Students continue their investigation of ratios by exploring graphical representations of the sum of two ratios. They should recognize that the sum of two equivalent ratios results in ratio equivalent to the original; and that the coordinates representing the ratio lie on the same line.
What to look forAt the end of the lesson, have students change the ratios for the blue and pink segments and explain what each segment represents. Discuss as a class the effects the rates associated with the two ratios have on the steepness of the segments.
The ratio 50:100 is equivalent to the ratio 1:2 and the ratio is 75:100 is equivalent to the ratio 3:4. Is the sum of the ratios 50:100 and 75:100 equivalent to the sum of the ratios 1:2 and 3:4? Why or why not.
Answer: One sum is the ratio 4:6 and the second is 125:200, which is equivalent to 5:8. The ratios are not equivalent so the sums are not equivalent.