Portfolio

Desmos: Marbleslides

Image retrieved from https://goo.gl/TNXPZJ

 The first item that I want to include is the Desmos Activity Marbleslides. This activity is a fun activity where students are asked to launch a ball and hit all the stars that are on the Cartesian plane. In order to do this the students have to use their knowledge of functions and transformations.

This activity covers many different courses and curriculum expectations because Desmos offers so many versions of Marbleslides. To date Marbleslides is offered for; Lines, Periodics, Parabolas, Exponentials, and Rationals. The activity would be appropriate to use in any course in which functions and graphs are present. The following courses would be appropriate to use this activity in:

Principles of Mathematics, Grade 9, Academic

• Linear Relations

Foundations of Mathematics, Grade 9, Applied

• Linear Relations

Principles of Mathematics, Grade 10, Academic

• Quadratic Relations

Foundations of Mathematics, Grade 10, Applied

• Modeling Linear Relations
• Quadratic Relations

Functions, Grade 11, University

• Characteristics of Functions
• Exponential Functions
• Trigonometric Functions

 Functions and Applications, Grade 11, University/College

• Quadratic Functions
• Exponential Functions
• Trigonometric Functions

Foundations for College Mathematics, Grade 11, College

•  Mathematical Models

Advanced Functions, Grade 12, University

•  Exponential and Logarithmic Functions
• Trigonometric Functions
• Polynomial and Rational Functions

Mathematics for College Technology, Grade 12, College

• Exponential Functions
• Polynomial Functions
• Trigonometric Functions

Additionally, this resource would address a group of process expectations:

• Problem Solving: students are given a task (hitting all the stars) and are asked to solve that problem using their problem solving skills.
• Communication: throughout the activity students are asked to communicate their reasoning and their understanding of the concept. 

The main mathematical ideas of this resource are equations, transformations, and properties of functions. In order to get all the stars, a student may have to stretch or compress a function. They may also have to shift or reflect it. This activity gets them to practice these skills by creating a fun objective of gaining all the stars.

I chose to include this item in my portfolio because I used it while I was in my first teaching block and my students absolutely loved it. Because of the format of my practicum, I used it as a minds on activity but it still worked beautifully. I chose a student to be my assistant and the class was tasked with going through each level as a group. This activity was very engaging and the students really enjoyed it.

If I was to use this activity in my class again, I would use it as the action piece and provide each student with a chrome book or an iPad to explore the activity individually. The students would have to sign in and I would be able to track each one of their progress through the activity. In addition to the game portion of the activity, students are asked to answer questions about the concept itself. Using these responses I should be able to assess their knowledge of the topic and if they have a proper understanding.

Speed Dating and Equation Making

This activity was presented to the class during our Learning Activities presentations and I needed to include it in my portfolio because I thought it was so great. The objective of this activity is to find your "match" out of all of your classmates. Some students may have multiple matches while some may have just one or two. The class is split into two groups. The first group of students receives purple cards indicating the slope and the second group receives yellow cards indicating the y-intercept. Each person in the first group is paired off with someone from the second group and are asked to use their information to graph a linear relation. After this has been done, you know if the person is your match if your linear relation goes through a red heart on the worksheet. After everyone's lines are drawn, everyone rotates and each student has a new partner.

This activity focused on teaching writing and graphing linear relations but could be adapted to a multitude of different functions depending on the grade level of students. Specifically this activity was for Grade Nine Academic Mathematics: Principles of Mathematics, Analytic Geometry strand.

Overall Expectations: 

1. determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity

2. determine, through investigation, the properties of the slope and y-intercept of a linear relation

3. solve problems involving linear relations

Additionally. this activity can be used to assess the following process expectations:

•  Problem Solving: students are asked to graph a linear relation using the given information using their problem solving skills
• Communicating: students must use their communication skills to work together and graph the correct line
• Representing: students will use graphical and algebraic representations of linear relations

The main mathematical ideas in this activity are putting equations together and graphing them based on that equation. Depending on the size of the class, each student may be asked to graph 10 to 15 linear functions. This activity is a great way for students to practice graphing and interpreting characteristics of functions, while having fun and trying to find their "match". 

I chose this item because when it was presented in class I thought it was very fun and engaging for students. I have not been given the opportunity to teach this concept in schools yet, but I will absolutely be using this activity in my own classroom. As a teacher sometimes I have a hard time making connections between fun activities and mathematical concepts, so having an activity like this in my toolkit is great. 

