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Proportional Thinking

Proportional Thinking. Decimals, Rate, Ratio and Percent. What is proportional thinking?. 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

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Proportional Thinking

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  1. Proportional Thinking Decimals, Rate, Ratio and Percent

  2. What is proportional thinking? • 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. What is ratio? • 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. Types of ratios • 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. Ratios and fractions • 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. Famous Ratio • 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. What is rate? • 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. Equivalent ratios and rates • 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. Onion Table

  10. Graphing Equivalents Ratios and Rates • 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. What is percent? • 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 Principles • 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. Unit Rates • 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. Relating and Comparing Ratios and 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.

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