The glue 20 of these together, small triangles on the inside, large triangles on the outside to make an icosahedron.
Monday, March 9, 2015
Pictures of the circle activity
The glue 20 of these together, small triangles on the inside, large triangles on the outside to make an icosahedron.
Tuesday, March 3, 2015
Flipped Intro to Quadrilaterals with Edpuzzle and Google Forms
The Common Core standards have brought us many changes to our Geometry curriculum, including less of an emphasis on special quadrilaterals and their properties. We used to spend an entire chapter talking about parallelograms, rectangles, rhombuses, kites, and trapezoids. Some of the newer curriculums such as Engage NY give this topic a couple of lessons worth of attention, with the focus being on proving properties of parallelograms. The Common Core Standard here is G-CO-11, which states:
My hope here is to get students to review vocabulary related to quadrilaterals such as sides, angles, and diagonals, and to make some observations about what is happening with the parallelogram in the video as it is being transformed.
The video above gives concrete measures for both angles and segment lengths, so to transition to abstract thinking I've made a few more videos for students to take a look at. Below is a Google Form that students can go through to both watch introductory videos and to answer some questions before we launch into a class conversation. There are additional videos on pages 2-3 of this form, and I will post the videos below so that you don't have to input answers into the form in order to proceed to the next page. If you want to fill out the form just for fun go right ahead, as this is a copy of my original form.
Video 2:
After this video the Google Form asks students to identify the pair of congruent angles that justifies why the marked pair of sides are parallel.
Video 3:
This video asks students to recall what a diagonal is, and also asks students to make an observation about congruences formed by intersecting diagonals.
These videos may need a bit more context, but basically I am hoping to show students how to see that all parallelograms are formed by rotating a triangle 180 degrees about the midpoint of one of its sides. From here, corresponding parts are congruent, and we begin to see why many of the parallelogram properties are true. Between the Edpuzzle video and the google form, I am asking students to make some of the observations about congruent parts of parallelograms that we will later prove. I'll note that this is still in draft form and my first attempt at flipping, so any feedback is welcomed.
Prove theorems about
parallelograms. Theorems include:
opposite sides are congruent, opposite angles
are congruent, the diagonals of a parallelogram
bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.
With the emphasis being on proving the properties/theorems, I am rethinking the way that I approach this material. Below is an Edpuzzle video that students can watch before we begin talking about parallelograms.
My hope here is to get students to review vocabulary related to quadrilaterals such as sides, angles, and diagonals, and to make some observations about what is happening with the parallelogram in the video as it is being transformed.
The video above gives concrete measures for both angles and segment lengths, so to transition to abstract thinking I've made a few more videos for students to take a look at. Below is a Google Form that students can go through to both watch introductory videos and to answer some questions before we launch into a class conversation. There are additional videos on pages 2-3 of this form, and I will post the videos below so that you don't have to input answers into the form in order to proceed to the next page. If you want to fill out the form just for fun go right ahead, as this is a copy of my original form.
Video 2:
After this video the Google Form asks students to identify the pair of congruent angles that justifies why the marked pair of sides are parallel.
Video 3:
This video asks students to recall what a diagonal is, and also asks students to make an observation about congruences formed by intersecting diagonals.
These videos may need a bit more context, but basically I am hoping to show students how to see that all parallelograms are formed by rotating a triangle 180 degrees about the midpoint of one of its sides. From here, corresponding parts are congruent, and we begin to see why many of the parallelogram properties are true. Between the Edpuzzle video and the google form, I am asking students to make some of the observations about congruent parts of parallelograms that we will later prove. I'll note that this is still in draft form and my first attempt at flipping, so any feedback is welcomed.
Monday, February 9, 2015
Highlight your correct answers in Geogebra
I've led a number of sessions over the past few months introducing teachers to Geogebra and Desmos. My general outline for presentation is to show the basics of what you can do with these programs, as well as to share some of the great pre-made resources that are available online, namely at geogebratube.org. After this we aim to have some playtime, during which teachers always ask me how to make the presentation below:
For this particular presentation, we asked students to perform a specific transformation of the graph of y=x^2. You move the 5 points according to the description, then you input the equation for the transformed graph and check your answer. I've been promising a how-to blogpost on this topic. Hope it is helpful! Follow the steps below to create a modified version of what you see in the above video, and please let me know if you have questions.
Stage 1: Create your objects
1. Type into the input bar g(x)=x^2 and f(x)=0. Press enter after each entry.
2. Use the add a point tool to add 3 points to the grid. Be careful not to put them on the axes or on an object. This will attach them to an object, and we need them to be movable. At this point in time I start changing the color and style of the objects.
right click-->object properties-->color (or style).
Stage 2: Boolean Variable and Conditions to Show
5. Add a boolean variable. My boolean variable is called sameGraph. It is true if function f goes through points A, B, and C. Otherwise it is false. You add the variable by typing into the input bar.
6. Type fcorrect=f into the input bar and press enter. This creates a new function called fcorrect(x) that is exactly the same as f(x).
7. Right click on function f and select object properties. From here you can change the color and style. I chose blue dashed. Under the Advanced tab we will type !sameGraph into the "conditions to show object" box. This means that function f will only show when our boolean variable sameGraph is false. This means function f will only show when points A, B, and C are not on f.
