Baker's Choice Portfolio:
Table of Contents:
1. Cover Letter
2. The 3 main steps to solving a Baker's Choice problem
3. POW Write Up - Kick It! (Link)
4. Other Quality Work - Profitable Pictures
5. Baker's Choice Revisited
6. In-class assessment - Baker's Choice
7. Personal Growth
1. Cover Letter
This unit of an mathematics that centers around graphs of linear equations and inequalities to help students build a deeper understanding of the content, not just simply memorize the "rules". Though this interactive unit students are expected to collaborate in groups and in class discussions. These collaborative efforts are designed around helping students feel comfortable with explaining their mathematical thinking through problems, either right or wrong. In the end it is about understanding but this unit really focus on the individual child and their unique approach to the problem is not only celebrated but it is expected. Creating a unit such as Baker's Choice creates a classroom environment where the content is accessible to all students. The goal of the unit is for student to see patterns, develop relationships and then make claims based on their evidence about solving a problem. This unit takes an abstract and difficult concept for students and creates problems that are relatable and relevant to the students.
Table of Contents:
1. Cover Letter
2. The 3 main steps to solving a Baker's Choice problem
3. POW Write Up - Kick It! (Link)
4. Other Quality Work - Profitable Pictures
5. Baker's Choice Revisited
6. In-class assessment - Baker's Choice
7. Personal Growth
1. Cover Letter
This unit of an mathematics that centers around graphs of linear equations and inequalities to help students build a deeper understanding of the content, not just simply memorize the "rules". Though this interactive unit students are expected to collaborate in groups and in class discussions. These collaborative efforts are designed around helping students feel comfortable with explaining their mathematical thinking through problems, either right or wrong. In the end it is about understanding but this unit really focus on the individual child and their unique approach to the problem is not only celebrated but it is expected. Creating a unit such as Baker's Choice creates a classroom environment where the content is accessible to all students. The goal of the unit is for student to see patterns, develop relationships and then make claims based on their evidence about solving a problem. This unit takes an abstract and difficult concept for students and creates problems that are relatable and relevant to the students.
2. The 3 main steps (in my opinion) to solve a Baker's Choice problem:
1. Student need time to think about the problem. During this think time students may begin to write down their ideas and thoughts about the problem. This may be the time that the student starts to pull out information they know and information they need to know to solve it. This step may include pictures, numbers and words or a combination of these three things. During this first step students are exploring the problem.
2. Once the first step is as complete as possible the student then transitions into trying to solve the problem. During this time students will be looking at all the information that is given and then attempt to solve the problem. During this step students look at solving the equations, graphing them and then looking for regions that fit the constraints of the problem.
3. The students then begin to transition into solving the problem or finding an "answer" that they came up with. During this step students are expected to not only find an answer but they are expected to back up that claim with evidence of their mathematical thinking. It is during this time int he process where students are building a deep understanding of the content because they found an answer but now they need to figure our "why".
I have an additional step here that is a very valuable aspect of this unit which is the collaboration part. This step is of course completed after solving a problem in Baker's Choice:
In Class Sharing: This in my opinion is at the core of Baker's Choice and that is the collaboration and sharing part of the process. It is this time in the problem where the students come together and share their individual mathematical thinking with either the class or in small group discussions. During these discussions students may find themselves "teaching" their thinking through the problem and how they approached it. The root of this is that the concepts are what is important not if the student got the correct "answer" or not.
3. POW: Kick It!
Click here to see my Kick It! Write up.
4. Other Quality Work - Profitable Pictures:
In this example of my work I started by removing what was known from the problem and while doing this I was thinking of the way I was going to set up the problem. It was clear to me that equations needed to be made that had the restraints that were given.
P = pastels (this would represent my x-axis)
W = water colors (this would represent my y-axis)
Profit =
P(pastels) = $40
W (watercolors) = $100
From there I started to work out the costs of making each type of painting
P (pastels) = $5 each
W (watercolors)= $15 each
My constraint (limits) were:
I could only make 16 pictures total
And I only have $180 total to spend
From there I sent up equations:
P + W < 16
5P + 15W < 180
I then plotted the two equations above (see in my photo) and saw where the two points intersected.
40P + 100W = Profits Max
From there I found where the equation above (max profits) = 1000, 600, 500 and put those numbers into
40P + 100W = Profits Max and graphed the three lines (as noted above in my photo, labeled $1000 profit, $600 profit, $500 profit)
The maximum profits are when the two equations hit the vertex point (10, 6).
This is what I came up with until we did the exercise in class with the straw and then I had an "ah-ha" moment:
It is very easy just to tell students to memorize that one of the vertices would give the maximum value so they can get a similar question right on the next exam. The real question is why is that true? We need to get our students to start asking why? It was seen after were were given straws to me that, in a profit equation the slope remains the same no matter what the profit. By physically sliding the straws up at this same slope I was able to see why the vertex, 6,10 was infact the maximum profit.
Click here to see my Kick It! Write up.
4. Other Quality Work - Profitable Pictures:
In this example of my work I started by removing what was known from the problem and while doing this I was thinking of the way I was going to set up the problem. It was clear to me that equations needed to be made that had the restraints that were given.
