Mrs Parore's Laundry
Use simple problem solving strategies;
Solve a simple problem involving number.
This problem is at the beginning of problem solving. It should help the students see how to use simple strategies such as use equipment and draw pictures. It’s also a good way to get them to start counting in twos.
The problem is also at the beginning of looking for patterns. By looking at different numbers of towels when two pegs are used, the students can begin to see that there is the pattern of doubling. If one peg is used between a pair of towels, the students can find another pattern.
Naturally patterns are at the base of mathematics. Almost all mathematical activity is aimed at finding a pattern of some sort. Theorems, the true statements of mathematics, are ways that sophisticated patterns are expressed. For instance, Pythagoras’ Theorem, that says that the square of the length of the hypotenuse is the sum of the squares of the lengths of the other two sides, is a pattern about the lengths of the sides in a right-angled triangle.
We’ve posed two types of problem here. One depends on using two different pegs for each towel. The other uses two pegs per towel but some pegs can be used on two different towels. You may like to use these two methods of hanging clothes in two different lessons.
- Mrs Parore is hanging out her towels to dry. She puts two pegs on each towel. If she has 4 towels, how many pegs will she need?
- Mrs Parore sees that her peg box is running low. So she puts one peg on the corner of two towels. This way she only needs 3 pegs for 2 towels. How many pegs will she need for 4 towels now?
- Talk about washing.
Does your family hang clothes out on a line?
Can you show me how she hangs out her clothes to dry?
How does she use the pegs?
- Get some of the students to hang out some ‘washing’ on a line in the classroom. Let them use two pegs per piece of clothing.
How many pegs did they use?
- Tell them Mrs Parore’s first problem. Let them go back to their seats to solve the problem.
- Help groups that need it. For the quicker groups, encourage them to try the Extension.
- Let a few groups report back to the whole class.
Mrs Parore needed to use 12 pegs to hang out her towels. (Two pegs per towel and each peg is only used to hang one towel.) How many towels did she wash?
If Mrs Parore is using the peg-saving method of hanging out her washing, how many towels can she hang with 9 pegs?
If students are using a drawing strategy, they will draw four shapes for the towels. Then they will put two ‘pegs’ per shape. Counting the peg shapes gives 8 pegs.
Using equipment for the second type of problem, they might link the ‘clothes’ with paper clip ‘pegs’. Once four towels have been strung together the students can count the 5 pegs that are needed.
Solution to the Extension:
The students first need to draw 12 pegs. Then they might draw a towel and joining two of the pegs. They then repeat this until they have joined all 12 pegs in pairs. It’s now just a matter of counting the 6 towels they have drawn.
Using equipment, the students should first count out the 9 pegs. They then join up the towels with the pegs. Finally they can count the 8 towels that they have hung up.