1. Good Grief, Ratios?!?! Lisa Herron – Cypress Bay High School Josh Cross – West Broward High School Jessica Flint – West Broward High School Venessa Smith – Blanche Ely High School

2. What is a Ratio? A ratio is an expression which compares quantities relative to each other. The most common examples involve two quantities. Example: What is the ratio of students to pizza slices?

3. The Ratio Is: 2:3or or Two students TO three slices of pizza.

4. Or there is 1 student to 1 ½ pizza slices? Is 2:3 the same as 1:1.5? Take another look…

6. It is often easiest to solve problems when the unit ratio is known. This is called the unit ratio.

7. Which row will give the students the most pizza?

8. Students : Pizza ANSWER: A & F

9. Same Ratio? If two ratios are equal then we have a proportion.

10. Proportions & Algebra How many ice cream cones should be in row B to have same ratio as row A?

11. Solution The ratio of students to ice cream is 1:2.

12. In row B there are 3 students:

13. Proportions & Algebra So, we need 6 ice cream cones to have the same ratio in A and B.

14. Algebraically

15. Ratios in the Classroom M&M Activity 1. Place M&M candies along the diameter and circumference of each circle. You may have to bite an M&M to get an exact fit. 2. Count the number of M&M’s and fill in the table below. Write the ratio as a decimal. 3. Calculate the average ratio of the 4 circles.

16. Ratios in the Classroom M&M Activity 4. What can be said about the ratio between the circumference and diameter of a circle?

17. M&M Activity 5.If the circumference of the Earth is 40,075.02 KM, and the diameter is 12,756.2 KM, how many M&Ms would be needed to go around the Equator?

18. What is Scaling? Applications of Ratios - Scaling is a linear transformation that enlarges or diminishes objects. - For similar figures, a scale factor is used to make this transformation. - A scale factor is the number by which each dimension of the original object is multiplied to find the corresponding dimension of the model.

19. The scale factor for HO scale trains is 1:87. Disney’s Haunted Mansion. The map on the right shows both the unit ratio and the scale used. Scaling is used…

20. Scaling Activity 1. Measure the length and width of the picture. 2. Find the side length of one square in the picture. 3. Measure the length and width of the graph paper. 4. What scale is needed to completely fill the graph paper with the Snoopy picture?

21. Scaling Activity 5. At the top of the Snoopy picture page label the boxes alphabetically A- H. On the left side of the page, label the boxes vertically from 1-11. 6. On the graph paper label the boxes in the same manner. 7. On the graph paper, enlarge the Snoopy Picture by reproducing each corresponding box. 8. After you sketch the entire drawing, use a pen to outline your drawing. You may also wish to color your drawing.

22. Geogebra Activity

23. Sunshine State Standards Grade 6Grade 7Grades 9 - 12 Big Idea 1 Big Idea 2 Big Idea 1Strand 2: Polygons Strand 4: Triangles Strand 6: Circles

24. Big Idea1: Develop an understanding of and fluency with multiplication and division of fractions and decimals. SSS – Grade 6 CodeBenchmark MA.6.A.1.1 Explain and justify procedures for multiplying and dividing fractions and decimals.

25. SSS – Grade 6 Big Idea2: Connect ratio and rates to multiplication and division. CodeBenchmark MA.6.A.2.1 Use reasoning about multiplication and division to solve ratio and rate problems. MA.6.A.2.2 Interpret and compare ratios and rates.

26. SSS – Grade 7 Big Idea1: Develop an understanding of and apply proportionality, including similarity. CodeBenchmark MA.7.A.1.1 Distinguish between situations that are proportional or not proportional and use proportions to solve problems. MA.7.A.1.6 Apply proportionality to measurement in multiple contexts, including scale drawings and constant speed.

27. SSS – Grade 7 CodeBenchmark MA.7.A.5.1 Express rational numbers as terminating or repeating decimals. Supporting Idea 5: Numbers and Operations

28. SSS – Geometry 9-12 CodeBenchmark MA.912.G.2.4 Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons. to determine congruence, similarity, and symmetry Standard 2: Polygons

29. SSS – Geometry 9-12 Standard 4: Triangles CodeBenchmark MA.912.G.4.4 Use properties of congruent and similar triangles to solve problems involving lengths and areas. MA.912.G.4.5 Apply theorems involving segments divided proportionally. MA.912.G.4.8 Use coordinate geometry to prove properties of congruent, regular, and similar triangles.

30. SSS – Geometry 9-12 Standard 6: Circles CodeBenchmark MA.912.G.6.2 Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles. MA.912.G.6.5 Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.