MFM 1P. Foundations of Mathematics Grade 9 Applied Mitchell District High School. Unit 2 Proportional Reasoning 9 Video Lessons

Transcription

1 MFM 1P Foundations of Mathematics Grade 9 Applied Mitchell District High School Unit 2 Proportional Reasoning 9 Video Lessons Allow no more than 14 class days for this unit! This includes time for review and to write the test. This does NOT include time for days absent, including snow days. You must make sure you catch up on class days missed. Lesson # Lesson Title Practice Questions Date Completed 1 Fractions Handout 2 3 Working with Rationals - Multiplying and Dividing Working with Rationals - Adding and Subtracting Handout (Same Handout as Lesson 2) 4 Equivalent Ratios 5 Ratio and Proportion Page 112 #1-5, 7-9 Page 117 # Ratio and Proportions Using Algebra Page 133 #1-6 7 Unit Rate Page 123 #1-9 8 Percent as a Proportion Page 137 # Putting it all Together - Applications of Proportion complete the proportional problems left on the note Test Written on :

2 MFM 1P U2L1 Fractions Topic : Goal : Fractions I know what a fraction is and how to change between fractions and decimals. What is a Fraction? A fraction compares pieces you have to the pieces that would be in a whole thing. If we cut a pizza into 8 slices, each slice is said to be one eighth.

3 MFM 1P U2L1 Fractions Working with Fractions Changing a Fraction to a Decimal Pull Pull Comparing Fractions Place the fractions in order of smallest to largest. Check you are right by turning them into decimals

4 MFM 1P U2L1 Fractions Changing Decimals to Fractions Change to a fraction. Step 1 Step 2 Step 3 Examples: Express in fractional form in lowest terms. a) 3.05 b) c) 8.75

5 MFM 1P U2L1 Fractions Practice

6 MFM1P U2L2 Working with Rationals - Multiplying & Dividing Today's Topic : Fractions Today's Goal : I can multiply and divide fractions If you don't have a calculator with a fraction button, now is a good time to get one. For today, you can trade me for one. Working with Rational Numbers (i.e. Fractions) Your fraction button will look like a b/c To enter a fraction a b/c 3 it may look like this - if so we need to talk :-) a b/c 2 a b/c 3 3

7 MFM1P U2L2 Working with Rationals - Multiplying & Dividing Mixed vs. Improper Fraction An improper fraction has a bigger number on top than the bottom. A mixed number has a whole number and a fractional part. Mixed to Improper Improper to Mixed

8 MFM1P U2L2 Working with Rationals - Multiplying & Dividing Multiplying Rationals x 2 5 Step 1 Change to an improper fraction Step 2 Multiply the numerators Step 3 Multiply the denominators Step 4 Reduce to lowest terms if possible. Dividing Rationals Step 1 Change to an improper fraction Step 2 Flip over the divisor (2nd fraction) Step 3 Multiply as normal. Step 4 Reduce to lowest terms if possible. Practice Questions - Handout Page

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10 MFM1P U2L3 - Adding and Subtracting Fractions Topic : Goal : Fractions I can add and subtract Rational Numbers (fractions). Adding and Subtracting Fractions

11 MFM1P U2L3 - Adding and Subtracting Fractions Adding and Subtracting a) Step 1 Change to an improper fraction Step 2 Look at both denominators and find the smallest number they both divide into. This is finding a common denominator. Step 3 Multiply both numerator and denominator of each fraction to get the common denominator. Step 4 Add/Subtract the numerators, keeping the denominators the same. Reduce your answer to lowest terms (if needed) b) c) Practice Questions - Handout Page

12 MFM1P U2L4 - Equivalent Ratios Topic : Goal : equivalent ratios I can recognize and write ratios that are equal in various forms. Equivalent Ratios A ratio is in lowest terms if there is no whole number that will divide evenly out of all parts of the ratio. Two ratios are equivalent if they are the same when reduced to lowest terms. Example 1. What fraction of each diagram is yellow? Reduce to lowest terms. What do you notice? Example 2. Write the ratios of Yellow:White for each of the above rectangles and reduce to lowest terms. Are the ratios equal? What is the difference between a fraction and ratio? This class has boys and girls. a) What fraction is boys? b)what fraction is girls? c) What is the ratio of boys to girls? d) What is the ratio of girls to boys?

13 MFM1P U2L4 - Equivalent Ratios There are three different ways to write a ratio - each are illustrated in the next example. Example 3. For each of the following ratios, determine and equivalent ratio by either dividing or multiplying. a) 1 : 5 b) 120 to 60 c) 3 5 Ratios can have a multiplication/division relationship between them or within them - as illustrated in the following example. Example 4. What are the two multiplication relationships in 12:36 = 24:72 Example 5. Find the missing number. 5 : 30 = 15 :? Example 6. Find the missing number. 7 : 12 = p : 48

14 MFM1P U2L4 - Equivalent Ratios Sometimes the question becomes easier if you simplify a ratio first. This means find it's LOWEST term value. Figure out what number can be divided out of each ratio, to produce an equal ratios with smaller numbers. Example 4. Find the missing number. 12 : 30 = 18 : p Example 4. You earned $200 last week working 20 hours. How long will you have to work to earn $550? Practice Questions - Page 112 #1-5, 7-9

