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What I Learned Today: Scale Drawings and Maps

I asked my 15-year-old what she learned today at school. She paused for a moment and then answered my question by asking me what I learned at school today.

It took me a while to think about what I had learned [which will make me more patient when I ask her the question again tomorrow], and then I remembered and shared with her:

We are working with some teachers who are using the Illustrative Mathematics 6–8 Math curriculum. The 7th grade teachers are in Unit 1, Scale Drawings. They are working with Scale Drawings and Maps. Today I learned to look more closely at the scale given for a map.

Look at the following for a moment. What’s the same? What’s different?

mapscale1.png

mapscale3.png

mapscale2.png

mapscale4.png

The last two are from Illustrative Mathematics, which you can download for free at openupresources.org.

What’s different about the scales on the last two?

Attend to precision, MP6, says, “Mathematically proficient students try to communicate precisely to others. … They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately.”

I’m not sure that we would have noticed a difference, except that we were trying to find some assessment items from another source and saw that many aligned to 7.G.A.1 included a scale in the form of “1 cm = 100 miles”. I’ve looked at lots of maps and I never noticed the incongruity of saying that 1 cm equals 100 miles. We don’t really mean that 1 cm equals 100 miles, right? Not in the same sense that we say 4 quarters equals $1 or 3+4=7. Is there any wonder that our students misuse the equal sign?

And so the journey continues, grateful for the authors of this curriculum who make me pay closer attention to attending to precision and grateful for my daughter who makes me think and share about what I’m learning, too …

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