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.
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.
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:
The context for this unit can be adapted to suit the interests and experiences of your students. For example:
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.
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.
For example:
Bull’s Eye Target $100
$90 + $10 = $100
$80 + $20 = $100
$75 + $25 = $100
$25 + $25 +$25 +$25 = $100
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).
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."
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.
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.
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:
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:
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.
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:
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.
Dear families 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 altogether that week. Find out how close they came with their estimate from Thursday!
Printed from https://nzmaths.co.nz/resource/money-marvels at 9:27am on the 2nd May 2024