Money Matters

Purpose

In this unit, students explore the place value system through engaging with a variety of money contexts including trading (\$1, \$10, and \$100 notes) and extended trades and operations into using thousands, millions, and billions of dollars.

Achievement Objectives
NA3-4: Know how many tenths, tens, hundreds, and thousands are in whole numbers.
Specific Learning Outcomes
• Create groupings of tens, hundreds, thousands, tens of thousands, etc. using play money and place value mats.
• Read and write large whole number money amounts.
• make sensible estimates for sums that are greater than / less than \$10, \$100, \$1 000
• Find the sum of collections of \$1, \$10, \$100, etc. notes and different combinations that total the same amount.
Description of Mathematics

In this unit students will explore the meaning of digits in whole numbers as well as developing deeper understandings about our place value system within the context of money problems.

The focus of the Number learning will be on developing better understandings about the fundamentals of our place value system, namely that:

• Our whole number system involves groupings in tens, and trading collections of ten.  (Powers of ten are therefore an important concept for learners to develop).
• The same digits are used in different positions to represent different values.  (This is often referred to as the distinction between the "face value" of a digit the "place value" of a digit and the " total value" of a digit. A digit is one of the numerals 0, 1, 2,3, 4, 5, 6, 7, 8, 9)
• Our system is called a base ten place value system.  (Which is reflected in the name decimal where "deci" means based on ten.)
• There are only ten digits (0 – 9) that we use in our system but there an endless number of place values that can be assigned to these digits – tens, hundreds, thousands – depending on their position.
• Understanding the role of zero is critical as it serves as an important place holder in our place value system as well as a symbol for ‘nothing of something’.

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:

• Vary the complexity of the numbers that students deal with.
• Vary the degree of abstraction required through access to materials (Play Money etc.) or removal of those materials.
• Modelling the use of symbolic recording to ease memory load.

The context of the unit is cash money. Although societal changes are limiting students’ experiences with money, the context is still highly motivating. Activities can be adapted to suit the interests and experiences of your students. For example:

• Use different place value materials alongside money to help students recognise the proportional relationships not obvious in cash.
• Discuss situations where large amounts of money are needed, such as fundraising to refurbish a marae, or pay for a trip back to a Pacific homeland.
• Share everyday situations where large amounts are commonly used, such as prices of items like cars, houses, and farms, amounts spent on big events, and money earned annually by enterprises like tourism, forestry, farming, and education, or large companies.
Required Resource Materials
• Calculators
• A large collection of Play money (
• Base 10 / Multi-base / Place value blocks (cubes, longs, flats, large cubes)
• Advertising circulars for sports gear / hardware/supermarket/clothing items for sale.
• Plastic bags or envelopes to create pay packets
• Hundred Charts
Activity

Session 1

The following activities are designed for students to work in collaborative groups of 6 –10 students. For the first day, students explore number patterns and relationships that they see in the play money, making amounts with the money by grouping it into ones, tens, hundreds, and other higher place values.

Hand out a mixed bundle of play money with denominations up to \$10 000 (from Copymaster 1) to each group of students and have them play "The Great Money Sort!" where they are asked to sort play money into denominations.

The Great Money Sort!

1. As students take the mess of play money and begin to sort the money into piles, have them discuss patterns that they observe as they look at the numbers in the play money.  Have students sort as much of the play money as possible. Have them discuss how they are choosing to organise the money into piles, and why.
Possible questions / prompts as students are sorting the money into piles:
• What do you notice about the amounts on these notes (the denominations)?
• Why were these amounts used?
• How is this toy money the same/different to the money we really use?
2. The money will get sorted into piles that replicate the place value house designations:
one
ten
hundred
thousand
ten thousand
If a greater denomination is needed, what amount should it be? Why?
3. Discuss how the denominations might be extended to the millions.
Encourage students to offer suggestions about patterns that they see in the numbers and to describe the same pattern in different ways, such as:
I see the 1 repeating at the start of each denomination (110, 100, 1,000, 10,000…)
I see zeros repeating. (10, 100, 1,000, 10,000…)
I see the zeros growing at the ends of the numbers… 1 zero here – 10 (tens), 2 zeros here - 100 (hundreds), 3 zeros here - 1 000 (thousands) etc.
I see 1, 10, 100 and that keeps repeating in the thousands (1 thousand, 10 thousand, 100 thousand), the millions (1 million, 10 million, 100 million) etc.
Be aware that seeing a symbolic pattern such as “adding zeros” is different from recognising that a given denomination is worth ten times as much as the next smallest denomination, e.g. \$100 note is worth ten times \$10 note.
Since money is a non-proportional representation of place value you might use a proportional representation as well to help students understand how the quantity changes although the notes all look the same size. Placing matching place value blocks on top of the \$1, \$10, \$100, and \$1,000 notes will help.
How big is the block that goes on the …\$10,000 note? …\$100,000 note? …\$1,000,000 note?
4. Once students have communicated their patterns with the group, turn their attention back to the piles of money.  Ask questions that will help students focus on the pattern that can be described as grouping by tens (ie. that 10 ones makes 1 ten, that 10 tens makes 1 hundred).  This can also be discussed and recorded as powers of ten though this is an interesting pattern, not a requirement at Level 3 (100 = 10 x 10 = 102; 1000 = 10 x 10 x10 = 103).
How many tens do you need to make… one hundred dollars?...one thousand dollars? etc.
How many hundreds do you need to make… one thousand dollars?...ten thousand dollars?etc.
How much do I add… to \$380 to make \$1,000? To \$4,900 to make it \$10,000? etc.
5. Set the groups challenges to find total amount for various collections of notes.
Good examples are:
Get 37× \$10 notes. How much have you got?
Get 24× \$100 notes. How much have you got?
Get 19× \$100 notes and 34× \$10 notes. How much have you got?
Get 29× \$10 notes, 17 \$100 notes, and 33× \$1 notes. How much have you got?
And other similar questions.
6. Gather the class to discuss structures and patterns they noticed. Particularly look for understandings related to place values, such as “If you have 23 × \$10 then you multiply 23 by ten to get \$230” of “If you have over ten of one note, that will make more of the next biggest note.”

