Length & Area – Sliding Triangles

05 May

We started our unit on Geometric Measure & Dimension with a Mathematics Assessment Project formative assessment lesson on Evaluating Statements about Length and Area.

I chose the card that each group would explore ahead of time. I only gave each group one card, and I had another task ready for them if they finished early. They didn’t. Students chose whether they wanted to explore on paper or using technology.

Screen Shot 2014-05-03 at 2.55.02 PM

Each card had a hint, which I held until I felt like the group might need it. While students were working, I monitored their progress.

Screen Shot 2014-05-03 at 2.56.05 PM

The second group had Sliding Triangles.

If you slide the top corner of a triangle from left to right, its area stays the same.

If you slide the top corner of a triangle from left to right, its perimeter changes.

They read through their card and drew a few diagrams, but they decided to spend most of their time building the scenario using our dynamic geometry software. This group did not need the hint card.

Screen Shot 2014-05-05 at 2.00.03 PM

Screen Shot 2014-05-05 at 2.00.31 PM

When it was time for this group to present their work, we sent the Quick Polls so that we would know what students instinctually thought, even though they had not all had time to explore the statements in depth. I am learning to make use of the TI-Nspire Navigator allowing me to send more than one Quick Poll at a time.

Screen Shot 2014-05-05 at 12.50.51 PM

I showed the results, but I deselected Show Correct Answer before doing so. I wanted the group to know what their peers thought before they just told them the results.

Screen Shot 2014-05-05 at 1.20.48 PM

Screen Shot 2014-05-05 at 1.20.58 PM

I used the Live Presenter feature of Navigator to make one of the student’s calculators live on the projector at the front of the room. They grabbed and moved the point that changed the top vertex of the triangle, noting with the square they had constructed off the base that the height of the triangle remained constant.

The area of the triangle will always be the same.

Screen Shot 2014-04-02 at 9.51.58 AM

What about the perimeter? The perimeter changes.

Does the perimeter always change? Sometimes the perimeter is the same.

When is the perimeter the same? When one triangle is a reflection of the other about the perpendicular bisector of the base.

Screen Shot 2014-04-02 at 9.52.27 AM Screen Shot 2014-04-02 at 9.52.43 AM

And so the journey continues …



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2 responses to “Length & Area – Sliding Triangles

  1. Travis

    May 5, 2014 at 11:03 pm

    Twofer…Insert Question1, Insert Question2, ctrl 4 (to group), Start Poll. Is that how you did it? Thanks for the tip (or reminder?).

    • jwilson828

      May 6, 2014 at 10:37 am

      Yes – or just split the screen when creating. I already had the two questions created for this document, so I grouped. I really didn’t realize until this year that questions on the same page all “polled” at once, so I’m just finding ways to incorporate. Sometimes helpful for differentiation … everyone works the first question & those who finish quickly move on to a more challenging second question.


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