Mathematical modelling: Year 7: Planning tool

Expected level of development

Australian Curriculum Mathematics V9: AC9M7N09

Numeracy Progression: Additive strategies: P10, Interpreting fractions: P8, Multiplicative strategies: P9, Proportional thinking: P2, Understanding money: P8

At this level, students are required to have knowledge of the other topics in the Number strand, so that applying knowledge and skills can be used in the mathematical-modelling process. This can be done in groups or as a whole class, as well as individually. Collaborative learning works well for practical problems.

Students are required to formulate problems, choose representations and efficient calculation strategies, using digital tools as appropriate.

Once identified, students are required to interpret and communicate solutions in terms of the situation, justifying choices made about the representation.

One practical example of the use of ratios is ‘best buy’ deals, using the unitary method to compare offers and evaluate which is better value. Students compare the cost of items to make financial decisions, both with and without technology. They make estimations to judge the reasonableness of results.

There are many real-world scenarios to pose to students that require students to draw on skills and knowledge of positive and negative quantities using all operations, proportion and reasoning to both financial and land area/perimeters. This is also an opportunity to create problems using cross-curriculum connections in Science, Design and Humanities subject areas.

This topic has many connections with other areas in the mathematics curriculum, for example, fractions, percentages, graphs and algebra.

Teaching and learning summary:

Revise all other strands of Number: rational numbers, percentages, ratios.
Ensure students can identify representations and use the correct calculation strategy as appropriate.
Give opportunities for students to communicate their reasoning and justify their choices.
Practical example: show how the unitary method can determine the ‘best buy’.
Use other real-world problems and guide students with recognition, representation, expression, computation, reasoning, communication and justification.

Students:

formulate problems, choose representations and use efficient calculation strategies
use digital tools appropriately to help with their investigation
use real-world scenarios, such as 'best-buy deals' to make connections between what they are learning and their everyday lives
bring together all knowledge and skills from the Number strand
listen to feedback and work collaboratively to work efficiently and to refine their model.

Some students may:

find it overwhelming to solve or investigate problems that are open-ended or could be tackled using different approaches.
be tentative to brainstorm, express their creative thoughts and communicate their ideas for solving problems.
find it difficult to work collaboratively.
not realise that it is the attempt of a complex problem rather than the result that counts at this stage.
attempt to use additive strategies for problems that require multiplicative thinking.
assume that everything is out of 100 for per cent rather than per 100.

Percentages are relative – teach students that they should not assume the larger percentage will result in the larger number; for example, 50% of 60 is less than 25% of 130. It is dependent on both the value of percentage and the whole (100%).

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

I am going to learn about 'best-buy tickets' from my local supermarket.
I am going to learn to make evidence-based decisions when deciding what products to buy.

Why do I need to know this?

Visiting a supermarket can be overwhelming. There are thousands of foods and products on the shelves and it can be difficult to know what to get. All sorts of questions arise when you look closely at the way a product or food is advertised. For example, you will be told the price, how much you will save if it is on sale and the unit price. But you can be tricked! You will now learn how to make sound decisions the next time you look at a ticket price at your local supermarket ... or any other shop for that matter!

What to do

Number	Product	Unit weight	Cost for product	Cost for 10 products	Best value
1.	Orange cordial	500 mL	$2.50	$25.00
2.	Orange cordial	1 L	$3.00 on sale	$30	This is the better value.

Choose 10 foods or products from your local supermarket. Perhaps pick foods or products you like.
Then choose a competing brand and pair it with each of your 10 products. You should have 20 products altogether.
You can find the products on the supermarket's website. Alternatively, you could go to the supermarket and check the ticket prices yourself beneath each product.
In a table, like the one above, create 21 rows and six columns.
The top row is for your headings and the remaining rows are for each of the products you have chosen.
Record the prices and fill out your table.
The final column is called 'best value'. This is where you decide which product of your pairs will give you the best value for the money you will spend. Remember, just because a product is on sale, doesn't mean it is the best value.
In my example, I also have a column called 'Cost for 10 products'. This was one way I could figure out how to find the best value of my pairs. However, there are other ways you could make comparisons depending on what information is on the ticket price.
Find an alternative way to make fair comparisons.

Success criteria

I have learnt about 'best-buy tickets' from my local supermarket.
I understand that it is important to make evidence-based decisions when deciding what products to buy.

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Planning tool

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