Working Mathematically I

Useful Terminology

• Sum - the sum of two numbers means to add the two numbers together.
• Difference - the difference between two numbers can usually be found by using subtraction
• Product - the product of two numbers is the answer when the two numbers are multiplied together
• Quotient - the answer obtained by dividing one quantity by another

 

When looking at 'word' problems

Problem solving can be a tricky process.  Here are a few points that might help you when tackling a problem.

• Read it once to get an idea on what the problem is about
• Read it again and highlight key words, or facts you will need to solve your problem
• Sometimes diagrams, sketches or pictures can help visualise the problem.  
• Identify the operations or mathematics you will need to use
• Go about solving the problem, this might involve trial and error, guess and check, algebra or number calculations.
• Answer the question - don't forget the right units

 

Let's look at an example of a question applying some of the problem solving ideas above.

Example

 

Question 1

Lachlan is four years older than Quiana. Twice Lachlan's age plus four times Quiana's age is 26. What are their ages?

Problem Solve:

• Read once to identify what the problem is about.  Ask yourself - what am I trying to solve?
• Read again to identify key parts of the problem and highlight key words.

Lachlan is four years older than Quiana. Twice Lachlan's age plus four times Quiana's age is 26. What are their ages?

• I might try a quick diagram to see if that helps me. Remember diagrams aren't for everyone, but if it helps then go for it!

So I know that Lachlan is older, (by 4 years)

And I know that 2 x Lachlans age + 4 times Quiana's age = 26.  I'm going to be systematic, but use a guess and check method.

Lachlan	Quiana	$2\times\text{Lachlan }+4\times\text{Quiana }$2×Lachlan +4×Quiana	Check
$5$5	$1$1	$2\times5+4\times1=14$2×5+4×1=14	not enough
$6$6	$2$2	$2\times6+4\times2=20$2×6+4×2=20	still not enough, but getting closer
$7$7	$3$3	$2\times7+4\times3=26$2×7+4×3=26	Perfect - this is what we need!

So Lachlan is $7$7 and Quiana is $3$3.  

 

Question 2

Question 3