Session 2

In the next three days, students will continue working with the play money, practise making pay packets in Pay Packet Play, carry out fair trades in the Go Fair Trading Game, and explore number problems by grouping money on Place Value Houses, thinking about rounding, grouping, and estimating to solve money story problems.

Pay Packets

1. For the first day of exploration, provide pairs or small groups of students with plastic bags or clear-faced envelopes into which they can put place collections of notes.  Discuss a scenario with the students where they control banking and payroll at a company.  It is their job to put together worker’s pay packets and keep track of the total amount of money needed to pay staff for the week.
2. Provide groups with Copymaster 2 that has amounts to pay people at the company. Ask students to make up a pay packet for each person and use a calculator or another method to find the total cost of the pay round.
Roam as students work. Look for:
Can students read the numbers, making use of the groups of digits separated by commas?
Can students recognise the place of digits in the numbers?
Do they understand the significance of zero as indicating none of a denomination?
Do they check to confirm the amount is correct in an organised way?
3. Rotate the groups so each group checks the pay packets of another group.
Where errors occur, the checking group needs to leave a note explaining the problem.
4. Bring the class together to discuss the task and strategies they employed to get the correct amounts.
The boss is feeling generous as the company has made a good profit this year.
Discuss what the term ‘profit’ means.
She decides to increase each payment by 10% as a bonus.
What does an increase of 10% mean?
Discuss that 10% means 10 in every 100 so each worker will get \$10 extra for every \$100 they earn.
How much extra will they get for every \$1,000 they earn? Every \$10 they earn? Every \$1 they earn?
Sorry pay clerks, it is your job to include the 10% bonus in every envelop. Get to it. You might get a bonus yourself.
5. Observe students as they work. Look to see if they develop efficient ways to add 10% to each pay packet. Methods might be cumbersome initially like calculating one tenth of each place value, but students should realise that multiplying the amount by 10% on a calculator gives the increase, as does 0.1 times the amount.
6. After a suitable time gather the class to discuss efficient ways to increase each amount by 10%.
How would you increase each payment by 20%? What would that mean?
Students might suggest dividing the amount by ten then adding the answer on to the original amount. You might offer multiplying the amount by 1.1. Why does that work?
7. Have students challenge each other in groups by one students naming a pay amount, recording the amount as \$___ and other students making up the envelope for the employee.
Encourage students to use place value structure rather than counting. Ask questions like:
I put 67× \$10 notes in the packet.  How much money do you have?
Can you work it out without counting?
I put in 19× \$10 000 notes.  How much money do you have?  How do you know?
I have put in 106× \$1 000 notes.  How much money do you have?  How do you know?
8. Throughout the pay packet play, have students discuss what patterns they are observing and how they are working out how much is in their pay packet.  Students take turns to make pay packets for each other.  Have them record their problems using words and numerals on pieces of paper.
Students can discuss possible ways to record the problems using only numerals and symbols.
For example:
10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = \$120 (Repeated addition than is tedious and inefficient)
or
12 x \$10 = \$120 (Multiplication that is very concise and efficient.)
9. Finally, vary the pay packet amount through scenarios like working overtime or paying tax. At the conclusion of the lesson tell students to make up a pay packet with a five-digit dollar amount in it. Encourage students to use a lot of notes, not simply use the digits, such as \$12,345 as 1×\$10,000  and 2× \$1,000, etc. Ask them to record their amount on a pay slip inside the envelope.

