Money: 2.0

• Indicator of Progress
• Teaching Strategies

Supporting materials

• Related Progression Points
• Developmental Overview of Numeration: Base Ten and Place Value Properties (PDF - 28Kb)

Indicator of Progress

At this level students can efficiently find the total amount of money in a pile of coins. Success depends on the ability to count by 5s, 10s and 20s, and students need to be able to think strategically about an efficient ways to approach the task. This is an important skill for real life. 

Before achieving this, they will be able to order amounts of money in dollars and cents, and group coins of the same denomination to make $1. They will be able to count piles of coins, but will not think ahead to choose an efficient method.

Dealing with our decimal money system builds understanding of whole number place value, and in turn it builds on these understandings. Since the withdrawal of 1 cent and 2 cent coins, as a model of number, money is most useful for counting in 5s and 10s.

 

Money has a place in building introductory ideas about decimals, but should be used cautiously, since students consider the cent to be a unit in its own right, rather than only as a hundredth of a dollar.

 

Illustration 1: Distinguishing size of coins from their value

Small children think that the size of a coin indicates its value. Many will think that a 50 cent coin is more desirable than a dollar coin. They will also think that it is always desirable to have more coins than fewer. An appreciation of the distinction between value of coins and their size and numerosity should be reached by Level 2.

Illustration 2: Counting money inefficiently leads to hard calculations and mistakes

Initially children count money one coin at a time in the order the coins are found. So if they are given a handful of coins (e.g. containing 2 five cent coins, 1 ten cent coin, a dollar and 2 twenty cent coins) they will take them in the order they pick them up. For example, they start with 1 five cent coin, add 1 ten cent coin to get 15 cents, add the dollar to get $1.15 and the  twenty cent coin to get $1.35 (a relatively hard calculation) and the next twenty cent coins to get $1.55 and then add the remaining 5 cents to get $1.60. This method presents many opportunities for mistakes.

Illustration 3: Efficient counting of money uses grouping

An efficient approach to counting money is to start by laying out the coins in easy groups and in order of size. For example, to count a handful of coins containing 2 five cent coins, 1 ten cent coin, a dollar and 2 twenty cent coins, it would be desirable to put the 2 five cent coins together noting they make ten cents, next put out the ten cents coin then the twenty cent coins then the dollar coins. The process is to then count the money starting with the coins of largest value first: $1, $1.20, $1.40, $1.50, $1.60.

Laying out large piles of coins prior to counting is an important strategy at any age. Eventually students can do this with a small number of coins in the hand without laying them out separately.

Starting with the largest coins first is not an unbreakable rule for efficient counting, but it is a good guideline. In real life, it is more important to get the dollars right than the cents right, so do them first. For example, to check change placed into the hand at a shop, a child needs to look for the large value coins first.

Illustration 4: Links to the Mathematics Online Interview

Examples of the types of tasks that would be illustrative of counting money and the associated number skills aligned from the Mathematics Online Interview:

• Question 4 – Counting from 0 by 10s, 5s and 2s
• Question 7 (a - c) - Counting money
• Question 14 – Ten more
• Question 15 – One hundred less

 

Teaching Strategies

Counting money is a practical skill which is very often used. Skills such as these need a combination of:

• specific teaching
• structured practice and
• incidental practice in many real life situations. (Parents can often help here).

Counting money also involves the development of strategic thinking. Although some children can develop efficient strategies for themselves, most children benefit from lessons where strategies are explicitly discussed and shared. Counting money builds on, and in turn builds up, place value knowledge, and should be considered in parallel.

Activity 1: Classroom corner shop provides opportunities for students to practice using money, counting change etc.

Activity 2: Capitalising on classroom events is an important way to give students practice and a good opportunity to discuss strategies.  

Activity 3: Focus on strategies is an activity to motivate students to use better strategies and provide another opportunity for class discussion.

Activity 4: Calculator alert warns teachers about pitfalls in using a calculator to do money calculations.

Activity 1: Classroom corner shop

Setting up a shop in one corner of the classroom can be a long term asset. Students can learn about the real world activity of shopping, goods, prices, getting change, and the expectations and good manners for shopping. They will enjoy the role play, taking turns to be customer and shop keeper, writing prices, keeping the shop clean and tidy, restocking the shelves etc. You could even bring out the dress up box, complete with old handbags and wallets!

NOTE: For mathematical benefit, price the items in various ways depending on your mathematical goals, including ‘3 for twenty cents’, ‘ten for two dollars’, ‘half price today’, ‘buy two and get another one free’ etc.

 

 

 

Imaginary play can continue with minimal teacher intervention, but take time to observe whether students are using the mathematical knowledge that you expect. Mathematical benefit may be increased if customers and shopkeepers work in pairs to check that the prices charged are correct, and the correct change is given.

 

 

 

Activity 2: Capitalising on classroom events

Working with money should principally be taught at this level with real or play money. Adults need to learn to calculate with amounts of money written down, and so older students must do this. However, the first priority is that children learn to work with real or pretend coins.

There are many occasions when children bring money to school. With appropriate safeguards, counting the money can be a shared activity. Effective strategies for counting and keeping track of the count can be demonstrated and discussed.

The main strategies are:

• grouping like coins, e.g. making piles of 5 twenty cents and 10 ten cents
• laying out dollars, e.g. putting coins together to make a dollar
• counting the dollars first, then the left-over coins
• getting another person to check your work when it is important
• writing down subtotals on paper when counting large numbers of coins.

Activity 3: Focus on strategies

As noted above, practical skills are best taught in practical lessons, but some instruction in strategies is worthwhile and requires a planned experience. This activity is designed for overhead projector or interactive whiteboard. For overhead projector, print onto transparencies. Download Efficient strategies for counting money (PPT - 1.2Mb). 

Explain to the students that the amounts of money on each slide will be shown for just a few seconds. Their task is to work out the total amount. Aim to make this a fast activity, where students concentrate hard for the few seconds that each one takes.

In reviewing, be sure to have students explain why some slides can be totalled easily and others can’t. Have students explain the strategies they used and emphasise the most powerful ones. Adapt the slides to suit your class using the images provided. This task could also be used with Level 3 and Level 4 students to assess the efficiency of their strategies. Be careful to maintain the relative size of the coin images.

Activity 4: Calculator alert!

Mathematics learning can be greatly enriched by using a calculator to explore numbers and their properties, and to check calculations. However, there are special alerts that students need to know when dealing with money. These cannot be fully understood until students learn about decimal notation. A calculator can be used to count a set of coins up to one dollar but problems arise for young children when dollars and cents are mixed. As a general rule, calculators can be used if children are only working with small numbers of cents, or small numbers of dollars, without any mixing. At the Level 2 stage, calculators can cause many problems.

Sample difficulties:

• A child who wants to add 15 cents to $1.25 with a calculator may enter: 1.25 + 15 and get the answer $16.25.
• A child who wants to add $1.15 to $1.25 with a calculator may enter: 1.15 + 1.25 and get the answer $2.4, which may then be interpreted as two dollars and 4 cents.

After students have some knowledge of decimal numbers it is important that they learn how to use a normal calculator for money calculations.