# Money marvels

Purpose

In this unit students are given the opportunity to explore various combinations of coins and dollars that add to make given totals.  Within the context of money problems students will practise using flexible mental strategies including rounding, estimating, and finding compatible numbers.

Achievement Objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Specific Learning Outcomes
• Find compatible numbers for totals such as 10, 20, 50 and 100.
• Use various dollar and coin amounts to make given totals.
• Round money amounts to the nearest 50 and 10.
• Use rounding to estimate totals.
Description of Mathematics

In this unit of work students will experience five activities that develop their ability to make sensible estimates, use rounding as a strategy to help in their estimation, combine money amounts to make compatible numbers for ease in adding and estimating totals.

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

• Use the hundreds board and Slavonic abacus to show compatible numbers.
• Ensure that all students know there are 100 cents in one dollar. Some students may need additional support before completing activities that involve dollars and cents.
• Have children record their additive and/or multiplicative thinking e.g., 20c + 20c + 20c + 20c = 80c or 4 x 20c = 80c
• Vary some of the activities to include larger numbers.
• Include other target options for the "Bulls eye target" activity.

The context for this unit can be adapted to suit the interests and experiences of your students. For example:

• Change the items in the "What's for lunch?" activity to items of interest to your students.
• Look at our history with coins (why do we start at 10c?) and compare with other countries.
• Discuss what giving a koha means if you were attending a tangi, wedding, christening or a conference at a local marae.  Are there similar situations in other cultures?
Activity

#### Session 1

Hit the Bulls Eye Target!

1. In this session, students will practise combining whole numbers in many different ways making different amounts of money. Using the context of dollar notes, students’ goal is to combine different amounts of money in as many ways as possible to create the target number in the Bulls Eye. Students can use actual play money to help them with the task as well as counters or calculators.
2. Before students are given the copymaster, it would be worth revising combinations to 10, 20, 50 and 100 with them.  Start by having the students sit on the mat.  Tell the students that the target number to make will be 10.   You will call out a number and the groups’ job is to tell you the other number that combines with it to make 10.  For example, if you call out the number 1, students will call out 9 because 1 + 9 = 10.  Make sure after you call out a number, you give students a few seconds to think of the compatible number that will make 10.  The aim is for the whole class in unison to call out the compatible number together when you point to them.
3. At first, call out numbers to make 10 in sequence, beginning with 1 + ? = 10, then 2 + ? = 10 and so on.  Eventually, with practise, you will be able to randomly call out a number and the students will wait, think, and in unison, call out the compatible number that combines with it to make 10.  Repeat this process over a series of days / weeks as a warm up building up compatible numbers to 10, 20, 50, 100 etc.
1. Students should now be ready for the Bull’s Eye Target activity. Copymaster 1 challenges them to find combinations that add to \$100.

If they need to use play money they can to figure out, for example, \$40 + ? = \$100 they can count out the play money to assist them.

1. Students record as many possible combinations to "hit" the \$100 target on a piece of paper. Their combinations will be shared with the class at either the end of the session or at the end of the week in Reflection time.
1. You may wish to model how you would like students to record their combinations.

For example:

Bull’s Eye Target \$100
\$90 + \$10 = \$100
\$80 + \$20 = \$100
\$75 + \$25 = \$100
\$25 + \$25 +\$25 +\$25 = \$100

#### Session 2

What is for Lunch? – Lunch Menu

1. In this session students are presented with a Lunch Menu with food choices and prices (see Copymaster 2).  Students are given \$5.00 with which to buy their lunch, choosing items from the Lunch Menu.  Play money dollar notes and coins should be available so that students can use them if required.  Students are to record as many possible lunch combinations that they can buy for \$5.00.
1. Before students complete the copymaster discuss your own school’s Lunch Menu.  Discuss with the students what types of things they can buy for \$5.00 from your school’s Lunch Menu.  Have them estimate whether two items together will cost more or less than \$5.00.  Ask students to explain how they estimate that something will cost more or less than \$5.00.  Encourage them to round off numbers that are near 50 or a dollar and look for compatible number combinations.

For example, if they are estimating if two lunch menu items costing \$3.50 and \$1.80 will be more or less than \$5.00 they might think:

"I know that \$3.00 and \$1.00 makes \$4.00.  I also know that \$0.50 and \$0.50 make another \$1.00.  That would be \$5.00 but I also have more because \$0.80 is more than \$0.50.  That means I cannot afford to buy those two items."

1. Give students Copymaster 2.  They can work in pairs to record as many possible Lunch Menu combinations that they can purchase with their \$5.00.

1.  Students can share their findings with another pair or small group at the end of day 2 or at the end of the week in Reflection time.  Challenge the students to try to find as many different combinations as possible that will make \$5.00.  The "winner" will be the person who discovers the most!

#### Session 3

Compatible Number Puzzle

1. In this session, students will attempt to match puzzle pieces (see Copymaster 3) in order to add two numbers that combine to make \$10, \$20, \$30.  In this activity, students will be required to round off numbers in their head involving dollars and cents.

For example, \$17.90 will be rounded off and thought of as \$18.00 and \$5.10 will be rounded off to \$5.00 and thought of as "just more than \$5.00".  In this activity, the "bits" or "extra" cents left over are not important to focus on as we are not trying to determine the exact amount.  The focus is merely on looking for compatible number combinations involving dollars and cents.  It is important for students to develop the ability to round off numbers to the nearest fifty and keep track of dollars and cents mentally.  At first, they may struggle to "hold onto" all of the pieces of information mentally.  If this is the case, have students record bits onto paper as they work out the totals of the puzzle pieces mentally.

