Wednesday, March 30, 2016

Area of Polygons Practice

After the students learned the area of triangles, parallelograms, and trapezoids, they needed to practice.

It would be easy to give them a worksheet with the shapes on it and all the measurements given and they just have to plug the numbers into the formula the solve.

Worksheets can be useful, but when there is a way to not do a worksheet, do it.

I did this activity last year and wish I would have saved all the shapes I made. So I remade them again and laminated them.

I drew 10-12 triangles, parallelograms, and trapezoids each. I spread them around the room and asked the students to find the area of the shapes. They measured everything to the nearest centimeters.

To make them talk to each other about it, I asked them to verify their answers with their classmates. I put a large poster at the front of the room with a table of the shapes. Once students have verified their answers with 3 other classmates, they could start adding the area of the shapes to the poster.

Once I made and laminated all the shapes, the activity was easy to put together. I didn't even use any copies! Just notebook paper.

If you dont want to draw your own shapes, you can use this file here. Download it for free. 

Here is another way for students to practice finding the area of polygons fro my TpT store. 

In Texas, 6th graders are to "determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers." 

Monday, March 28, 2016

Decomposing a Trapezoid--Finding the Area

This has been one of my most favorite and wonderful lessons of my entire teaching career. My students pleasant surprised me with how awesome they are.

Students need to be able to explain how shapes can be decomposed into other shapes to find the area--that is how the formulas are derived.

There are several different ways trapezoids can be decomposed and rearranged to make other shapes. Before this lesson, the students had a guided lesson to decompose parallelograms to rectangles and triangles to parallelograms. So they had previous experience with cutting and rearranging shapes.

I wanted to see if they could take what they had done and apply it to trapezoids.

And they did awesome.

I gave them a sheet of trapeziods and a ruler. I asked them to pick any trapezoid and find a way to decompose it, rearrange it, and find the area.

My advanced class found 8 different ways to find the area. My on-level class found 5 different ways.

I don't have the list we made in front of me, but these are some of the ones I remember they were able to find.

  • Cut the trapezoid by the diagonal to make two triangles
  • Cut off two triangles at the ends to make one square and one rectangle
  • Cut off one triangle and you have a triangle and a rectangle (When one of the sides of the trapezoid is also the height
  • Cut the trapezoid by the height, rearrange and make a rectangle
  • Double the trapezoid to make a parallelogram
  • Cut off one triangle, add to the other side to make a rectangle

After the students spent some time exploring, I had students share what they found. We looked at the measurements of the original trapezoids and of the new shapes they created and found some patterns.

Sometimes, the new base was in between the two original bases(specifically it was the average of the two bases). When you had a triangle, you used the formula 1/2bh and added to the area of the other piece. If you doubled the trapezoid, you would have to half the area of your new shape. 

The last step was to write a formula that they could use to find the area of a trapezoid so they wouldn't have to decompose a trapezoid every time they wanted to find the area. I'll need to improve this part of the lesson. Students got the adding something, the multiplying the height and either multiplying by 1/2 or dividing by 2, just not in a way that would work. 

It was a fun lesson and I was walking around so excited all day long because they were doing such a good job trying and finding ways to decompose the trapezoids!

If you want pdf of the printable with the trapezoids, you can download it here

If you want some notebook pages that show decomposing shapes to find the area, I have some in my store. 

Thursday, March 24, 2016

Measures of Center

We started our unit on Statistics after spring break. It is one of my favorite things to do and teach and it is not easy for students to understand. There are so many little things about that you understand once you've studied statistics for awhile. I took some pretty intense statistics classes in college, so I feel like everyone should learn everything about it--I have to remind myself that my 6th graders need to be gradually introduced to it.

So this is the foldable we created for Mean, Median, Mode, and Range--I let my students use my markers and they loved it--I'll have to pull out markers more often.

I read this book in college and it is so interesting. It's been a few years since I've read it, I might have to pull it out again.

Sunday, March 20, 2016

Properties of Operations Pockets

I love little pockets in notebooks. They are also a great way for students to sort things and resort them later to quiz themselves.

This properties of operations page is my favorite.

All the cards with 10 different properties of operations is available on Teachers Pay Teachers. 

Wednesday, March 9, 2016

Classifying Numbers--Nesting Containers

6th grade is the first time students in Texas have to classify numbers. It has been a difficult concept for my students to understand--especially that numbers can "fit" into several different classifications.

I found some "nesting" tupperware to help my students visualize it. I have kept this handy in my classroom so every time we talk about classifying numbers, I pull these out.

So if we classify a number as a natural number, it is also a whole number, integer, and rational numbers since it "fits" into the bother containers. 

I have 7 different classifying rational numbers stations available in my store

Monday, March 7, 2016

Triangle Inequality Theorem

This is the second year I have taught the Triangle Inequality Theorem using spaghetti and I love doing it this way. 

First I had students copy the table into their notebook and gave them a piece of spaghetti. Their instructions were to break it into three uneven pieces, measure the three pieces, and record their measurements under the columns short side, medium side, and long side. (I asked them to do three uneven pieces because last year too many students broke them into the exact same length and it was more difficult to illustrate the concept)
As the students were measuring, I was walking around the room asking students to write their measurements on the board. I looked for a mixture of those who lengths that would make a triangle and those who did not. I asked a few students to come to the board and share their triangle lengths. 

BEFORE filling out the short + medium column, I ask students to try to make a triangle with their pieces. I asked the students who wrote their measurements on the board if their length pieces made a triangle and we added a "yes" or a "no" to the last column.

I didn't have the column labeled Short+Medium yet. So with 4/5 columns filled in, I asked the students to look for a pattern. Some classes were able to see that when two small side lengths were more than the large one, there was a triangle.

For the class that did not come to that conclusion, we added the short+medium, then added up those two sides and I asked them to look again.

It is one of my favorite lessons of the year. After we determined what the Triangle Inequality Theorem says, we put this foldable into the student notebooks.  My students did really well explaining when a triangle could be formed.

This foldable is now available in my store. 

Saturday, March 5, 2016



I finally did this for my class. I read about it here and here .

I really liked it and I loved watching them do it. They had some great conversations about what models to use to represent integer operations and it helped me see where they need more help.

I  made cards with various integer problems on it like -5+3 and 4*-2 and they had to model the expression and their partner had to write the expression that matched it.

I think this could also work with algebraic expressions and equations--and that will be my next station to try with my students. 

Thursday, March 3, 2016

Lucky to Be a Teacher Giveaway

There is a giveaway going on RIGHT NOW for all types of products. I have a product in the Middle-High School Category. 

Why Am I Lucky to be a Teacher?

Right now, I am thinking it is because Spring Break is coming up! Only 6 more school days before all the sleeping in begins!

But real talk (that's what the kids say), I am lucky to watch kids grow and change and try to become their best selves. I love watching kids get the math I'm teaching. I love watching kids explain math concepts to their peers and being successful!

Teachers have a responsibility to nurture and help students grow to be responsible citizens. I get to be a part of that! 

The more stores you follow, the more entries you get! The giveaway ends Sunday Night.

Thank you to Countless Smart Cookies for hosting this giveaway!

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