Mathematical modelling: Year 5: Planning tool

Expected level of development

Australian Curriculum Mathematics V9: AC9M6N08, AC9M5N09

Numeracy Progression: Additive strategies: P8, Multiplicative strategies: P6, Understanding money: P7

At this level, students use mathematical modelling to solve practical problems involving additive and multiplicative situations 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.

The 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 applying their knowledge and understanding of mathematics concepts, structures and relationships and 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 enabling prompts, questioning and feedback to guide students through the process. Use resources that have relevant problems to solve, however, do not include the scaffolding and allow students to choose which mathematical operations to use.

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 mathematics skills depending on the richness of the problem.

Look for opportunities to highlight different approaches students’ use and encourage a discussion about the range of approaches and the 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 relevant mathematical operations and efficient calculation strategies.
Explicitly teach and provide guidance to support students to fluently solve calculations as the opportunity arises.
Encourage students to make estimates for solutions involving rational numbers and percentages to check the reasonableness of solutions.

Students:

use additive and multiplicative thinking to solve mathematical problems
use appropriate estimation strategies
model practical situations choosing an additive/multiplicative model and use a number sentence to represent it
using physical materials, arrays and bar models to assist with calculations
choose and evaluate calculation strategies in terms of efficiency and solutions in terms of reasonableness
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

The bathroom in Adam’s house has a leaking pipe. He realises there is an issue with the plumbing so he has contacted three plumbers to see if they can help him figure out what is going on. Here is some information from each plumber:

	Plumber 1	Plumber 2	Plumber 3
Callout fee	Nil	$50	$80
First 3 hours	$500	$330	$420
Every additional hour	$85	$70	$50
Unexpected additional costs	$100	$50	$50

Which plumber should Adam choose? List all the possibilities and show your calculations.
Why should Adam choose this plumber?
Is there a plumber who would be ideal for quick jobs? Is there another plumber who would be better to call in in the event of extended works to the plumbing?
How might Adam save some money?

Success criteria

I can:

select an approach to solve a practical problem
use mathematical modelling to specify the mathematical problem and then formulate and solve the problem
evaluate my approach (calculation strategies used) and my solution in terms of the problem.

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Planning tool

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