Proportional ThinkingDecimals, Rate, Ratio and Percent

How are two things related multiplicatively. Example: thinking of six as two threes

instead of 4 + 2. 16 = 8 x 2 rather than 16= 8 + 8 Give other examples of your whiteboards Learning Goal: to think about thinking

proportionally

What is proportional thinking?

Compares quantities within the same unit For example: Grade 7: Grade 8 in the class (the unit

would be students) What would this ratio be?

17:8 We would call 17 the first term of the ratio. We would call 8 the second term of the

ratio.

What is ratio?

Part to whole ratios compare one part to the whole thing. So 8:25 would describe what ratio in our class?

Grade 8: whole class Part to part ratios compare two parts of

something. What would be the ratio if we compared girls to boys in the class?

14:11 On your whiteboards, come up with other

ratios to describe the class.

Types of ratios

How would we write the ratio of grade 8: Grade 7 as a fraction?

8/17 How about the ratio of boys to girls? 11/14 The ratio 1: 14 represents the number of

girls named Amber to the number of girls in the class. What would it be as a fraction?

What can we observe about fractions and ratios?

Ratios and fractions

One of the most famous ratios is the ratio of the circumference (outside) of a circle to the diameter (across the middle) of a circle.

This ratio is 3.14:1. What else is this know by?

Pi

Famous Ratio

Rate compares quantities with different units but are very similar to ratios. Some mathematicians don’t see any difference at all. Do you?

Rates include things such as distance to time or price per number of items.

Come up with an example of a ratio problem on your whiteboard.

What is rate?

Remember equivalent fractions? Write equivalent fractions for ½ Now write equivalent ratios for 1:2 This is very handy when shopping. For

example, if 6 onions are $5 but I only want 3 onions, I know it will cost $2.50 because they are equivalent rates.

Make a table on your whiteboard to show how much 12, 18, 24 and 30 onions would cost.

Equivalent ratios and rates

Onions Cost ($)

612182430

510152025

Onion Table

You can also use a graph to represent rates or ratios and find equivalent ratios or rates.

make a line graph of our onion table with your table group on a whiteboard.

What do you notice? each ordered pair (6,5), (12, 10) is an

equivalent ratio.

Graphing Equivalents Ratios and Rates

A percent always compares a quantity to 100.

Think of percent as a special ratio in which the second term is always 100.

Give an example of a percent problem on your white board.

When do we use percent in real life?

What is percent?

Percent can be written as x:100 or x/100 or as an equivalent decimal.

Percent can be as low as zero and more than 100

Comparing presents is easy as you are comparing whole number values. Ex: what is more 25% or 75%?

Sometimes presents describe change

Percent Principles

A UNIT RATE is an equivalent rate where the second term is 1.

For example, if I drive 30km in 20 minutes the rate is 1.5 km per minute or 1.5:1

This is also handy for shopping! Solve the following problem in your table

groups on white boards: Which is the better buy: 3.6 litres of brand A

dish soap for $3.69 or 4 litres of brand B for $4.29?

Soap A

Unit Rates

Similar to fractions, we can easily compare ratios or rates with the same second term (what does this remind you of???)

So…if 6:25 represents the number of equestrians in the class and 15:25 represents the number of teams sports players, it is easy to see that there are more team sports players in the class.

Relating and Comparing Ratios and Rates