Check out the youcubed.org website for links to resources from Jo Boaler. Her most recent post is a collection of her 7 favorite messages to set positive classroom norms for the start of the school year. She also includes a summary page that can be posted in the classroom. Additionally, there is a document with 10 formative assessment strategies for the math class included towards the bottom of this post.
Thursday, August 21, 2014
Monday, August 11, 2014
Presentations
Below is a list of MVLA math presentations along with links to the info from each presentation. Some of the presentations are specific to a site or course team, though the information can be useful to everyone.
MVHS Trig/Math Analysis 2-11-2015
LAHS Trig/Math Analysis 1-15-2015
LAHS Geo H 1-14-2014
LAHS 1-7-14
MVHS 1-7-14
GeoH 2-12-14
GeoH 3-26-14
MVHS Trig/Math Analysis 2-11-2015
LAHS Trig/Math Analysis 1-15-2015
LAHS Geo H 1-14-2014
LAHS 1-7-14
MVHS 1-7-14
GeoH 2-12-14
GeoH 3-26-14
MVLA Math Resources
The linked document was developed during the 2013-2014 school year, and includes resources related to the following:
-Online Curriculum and course maps
-Online problem banks
-Smarter Balanced Test released items
-Sample Performance Tasks from Smarter Balanced
-Technology Tools
MVLA Math Resources
-Online Curriculum and course maps
-Online problem banks
-Smarter Balanced Test released items
-Sample Performance Tasks from Smarter Balanced
-Technology Tools
MVLA Math Resources
Geogebra Tools
Geogebra Tools Spreadsheet
The tools in this spreadsheet are designed for easy use during either a lecture/demonstration, or by students to complete their work. There is much value in having students create some of these presentations on their own, but if there are time constraints, a premade tool can be a great support in the learning process. These tools can be downloaded for free from geogebratube.org website as well if you'd like to make modifications. To download, open the file from the spreadsheet (it opens as a geogebratube file), and remove the m from the beginning of the 6-digit code at the end of the url. This takes you to the teacher page, where there is an option to download the file.
There are countless Geogebra presentations available on Geogebratube and other blogs, and I feel like I have only skimmed the surface. The second tab of the spreadsheet contains links to Geogebra presentations from other authors. If you have found a presentation that has been useful, please share the link and I will add to the spreadsheet.
The tools in this spreadsheet are designed for easy use during either a lecture/demonstration, or by students to complete their work. There is much value in having students create some of these presentations on their own, but if there are time constraints, a premade tool can be a great support in the learning process. These tools can be downloaded for free from geogebratube.org website as well if you'd like to make modifications. To download, open the file from the spreadsheet (it opens as a geogebratube file), and remove the m from the beginning of the 6-digit code at the end of the url. This takes you to the teacher page, where there is an option to download the file.
There are countless Geogebra presentations available on Geogebratube and other blogs, and I feel like I have only skimmed the surface. The second tab of the spreadsheet contains links to Geogebra presentations from other authors. If you have found a presentation that has been useful, please share the link and I will add to the spreadsheet.
Modeling with Trig Functions
The activity below was used by some of the Algebra 2 teachers at LAHS last year, but it is also a great activity for trig/math analysis. If you'd like to use this activity with a different context, please let me know.
I wanted to share this as blogpost to give an example of what we can do with the blog. In this case, I am sharing parts of an activity that took place in a class, and some of the questions that a teacher might ask as they go through the activity. So the blogpost can serve as a script if you find that to be helpful.
Towards the end of this unit in Algebra 2, students were asked to model real world situations using trigonometric functions. We picked a few problems involving tides and ended with a problem from Illustrative Mathematics called Foxes and Rabbits 2. We used a series of scaffolded Geogebra presentations to help students get started. The first presentation is below, and is an embedded applet that you can play with. Type a function into the f(x) input bar and press enter to see it on the graph. You should try this right now. It is fun! The goal is to get the sine graph to pass through all of the data points.
We introduced this to students by first talking about the data and how tides are measured. You can talk about how the moon impacts tides and how the data is roughly periodic. At this point students should know the amplitude and period for y=sin(x). Next, have a class conversation about how to transform this graph to pass through the given points. The power of a premade interactive model is that you can pause during the conversation to allow students time to process. I make use of the think-pair-share structure with the expectation that students may be called on to explain what they know or discussed with a partner. Below is a list of questions that can be used with this presentation after the initial conversation about the data. Feedback on this list of questions would be great!
1. What is the midline for the Santa Cruz Tides data? (Discuss first, then reveal the midline by selecting the midline box.)
3. What is the maximum value of this function? What does it represent with respect to the tides? Find the minimum value as well. Discuss and then reveal the max and min lines by selecting the appropriate box.
