies to provide solutions to problems
communicate findings of their investigations in the context of the problem situation.

Some students may:

not yet be able to choose the correct operation to solve a mathematical problem. Often, we suggest an operation to solve a number problem or provide scaffolding to the extent that students are not given an opportunity to think about how to solve a problem. Prompt student thinking using questioning and encourage different ways to solve problems.
require support to evaluate and explain their choices. Often students focus on finding a solution without justification for this choice. Help students to slow down and think about whether the choices they made were effective or not, and why.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

We are learning to choose relevant approaches and mathematical strategies to solve problems.

Why are we learning about this?

We solve maths problems everyday in life and work.

What to do

Sam is looking to replace an existing family car with a new or second-hand vehicle, but can’t decide whether an electric vehicle (EV) is more cost effective than a petrol-fuelled vehicle. He has a total budget of $45,000 and has narrowed his decision to two cars: BYD Atto 3 or the Hyundai Santa Fe. Which vehicle should Sam buy and why?

Success criteria

I can:

select an approach to solve a practical problem
use a mathematical modelling process to specify the mathematical problem and then formulate and provide a solution to the problem
evaluate the reasonableness of my solution in relation to the situation.

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Planning tool

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