1. Decimals, Rate, Ratio and Percent

2.  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

3.  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.

4.  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.

5.  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?

6.  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

7.  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.

8.  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.

9. OnionsCost ($) 6 12 18 24 30 5 10 15 20 25

10.  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.

11.  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?

12.  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

13.  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

14.  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.