Before you give students the copymaster, you may need to spend some time working on rounding off strategies with them.  This may involve looking at a number line and deciding whether to round numbers up or down to the nearest 50 depending on where they are located in relation to the nearest 50.

For example, you may pose questions for students to answer such as:

• If I have \$0.70 do I have closer to \$0.50 or \$1.00?  How did you decide?
• If I have \$1.40 do I have closer to \$1.00 or \$1.50?  How did you decide?
• If I have \$6.40 do I have closer to \$6.00 or \$7.00?  How did you decide?
• If I have \$10.60 do I have closer to \$10.00 or \$11.00?  How did you decide?
• If I have \$16.30 do I have closer to \$16.00 or \$16.50?  How did you decide?
1. Give students Copymaster 3.  They can either work alone or with a partner to try to match the Compatible Number Puzzle pieces.  Students should record their number combinations on a piece of paper to share at discussion time later.
1. Before students begin recording their answers, you may need to discuss how you want students to record their found combinations.

For example, if they are finding combinations to \$20, they might record:

\$17.90 + \$3.10 = approximately \$20 (more)

\$15.90 + \$3.50 = approximately \$20 (less)

1. At the end of the session or at the end of the week during Reflection time, have students compare their Compatible Number Puzzle decisions.  See if they agree with each other about which puzzle pieces equal more than or less than \$10, \$20, \$30.  Have them justify their decisions and explain their rounding off strategies with each other.

#### Session 4

More or Less than \$20?

1. In this session, students will look at combinations of number tags to estimate whether the total amounts added together equal more or less than \$20 (see Copymaster 4).  Students will need to have strategies to approach rounding off cents to make the next nearest ten (or dollar).  However, in this activity, it will be more important for them to also pay attention to the "extra bits" left over in order for them to determine, once they have added the rounded off amounts, whether the total of the number tags will be just more, or just less, than \$20.
1. Begin at the mat by having students practise rounding off numbers that are made up of dollars and cents.  With the students, develop effective mental strategies to add two numbers together that are made up of dollars and cents such as \$4.99 and \$4.99.  Have the students determine whether the total is just more or just less than \$10 by using strategies such as:
• Rounding to the nearest 10 (or dollar)
• Looking for compatible number combinations

For example:

Pose the following problem with the students:  Two number tags say:  \$4.99 and \$4.99.

Ask students:  How could you work out if the total amount will be less than, or more than \$10?

A possible answer from a student might be:  I know that \$5.00 and \$5.00 makes \$10.00 exactly so \$4.99 is less than \$5.00.  Therefore, 2 groups of \$4.99 will be just less than \$10.00.

Other warm up problems you could pose to have students practise adding numbers to make more than or less than \$10 could be:

• \$5.45 and \$4.55
• \$9.10 and \$0.85
• \$3.75 and \$6.20
• \$2.50 and \$2.50 and \$5.10
• \$3.33 and \$3.33 and \$3.33

… and so on until students have developed confidence using mental strategies like rounding off, using compatible numbers and adding dollars first to make sensible estimates about total amounts.

1. Before students are given the copymaster, make sure they understand their task is still to estimate whether the total of the number tags will be more or less than \$20.  They are not to work out the exact total but merely to work out, as closely as possible through rounding off to the nearest tens and looking for compatible coin combinations, whether or not the number will "bump over" or "bump under" \$20.
1. If students struggle with this task of estimation, they may need to go back and practise combining 10c, 20c and 50c coins to make \$1.00 in many ways.

For example, you may need to pose problems of the sort:

• If you have 50c, 20c and 20c do you have more or less than \$1.00?
• If you have 30c, 50c and 30c do you have more or less than \$1.00?
• If you have 30c, 30c, 30c and 20c do you have more or less than \$1.00? etc.
1. Working alone or with a partner, students try to estimate whether the number tags combined total more or less than \$20.  They record their estimates, whether they are more or less than \$20 and then, at the end, they can check the accuracy of their estimates by adding the amounts of the number tags using a calculator to check their answers

#### Session 5

Does it Stack Up?

1.  This session offers students a problem solving task, which requires them to make a choice between various stacks of coins.   Students will need to work out the relative values of the stacks of coins before they decide on the stack they would like to keep from themselves.  Play money coins can be used  for those students who will actually need to physically count coins in order to solve the task.

1. Before students go to carry out the task, it may be helpful to brainstorm some possible solution methods with them.  For example, students may need to actually make the amounts using the play money coins.  Other students may like to draw the coins using pictures and numbers.  Some students may simply like to record the numbers such as 18 \$2.00 would be 2 + 2 + 2 + 2 and so on.  More advanced students should be encouraged to think of basic multiplication and addition facts they can use to solve the task.

1. If you wish to use the task as a formative assessment task, have students work on their own to solve the problem (see Copymaster 5).  Otherwise, students may choose to work with a partner to decide on their choice of coins from the possible stacks.

1. Students work on the problem and record their solution and problem solving strategy on paper.

1. Either at the end of day 5 or on the following day provide time for students to compare their solution.  Ask them some of the following questions to prompt a discussion about the task:

• Which stack of coins did you choose and why?
• Did anyone else choose a different stack of coins?  If so, why?
• Does anyone want to change their mind now that they have heard some different choices?  If so, why?
• What problem solving strategies did you use to make your decision?
• Did anyone else solve the problem using a different strategy?
• Who do you think used the most efficient problem solving strategy?  Why?
• Do you think all of the grandchildren will be equally happy?  Why?  Why not?