RP Progressions

[Bill McCallum]

Will there be an updated progressions document for RP soon? I have been reading lots of discussions about the terms rate and unit rate, and how they are defined in the progressions (and how they are NOT defined in the standards). I am hoping an updated version of the progressions will help to clarify the meanings of these terms.

[Susan Forbes]

I have some comments about the RP Progressions that I would like to put out there. I welcome any and all input. Sue

When I looked at “Progression on Ratios and Proportional Relationships” I noticed no mention of the importance of ordering a ratio expression when it is placed into a table. My thought here is that the order in which two quantities are related makes a difference when these two quantities are displayed in a table and then later graphed. Further, the language surrounding the words that describe a ratio should be consistent so that students can more easily discern this relationship. When I look at standards 6.RP. 1 – 3, and standard 6.EE.9, I note a disconnect. I found this same disconnect between pages 5 and 6 of the RP Progressions article and also within a recent Texas Instruments webinar. On page 6 of the RP Progressions article and in the TI webinar, I noticed that the ratio expression was not properly treated when it was placed into a table where units were attached.

The first treatment of the ratio expression on page 5 of the RP Progressions article differs from the second treatment of the ratio expression on page 6. I believe that the first treatment of the ratio: ““for every 5 cups grape juice, mix in 2 cups peach juice” was correctly represented within the table with grape juice being shown within the first column and then later graphed as the independent variable on the x. However, I noticed that this was later reversed in the tables shown on page 6 when the ratios: “1 cup red paint for every 3 cups yellow paint and … 3 cups red for every 5 cups yellow” were arranged within the table with red paint as the independent variable.

In a like manner I found similar flip-flopped reversals of ratios displayed within a graph during a recently viewed Texas Instruments on-demand webinar entitled: “Deciphering Ratios with TI- Inspire Technology: Are They Fractions?” Fifty minutes into this webinar, when it came time to display the rate 3m for every 2 seconds in a graph, the points were labelled in reverse order with distance listed first. I have captured this in a screen shot attachment below. I am wondering if this was done to maintain the ratio as it was originally read. I am also wondering if this is an ideal representation.

I am also wondering if we shouldn’t explicitly teach rate as a special type of ratio in which units are attached and order matters. If we discuss this order, the language clues, semantics, and relationship contexts prior to placing a ratio into a table and graphing it, the potential for later student confusion might be avoided.

Any thoughts on this???

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