Digging Deeper into … Money (all classes)
Category : Uncategorized
Similar to the strand unit of time, money is an integral element of our daily lives and therefore an essential, “need-to-know” topic in primary maths, particularly for those children with special educational needs or learning difficulties. And, while it is not as abstract as the topic of time, it still can be a concept with which many children struggle. Consider the nature of money itself:
- It comes in different shapes and sizes, and in metal and paper forms (i.e. coins and notes) each of which has its own value.
- The sizes of the coins and notes are not proportional to their value i.e. a 20c coin is not twice as big as a 10c coin; a €100 is not ten times the size of the €10. Therefore, while money can be used as a base-ten material, unlike the base-ten blocks, it is not proportional.
- Money can be expressed as € or c, but not as both. And when using the € sign it precedes the numbers (even though it is verbalised as “six euro” as opposed to “euro six”), where as the c sign comes after the numeral.
- Countries often use different currencies; this can lead to confusion when children presume that dollars and pounds are used in this country, because they hear this terminology regularly from imported TV programmes.
- When changing currencies you cannot do a straight swap i.e. €1 doesn’t equal £1 or $1; the new value must be calculated using an exchange rate, which also varies.
- More and more, transactions are becoming cashless, as people use credit and debit cards more than ever before. Thus, children are missing out on essential opportunities to handle cash, or see it being handled in real-life situations. The increased use of plastic and contactless payments also limits the opportunities for people to total mentally, calculate change etc.
Elicit prior knowledge & concrete exploration
At every class level, it is always a good idea to elicit the children’s prior knowledge, which can be very varied, depending on the experiences they’ve had with money. Even some simple revision questions can be very revealing, such as these:
- ‘What currency/money do we use in Ireland?’
- ‘Do you know of any other countries that use the euro?’
- ‘Can you name the coin/note with the least value? And the next? And the next?’ etc
Even in a senior class, the answers to the last question can often be ‘1c, 2c, 3c, 4c…’ as the children forget or don’t realise that there is not a single coin for each value. In keeping with the CPA approach of Operation Maths, these type of questions should be followed with opportunities to explore and examine the actual notes and coins, and the similarities and differences between them. And, if there is not enough real or replica money, the Sorting eManipulative, accessible via edcolearning.ie, can be a very useful way to display the coins and notes (see below).
Do you notice any pattern? Many children, and even some adults, don’t recognise that our euro money follows a ‘1, 2, 5’ pattern i.e. every note or coin has either 1, 2 or 5 as its most significant digit (look at the columns above). Once the children recognise this, they are less likely to suggest using a ‘3c coin’ or a ‘7c coin’ etc to make a value. To improve their familiarity with the coins, even children in junior infants could use them for pre-number sorting purposes, eg using coins for sorting by size, colour, shape etc. They don’t need to be restricted to just coins up to 5c (the traditional limit for junior infants), as the focus is not on number. Play activities based on money e.g. the shop, post office, restaurant etc should also be encouraged, particularly as the basis for Aistear themes.
Exploring the value of the coins
Recognising the value of each individual coin is one thing, recognising that one coin can be exchanged for a number of coins of equal value is very different. This is why it can be very useful to represent the value of the coins concretely. This can be done by attaching coins to large squared card and/or ten and five frames. Grid paper with 2cm squares is perfect for this. Just print out/photocopy onto white or coloured paper or light card and then cut out into sections that relate to five and ten frames (see image below):
- 1c, 2c, 5c on to strips of 1, 2 or 5 squares respectively
- 10c onto a 2×5 section i.e. ten frame
- 20c onto a 4×5 section, with a bold line through centre to show each ten
- 50c onto a 10×5 section, with 4 bold lines to show each ten
This reinforces the benchmarks of five and ten, while building on the children’s ability to subitise (recognise at a glance) these quantities.
These materials can then be used for exchanging activities, where the children identify different ways to make various values, i.e “same value, different appearance”, e.g. what coins could we use instead of 2c, 5c, 10c, 20c, 50c, etc. When the children are comfortable making these values they should then make values that are not equivalent to a single coin e.g. 6c, 13c, 23c etc. Ultimately, it is hoped that the children will be able to visualise the value of the coins without needing the visual supports shown above.
Mental calculations with money
Despite the face that our society is becoming increasingly cashless, mental calculations with money should still be emphasised and, in particular, the strategy of making change. Officially referred to a complementary addition, where you add on to subtract, it has also been known as “shopkeepers arithmetic” given its application in those situations. It is also one of the specific subtraction strategies dealt with in Number Talks, where it is referred to as Adding up (all of the other Number Talks strategies are also relevant to calculations involving money, but this one is worthy of a special mention). Complementary addition is also one of the strategies used in Operation Maths, where it is shown using the visual strategy of an empty number line (see below).
Visual Strategies for Problem Solving
A key element of Operation Maths is the use of three specific visual strategies to support the development of problem solving skills. These are empty number lines (as shown above), bar models and T-charts. T-charts are particularly useful to solve problems based on the unitary method, as shown below.
Bar models can be very useful to model addition and subtraction problems e.g. where the whole amount is known and a part is missing or where the parts are known and the whole is missing. The type of models shown below are referred to a part-whole models.
For more information on the visual problem solving strategies used in Operation Maths 3-6, please read this post.
Other tips and suggestions for teaching money
- Emphasise that money is based on the euro. Cent coins are merely fractions of that unit; euro coins and notes are multiples of that unit. In this way money can also be used to help teach other strand units, including place value, operations and decimals (see examples below).
- Emphasise the importance of using an efficient estimation strategy when calculating with money:
- front-end estimation: where you only consider the most significant digit i.e. think of €26.95 as €20
- rounding: where you round to the nearest unit, ten etc, i.e. think of €26.95 as €27 or as €30. Rounding produces more accurate estimates than front-end estimation; however, it can also be more time-consuming for some children and thus less efficient.
- Value for money: Encourage the children to compare prices in different shops and/or catalogues to identify the best price and when comparing items being sold as multiples to compare their values using the unitary method and T-charts, as shown above.
- Use That Quiz for an interactive quiz based on euro. Use the options on the left hand side to change the difficulty (level) and the scope of questions (identify, compare or make change). For more on using That Quiz in the classroom read on here.