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Arithmetic: Ratios and Proportional Reasoning -Ratio (& Proportions) -Scale Drawings: Increase/Decrease -Percent -Rate.

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Presentation on theme: "Arithmetic: Ratios and Proportional Reasoning -Ratio (& Proportions) -Scale Drawings: Increase/Decrease -Percent -Rate."— Presentation transcript:

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2 Arithmetic: Ratios and Proportional Reasoning -Ratio (& Proportions) -Scale Drawings: Increase/Decrease -Percent -Rate

3 Overview HINT: Read the brief text in each slide BEFORE going to any website or looking at a file. There will be instructions on HOW best to use the resource/website. This is the first modular, and serves as a precursor to the algebra and beyond courses. In this module you’ll be learning about Ratio and Proportional Reasoning. A ratio describes a relationship between two quantities. Some distinguish ratios from rates, using the term “ratio” when units are the same and “rate” when units are different; others use ratio to encompass both situations. Relationships of two quantities may be described in terms of ratios, rates, percents, or proportional relationships. Rates can be indicated in terms such as “for each 1,” “for each,” and “per.” The unit rate is the numerical part of the rate; the “unit” in “unit rate” is often used to highlight the 1 in “for each 1” or “for every 1.” ” Notation for ratios can include the use of a colon, as in 3 : 2. Ratios are used in many applications.

4 Topics Ratio Foundation Determining and expressing a ratio Creating Ratio Proportional Relationships Ratio: Scale Drawings Ratio: Percent Ratio: Rates

5 A ratio expresses the relationship of two quantities. Ratios can be indicated in words as “5 to 6” and “3 for every 5” and “5 out of every 7” and “5 parts to 6 parts.” This use might include units, e.g., “5 cups of flour for every 6 eggs” or “3 meters in 2 seconds.” Notation for ratios can include the use of a colon, as in 3 : 2. This video will show you how to determine a ratio as well as how to express a ratio. The video is 14 minutes long; however, you may only need to watch the first 4 minutes demonstrating HOW TO DETERMINE and WRITE A RATIO of horses to dogs. There are thee more examples that follow horses : dogs ratio. You might want to use these to test your skills. After the problem is introduced, stop the video and try to write the ratio, restart the video to check your answer. Continue through the video until you feel you can suffessfully write a ratio. ratios/ratios_and_proportions/v/introduction-to-ratios--new-hd- version ratios/ratios_and_proportions/v/introduction-to-ratios--new-hd- version Ratio Determining and Expressing a Ratio

6 Often you might be asked to use a ratio to determine missing information such as: If the ratio of girls to boys is 5 to 8, and there are 65 students in the class, how many of those students are girls? This 2 minute step-by-step video demonstrates the above problem. You should stop the video after the problem is introduced to determine the ratio before going on to check your answer with the one demonstrated on the video. https://www.khanacademy.org/math/cc-sixth-grade-math/cc- 6th-ratios-prop-topic/cc-6th-ratio-word-problems/v/ratio- word-problem-exercise-example-1 https://www.khanacademy.org/math/cc-sixth-grade-math/cc- 6th-ratios-prop-topic/cc-6th-ratio-word-problems/v/ratio- word-problem-exercise-example-1 There is a second problem you can try. To get to the second problem click on “Ratio word problem exercise 2” in the left side bar. Ratio Determining and Expressing a Ratio

7 Creating Ratio Proportional Relationships A ratio expresses the relationship of two quantities. Proportions are determined by using a given ratio to create multiplicative relationships of the same two given numbers used in the ratio, thus when two ratios are the same, they are proportional. For example: This 5 minute video will demonstrate the use of multiplication to find proportions equal to a given ratio. Note that one factor is used to multiply both numbers in the ratio to find a proportion equal to the given ratio. proportion-topic/ratios_algebra/v/ratio-problem-with-basic-algebra- -new-hdhttp://www.khanacademy.org/math/algebra/ratio- proportion-topic/ratios_algebra/v/ratio-problem-with-basic-algebra- -new-hd Ratio