8. Right click on function fcorrect and select object properties. From here you can change the color and style. I chose green. Under the Advanced tab we will type sameGraph into the "conditions to show object" box. This means that function fcorrect will only show when our boolean variable sameGraph is true. This means function f will only show when points A, B, and C are on f.
9. I also want my "you got it" textbox to show only when A, B, and C are on f. The steps are the same as those above. The tricky part is that your textbox may not be showing on the screen, so you can't right click on it. If this is the case, right click on another object, select object properties, and then find your textbox in the objects list.
For this particular presentation, we asked students to perform a specific transformation of the graph of y=x^2. You move the 5 points according to the description, then you input the equation for the transformed graph and check your answer. I've been promising a how-to blogpost on this topic. Hope it is helpful! Follow the steps below to create a modified version of what you see in the above video, and please let me know if you have questions.
Stage 1: Create your objects
1. Type into the input bar g(x)=x^2 and f(x)=0. Press enter after each entry.
2. Use the add a point tool to add 3 points to the grid. Be careful not to put them on the axes or on an object. This will attach them to an object, and we need them to be movable. At this point in time I start changing the color and style of the objects.
right click-->object properties-->color (or style).
3. Add an input box. The caption should be "f(x)", and we attach it to object f.
4. Add a text box. I chose the "You got it!" as my text. Drag your textbox and input box to an appropriate location.
Stage 2: Boolean Variable and Conditions to Show
5. Add a boolean variable. My boolean variable is called sameGraph. It is true if function f goes through points A, B, and C. Otherwise it is false. You add the variable by typing into the input bar.
6. Type fcorrect=f into the input bar and press enter. This creates a new function called fcorrect(x) that is exactly the same as f(x).
7. Right click on function f and select object properties. From here you can change the color and style. I chose blue dashed. Under the Advanced tab we will type !sameGraph into the "conditions to show object" box. This means that function f will only show when our boolean variable sameGraph is false. This means function f will only show when points A, B, and C are not on f.
8. Right click on function fcorrect and select object properties. From here you can change the color and style. I chose green. Under the Advanced tab we will type sameGraph into the "conditions to show object" box. This means that function fcorrect will only show when our boolean variable sameGraph is true. This means function f will only show when points A, B, and C are on f.
Below is what your final product will look like when you have a correct answer. For this example, we transformed the points on y=x^2 three units right and one unit up. Then we typed in the correct function into the input box.
Side note: If I intend for students to interact with my presentation, I always change the point capturing to "fixed to grid". This saves valuable class time, as points will automatically go to the nearest point with integer coordinates (or where gridlines cross, depends on your settings). I haven't found this feature yet in Geogebra 5, so I use Geogebra 4 for these types of presentations.
Wednesday, January 7, 2015
SBAC Calculators
Basic Calculator
This is the calculator that is embedded into the practice problems released by SBAC. Students can work through the tutorial to learn how to enter fractions, exponents, etc.
Graphing and Regression Calculator
Here you will find the calculator that is embedded more so into the performance tasks.
There will be opportunities to learn more about these calculators soon, as well as class activities.
This is the calculator that is embedded into the practice problems released by SBAC. Students can work through the tutorial to learn how to enter fractions, exponents, etc.
Graphing and Regression Calculator
Here you will find the calculator that is embedded more so into the performance tasks.
There will be opportunities to learn more about these calculators soon, as well as class activities.
Tuesday, January 6, 2015
LAHS Geogebra Training 1-6-2015
Please sign in, then fill out this quick form to help us guide our time together.
Vision: Teachers and students will be proficient at using Geogebra to demonstrate thinking and to solve problems.
Goals:
-Learn about support available for integrating Geogebra into your class
-Learn how to locate and use pre-made Geogebra presentations
-Learn some basics for using Geogebra
Basics Tutorial
Screencasts
Functions
Geogebra Tools Page
Vision: Teachers and students will be proficient at using Geogebra to demonstrate thinking and to solve problems.
Goals:
-Learn about support available for integrating Geogebra into your class
-Learn how to locate and use pre-made Geogebra presentations
-Learn some basics for using Geogebra
Basics Tutorial
Screencasts
Functions
Geogebra Tools Page
Monday, January 5, 2015
Piecewise Functions for Trig/Math Analysis
We are about to start functions and transformations in trig/math analysis, so I made some piecewise functions in Desmos to use for the intro.
Then we can view transformations of f by typing the transformation on an input line to the left of the graph.
All of these functions were taken from Calculus AB free response questions, hence the link back to the website. I also made a table of values to use for by-hand practice.
Watch this video by Meg Craig for a fantastic demo of how to use the table above. Scroll down to the embedded video to view.
The above function is named f(x). Below is what I entered to graph the function.
Then we can view transformations of f by typing the transformation on an input line to the left of the graph.
You can show or hide each graph by clicking on the colored circle to the left of the equation. Below is 2f(x).
And f(2x).
Here are the links to the Desmos graphs. Graphs 3 and 4 include questions for students to answer. Hope some of you can use them!
All of these functions were taken from Calculus AB free response questions, hence the link back to the website. I also made a table of values to use for by-hand practice.
Watch this video by Meg Craig for a fantastic demo of how to use the table above. Scroll down to the embedded video to view.
Sunday, January 4, 2015
SBAC Test Resources 2015
Updated links. Also available on the mvla website under the common core tab, as well as on our common core resources page from 2013-2014.
Clovis Unified School District SBAC Page. Organized by claim for easy navigation.
SBAC Calculator
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