5. Now that I know that the amplitude is 1.5, how can I change my function f(x)=sin(x)+2.5 to account for an amplitude that is not 1?
6. Discuss with your partner what one period of y=sin(x) looks like. My current graph has been shifted horizontally from the parent graph y=sin(x). Can you find a new starting point? How can we change our function y=1.5sin(x)+2.5 so that it has been shifted horizontally to your new starting point? (There are multiple answers here, which can be discussed now or later depending time.)
7. What about the period? Note: Most classes will have a formula to use to account for a change in period. I haven't taught trig in years, so I just use horizontal stretch/shrink reasoning. y=sin(x) has a period of 2pi, and Santa Cruz tides has a period of 12. Since 12 is larger than 2pi, I will multiply x by a factor of (2pi)/12. My new function is f(x)=1.5sin(2pi/12(x-9))+2.5.
One of the teachers from this team made a worksheet for students to use as we modeled the thinking. I find this to be an important step so that students can refer back as they practice and study. Please let me know if you are interested in having this worksheet, and I can get you a copy.
Below is a list of all the tide problems that students worked on.
Santa Cruz Tides
San Mateo Bridge Tides
Bay of Fundy Tides
Students also worked on Foxes and Rabbits from Illustrative Mathematics.
Illustrative Mathematics Foxes and Rabbits 2 Problem
Illustrative Mathematics Foxes and Rabbits Geogebra Tool
I wanted to share this as blogpost to give an example of what we can do with the blog. In this case, I am sharing parts of an activity that took place in a class, and some of the questions that a teacher might ask as they go through the activity. So the blogpost can serve as a script if you find that to be helpful.
Towards the end of this unit in Algebra 2, students were asked to model real world situations using trigonometric functions. We picked a few problems involving tides and ended with a problem from Illustrative Mathematics called Foxes and Rabbits 2. We used a series of scaffolded Geogebra presentations to help students get started. The first presentation is below, and is an embedded applet that you can play with. Type a function into the f(x) input bar and press enter to see it on the graph. You should try this right now. It is fun! The goal is to get the sine graph to pass through all of the data points.
We introduced this to students by first talking about the data and how tides are measured. You can talk about how the moon impacts tides and how the data is roughly periodic. At this point students should know the amplitude and period for y=sin(x). Next, have a class conversation about how to transform this graph to pass through the given points. The power of a premade interactive model is that you can pause during the conversation to allow students time to process. I make use of the think-pair-share structure with the expectation that students may be called on to explain what they know or discussed with a partner. Below is a list of questions that can be used with this presentation after the initial conversation about the data. Feedback on this list of questions would be great!
1. What is the midline for the Santa Cruz Tides data? (Discuss first, then reveal the midline by selecting the midline box.)
2. How can I change (transform) the function f(x)=sin(x) so that it has this midline? (Discuss, then type in the correct function and reveal the change in the graph.)
3. What is the maximum value of this function? What does it represent with respect to the tides? Find the minimum value as well. Discuss and then reveal the max and min lines by selecting the appropriate box.
4. What is the difference between the highest and lowest tide measurements? Does this help me find the amplitude, period, or vertical shift of my function?
5. Now that I know that the amplitude is 1.5, how can I change my function f(x)=sin(x)+2.5 to account for an amplitude that is not 1?
6. Discuss with your partner what one period of y=sin(x) looks like. My current graph has been shifted horizontally from the parent graph y=sin(x). Can you find a new starting point? How can we change our function y=1.5sin(x)+2.5 so that it has been shifted horizontally to your new starting point? (There are multiple answers here, which can be discussed now or later depending time.)
One of the teachers from this team made a worksheet for students to use as we modeled the thinking. I find this to be an important step so that students can refer back as they practice and study. Please let me know if you are interested in having this worksheet, and I can get you a copy.
Below is a list of all the tide problems that students worked on.
Santa Cruz Tides
San Mateo Bridge Tides
Bay of Fundy Tides
Students also worked on Foxes and Rabbits from Illustrative Mathematics.
Illustrative Mathematics Foxes and Rabbits 2 Problem
Illustrative Mathematics Foxes and Rabbits Geogebra Tool
Saturday, July 19, 2014
Google Auto Awesome: Santa Cruz Tides
I found this one day through an alert from Google. It was made automatically by Google Auto Awesome! When you upload pictures to Blogger, they are automatically saved in Google Photos, and when there are several related photos Google Auto Awesome makes a little movie for you. Pretty Awesome!
Saturday, July 12, 2014
Geogebra Tool: Domain and Range for a Set of Points
You can view more tools on the Geogebra Tools page. There are several more tools for students to use to explore domain and range. Use these tools in Algebra I, Algebra II, or Math Analysis as an introduction or refresher for domain and range.
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