Hmm, your blog collapsed the spacing between the points I made with the x’s. I meant some kind of spacing like this:

https://teacher.desmos.com/activitybuilder/custom/5811fa44298b5ee6059022ed

Anything’s good as long as it ensures that kids are processing what the x- and y-coordinates of those points represent. I work with a population that needs to be very inclusive of ELL and special education students, so I was trying to avoid a long sentence saying, “Now graph the points for each body part, where x represents Dan’s measurement of the part, and y represents Marcellus’ measurement”.

In addition, I think there’s something beneficial about having kids make some kind of a double number-line to represent the relationship initially. I want them to see that if the original body parts are spaced like this on the number line:

x x x

then the new body parts will be spaced like this:
x x x

The points spread out, but the ratio of the distances between the points is preserved. Dragging the points to the right locations is a feeble attempt to give some tactile sense of that. After which, of course, students need to turn the second number line vertically and make an x-y graph. For a novice, it’s not easy to see that when the second number line has bigger spaces between points, it means the graph will get steeper. Will they get that understanding out of what I’ve proposed? I’m not sure, but that’s what I’m trying to drive at here.

And that the

1. “Desmos is too accurate!” (a student received “Oh biscuits” feedback regarding the mouth being 1.95 times larger instead of 2 times larger, and Desmos called him on it, ha!)

2. “That was so dorky! But the dorkiest things are often the funnest things!”

Two comments from me:

1. I was very impressed with student language on screen 14. Students really did a fine job explaining what they’d learned.

2. Maybe it’s just my silly kids, but for the life of me, I couldn’t get anyone to do anything on screen 15 but doodle! I sketched a sample accessory for them, but alas, they just wanted to have fun. Can’t blame ’em really. They loved this activity’s playful tone.

However, I ALSO make sure to ask a question about the NUMBER of some item. (the number of handles on the chest, the number of windows on the front, the number of eyes on the giant). You would be surprised how many students will apply the length scale factor to such problems.

Awesome. I’m sure I would.

Students are given (essentially) three or four tables of values and dot-to-dot instructions. Each graph becomes the face of a cat. Students are then asked to decide which ones have the same shape. What is the criteria?

The activity leads to students developing/constructing the definition to include congruent corresponding angles and proportional corresponding lengths.

When assessing students at the end of such a unit, I like to include a question in which the scale factor is given and I ask the students the typical questions about angles, lengths, areas, and volumes. However, I ALSO make sure to ask a question about the NUMBER of some item. (the number of handles on the chest, the number of windows on the front, the number of eyes on the giant). You would be surprised how many students will apply the lenght scale factor to such problems.

That is, it wasn’t the entire person that wasn’t scale but just parts. Was that a conscious decision? I wonder if that slide needs some teacher notes to so they can anticipate that issue?

Thanks for the feedback, David. We’ll take it all into consideration. In the quoted piece above, are you saying you wanted every body part to be disproportional?

Wait. Why not have them plot three points out in the plane?

Ideally, after they got this Screen 9.5 right, you’d have a nice animation that would then make a point a point appear in the x-y plane to for each body part, e.g., the point (Dan’s eyes, Marcellus’ eyes) would appear. Those are the points that are displayed in Screen 10, so you could make sure students understand what those points mean.

Super interesting. I like it.

I was just wondering, though, if there was a way to grab measurements from the last screen where they make an accessory to determine whether or not their drawings were actually proportional?

Thanks for the feedback, Rachel. I wish that were possible. Perhaps in the future.

Lots of helpful feedback here, Andrew. No follow-up questions. I think we’ll take them all on.