# Investigating Ratios As Instructional Tasks MTL Meeting April

Investigating Ratios As Instructional Tasks MTL Meeting April 15 and 27, 2010 Facilitators Melissa Hedges Kevin McLeod Beth Schefelker Mary Mooney DeAnn Huinker Connie Laughlin The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

WALT We are learning to explore ratios (part to part, part to whole) We will be successful when we analyze ratios in instructional tasks. Ahhh Grasshopper

A grasshopper can jump further than a person. Do you agree or disagree? What justification do you have for your answer. Turn and talk with a person at your table. Two Types of Thinking

Absolute thinking - thinking additively Relative thinking - thinking multiplicatively Which type of thinking were you using? If you used relative thinking what comparisons did you use to justify your reasoning?

What is a ratio? An ordered pair of numbers that express A multiplicative (relative) comparison of two quantities or measures. Types of ratios Part-to-Part: number of girls to number 2:3 Part-to-Whole: number of girls to number children in the family 2:5

of boys of Studying ratios Proportional thinking is developed through activities involving comparing and determining the equivalence of ratios and solving proportions in a wide variety of problem based contexts and situations without recourse to rules or formulas

To the student beginning to develop an understanding of ratio, different settings or contexts may seem like different ideas even though they are essentially the same from a mathematical viewpoint. Van de Walle,J. (2009). Elementary and middle school teaching developmentally. Boston, MA: Pearson Education. Interpreting Ratios in Instructional Tasks If you are told the ratio of girls to boys in a class is 3:4, what can you tell about the

class? Orange Juice To Water You have a 30% concentration of orange juice in water. If you take a cup of the mixture, what percent will be orange juice? What is the ratio in this situation? How is this situation similar to the previous task? How is it different?

Interpreting information in ratios situations In order to understand the different nuances that ratios bring to a contextual situation, it is important to discuss all of the issues and understandings related to that situation. Explicit information Implicit information

Lamon,S. 2005. Teaching Fractions and Ratios for Understanding. Lawrence Erlbaum Associates. Auditorium problem There are 100 seats in the theatre with 30 in the balcony and 70 on the main floor. Eighty tickets were sold for the matinee performance, including all of the seats on the main floor.

What fraction of the seats were sold? What is the ratio of balcony seats to empty seats? What is the ratio of empty seats to occupied seats? What is the ratio of empty seats to occupied seats in the balcony? Does the ratio remain the same? John is 25 years old and his son is 5 years old.

Does this ratio remain constant as John and his son age? Is this relationship multiplicative or additive? Fathers and Sons The ratio of a fathers age to his sons age is 5:1 What are some possible ages that the father and son could be?

Big Idea A key developmental milestone is the ability of a student to begin to think of a ratio as a distinct entity, different from the two measures that made it up. Ratios and proportions involve multiplicative rather than additive comparisons. Equal ratios result from multiplication or division not from addition or subtraction. Van de Walle,J. (2009). Elementary and middle school teaching developmentally. Boston, MA: Pearson Education.

## Recently Viewed Presentations

• Large reduction in cost as the system eliminates expensive foundation. Eliminates the need for piles or caissons. Floating foundation system that can resist liquefaction phenomenon of soil that might occur after an earthquake. Does not require large easement to construct....
• Capturing and Billing Pre-Transplant Services for Cost Reporting, Increased Revenue, and Donor Financial SafeguardsTFCA Annual Workshop forFinancial CoordinatorsSeptember 27th, 2017. Debbie Mast. Manager-Finance and Data. Stanford Health Care
• Mise-en-scène. The arrangement of everything that appears in the framing - actors, lighting, décor, props, costume - is called mise-en-scène, a French term which means "placing on stage." The frame and camerawork also constitute the mise-en-scène of a movie. It...
• The primary advantage of the corporate form is the ability to raise large amounts of capital by issuing shares of stock. Limited legal liability. is a concept in which owners bear no personal liability for the corporation's debts and risk;...
• Hobbies, Leisure and Lifestyles Leisure Free time after school or work is called leisure time. It is time when we don´t have to go to work or school. It is the time of fun and entertainment. We devote time to...
• This lowers the world price to P 1 W and increases quantity traded to Q. 1 The CVD is a tariff, t, equal to the subsidy, which shifts the demand curve for imports down by t. Quantity traded returns to...
• The TLP are designed to help solve tactical problems. Leaders at battalion-level and above use the military decision making process (MDMP). For further discussion on the MDMP see FM 101-5 (Staff Organizations and Operations). Both TLP and MDMP are established,...
• screen = pygame.display.set_mode((640,480))The window is 640 pixels wide by 480 pixels high. a pixel is a drawing square on the screen . surface. Pygame can create many surfaces which can all be drawn on