8 Creating Ratio Proportional Relationships This 5 minute step-by-step video will show you how to determine and express a ratio proportionally. Use this video to practice practical applications problems using ratios. Begin the video, and once the problem is established; stop the video and determine the ratio, before going on to check your answer with the one demonstrated on the video. Note on the left side bar of this web site that there are several examples you can work through. You can determine how many problems you need to do. Continue doing problems until you are successful. https://www.khanacademy.org/math/algebra/ratio- proportion-topic/ratios_algebra/v/writing-proportions https://www.khanacademy.org/math/algebra/ratio- proportion-topic/ratios_algebra/v/writing-proportions Ratio

9 Scale Drawings ~ Increase Scale drawings use proportional reasoning to create a smaller or larger drawing of the given drawing. Scale drawings are created by using multiplication to increase the size of the drawing; or division to decrease the size of the drawing. This 4 minute video will show you how to use a scale factor used in creating a floor plan to determine the actual size of the house. Watch this video and note the multiplication used to determine the actual size of the house. Note that one factor is multiplied by all sides to maintain the ratio. geometry/cc-7th-scale-drawings/v/scale-drawings-example geometry/cc-7th-scale-drawings/v/scale-drawings-example Ratio: Scale Drawings

10 Scale Drawings ~ Decrease Scale drawings use proportional reasoning to create a smaller or larger drawing of the given drawing. Scale drawings are created by using multiplication to increase the size of the drawing; or division to decrease the size of the drawing. This 3 minute video will show you how to use a scale factor to create a floor plan. Watch this video and note the division used to create the scale drawing. Note that the same number is used to divide all sides to maintain the ratio. https://www.khanacademy.org/math/cc- seventh-grade-math/cc-7th-geometry/cc-7th-scale- drawings/v/Constructing%20scale%20drawingshttps://www.khanacademy.org/math/cc- seventh-grade-math/cc-7th-geometry/cc-7th-scale- drawings/v/Constructing%20scale%20drawings Ratio: Scale Drawings

11 Percent A ratio can be expressed as a percentage. In expressing the percent keep in mind the two quantities in the ratio combined to make the whole. Thus one can compare one quantity to the other; or compare one quantity to the whole of the set. This 3 minute video explains what a percent is, and how to find a percent. topic/cc-6th-percentages/v/finding-percentages-example topic/cc-6th-percentages/v/finding-percentages-example Now that you have watched the video, think about all the ratio problems you have done and how a ratio can be expressed as a fraction. Use the next two web resources to test your understanding of percent. Each website has percentage problems. Work the problem, then click on ‘answer’ to see if you are correct. Ratio:

12 A quantity measured with respect to another measured quantity (sometimes called a unit rate) Ratio: Rate

13 A quantity measured with respect to another measured quantity (sometimes called a unit rate) Rates are often found in respect to an time. To see how a rate per hour is determined, click on the link below. After you view this two and one-half minute video, click the left sidebar to continue. https://www.khanacademy.org/math/cc-sixth-grade-math/cc- 6th-ratios-prop-topic/cc-6th-rates/v/finding-unit-rates To skip the video, advance to the next slide. Ratio: Rate

14 A measure of a part with respect to a whole Example: a sales tax rate. This rate compares the taxes to be paid to the state based on the total dollar amount being spent. Ohio’s state sales tax is 5.75%. To see how to calculate sales tax, watch a one minute video at tax.html tax.html After you view this one minute video, click the left sidebar to continue. To skip the video, advance to the next slide. Ratio: Rate

15 The cost per unit of a commodity or service Example: a postal rate. This rate compares amount of money to be paid to the post office based on the weight of the mail being spent. The cost to mail a letter weighing one ounce or less is $0.46 The postage rate for first class letters of one ounce is $0.46 This is sometimes written as Ratio: Rate