Session 3

1. This activity can be played in a small group or as a whole class.  Ask students to sit in a circle.  Tell them you are going to give them some money in a pay packet that is theirs to keep and trade with throughout the "Go Fair Trading Game".  The aim is to not lose any money as they play each round of the game. Hand out "packets" of pay that were created yesterday. Ask students to check their pay packet of money to see that it matches the pay slip.
2. The moves in the Go Fair Trading Game are:
• Find someone else in the group who has an equivalent amount of money made from different denominations with whom they can make a fair trade for their money. For example, one student trades twenty \$10 notes with another student in the circle for two \$100 notes.  These students can make a fair trade as they do not lose any money in the transaction and they both have different denominations of money to make \$200.
• Each student must complete five acts of trading and check at the end whether, or not, the packet still contains the correct amount.
3. Play many rounds with students receiving different pay packets each round.  Money returns to the teacher at the end of each round.
Encourage students to avoid counting or repeated addition to work out the total of their pay packet.  Push them to adopt more efficient strategies such as:
I have thirty \$100 notes.  I know that ten \$100 notes make \$1 000 so three groups of ten \$100 would be \$1 000 + \$1 000 + \$1 000.  That make 3 x \$1 000 or \$3 000 altogether that I have.
Also encourage efficient recording strategies, such as a table, with amounts arranged in vertical alignment.
 Note Number Total amount \$1 5 \$5 \$10 12 \$120 \$100 34 \$3,400 \$1,000 6 \$6,000 \$10,000 17 \$170,000 \$100,000 9 \$900,000 \$1,000,000 3 \$3,000,000 Sum \$4,079,525

Continue discussing the trades increasing the complexity and number size with each round.  Have students share and record their strategies for each round.

4. Provide a challenging problem to complete the lesson:
[Name] has \$27,094 in his/her pay packet.
How many notes are in his/her pay packet?
How many different answers can you find?
Encourage the students to think beyond the simplest answer of 2 + 7 + 9 + 4 = 22 notes.

Session 4

Place Value Houses and Problems

In this lesson students make further links between the play money and our the number place value system by placing money on the Place Value Houses template.  Students will gain confidence reading multi-digit whole numbers using the Place Value Houses to help them to structure large whole numbers.  Finally, they solve addition and subtraction problems by using their knowledge of grouping play money in tens/hundreds/thousands etc. and by making sensible estimations that they can check with the money.

1. Use A3 laminated Place Value Houses (Material Master 4-11) along with the Play Money that has been used throughout the past lessons.  Ask students to explain the structure of the Place Value Houses template.
2. Students should connect the Place Value Houses in order starting with the "Trend setter house" on the far right. These three columns refer to the ones period. Each set of three places is a period. Next left from ones, is the thousands period, then the millions period, etc. It is helpful to record \$1, \$1,000, \$1,000,000, \$1,000,000 so students understand how commas are used to separate periods when money amounts are written. That system makes reading large numbers easier than a string of digits. Not that we write numbers with a gap between periods, not a comma.
3. Ask students to read the amount \$111,111,111 and make that amount using play money on the Place Value Houses template. Ask them to remove notes and read the resulting amount, e.g. \$101,111,111.
4. Have pairs or trios of students place all their play money into piles in the appropriate places in the House template, e.g. \$100 notes in the hundreds place.
5. Tell students to remove most notes from each column, so there are just a few notes in each place. Ask them to work out how to read and write the amount they have left. Students can swap their amounts with a neighbouring pair or trio for more practice.
6. On the whiteboard or on a piece of paper, write amounts of money. Ask students to read then make the amounts, such as:
\$3,450
\$75,010
\$407,908
\$37,090,324
7. Let students challenge another pair or trio beside to tell them what piles of money they would place on the Place Value Houses for an amount that they write on paper. Practise reading the amounts as well.
8. Help students decode the reading of large numbers by always having them begin reading numbers at the far left and saying first the "ones, tens and hundreds" and then the Place Value House name and so on.
In this way, the number \$45 874 230 would be explained and read as:
(Always start reading with the far-left-hand side of the number):
(ones, tens, hundreds) 45 (millions house) million, (ones, tens, hundreds) 874 (thousands house) thousand, (ones, tens, hundreds) 230 (trend setter house so we just say the number of ones, tens, hundreds).
9. Practise reading each other’s large numbers written on paper and making them on the Place Value Houses.

Session 5

For the final day, students will be given an open-ended task involving Advertising circulars (such as a Warehouse, Rebel Sport or Farmers advertising flyer) and play money.

1. The teacher should discuss the learning task with students and then move from student to student observing the students’ strategies.  Students can use the play money, Place Value Houses, number lines and hundred charts to assist them as they work and reflect on the following task.