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Symmetry, Solving Word Problems (routine
and non routine)
(a) PROBLEM SOLVING TIPS
(i) KEEP TRYING
When you work on a problem, your first try may not work out.
Don't worry and don't give up. Just look at what you've done
and give it another try.
(ii) TAKE CHANCES
You can't solve a problem without giving it a try. Take your
best shot. You've got nothing to loose.
(iii) STAY POSITIVE
Next time you're working on a tough problem, remind yourself
how good you'll feel when you find a solution.
(iv) USE WHAT YOU KNOW
When you have to solve problems, use your experience. Look
for things that are familiar. Maybe you'll remember a method
that you've used or seen before.
The more you practice the better you'll get. With each prob-
lem you work on, you learn something new, and you become
better prepared to solve problems.
(vi) WATCH WHAT YOU DO
As you work on a problem, keep an eye on the method you're
using. If you think you're on a road to nowhere, you should try
a different method.
(vii)TAKE A BREAK
When you feel you've tried everything you can think of, it may
be time to take a break for a while. Give your brain a chance to
STRATEGIES FOR SOLVING ROUTINE PROBLEMS
Strategy 1 - Using the 5 point checklist.
To Solve a Problem the 5-point checklist can help you organise
your attack. This works for Routine problems
1. Understand the Problem
2. Find the data you need
3. Plan what to do.
4. Do the computation
5. Check back
EXAMPLE: One year Mr Lewis grew 356 hectares of toma-
toes, Mr Jones grew 274 hectares and Mr Lalla grew 519
hectares. How many less hectares of tomatoes did mr Lalla
grow than the combined hectares of Mr. Lewis and Mr. Jones?
To solve the Problem
UNDERSTAND THE PROBLEM
You need to find out how much less hectares Mr Lalla grew
than Mr. Lewis and Mr. Jones combined.
Find the data.
PLAN WHAT COMPUTATION YOU SHOULD DO
To find the combined hectares you must add, then subtract
Mr. Lalla's hectares.
Do the computation
356 + 274 is 630.
Mr Lalla grew 111 hectares less than Mr Lewis and Mr Jones com-
CHECK BACK: 356 + 274 is 630
Strategy 2:- Follow this four step plan that acts like a map to help
you. It won't work the problem for you, but it can help you find a
way to solve it. When you get stuck on a problem, you should try
the four step plan.
Step 1: Use these hints to help you understand the problem;
Read it over, slowly.
Take notes or draw pictures to help.
Study any charts or drawings given.
Look up any words or symbols you don't know.
Step 2: Take a little time to plan what you can do to solve it.
You can try one or more strategies.
Step 3: Carry out your plan. Work carefully and keep thinking
while you work. Remember, if your first try does not work,
try something else.
Step 4: After you find an answer, go over what you've done.
Does the answer make sense?
Does it really answer the question asked?
Is your computation correct?
If you try another way would you get the same answer?
(c) PROBLEM SOLVING for routine and non routine problems
There are many problem solving strategies to choose from.
REMEMBER! You can use more than one strategy to solve a
You can use a strategy that is not on the list.
You can use whatever strategy works for you.
Act it out
Draw a diagram.
Make a table.
Use simpler numbers.
Make a graph.
Write an equation.
Guess, check and revise
Finding a pattern
Logical reasoning, etc.
Samples: Let us look at 3 strategies.
(1) WORK BACKWARDS
If you know the end and you know the steps in between, you can
find the beginning by going step by step in reverse order.
A good plan is to start with some given information and then work
Some problems start with the end result and ask for something
that happened earlier. The strategy of working backwards or back-
tracking can be used to solve these problems.
To use this strategy, start with the end result and undo each step.
Hint: use the opposite operation when going backwards.
A school held a cake sale to raise money for the sports fund, the
field trip fund and the charity fund.
The money collected was divided in the following way; Sports 1/3 of
the total, field trip 1/6 of the total and the rest to charity.
If Charity received $900, what was the total collected?
1/3 + 1/6 + $900 = Total money collected.
1/2 + $900 = Total
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