Category Archives: Quadrilaterals

Dice #tlapmath

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Well, @druinok shared this amazing find from Dollar Tree!

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First of all, let me just say, JEALOUS!  But soon after, she shared an idea from #tlapmath Walk the Plank ideas to make lessons Pirate-Worthy.  So, being on the road home from a visit to my brother’s near St Louis, I had plenty of time to think. Hmmmm.

Here are a couple of  thoughts. 

Roll the dice, generate 3 sets of coordinates.  Prove what type of triangle they form.  Find the perimeter. 

OR roll 6 sets of coordinates.  Which triangle is “closest to being equilateral”?

Create coordinates for a quadilateral.  Prove what type of quadrilateral.

In a group, compare your quadrilaterals.  Who has the one closest to being a square? Rectangle? Or other polygon. Why?

Use your 8 coorindates and can you arrange (x,y) pairs to create quadilateral closest to _____?

Quadrilateral Diagonals Properties

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Over spring break, I was surfing online resources, searching for ideas and suggestions on how to plan and be more purposeful with the Mathematical Standards, which I have realized this year just how key these are to the success of CCSS. As I looked through Inside Mathematics , I ran across some PD training materials. I watched clips from Cathy Humphrey’s class. The Kite Task, an investigation of quadrilateral properties from seemed like a great activity to ease back on day 1 when we returned.

The task in short is for a kite company, who wishes to launch a new line of kites consisting of all types of qudrilaterals. The students are asked to devise a plan for how to cut/assemble the braces for each type of kite. They are only working with the diagonals in the investigation.

Rather than running copies and cutting out, I used my paper cutter to cut 1″ strips one color card-stock lengthwise and 1″strips width wise of a different collor (I didn’t realize how helpful this would be until later on). I created a strip to use as a guide on each strip, placed 7 holes equally spaced. Odd amount is best since they will be looking at bisectors some.
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Each student would receive 2 of one color and 1 of another color.
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Here are some snapshots of possible braces built.
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For anyone who is having trouble visualizing, I’ve added some “sides” to the diagonals:
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As we began the 2nd day of class, a few groups needed just a bit more time to wrap up their investigation. Using fist to five, I asked how many they still needed to determine. Most groups only 2 or 3, so I set the timer to keep us on track. I love days like this to walk around and just listen.

As I was questioning one of the groups, trying to ensure an absent student was on track, I asked the group’s members to “fill an order” – pick 2 sticks and construct the diagonals needed to brace…kite that was a rhombus, then another shape, etc to quiz them for understanding. AHA! Why couldn’t I use this as a formative assessment for the entire class?!?! Perfect.

When all groups had completed and debriefed a bit, I placed orders for kites and the students had to build the braces and pop up to show me for a quick assessment.

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These pics were actually a geometrically defined kite. If you look closely, you can see a few wrong repsonses. To address these, I used extra sets of sticks to build a correct example and an incorrect example. To ask for suggestions why one was and the other was not correct. Why was one example actually a rhombus, allowing them to really compare/contrast the two figures.

Another great mistake I saw…when asked to create a rectangle, the top sketch is what I saw from about 6 students. Of course, my initial thought was, they dont understand the diagonals must be congruent.
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Then I saw a student trace their shape in the air…second sketch. I literally saw their thinking. They had not used the sticks as diagonals. Clarified and corrected!

A post-it note quiz today, I built the braces, they had to tell me the quadrilateral name. A stop-light self assess, revealed most were confident, of the 10 yellows, 7 got all parts correct. The others missed 1, 2 or 3. All green students had each part correct.
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We did a little speed dating to use properties to solve problems. As I listened to their approaches, most everyone seemed on track. Overall, I was very pleased with the results of the lesson.

Chalk Talk part 2 #makthinkvis

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Another task I presented students in the form of a Chalk Talk

We had previously used a patty paper lesson to construct our kites. image

Simply enough, we constructed the kite by first creating an obtuse angle, with different side lengths. Folding along AC, tracing original obtuse angle using a straightedge to form the kite. Immediately students made comments about the line of symmetry. They were given time to investigate side lengths, angles, diagonals, etc. forming ideas and testing them to prove properties.

Their Chalk Talk task was to devise a plan to calculate the area of a kite.

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Most every group approached the problem by dissecting the kite into right triangles, then combining areas. Several approached dissection as top triangle/bottom triangle, but would have to adjust their thinking when I asked them test their idea with specific total diagonal lengths. Some even extended the kite to create a rectangle. In the end, our discussion centered around 3 statements/procedures for finding area of a kite.

1/2(d1*d2) (d1*d2)/2 d1*d2

Allow them to determine which will /will not work and share evidence as to their conclusions. (Hello! MP3 critique reasoning of others.)

Sure, it would have been quicker to say here’s the formula, here’s a worksheet, practice, learn it. But its so much more fun “listening” to their Chalk Talk. Again, the end discussion is key-allowing them to think / work through each group’s findings, address any misconceptions and finally coming to a concensus as a class.