Money marvels

Session 1

Hit the Bulls Eye Target!

In this session students practise combining whole numbers in different ways, therefore 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 play money to help them with the task as well as counters or calculators. 

1. Before introducing the Hit the Bulls Eye Target!, revise combinations to 10, 20, 50 and 100 with students.  Start by having them 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. 
    
2. At first, call out numbers to make 10 in sequence, beginning with 1 + ? = 10, then 2 + ? = 10 and so on. Eventually, with practice, you should be able to randomly call out a number and have students 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. Students ready for extension could repeat this in small groups, perhaps with larger numbers, whilst students in need of greater support might benefit from working in a small group with the teacher.
    
3. Use Copymaster 1 to introduce Hit the Bulls Eye Target! This challenges student to find combinations that add to $100. Provide play money for students to use. Model its use and have students work with a partner to make a combination using the play money. E.g. $40 + ? = $100. Revise relevant addition and multiplication strategies in reflection of your students' needs.
    
4. Have students record as many possible combinations to "hit" the $100 target on a piece of paper (you might provide a table or model constructing a list). 

For example:

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

5. Share their combinations with the class.

Session 2

What is for Lunch? – Lunch Menu

In this session students are presented with a Lunch Menu with food choices and prices (see Copymaster 2).  Students are given $5.00 in play money with which to buy their lunch, choosing items from the Lunch Menu.  Students are to record as many possible lunch combinations that they can buy for $5.00. You could change the context of this session to focus around different culturally relevant food items at an imaginary tuck shop (perhaps your students could each contribute the name of one item).

1. Discuss your own school’s Lunch Menu, favourite lunches, favourite cafes, favourite shared meals etc. (whatever is relevant to the context you have posed). You might also look at lunch menus from the past, or have students ask members of their whānau what they could buy to eat when they went to school. 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
• 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."

2. 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. Students ready for extension could be challenged to find as many different combinations as possible that will make $10.00, $15.00 etc. 
3. Provide time for students to share their findings with another pair or small group.  

Session 3

Compatible Number Puzzle

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, and $30.  Students will be required to round off numbers, mentally, 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.

1. Revise rounding off strategies with students.  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. You might pose the following questions for students to answer:
   • 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?
      
2. 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. Model how to record the answers. For example, when finding combinations to $20, you might record:

• $17.90 + $3.10 = approximately $20 (more)
• $15.90 + $3.50 = approximately $20 (less)
   

1. 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?

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 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 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

   Continue with warm up problems until students demonstrate confidence using mental strategies like rounding off, using compatible numbers and adding dollars first to make sensible estimates about total amounts. You might work with some students in a more targeted manner, whilst others work in pairs or small groups on the problems.

2. Introduce the More or Less than $20? task. Ensure students understand that they need 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.

3. 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.
4. Have students work alone or with a partner and estimate whether the number tags combined total more or less than $20.  They should 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. 
    
5. Provide time for students to share their work with another pair, group, or individual.

Session 5

Does it Stack Up?

This session introduces a problem solving task which requires students 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. 

1. Introduce the problem. Brainstorm some possible solution methods with students.  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. Students ready for extension should be encouraged to think of basic multiplication and addition facts they can use to solve the task.
2. Have students work on their own to solve the problem. Ensure they record their solution and problem solving strategy (you might model how to do this).
3. 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?
4. Revisit all of the tasks used throughout the week. You could have students compile a Money Marvels book with their mathematical work and learning about money from other curriculum areas (e.g. pictures of different currencies, facts about money). Alternatively, you could create one large book, video, or poster as a class.