Teaching scale drawings always seems like a fun, activity based concept to learn. But what makes it really important for students is that it helps them apply proportions in a real-life way. When they really understand scale drawings, they are also that much better at solving and understanding proportional relationships. I already talked about how I chunk out the learning targets for this skill here. And I’ve shared in an earlier post about my first experience teaching with a discovery lab. Now I’m excited to share with you all the discovery lab and foldable notes I used to teach scale drawings and proportional relationships.
As I’ve talked about before, I believe it is so powerful to start a new unit with a discovery, or inquiry, activity. This way, students grapple with the math concept, identify patterns, and draw conclusions, all before they have any formal instruction about it. I like calling these “labs” because that reinforces the idea that we are trying and testing things, just like mad scientists! (Or, I guess, scientist in general). At the conclusion of this discovery lab, students are better primed and prepared for the direct instruction, and they show a better long-term grasp of it. In keeping with this new lesson sequence, I wanted to start this unit off with students recognizing and describing proportional relationships.
Step 1- Building Background
To start off, I wanted students to write down everything they already knew about proportions, ratios, and scale drawings. It helps prime the pump, so to speak, by activating their prior knowledge.
This only takes about 3 to 5 minutes for students to write down their thoughts, and then share with the class. I have students listen to others’ responses and add them to their paper if they hear something they didn’t already write down.
Step 2- Conducting trials with scale drawings
Next comes my favorite part- conducting trials with scale drawings. During this section, I want students to become mad scientists. I want them to look at things deeply, to really analyze what is going on, and to try to explain it. To get students into *mad scientist mode* with scale drawings, I used candy bars. Well, I used paper candy bars any ways. Students cut apart the six candy bars, three arrows, and three labels. Then, I reminded students of the definition of proportional relationships.
Finally, I presented students with this challenge: “Using the definition of proportional, take the 6 candy bars and put them into pairs that are proportional. Then, explain your pairs using ratios and words.”
I think of this step as students conducting trials and making observations. I liked watching them physically move the pieces around and matching up different pairs.
Discovery in Action
What my students struggled with the most was finding patterns. Many of them just couldn’t see a pattern in any of this. Now, I work with students who struggle more than most of their peers in math, so some of that is to be expected. But to be honest, it surprised me how much they struggled to find patterns. It reinforced to me how very important it is to keep using these kind of activities in math. They NEED to struggle a bit. These students desperately need to learn skills like pattern seeking to improve as problem solvers overall. And this activity provided them such a great, low stress way of doing some of that work.
In this case, I wanted to make sure that their struggle was still productive, so at certain points I did give them hints. I prompted them to look at the overall shapes and see if any looked similar. If that didn’t work, I pointed out one that was a square and asked them to just focus on this shape. Did they see anything else on the table that reminded them of this piece? If they still didn’t pick out the other square, I pointed it out and talked with them about how the two squares were similar to each other, even though one was smaller than the other. Then, I asked them to examine the remaining four pieces in the same way.
Step 3- Drawing Conclusions
Finally, students reflected on their experience. They answered the question, “What did you learn about proportional objects?”
I asked two more questions to close out this activity. First, “What is a proportional candy bar to one that is 3 squares by 4 squares.” And finally, I wanted them to pull it all together and answer this question, “If scale drawings are proportional, what does that mean?”
I paid careful attention to students’ responses. They were very helpful in knowing what to emphasize and what misconceptions to address when I started formal instruction.
Taking notes about scale drawings
I began giving direct instruction by giving students notes to add to their interactive math notebook. During this lesson I wanted to model for students how to read a scale drawing situation, represent the proportional relationships in that problem, and then solve for an unknown value. Students added this foldable graphic organizer to their math interactive notebook:
First, students read and annotated a situation. I modeled the thinking and we underlined key words together.
After having a clear idea of the question, I modeled how to represent that information in a proportion.
I emphasized for students that we need to make sure that the same units are being compared. So, in this example, the inch is in the numerator and the feet are in the denominator. I explained that we know this because the problem states that the proportion is 1 inch for every 20 feet, so that is written 1/20. Then, when setting up the second proportion with an unknown value given for inches, this proportion needs to be set up in the same way, so x/1200.
This was, without a question, the part that they struggled with the most throughout the unit. So having a worked example in their math notebook was a huge help. Also, I wanted to make sure they all wrote the unit, not just the number. So 20 f, not just 20. This helped them keep everything in the right place, rather than just randomly writing numbers based on where they *felt like* they should go. (Right?! Anyone else have students who like to be creative when writing equations? Students who like to “express” themselves by doing things no one else is doing with numbers?)
Incorporating math talk with scale drawings foldable
After making sure everyone recorded the proportion in their notebook, we practiced actually reading the proportion out loud. I reminded students that the fraction bar means something too. In these proportions, it means “to” or “per”. So, we practiced reading out loud, 1 inch/20 feet as “one inch to 20 feet.” This helped students later when they needed to justify their answers. Incorporating speaking into the lesson with the foldable really got them more comfortable with how we talk about proportions.
For the final step, we solved for x. I walked students through the strategy of multiplying the 2 diagonals, and then dividing by the other one.
Reflecting on discovery labs and foldable notes
Using discovery labs and math interactive notebooks has revolutionized my classroom over the past two years. Together they make a powerful way to combine student centered learning and meaningful class notes that students will actually look back at and use. Throughout this scale drawings discovery lab students were hands-on working with this concept right from the start. I loved seeing students start this way, and it gave the class a concrete example to refer back to during the notes and the rest of the unit.
The foldable notes provided students a simple, clear way to organize the new information about scale drawings. Watching students refer back to their notes throughout the unit reminded me of what a great resource the interactive notebook really is for my students.
Try it out!
Want everything I used in my classroom for this unit to teach scale drawings? The entire discovery lab can be found here.
This interactive notebook foldable is also ready to just print and go here.
Get even more practice ideas, activities and resources for studying scale drawings in our next post here.
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