Shopping for Savings

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Purpose

This unit involves students in calculating savings and finding the best value items from a list of products. It would ideally be carried out prior to a school camp or similar event, with students given the challenge of finding the best bargains for the situation.

Achievement Objectives
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
Specific Learning Outcomes
  • Calculate the amount saved from given prices and percentage savings.
  • Identify the best value item from a list of similar grocery items.
  • Check the reasonableness of answers obtained using a calculator.
Description of Mathematics

This unit involves students in calculating savings and finding the best value items from a list of products. It is suitable for students working at Stages 7-8, Advanced Multiplicative-Advanced Proportional, of the Number Framework. Students working at these levels use a range of multiplication and division strategies to estimate answers and solve problems with whole numbers, decimals, fractions, proportions and ratios.

Calculators are included in this unit as tools for calculation, and as tools which enables students to justify the reasonableness of answers obtained.

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing support to students, and by varying the task requirements. Ways to differentiate include:

  • selecting items where the prices are simple to work with. Most supermarket items can be rounded to the nearest dollar or fifty cents to make calculation easier
  • supporting students with toy money or diagrams of amounts that show the place value structure.
  • allowing students to use a calculator to help them with their calculations (especially in predictive ways). Students should be encouraged to anticipate an answer before using  a calculator to check. Emphasise that students need to be able to justify the reasonableness of answers obtained
  • for each task, providing direct and explicit teaching, modelling; and opportunities for students to make calculations with a partner and independently, ensuring they feel confident before beginning to work independently on the task 
  • providing opportunities for students to express their mathematical understanding, and the ideas developed in this unit, in different ways (e.g. as a video, by acting it out, with the use of digital tools, or as a poster, PowerPoint, or movie)
  • validating the mental calculation strategies used by students, and encouraging them to work in an increasingly efficient and systematic manner
  • providing opportunities for students to work collaboratively in groups, share ideas, and develop explanations and justifications.

The context for this unit is supermarket shopping. For some (e.g. rural) students the experience may be less familiar than it is for urban students. Use online shopping sites to find prices of items. Major supermarket chains have websites through which items can be ordered remotely and delivered. The context of shopping for supermarket items can be adapted to other items that are of high interest to students, such as shopping for sports or kapa haka equipment, or for holiday deals. Consider which shopping-related contexts will be engaging and relevant to your students, and relevant to their current interests and learning from other curriculum areas. This context will be integral to the development of this unit, and its relevance to your students.

Te reo Māori kupu such as ōrau (percent) could be introduced in this unit and used throughout other mathematical learning

Required Resource Materials
  • Copymasters One, Two, Three, Four and Five
  • Calculators
  • Supermarket receipts containing items that have been reduced in price
  • Paper and pencils for working
  • A selection of grocery advertising flyers or access to online information about special prices
  • Computers with access to the internet and relevant shopping sites
Activity

This unit is presented as a series of five activities, or stations, based around the same theme. If appropriate,  after introducing and modelling each activity, your whole class could rotate around these stations over the course of a week. Ensure that your students have developed the knowledge necessary to complete each activity independently or with a partner. During this time, you could also hold small group teaching sessions to address gaps in knowledge and misconceptions that have become apparent during your introduction (or other whole class teaching).

Station One

At this station students practise calculating reduced prices, using given prices and percentage reductions.

Copymaster 1 contains problem sets for students to work through.

To succeed at this task, students need to be able to find 5%, 10%, 20%, 25%, and 30% of a given price, and then subtract this to calculate the ‘sale price’. Complete a few examples with the class, using these percentages and the prices given on Copymaster 1. You should also model how to calculate a percentage using the calculators you have access to in the class. Ensure students understand the difference between the two price options at the different supermarkets and help them to compare these in a logical way.

Station Two

At this station students use supermarket receipts to calculate percentage reductions on sale items, before calculating the overall percentage saved. Model how to identify the items on the receipts that were on special when purchased and find the original price, how to find the amount saved for these items. Once these numbers have been found, students should use them to calculate the percentage reduction for each item on special. 

See Copymaster 2 for student instructions.

Once all items on special have been found, students calculate the total amount saved and the total amount spent. This can be done in two ways, either calculating a percentage saved on just the items on special, or the percentage saved on the supermarket bill overall. If time allows have students do both calculations to enable comparison. Discuss how choosing items on special increases the percentage saved but often percentage savings is not the only consideration when shopping.

Note: Not all supermarkets present information on receipts in this way. New World and Countdown are two supermarkets that do indicate items purchased on special.

Station Three

Students participate in the ten dollar challenge. Working from a list of grocery items and their prices the challenge is to spend a total less than $10 on any selection of items while making the biggest savings possible. 

See Copymaster 3 for student instructions.

To complete this task, students will first need to calculate the reduced price and the amount saved for each item. Support students in this as required, modelling the required calculations and helping students to work systematically on the problem. Once this is done discuss with students the strategies they might use to solve this problem. These might include:

  • Trial and error, experimenting with different combinations of items to maximise savings.
  • Selecting the maximum number of items with the highest percentage saving possible.

Encourage students to discuss the strategies they are using as well as the answers they come up with?

 How did you choose those items?
Why did you do it that way?

Station Four

At this station students use a collection of grocery advertising flyers to make a list of all drinks on special and then work out which drink is the best value in terms of cost per litre of drink. 

See Copymaster 4 for student instructions.

Once students have listed the drinks and identified the price per litre, ask them to look at the problem another way. For each drink, how many litres are being purchased per dollar spent? Either way of looking at it will identify the better value products but the cost per litre is easier to calculate mentally as you do the shopping. Why? (The number of litres is usually a whole number and the number of dollars usually isn’t so it’s easier to divide by the number of litres than the number of dollars).

As an alternative to using flyers, students could access information about prices of drinks through supermarket websites.

Station Five

At this station students use online shopping sites to look for the best value items. 

See Copymaster 5 for student instructions.

Students can use either the browse or the quick-list functions on these sites. Full information on using these features can be found online.

In this task, students need to find the items they are looking for, and evaluate the products displayed, to find the best value. To compare products, students will need to calculate the cost per kg, g or litre as appropriate for each item and may need some support to do this.

Student’s efficiency with mental calculation strategies and calculators will be particularly important in solving this task. For example, if calculating the cost per litre of juice when 3 litres costs $5.90, it is reasonable to use the strategy of tidy numbers and round the $5.90 up to $6.00. This makes the calculation 6 ÷ 3 which is a much simpler problem. Using this strategy, students can estimate the cost per litre to roughly $2.00. To support students, ask questions like:
How do you know that is the right answer?
What simpler calculation could you use to check?

Have students make a list of the items they have selected, including brand name, and the price for these as they work so they can calculate the total price when finished.

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Level Four