Half of a Square

29 Jan

Sketch a smaller square inside the given square so that the area of the smaller square is half the area of the larger square. Write an explanation to convince another that your new, smaller square is truly half the area of the original square.

1 Square

I’m sure that I didn’t write this question, but I don’t remember from where it came.

What would your students get right?

What misconceptions might they have?

I was surprised at some of my students’ misconceptions (and miscalculations) and explanations.

2 Screen Shot 2015-01-28 at 12.56.54 PM

3 Screen Shot 2015-01-28 at 12.57.49 PM 4 Screen Shot 2015-01-28 at 12.59.22 PM 5 Screen Shot 2015-01-28 at 12.59.57 PM 6 Screen Shot 2015-01-28 at 1.00.34 PM 7 Screen Shot 2015-01-28 at 1.00.55 PM

Measuring errors.

Calculation errors. Lots of “simple” calculation errors: Half of 36 is 16. Half of 25 is 13.25. Half of 5 is 3.5.
More measuring errors.

Square vs. rectangle errors.

And someone getting at the immeasurability of irrational numbers.

The test was summative. But even though the test was summative in my gradebook, I can still use the responses to inform the learning experiences that I give my students in the future. And so I will, as the journey continues …


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2 responses to “Half of a Square

  1. Rudolph, Heidi

    January 29, 2015 at 6:21 pm

    Do you know anything about the high school webinar tonight with Illustrative Math? I didn’t get the email with the link today…. 😦

  2. howardat58

    January 29, 2015 at 8:31 pm

    I was intrigued by the variety of answers to the other two questions as well.


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