P = pastels (this would represent my x-axis)
W = water colors (this would represent my y-axis)
Profit =
P(pastels) = $40
W (watercolors) = $100
From there I started to work out the costs of making each type of painting
P (pastels) = $5 each
W (watercolors)= $15 each
My constraint (limits) were:
I could only make 16 pictures total
And I only have $180 total to spend
From there I sent up equations:
P + W < 16
5P + 15W < 180
I then plotted the two equations above (see in my photo) and saw where the two points intersected.
40P + 100W = Profits Max
From there I found where the equation above (max profits) = 1000, 600, 500 and put those numbers into
40P + 100W = Profits Max and graphed the three lines (as noted above in my photo, labeled $1000 profit, $600 profit, $500 profit)
The maximum profits are when the two equations hit the vertex point (10, 6).
This is what I came up with until we did the exercise in class with the straw and then I had an "ah-ha" moment:
It is very easy just to tell students to memorize that one of the vertices would give the maximum value so they can get a similar question right on the next exam. The real question is why is that true? We need to get our students to start asking why? It was seen after were were given straws to me that, in a profit equation the slope remains the same no matter what the profit. By physically sliding the straws up at this same slope I was able to see why the vertex, 6,10 was infact the maximum profit.
5. Baker's Choice Revisited
Elements I want to see from my students using Baker's Choice:
1. The build a deeper understanding of linear equations and inequalities by given a in-depth problem that requires critical thinking skills.
2. Students get in the habit of thinking mathematically
3. Students feel comfortable with showing and explaining their way of thinking, either right or wrong
4. Students show evidence to back up their claims
5. Students show their fellow classmates respect while they are presenting their findings/mathematical thinking
6. Students get comfortable with failing and see it as growth both socially and academically
7. By providing students with only one or two problems versus many in the standard "drill and kill" students gain a new understanding of mathematics.
6. In-Class Assessment For Baker's Choice
ABOVE: My work for in-class assessment #1. (Please note that I used the same graph for all 3 assessments) :)
Elements I want to see from my students using Baker's Choice:
1. The build a deeper understanding of linear equations and inequalities by given a in-depth problem that requires critical thinking skills.
2. Students get in the habit of thinking mathematically
3. Students feel comfortable with showing and explaining their way of thinking, either right or wrong
4. Students show evidence to back up their claims
5. Students show their fellow classmates respect while they are presenting their findings/mathematical thinking
6. Students get comfortable with failing and see it as growth both socially and academically
7. By providing students with only one or two problems versus many in the standard "drill and kill" students gain a new understanding of mathematics.
6. In-Class Assessment For Baker's Choice
ABOVE: My work for in-class assessment #1. (Please note that I used the same graph for all 3 assessments) :)
ABOVE: My work for in-class assessments #2-3 (graph is in above pic)
7. Personal Growth
Baker's choice to me could have been called student choice because I believe this unit is designed to give student's choices. These choices include both right and wrong answers. The one important aspect of this unit is the interactive quality of the problems. Each week we were asked to complete a problem. When we returned to class hand discussed these problems, that's when I really was able to see the value in collaboration and development of a deep understanding of mathematical thinking. It was during these discussion both as a small and large group where I really was able to see the importance of mathematical thinking. As the problems were presented week after week I started to really value the importance of an open-ended problem with maybe one or maybe many answers as.
In the beginning of this course I was very nervous about sharing in front of the class. I felt like everyone who chose to show their work was then drilled with more questions and comments about their choice in using the mathematical steps they choose. It was not until one day that the instructor ask the students in our class to focus only on the student who is presenting mathematical thinking, that is ask questions that only pertains to the information they are giving you, nothing more. To me this was a turning point about Baker's Choice and about setting a classroom expectation for all students. This is very important as a future teacher because we want to encourage an environment where all ideas and thoughts are welcome and appreciated as valuable learning steps for each individual student.
Mistakes = Personal Growth (Academically, Socially & In Life)
Baker's choice to me could have been called student choice because I believe this unit is designed to give student's choices. These choices include both right and wrong answers. The one important aspect of this unit is the interactive quality of the problems. Each week we were asked to complete a problem. When we returned to class hand discussed these problems, that's when I really was able to see the value in collaboration and development of a deep understanding of mathematical thinking. It was during these discussion both as a small and large group where I really was able to see the importance of mathematical thinking. As the problems were presented week after week I started to really value the importance of an open-ended problem with maybe one or maybe many answers as.
In the beginning of this course I was very nervous about sharing in front of the class. I felt like everyone who chose to show their work was then drilled with more questions and comments about their choice in using the mathematical steps they choose. It was not until one day that the instructor ask the students in our class to focus only on the student who is presenting mathematical thinking, that is ask questions that only pertains to the information they are giving you, nothing more. To me this was a turning point about Baker's Choice and about setting a classroom expectation for all students. This is very important as a future teacher because we want to encourage an environment where all ideas and thoughts are welcome and appreciated as valuable learning steps for each individual student.
Mistakes = Personal Growth (Academically, Socially & In Life)