1 / 34

M & M Ratio Activity/ Chapter 8/ Flashlight Activity

M & M Ratio Activity/ Chapter 8/ Flashlight Activity. MA.912.G.2.2 MA.912.G.3.4. 8.1 Ratio and Proportion. MA.912.G.2.2 MA.912.G.3.4. 8.1 Ratio and Proportion.

pekelo
Download Presentation

M & M Ratio Activity/ Chapter 8/ Flashlight Activity

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. M & M Ratio Activity/ Chapter 8/Flashlight Activity MA.912.G.2.2 MA.912.G.3.4

  2. 8.1 Ratio and Proportion MA.912.G.2.2 MA.912.G.3.4

  3. 8.1 Ratio and Proportion • Ratio of a to b – if a and b are two quantities that are measured in the same units then the ratio of a to b can be written as and as a:b. • Ratios are usually written in simplified form. The ratio 6:8 would be written 3:4.

  4. 8.1 Ratio and Proportion • The perimeter of a rectangle ABCD is 60 centimeters. The ratio of AB : BC is 3:2. Find the length and width of the rectangle.

  5. 8.1 Ratio and Proportion • The perimeter of a rectangle ABCD is 60 centimeters. The ratio of AB : BC is 3:2. Find the length and width of the rectangle. • Solution: Because the ratio of AB : BC is 3:2, you can represent the length AB as 3x and the width BC as 2x. • 2l + 2w = P (formula for perimeter) • 2(3x) + 2(2x) = 60 • 6x +4x = 60 • 10x = 60 • X = 6 • So, ABCD has a length of 18 centimeters and a width of 12 centimeters.

  6. 8.1 Ratio and Proportion • Proportion – an equation that has two ratios. IF the ratio of is equal to the ratio , then the following proportion can be written: • = • The numbers a and d are extremes of the proportion. The numbers b and c are the means of the proportion.

  7. 8.1 Ratio and Proportion • Properties of Proportions • 1. Cross Product Property – The product of the extremes equals the product of the means. IF =, then ad = bc • 2. Reciprocal Property – IF two ratios are equal, then their reciprocals are also equal. IF =, then =

  8. 8.1 Ratio and Proportion • = • =

  9. 8.1 Ratio and Proportion • Homework: Page 461 10-16, 26-28, 34-46 even

  10. Steps to the activity • Open your package of M & Ms • Sort all your colored M & Ms • Count each color separately and record the amount on your piece of paper • Count the TOTAL number of M & Ms and record that amount

  11. Let’s Begin • Write the answer to all the ratios as a fraction, using a colon, and the word to. • Example: What is the ratio of blue M & Ms to red M & Ms (In my bag: blue= 4 And red= 8) • 4/8 = ½ , 1:2 or 4:8, 1 to 2 or 4 to 8

  12. Now answer the following: • What is the ratio of greenM & Ms to yellow M & Ms • What is the ratio of blue M & Ms to Red M & Ms • What is the ratio of brownM & Ms to the total number of M & Ms

  13. Ready for some more? • What is the ratio of greenand redM & Ms to the total of M & Ms • Record the ratio of blueM & Ms to the total number of yellowand orangeM & Ms • Record your favorite color of M & Ms to the total number of M & Ms (You must write down your favorite color)

  14. Need just a little more practice. • Record the ratio of orangeM & Ms to greenand yellowM & Ms • What is the ratio of your least favorite M & Ms to the total M & Ms • My favorite color is green. What is the ratio of my favorite color & your favorite color of M & Ms to the total number of M & Ms

  15. Are you getting hungry? • Create a table showing your color of M & Ms and the amounts

  16. You are almost finished! • Please put your name on your paper • Now you may eat your M & Ms!!!!! • I hope you had fun with ratios

  17. 8.3 Similar Polygons MA.912.G.3.4

  18. 8.3 Similar Polygons • Similar Polygons – the correspondence between two polygons such that their corresponding angles are congruent and the lengths of corresponding sides are proportional. • Scale Factor – the ratio of the lengths of two corresponding sides of similar polygons.

  19. 8.3 Similar Polygons • Theorem 8.1 If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths. If KLMN ~ PQRS, then = = = =

  20. 8.3 Similar Polygons • Homework: Page 476 8-42 even

  21. 8.4 Similar Triangles MA.912.G.3.4

  22. 8.4 Similar Triangles • Postulate 22 Angle – Angle Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. If JKL = XYZ and KJL = YXZ, then JKL ~ XYZ

  23. 8.4 Similar Triangles • Homework: Page 484 18-26, 34-46 even

  24. 8.5 Proving Triangles are Similar MA.912.G.3.4

  25. 8.5 Proving Triangles are Similar • Theorem 8.2 Side-Side-Side (SSS) Similarity Theorem If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar. If = = Then ABC ~ PQR

  26. 8.5 Proving Triangles are Similar • Theorem 8.3 Side-Angle-Side (SAS) Similarity Theorem IF an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar If X = M and = Then XYZ ~ MNP

  27. 8.5 Proving Triangles are Similar • Homework: Page 492 6-26 even

  28. 8.6 Proportions and Similar Triangles MA.912.G.3.4

  29. 8.6 Proportions and Similar Triangles • Theorem 8.4 Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. If TU ǁ QS, then =

  30. 8.6 Proportions and Similar Triangles • Theorem 8.5 Converse of the Triangle Proportionality Theorem IF a line divides two sides of a triangle proportionally, then it is parallel to the third side. If = , then TU ǁ QS.

  31. 8.6 Proportions and Similar Triangles • Theorem 8.6 IF three parallel lines intersect two transversals, then they divide the transversals proportionally. If r ǁ s and s ǁ t, and l and m Intersect r, s, and t, then = .

  32. 8.6 Proportions and Similar Triangles • Theorem 8.7 IF a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. If CD bisects LABC, then =

  33. 8.6 Proportions and Similar Triangles • Homework: Page 502 12-30 even

  34. End of Chapter Review • Homework: Page 519 1-18

More Related