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not watered down) HS Geometry text (10th grade)": Remark.Students should have mastered these in elementary school. Students will need to be told that "2 1/2 blocks per minutes" means "2 1/2 blocks each minute".He says that in the first step we should cross multiply the numbers across the diagonal.
This will increase instructional time for these problems.
If students go on automatic pilot, while setting up these tables, they will sometimes do it when it is not valid.
Correctly, multiplying numbers when multiplication is not justified is wrong.
Darcy Conant wrote: "Many students -- even 'good' high school students have difficulty with rate problems.
Jack picked 12 apples 15 pears and Jill picked 16 apples and some pears.
The ratio of apples to pears picked by Jack and Jill were the same. Solution Jack 12 15 1 15/12 Jill 16 16 x 15/12 = 20 Remark.Now, lets convert back: It is absurd that a high school biology teacher had not learned how to change centimeters to meters; -- unless he too, had been taught by the rule for idiots: "move the decimal two places", in which case, it is predictable. Similarly, 2.365 dollars and 2.365 can be converted to 236.5 cents and 236.5%, resp. "Ratio" and "Proportion" basically, mean that we can set up tables, (as in the previous problems) and then it is valid to multiply or divide a line by a number. Jack and Jill went up the hill to pick apples and pears.The new 1999 California Standards require that students learn this in Grade 4. Jack picked 10 apples 15 pears and Jill picked 20 apples and some pears.This will include several problems, which are normally solved using Algebra; including five of the more difficult problems on the Maryland High School Assessment on Functions, Algebra, Data Analysis and Probability (MD Algebra) sample test, an about-to-be-implemented high school graduation requirement in MD.The arithmetic solutions presented herein, provide more conceptual-understanding of the problems than the expected Algebraic solutions.Also, many "good" high school students have difficulty in dealing with times (hours and minutes).Look at the types of rate problems in a 'regular' (i.e.Dickler, was principal.) In fact, such problems can and should serve as background for formal proportional thinking. Of course, this problem should be presented only after the students are fluent with the parts, namely, * If one T-shirt cost 5 dollars, how much do 5 T- shirts cost? Multiplying 2 x 16 = 32 whether directly or by setting up a table as in Problems 1,2 and 3, will produce a wrong answer.And * If three T-shirts cost 15 dollars, how much does one T- shirts cost? While the falling distance is a function of time, it is not a linear function; it is not proportional to time.This report will present simple, conceptual-understanding based arithmetic methods that will allow students to solve a wide variety of problems.These better methods of instruction are in the spirit of my version of KISS , that is "Keep It Simple for Students", while emphasizing conceptual-understanding.