16 The cost per unit of a commodity or service Click on the link below to find the cost of cleaning one office when the cost of cleaning eight offices is known. After you view this two minute video, click the left sidebar to continue. https://www.khanacademy.org/math/cc-sixth-grade-math/cc- 6th-ratios-prop-topic/cc-6th-rates/v/finding-unit-prices To skip the video, advance to the next slide. Ratio: Rate

17 If you would like to read more about rates and unit rates, click on the link below. If you do not need to read further information, advance to the next slide. Ratio: Rates

18 Unit Price Practice If you would like to practice finding unit rates click on the link below to access 10 multiple choice problems. When you are finished, click the left sidebar to continue. To skip the practice, advance to the next slide. 1&ref=/measure/unit- price.html&qs=1049_1050_1937_1938_2210_2211_3745_37 46_3747_ &ref=/measure/unit- price.html&qs=1049_1050_1937_1938_2210_2211_3745_37 46_3747_3748 Ratio:Rate

19 Rate of Change We often talk about how something changes. A graph is a picture of the rate of change of one thing to another. Some examples for rate can be found in the 13 minute video at the link below. You will learn about Usain Bolt’s average speed. https://www.khanacademy.org/math/arithmetic/rates-and- ratios/rates_tutorial/v/usain-bolt-s-average-speed https://www.khanacademy.org/math/arithmetic/rates-and- ratios/rates_tutorial/v/usain-bolt-s-average-speed After viewing the video, click the left sidebar to continue on with examples of finding unit rates. To skip the video, advance to the next slide. Ratio: Rate

20 Game for practice Build your own potions based on what you have learned about unit rates. Click on the link below to access the game. Once you are finished playing the game, click the left sidebar to continue. To skip the game, advance to the next slide. Ratio: Rate

21 Game for practice In this Ratio Stadium game, play against the computer or with up to three other people. Click on the link below to access the game. stadium.html stadium.html Once you are finished playing the game, click the left sidebar to continue. To skip the game, advance to the next slide. Ratio: Rate

22 Slope Ratio: Rate

23 Slope – Mathematical Definition Ratio: Rate

24 Slope – Problem Ratio: Rate

25 Slope – Problem Ratio: Rate

26 Linear Equations See what happens when the values of “x” and “y” change using a virtual manipulative. Click below to access a place where you can see how the slope of the line changes. See what happens when you enter a value of zero for slope and a value of 5 for the y intercept. Try other values for the slope and the y intercept to see what happens to the line. Once you have finished exploring, click the left sidebar to continue. To skip the exploration, advance to the next slide. Ratio: Rate

27 Song about slope If you want to remember the formula for slope, watching this YouTube video may help. Click on the link below to watch the 2 ¼ minute video. If you wish to skip the song, advance to the next slide. Ratio: Rate

28 How to calculate the slope on a ramp There are many practical applications of using the slope formula. Calculating the slope of a ramp is one such application. Click on the link below to try it! After you have visited the website, click the left sidebar to continue. ramp.html#ixzz2nbf9VQj7 ramp.html#ixzz2nbf9VQj7 To skip practice, advance to the next slide. Ratio: Rate

29 Rate of Zero Ratio: Rate

30 Slope – Problem – Rate of Zero Ratio: Rate

31 Undefined slope Can you travel a distance and no time passes. Is this possible? Not in our universe! Remember that the rate is defined by distance over time. If the time is zero, then the rate is undefined. The graph for this situation would be a vertical line. The slope is undefined. We may also say vertical lines have no slope. Ratio: Rate

32 Slope – Problem Ratio: Rate

33 Slope Rap Song Slope Rap Song If you like to remember things by singing a song, you might wish to click on the above link to watch a four minute video, otherwise advance to the next slide. Ratio: Rate

34 Save the Zogs Play this game to practice finding the slope of a line by capturing the Zogs sitting on the line. Click on the link below to access the game. html Once you are finished playing the game, click the left sidebar to continue. Ratio: Rate

35 Ratios and Proportional Reasoning Congratulations, you have completed the Ratio module. You can revisit this module at any time.


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