Transcript Calc10a-Problemsx

MATHEMATICS
Solving Wordy Problems
• The aim of this powerpoint is to teach you techniques
which should help you solve worded problems.
EITHER
• Take notes as you go along, include some examples and
write down any questions and your answers (which you
can mark as you go along)
OR
• At the end of both this powerpoint and the calculators
powerpoint, printout the notes called Calc-10
Words that imply ADD
• These words all mean add…
Sum
Total
Altogether
Increase (by a value)
• but there are many others that imply it in context…
Words that imply ADD in context
E.g.
Amy has 23 marbles. Bob gives her another 17.
How many marbles does she have now?
Solution: 23 + 17 = 40
E.g.
Cathy has 14 more sweets than Dan who has 45.
How many sweets does Cathy have?
Solution: 45 + 14 = 59
E.g.
In January Scott was 134cm tall. By June he had
grown another 4cm. How tall is in June?
Solution: 134 + 4 = 138cm
Words that imply SUBTRACT
• These words all mean add…
Minus
Difference
Take away or Take off
Less (a value)
Deduct (a value)
Decrease (by a value)
• but there are many others that imply it in context…
Words that imply SUBTRACT in context
E.g.
Fred has 23p. He spends 9p.
How many money does he have left?
Solution: 23 – 9 = 14p
E.g.
May has 14 fewer marbles than Tom who has 45.
How many marbles does May have?
Solution: 45 – 14 = 31
E.g.
Phil’s t-shirt was originally 55cm long but it shrank in
the wash to 48cm in length. By how many
centimetres did it shrink?
Solution: 55 – 48 = 7cm
Words that imply MULTPLY
• These words all mean add…
Multiple
Times (by)
Lots of
Product
Increase (by a factor or multiplier)
each
Double, Triple or Quadruple
*fold
Square or Cube
• but there are many others that imply it in context…
Words that imply MULTIPLY in context
E.g.
Each coach can transport 48 people.
How many people can be transported by 5 coaches?
Solution: 5 x 48 = 240
E.g.
A rectangle has measurements 6m by 8m.
What is its area?
Solution: 6 x 8 = 48m²
E.g.
Barbara gets paid £5 per hour.
How much would she get paid for working 24 hours?
Solution: 24 x 5 = £120
Words that imply DIVIDE
• These words all mean add…
Factor
Divide (by)
Share (by)
Quotient
Decrease (by a factor or multiplier)
per
Halve, Third or Quarter
(the bottom value of a fraction)
• but there are many others that imply it in context…
Words that imply DIVIDE in context
E.g.
Each box contains 6 eggs.
How many boxes can be filled by 84 eggs?
Solution: 84 ÷ 6 = 14
E.g.
A car travels at 30 miles per hour. How many hours
does it take to cover a distance of 240 miles?
Solution: 240 ÷ 30 = 8
E.g.
A basket scores 2 points. If Ben scored 32 points in
one match, how many baskets did he score?
Solution: 32 ÷ 2 = 16
Multi-Step Problems
• Some problems mean you have to undertake several
calculations before you get to the final answer.
• Work through the problem one step at a time
• Sometimes unnecessary information is given.
• Discard this! It’s been put in to trick you!
• Let’s look at an example…
Example
E.g.
Michelle had 45 marbles. She gave 17 of them to
her friend Mavis who already had 5 marbles.
Michelle then gave half of what she had left to Gary.
How many marbles did Michelle give to Gary?
The un-necessary information is that Mavis had 5 marbles!
Step by Step: Michelle had 45 marbles.
She gave 17 of them to Mavis
She then had 45 – 17 = 28
She gave half of these to Gary
So she gave Gary 28 ÷ 2 = 14
What next?
• Work through the MyMaths lesson (and then the online
homework) called Word Problems found at:
http://app.mymaths.co.uk/1425-resource/word-problems
•
http://app.mymaths.co.uk/1425-homework/word-problems
• Work through pages 2, 5, 7 & 8 of the MyMaths lesson
(and then the online homework) called Introducing
Money found at:
• http://app.mymaths.co.uk/102-resource/introducing-money
• http://app.mymaths.co.uk/102-homework/introducing-money
• Save and complete the worksheet called: Probs-S1.xlsx
• Now move on to the Calc10b-Calculators powerpoint