Money marvels
In this unit students are given the opportunity to explore various combinations of coins and dollars that add to make given totals. Within this context of money problems students will practise using flexible mental strategies including rounding, estimating, and finding compatible numbers.
About this resource
Specific learning outcomes:
- Find compatible numbers for totals such as 10, 20, 50, and 100.
- Use various dollar and coin amounts to make the given totals.
- Round money amounts to the nearest 50 and 10.
- Use rounding to estimate totals.
Money marvels
Achievement objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Description of mathematics
In this unit of work, students will develop their ability to make sensible estimates, use rounding as a strategy to help in their estimation, and combine money amounts to make compatible numbers for ease in adding and estimating totals.
Opportunities for adaption and differentiation
The learning opportunities in this unit can be differentiated by providing or removing support for students and varying the task requirements. Ways to support students include:
- Using materials (e.g., hundreds boards, Slavonic abacus) to show compatible numbers Some students might be encouraged to move to imaging and mental operations.
- Preparing students for this unit with additional activities that build their understanding of 100 cents in one dollar.
- having children record their additive and/or multiplicative thinking, e.g., 20 cents + 20 cents + 20 cents + 20 cents = 80 cents or 4 x 20 cents = 80 cents
- Varying the complexity of the numbers used in each activity.
- including other target options for the "Bulls eye target" activity
- providing time for students to make up new problems to be solved by their peers
- providing opportunities for individual, grouped, and paired work
- strategically organising students into pairs and small groups in order to encourage peer learning, scaffolding, and extension
- working alongside individual students (or groups of students) who require further support with specific areas of knowledge or activities.
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 10 cents?) and compare with other countries.
- Discuss what giving a koha means if you are attending a tangi, wedding, christening, or conference at a local marae. Are there similar situations in other cultures?
Te reo Māori kupu, such as moni (money), tāra (dollar), hēneti (cent), and tatau (count), could be introduced in this unit and used throughout other mathematical learning.
You could also encourage students who speak a language other than English at home to share the words related to money that they use at home.
Required materials
- play money
- calculators
- materials to support thinking (e.g., counters, number lines, slavonic abacus)
See materials that come with this resource to download:
- Money marvels bull's eye target CM (.pdf)
- Money marvels compatible number puzzle CM (.pdf)
- Money marvels stack it up CM (.pdf)
- Money marvels more or less than CM (.pdf)
- Money marvels what's for lunch CM (.pdf)
Activity
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 group's 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 that after you call out a number, you give students a few seconds to think of a 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 or 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, while students in need of greater support might benefit from working in a small group with the teacher.
3.
Use Money marvels bull's eye target CM to introduce Hit the Bulls Eye Target! This challenges students to find combinations that add up 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 for 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.
What is for lunch? - lunch menu
In this session, students are presented with a lunch menu with food choices and prices (see Money marvels what's for lunch CM). 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 on 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 Money marvels what's for lunch CM. 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.
Compatible number puzzle
In this session, students will attempt to match puzzle pieces (see Money marvels compatible number puzzle CM) 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 Money-marvels-compatible-number-puzzle-CM. 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 of $20, you might record:
- $17.90 + $3.10 = approximately $20 (more)
- $15.90 + $3.50 = approximately $20 (less)
3.
Have students compare their Compatible Number Puzzle decisions. See if they agree with each other about which puzzle pieces equal more or less than $10, $20, or $30. Have them justify their decisions and explain their rounding-off strategies to each other.
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 Money marvels more or less than CM). Students will need to have strategies for 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 to 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 make $10.00 exactly, so $4.99 is less than $5.00. Therefore, two 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, $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, while 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 number of 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.
Does it stack up?
This session introduces a problem-solving task that 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 to 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, which 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 solutions. 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 about 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 learn 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.
Home link
Dear parents and whānau,
This week, your child would like to do some chores and jobs at home for 10c, 20c, or 50c. Each day, they are to record the jobs they have done in a diary and how much each job is worth. On Thursday, they are to estimate whether or not by Friday they will make more than, less than, or exactly $3.00. On Friday, they will total the jobs and the amount they have earned so far that week. Find out how close they came with their estimate from Thursday!
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