15 MFM1P U2L5 - Ratio and Proportion Topic : Goal : Ratio and Proportion I can solve proportional relationships using a variety of methods. Ratio and Proportion Ratio and proportion is one of the most useful skills you'll get from your math classes. Here are some following situations where it could be useful in every day life. A paediatric nurse (children's nurse) is working in the OR following a child's surgery. The dosage of pain medication says 5 mg / 100 kg of bodyweight. How much medication should she give a 15 kg child? You decide to paint the living room in your house. A gallon of paint will cover about 375 ft 2. You calculate your living room walls to have a surface area of 525 ft 2 and you are using a dark colour so you will need to use 3 coats. How many gallons of paint do you need? To open your swimming pool you will need to treat it with an algaecide to get rid of algae growth. The package says that you need to use 1 cup for every 1000 gallons of water. How many cups do you need for a gallon swimming pool? Example 1. A child is given pain medication based on how heavy they are. The dosage says 2mg for each 6 kg of bodyweight. How many milligrams should be given to an 18 kg child? Let's set up ratios. There are two ways to do this. Look for a multiplication relationship between ratios OR look at a multiplication relationship inside a ratio. between inside

16 MFM1P U2L5 - Ratio and Proportion Example 2. What are the two multiplication relationships in Between ratios 6:18 = 30:90 inside the ratio Example 3. Find the missing number. 7 : 10 =? : 40 3 : 21 =? : 49 Example 4. Find the missing number. 18 : 30 = 21 : p

17 MFM1P U2L5 - Ratio and Proportion Example 5. Example 6. A car travels 125 miles in 3 hours. How far would it travel in 5 hours? Example 7. The scale on a diagram is 1 : 250. This means that every unit on the diagram represents 50 units in real life. If a tree measures 4 cm on the diagram, how tall is it in real life? Practice Questions - Page 117 #1-12

18 MFM1P U2L6 - Ratio and Proportion Using Algebra Topic : Goal : Ratio and Proportion using Algebra I can solve proportional relationships using algebraic methods. Using Algebra to Solve a Proportion If we write a ratio as a fraction, we can find two different ways to solve the proportion using our algebra skills. Method 1 : Isolate the unknown (letter) Example 1. the variable would be by itself if the 15 were gone. 15 is dividing the variable, so to make it go away we do the opposite The opposite of dividing is multiplying. Example 2. You have to do the same on the other side, to keep the equation equal.

19 MFM1P U2L6 - Ratio and Proportion Using Algebra Example 3. Try a few more... a) b) c) d) e) f)

20 MFM1P U2L6 - Ratio and Proportion Using Algebra Method 2 : Cross Multiplying (a property of equal fractions/ratios) This property can be useful when solving a ratio. Example 4. Try a few more use cross multiplying...

21 MFM1P U2L6 - Ratio and Proportion Using Algebra Example 5. At the same time of day, all shadows cast by the sun will be proportional to the height of the object casting the shadow. I'm 1.53 m tall. I measure my shadow to be 2.6 m long at the same time as I measure the shadow of a tree to be 9.8 m long. How tall is the tree. Practice Questions - Page 133 #1-6

22 MFM1P U2L7 Unit Rate Topic : unit rates Goal : I know what a unit rate is and I can solve problems with it. Unit Rate A unit rate is a comparison between two things, where the second quantity being compared is ONE. Some examples of unit rate. * kilometres per ONE hour of driving * Cost per ONE ml of pop * goals per ONE game A unit rate can be written in 3 different ways... * Using words : 90 kilometres per hour * Using numbers, symbols and words : 90 km per hour * Using numbers and symbols : 90 km/h Since speed is one of the most common unit rates, we will take a moment to examine that. Let's say it takes 15 minutes to drive 20 km. What is the unit rate?

23 MFM1P U2L7 Unit Rate Example 1. Find the unit rate in each situation... a) $6 for 12 cans of pop b) 650 kilometres in 7 hours Example 2. At Walmart you can buy a case of 12 cans of Coke for $6.99 or a case of 24 cans for $ Calculate the unit rate for each case. Which is the better deal? Practice Questions - Page 123 #1-9

24 MFM1P U2L7 Unit Rate EQAO Check :

25 MFM1P U2L7 Unit Rate

26 MFM1P U2L8 Percent as a Proportion Topic : Goal : Percent as a Ratio I know what percent means and I can use proportion to solve percentage calculations. Percent as a Ratio Two students take a test on the same topic with different teachers. One student gets 30/32 the other gets 24/25. Who did better on that topic? It's hard to compare if they aren't out of the same thing, so we change them to make them both out of 100. This is called the percent. Anytime you take a situation and change it to be out of 100, you are dealing with percent. Example 1. Changing a fraction to a percent Method 1 - set up a proportion Method 2 - divide and X 100% Rule: Example 2. Changing a percent to a decimal. 14% 4% 104% Rule: d

27 MFM1P U2L8 Percent as a Proportion Example 3. Finding the percent of a number using ratios. a) What is 10% of 45? b) What is 63% of 230? Example 4. Finding the percent of a number by remember that 'of' in math means to multiply. a) What is 10% of 45? b) What is 63% of 230? Example 5. The yearbook committed conducted a survey to find out how many students in the school had a cell phone. of the 63 students they surveyed, they found that 83% said they had a cell phone. How many students were carrying a cell phone? Method 1 - ratio method Method 2 - 'of' method

28 MFM1P U2L8 Percent as a Proportion Example 6. A pair of jeans you've been waiting for goes on sale for 25% off. How much will you have to pay if they were $75.99 originally? Example 7. In Ontario we pay 13% sales tax (HST). So really what we are paying is 113% of the sale price. How much money do we have to pay in total for an ipod that sells for $159.75? Practice Questions - Page 137 #1-11

29 MFM1P U2L9 Putting it all Together - Proportional Problems Topic : Goal : Proportional Problems I can set up ratios and proportions to solve word problems dealing with "real life" situations. Proportional Problems

30 MFM1P U2L9 Putting it all Together - Proportional Problems

31 MFM1P U2L9 Putting it all Together - Proportional Problems

32 MFM1P U2L9 Putting it all Together - Proportional Problems