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Using Algebra to Solve Proportional Reasoning Problems

Learn how to use algebraic structures to solve real-world problems involving proportional reasoning. Explore scale factors and their representation in scale drawings. Friday, 20181109.

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Using Algebra to Solve Proportional Reasoning Problems

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  1. B.A.SSE.A.2. Use algebraic structures to solve problems involving proportional reasoning in real world context. Friday, 20181109Proportional Reasoning EQ10: How do we use algebraic structures to solve proportional reasoning problems? Objective: Compare two different proportional relationships represented in different ways. Figure Scale Factors from Scale Drawings

  2. Friday, 20181109 Essential Questions • EQ10: How do we use algebraic structures to solve proportional reasoning problems? Vocabulary: • Unit rates • Fractions • Solving Proportions • Ratios • Finding percent and calculating percent of a number • Determining constant of proportionality (slope) from tables of values, graphs, and algebraic relations • Interpreting constants of proportionality (slope) on a graph • Proportional Reasoning • Scale Factor No Sleeping! Agenda Bridge Math • Store your phones • Find your seat • Bellwork: Bridge Bellwork • EQ10 QUIZ: Join.Quizizz.com • Scale Drawings • Calculator • Proportional reasoning problems/ Scale Factors • Join.Quizizz.com • No Exit Ticket • Remain in seat until bell rings. Teacher Dismisses NOT the bell. It’s always a great day to be a Wolverine!

  3. Bellwork: Friday, 20181109 • You are a detective assigned to work on the robbery of your local grocery store. The surveillance film shows the suspect standing next to the check out counter. Describe a method that you could use for finding out the actual height of your suspect. (Hint: Think about scale models and your scale drawings.)

  4. AUSTIN’S CLASS:Join.quizizz.com 20181109≥ 90% is your goal!

  5. DILL’S CLASS:Join.quizizz.com 20181109≥ 90% is your goal!

  6. Throneberry’s CLASS:Join.quizizz.com 20181109≥ 90% is your goal!

  7. Finish Scale Drawings and Hang on Wall

  8. Remember…. • A ratio is a comparison of two quantities by division. • A ratio compares part to part or part to whole. • A ratio can be written 3 different ways… n/d n:d or “n to d” or “n out of d”

  9. Word Wall • Indirect measurement - is a method of using proportions to find an unknown length or distance in similar figures.  • Scale drawing - A drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale).  • Scale - a reference standard in measurement, in which each number corresponds to some physical quantity • Dilation - is a transformation that produces an image that is the same shape as the original, but is a different size.

  10. Word Wall Continued SCALE FACTOR

  11. Cartoon Scale Drawings Using cartoons to draw similar figures

  12. Objectives Use ratios to make indirect measurements. Use scale drawings to solve problems.

  13. The Cartoon What to do with your cartoon: 1.Select a cartoon 2.Print it out with: Coach Dill’s Classes and Mrs. Austin’s Classes today!

  14. The Grid Use a ruler to measure the length and width of your cartoon in centimeters and write it on your paper – near your cartoon

  15. The Grid Use a ruler to measure the length and width of your cartoon in centimeters and write it on your paper – near your cartoon 10cm Yours may not be 10cm – this is just an example 10cm

  16. The Grid Now…Time to draw the grid! On the paper (not on the cartoon), Make two centimeter marks on opposite sides Start on the left and go towards the right across the top and bottom Be careful measuring – your grid will turn out better the last block may be smaller than two centimeter 2cm 2cm 2cm 2cm 2cm 2cm 2cm 2cm 2cm 2cm

  17. The Grid Now…Time to draw the grid! Connect the marks… BE careful you have one shot at this! 2cm 2cm 2cm 2cm It is okay if all your squares aren’t exactly the same size – but try to get them as close as possible 2cm 2cm 2cm 2cm 2cm

  18. Scale Drawing • 43.2 cm x 50.8 Large paper • 10 cm x 10 cm cartoon • Scale Factor of my scale drawing is • 50.8 cm/10 cm = 5.08 • Which means my drawing with the scale factor of 5.08 is 5 times bigger than the cartoon I started out with.

  19. The Scale Drawing Time to draw your cartoon on to a larger paper with a larger grid. What is the scale factor of your drawing?

  20. The Scale Drawing Time to blow up your cartoon. The scale factor is 3. You are making your cartoon 3 times as large. What do you do? 2cm 2cm 2cm 2cm 2cm 2cm 2cm 2cm 2cm 2cm multiply everything by 3!

  21. The Scale Drawing You need to create a grid that is three times as large as your original. My original is 10cm by 10cm.

  22. The Drawing To draw the large grid you need to multiply the length and width of the small cartoon by three.

  23. The Scale Drawing You need to create a grid that is three times as large as your original. My original is 10cm by 10cm. I’m choosing scale factor of 3cm, so my new grid is 30cm to 30cm Now mark off five 6cm marks! – Left to right and top to bottom

  24. The Drawing Now you can draw! You do not have to know how to draw to do this. The grid helps you with spatial relationships…

  25. The Drawing Now you can draw! You do not have to know how to draw to do this. The grid helps you with spatial relationships… Draw the new picture one square at a time Notice spatial relationships here and it will look Exactly like original

  26. Cartoon Similarity Finished Product

  27. EQ9 Proportional Reasoning/Ratios That's All Folks! Get Ready for the EXIT TICKET!!!

  28. EXIT TICKET Solve each proportion for x:

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