 |
|---|
Problem
Lee and Jamie have decided to buy their father a card for Fathers’ Day. The card is going to cost $5.95. Lee puts in 35c more than Jamie. How much does each child contribute to the card?
What is this problem about?
At its simplest this problem involves a two-digit subtraction and then a division by 2. But the problem can be done equally well with equipment to represent money or by guessing and improving or by a number of other ways. The problem becomes more interesting and linked to number understanding when you consider the suggested extensions.
When the children write their own problem it’s very important that when they take the difference between what the two children have, away from the cost of the object, the answer is even. Otherwise they can’t divide the answer by two!
In the three-person problem there are similar hurdles to overcome. Not every set of numbers will work. These extensions require the children to think about the multiples of numbers.
Achievement Objectives
- write and solve problems which involve decimals and which require a choice of one or more of the four arithmetic operations
Mathematical Processes
- devise and use problem solving strategies (act it out, draw a picture, guess and
improve, make a table)
- use equipment appropriately
Resources
Blackline master of the problem (Maaori)
Specific learning Outcomes
The children will be able to:
- subtract using decimals
- find ½ of a decimal number
Teaching Sequence
- Read the problem with the class. Ask them to identify the important pieces of information.
- Give the children time to think about a possible way of solving the problem before requiring them to work with others. Often it is the child who first comes up with an idea that determines the strategy that the group follows.
- Circulate asking children to explain the strategy that they are using.
- Focus their thinking on the maths by asking them to explain their subtraction/division of decimals and how they know that their answer is reasonable.
- Share solutions.
Extension to the problem
Get the children to write a similar problem but with bigger numbers.
When they’ve done that they might like to try one with three people buying something.
Other contexts for the problem
Purchasing presents
Solution
Perhaps the neatest way to do this is to notice that if Lee had not put in the extra 35c, they would have only paid $5.60. However, they would have each given the same amount then. So first subtract Lee's additional contribution 5.95 - .35 = 5.60.
Now divide the remainder by 2 to find Jamie's share 5.60 ¸ 2 = $2.80.
Lee contributed 2.80 + .35 = $3.15.