Understanding Problems

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Understanding Problems
Lesson 1.2.7
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Lesson 1.2.7
Understanding Problems
California Standards Algebra and Functions
4.1 Solve two-step linear equations and
inequalities in one variable over the rational
numbers, interpret the solution or solutions in
the context from which they arose, and verify the
reasonableness of the results. Mathematical
Reasoning 1.1 Analyze problems by identifying
relationships, distinguishing relevant from
irrelevant information, identifying missing
information, sequencing and prioritizing
information, and observing patterns.
What it means for you
Youll learn how to spot which pieces of
information are important in answering a
question, and how to check that your answer has
the correct units.
Key Words

• relevant
• irrelevant
• unit

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Lesson 1.2.7
Understanding Problems
Math problems are full of all kinds of details.
The challenge is to work out which bits of
information you need and which bits you dont
need.
To be able to do this you need to understand
exactly what the question is asking.
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Lesson 1.2.7
Understanding Problems
You Cant Solve a Problem with Information Missing
Sometimes a piece of information needed to solve
a real-life problem will be missing.
You need to be able to read the question through
and identify exactly what vital piece of
information is missing.
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Lesson 1.2.7
Understanding Problems
Example 1
Brians mechanic charged 320 to fix his car.
The bill for labor was 157.50. How many hours
did the mechanic work on the car?
Solution
The question tells you that Brians total bill
for labor was 157.50. But to use this piece of
information to work out how many hours the
mechanic worked on the car you would also need to
know what the mechanics hourly rate was, as
hours worked bill for labor hourly rate.
You cant solve the problem as the mechanics
hourly rate is missing.
Solution follows
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Lesson 1.2.7
Understanding Problems
Guided Practice
In Exercises 14 say what piece of information is
missing that you need to solve the problem. 1.
Samantha is 20 inches taller than half Adams
height. How tall is Samantha? 2. A coffee bar
charges 2 for a smoothie. Sol buys a smoothie
and a juice. How much is his check? 3. Erin has
36 and is going to save a further 12 a week.
How many weeks will it take her to save enough
for a camera? 4. A box contains 11 large tins and
17 small tins. A large tin weighs 22 ounces.
What is the weight of the box?
Adams height is missing.
You need to know the cost of a juice.
The cameras price is missing.
You need to know the weight of a small tin.
Solution follows
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Lesson 1.2.7
Understanding Problems
Some Information in a Question May Not Be Relevant
You will often come across real-life problems
that contain more information than you need to
find a solution.
Information that you dont need to solve a
problem is called irrelevant information.
You need to be able to sort out the information
you do need from the information you dont.
A good example of this is a question where you
have to pick out the information that you need
from a table.
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Lesson 1.2.7
Understanding Problems
Example 2
At the hardware store Aura spent 140 on paint.
She bought four cans of blue paint and spent the
rest of the money on green paint. Use the table
below to calculate how many liters of green paint
she bought.
Solution
Aura only bought blue paint and green paint. So
you only need the circled data in these two rows
to answer the question.
The data about yellow and red paint is irrelevant.
This is all the information you need.
First work out how much Aura spent on blue paint.
You know that she bought four cans of blue paint
that cost 20 each. So she spent 80 on blue
paint. That means she spent 140 80 60 on
green paint.
To answer the question you need the price of a
can of blue paint, and the volume and price of a
can of green paint.
Each can of green paint is 30. So she bought
60 30 2 cans.
The volume of cans of blue paint is irrelevant,
as is the information about red and yellow paint.
A can of green paint is 1.5 liters. So she
bought 1.5 2 3 liters.
Solution follows
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Lesson 1.2.7
Understanding Problems
Guided Practice
Use the table from Example 2 in Exercises 57.
5. Eduardo bought one can of yellow paint and
three liters of blue paint. How much did he
spend? 6. Lamarr bought 2 cans of green paint and
some yellow paint. He spent 165. How many
liters of yellow paint did he buy? 7. Amber spent
120. She bought twice as much red paint as blue
paint. How many cans of red paint did she buy?
95
6 liters
4 cans
Solution follows
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Lesson 1.2.7
Understanding Problems
Answers Should Always Have the Correct Units
When you work out the answer to a problem, you
need to think about the right units to use.
If you apply the same operations to the units as
you do to the numbers, youll find out what units
your answer should have.
You can do this with any calculation to find the
correct units for the answer.
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Lesson 1.2.7
Understanding Problems
Laura drives her car 150 km in 2 hours. Use the
formula speed distance time to calculate her
average speed.
Solution
Speed distance timespeed 150 2 75
Now do the same operations to the units of the
numbers speed distance timespeed km
hours km/hour.
So the average speed of the car is 75 km/hour.
Solution follows
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Lesson 1.2.7
Understanding Problems
Solution
First do the numerical calculation.
Power Consumption Time Used Energy Used
0.5 4 2
Then work out the units.
kilowatts hours kilowatt-hours
The computer will use 2 kilowatt-hours of energy.
Solution follows
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Lesson 1.2.7
Understanding Problems
Guided Practice
Say what units the answers will have in Exercises
811. 8. 40 miles 2 hours 20 ? 9. 5 newtons
3 meters 15 ? 10. 6 persons 4 days 24 ? 11.
25 5 hours 5 ?
miles/hour
newton-meters
person-days
/hour
Solution follows
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Lesson 1.2.7
Understanding Problems
Independent Practice
1. The sale bin at a music store has CDs for 4
each. Eric buys four CDs and some posters, and
uses a coupon for 2 off his purchase. He pays
26. How many posters did he buy? Say what
information is missing from the question that you
would need to solve the problem.
You need to know the price of a poster.
Solution follows
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Lesson 1.2.7
Understanding Problems
Independent Practice
2. Liz meets Ana to go ice-skating at 7 p.m.
Admission is 8 and coffee costs 1.50. Liz has
14 and wants to buy some 2 bottles of water for
her and Ana to drink afterwards. Calculate how
many bottles of water Liz can buy. What
information are you given that isnt relevant?
3 bottles
You dont need to know who Liz meets, when they
meet, or the price of a cup of coffee.
Solution follows
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Lesson 1.2.7
Understanding Problems
Independent Practice
3. Sean has 60 to buy books for math club. A
book costs 9.95. He orders them on a Monday.
Shipping costs 10 an order. How many books
could he buy? What information are you given
that isnt relevant? Say what units the answers
will have in Exercises 47. 4. 4 persons 4
hours 16 ? 5. 100 trees 10 acres 10 ? 6. 6
meters 7 meters 42 ? 7. 21 meters/second 7
seconds 3 ?
He could buy 5 books.
You dont need to know what he gets them for or
when he orders them.
person-hours
trees/acre
meters meters, or meter2
meters/second/second, or meters/second2
Solution follows
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Lesson 1.2.7
Understanding Problems
Round Up
When youre solving a math problem, you need to
be able to pick out the important information.
Then you can use the relevant bits to write an
equation and find the solution.
Always remember to check what units your answer
needs to be written in too.