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Problem Solving Series Book 1

Strategies and techniques covering all strands of the curriculum, with activities to reinforce each problem solving method.

Problem Solving Series Book 1 by Val Morey
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This blackline masters book contains a learning outcomes approach to mathematics education meaning students and teachers need many and varied opportunities for students to demonstrate their learning and their understanding.  In order to make more accurate assessments of students’ understanding, and therefore place them carefully within the levels described in the curriculum document, activities are needed which address two important aspects: The activities provided in this book are based on realistic situations which school students of age 9 - 10 could expect to be familiar with or to face. The strategies in this book include: Guess and Check;  Create a Diagram;  Use a Table;  Logical Reasoning;  Make a Table;  Find a Pattern;  Work Backwards;  Solve an Easier Version. Each strategy is applied to problems across the math curriculum incorporating the strands of: Number Space Measurement Chance & Data

To be as accurate as possible in determining students’ current level of numeracy, those students must be given opportunities to demonstrate their understanding through activities which really show what they are able to do, as well as what they are not. Scoring 100% in a page of exercises tells teachers that a student has learnt what was taught, and can be useful information for checking that criteria have been met, but may not be a demonstration of their true or full mathematical understanding.

Ready-Ed Publications; June 2002
52 pages; ISBN 9781863974622
Read online, or download in secure PDF format
Title: Problem Solving Series Book 1
Author: Val Morey; Terry Allen
 
Excerpt

Student Information Page: Make a List

This strategy is easy to use and helps you to "think straight". Sometimes a problem does not involve any real calculating, but there is just too much information for you to handle in your head – so, you write it down.

Making a list means you can think about each part in turn without worrying that you will forget the parts that came before.

Let’s say you wanted to buy a birthday present for your friend and your Mom said you could buy one box of Lego® and one toy car. When you went to the toy shop, you found 5 different Lego® sets and 4 different toy cars to choose from. How many different ways could you make a present of a toy car and a Lego® set?

It would be very hard to try and think of all the ways you could do it without writing them down. But there is nothing difficult to actually work out. You only have to make sure you haven’t missed any items out.

Here’s how the "Make a List" strategy helps.

You need to find a system to write down all the possible ways you can do it and stay "in the rules". The rule this time is to have one Lego® set and one toy car.

Start by listing all the Lego® sets and toy cars separately:

  • Pirate Pete Porsche
  • Bob the Builder Mercedes
  • Jack Stone Ford
  • Dinosaur Chrysler
  • Space Vehicle

Now start with the first Lego set and match it to each toy car in turn:

  • Pirate Pete with: Porsche
  • Pirate Pete with: Mercedes TOTAL: 4 combinations
  • Pirate Pete with: Ford
  • Pirate Pete with: Chrysler

Now do the same for the next Lego® set:

Bob the Builder with: Porsche, Mercedes, Chrysler, Ford. Total = 4.

You should be able to see that for each one of the Lego® sets, there will be 4 different ways you could make the present.

You know there are 5 different Lego® sets, so there will be 5 lots of 4. Altogether, there are 20 different ways you could make a present from the toys at that shop.

Can you work out how many there would be if you found another different Lego® set?