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Everyday Math Book 3

Stimulating word problems for upper primary students

Everyday Math Book 3 by Jane Bourke
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The idea of problem solving activities often conjures up images of numbers and objects that have no direct meaning for students other than teaching the basic problem solving strategies. The blackline master activities in this book are designed to present real-life problems in a realistic context so as to provide children with situations in which everyday problem solving and comprehension skills are required.

The activities are based around recurring cartoon characters ? named Archimedes, Pythagoras and Gaileo ? who find themselves exposed to a range of problems that need to be solved; the sort of problems that students may one day encounter.

Most sheets include a challenge activity, usually an extension of the main problem, which will further consolidate comprehension skills. Included throughout the book are brainteaser Sheets which focus on a particular problem solving strategy, highlighted at the foot of the Page. These brainteasers can be photocopied and individually glued on to card so as to create a set. Students might like to think up their own brainteasers to add to the set.

Problem Solving Strategies

There are many strategies for solving everyday math problems. Some of the main problem solving strategies have been explained below. In some cases examples of problems are given where the particular strategy can be applied.

Guess and check:
Probably the first strategy children might try and definitely the easiest. By making a guess and checking their answer, children have a point of reference on which to base all other guesses.

An example:
I am thinking of two consecutive numbers that when multiplied give 182. A guess might be to try 14 x 15 which would give 210. Obviously the next guess would try lower numbers.

Act it out:
Students quite often need to visualize the problem, especially where people or objects are concerned. Counters, coins and students can be used to help solve the problem.

Examples:
There are 48 players in the darts championships. Each player stays in the competition until they lose a game. How many games must be played to find the club champion?

A caterpillar crawls 2 m up a tree every day. Every night it slips back 50 cm. The tree trunk is 10.5 m tall. How long will it take for the caterpillar to reach the top of the trunk?

Make a model:
When problems cannot be acted out the next best thing is to make a model using cubes, matches, and so on.

Make a drawing, diagram or graph:
Graphs and diagrams are particularly useful for trying different combinations or clarifying information.

An example:
Jack has a rectangular field that has an area of 360 m. What are the possible dimensions of the rectangle?

Look for a pattern:
This strategy can be used in many number and space activities to help simplify the problem.

Number patterns: It takes three matches to make a triangle, 5 matches to make 2 triangles. How many matches are needed to make 3 triangles?

Spatial Patterns: How many squares are there on a checker board?

Construct a table:
By organizing data in a more meaningful way children can better see relationships, patterns and possibly missing information. This strategy is best used where different information is given about each person or object in the problem. A table can include all the information and eliminate irrelevant information.

An example:
Tim, Peter, Max, Jane, Tarnie and Kelly each play sport over the weekend. They all play a different sport. Match the person to their sport based on the following:
Tim doesn?t like swimming but enjoys baseball;
Peter likes tennis more than swimming;
Kelly enjoys netball;
Max won?t play hockey;
Jane doesn?t like baseball or diving;
Tarnie plays the sport that Max doesn?t like.

Ready-Ed Publications; January 2001
40 pages; ISBN 9781863971690
Read online, or download in secure PDF format
Title: Everyday Math Book 3
Author: Jane Bourke; Rod Jefferson
 
Excerpt

Life in the Wheel World

Pythagoras has been cycling around the lake. His bike is fairly old and one brake pad has worn away on the front wheel. A certain part of the wheel always touches the brake pad making a short grinding noise. It only does this once every revolution.

Pythagoras has been meaning to buy an odometer for his bike so he can measure the distance around the lake. However he has decided to use his brain instead. He knows that he has 48 cm diameter tires on his bike and thinks he can work out the circumference. He has placed the wheel so that it will grind immediately and is going to count the noises he hears.

Pythagoras counted 250 grinding noises when he rode once around the lake.

1. Approximately how far in meters is the distance around the lake?

How many grinding noises should Pythagoras expect to hear if he rides:

2. Three times around the lake?

3. Five times around the lake?

4. Exactly half way around the lake?

5. If he rides for exactly four and a half kilometers?

6. If he rides at twice the speed around the lake once?