In order to create formative assessment in this activity, I would follow up with a consolidation discussion with students about what they learned. This discussion would include questions about what they liked, what they found difficult and want they still have issues understanding. Alternatively, I could also create an exit card for students to complete which gives them a slope and y-intercept and asks them to graph just as they have in this activity. The exit card would also contain questions similar to the discussion questions. This would provide me with an idea of how each student is doing individually and what needs to be reviewed in the coming classes. 

Logarithm Dominoes
 
The third item that I will be including in this portfolio is Logarithm Dominoes.I chose this activity as an item in my portfolio because when we were presented with this activity in class it was extremely fun and I could see using this activity in my own classroom. This activity is very similar to the dominoes that most of us grew up playing, but instead of dots on the dominoes, each domino has two logarithms on it. (Each representing a number) The students would be put into groups of three or four, and given a set of dominoes.

The rules are as follows: 

1. Each player draws 5 dominoes. You start by playing a double domino (one end equals the same number as the other end)
2. You can build off the double domino in 4 directions - above, below, left or right. To play off a domino, you must match the ends that have the same value.
3. Players take turns placing dominoes.
4. Each turn is 45 seconds, if you do not play in time or you cannot play a domino,  pick a new domino and move to the next player. 
5. If a player places a domino that does not have the proper value/doesn't match and the other players notice, the player must pick a new domino in place of their turn.
6.  The game ends when a player runs out of dominoes in their hand. Second and third places are determined by who has the dominoes with the lesser overall value. 

This activity was geared towards Grade Twelve University Advanced Functions.

Overall Expectation from the Exponential and Logarithmic Functions strand:
 1. demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions

 This activity can be used to assess the following Process Expectations:

• Communicating: this activity allows students to show their communication skills through words, visuals and in writing, through the playing of logarithm dominoes. 
• Problem Solving: through this activity, students will use their problem solving skills to play and advance through the game

The main mathematical idea in this activity is understanding how to simplify and evaluate logarithmic expressions. As students are playing the game, they must continue to evaluate these expressions. The students are constantly practicing their skills in a fun and exciting way.

I decided to choose this activity as an item in my portfolio because of how engaging it was for me to play with my colleagues and because of the versatility of the game (it can be modified for many different grades and levels). When we played this in class, it was a great way to practice and we had so much fun as a class. I know that this would be a great game to play in my own classroom.

A formative assessment plan for this activity would include a consolidation discussion at the end of class to use as a check for understanding. This discussion would be a series a questions asking students how this activity helped improve their knowledge and if there is any concepts that we still need to focus on as a class.

Polygraph

Retrieved from https://teacher.desmos.com/polygraph/

For the last item of my portfolio I decided to include another Desmos activity because I love Desmos so much. This time I will be focusing on the Desmos activity Polygraph. This is an activity on Desmos which is very similar to the popular board game Guess Who?. This activity is done in pairs; one partner chooses a card and the other partner has to guess what card it is based on a series of mathematical questions.

Polygraph has activities for the following topics:
Lines
Parabolas
Hexagons
Rational Functions
Basic Quadrilaterals
Advanced Quadrilaterals

Retrieved from https://mathcoachblog.com/category/algebra-2/

I will be focusing on the Polygraph dedicated to Lines (which is the specific activity that we played in class).

This activity could be used in Grade Ten Academic Mathematics, Principles of Mathematics, but could be used in any course that explores parabolas and quadratic functions.

Overall Expectations from the Quadratic Relations strand:
1. determine the basic properties of quadratic relations
2. relate transformations of the graph of y = x^2 to the algebraic representations y = a(x - h)^2 + k

 This activity can be used to assess the following Process Expectations:

• Communicating: students must communicate to their partner effective and accurate mathematical questions, in order to guess the correct parabola
• Reflecting: students are required to use their reflecting skills to understand their partners questions and then answer them correctly based on the parabola that they selected

 The main mathematical idea in this activity are being able to describe the characteristics of a quadratic relation. Students are asked to ask questions that relate to the properties of quadratic relations such as;

• the equation of the axis of symmetry
• the coordinates of the vertex
• the y-intercept
• the zeros
• the maximum or minimum value

Students are required to use these mathematical properties accurately with the appropriate terminology. 

I chose this item for my portfolio because Desmos is such an engaging and interactive tool. I have used this activity myself in teacher education classes and used Desmos activities in my own classroom, and each time I have been impressed with Desmos. Every time I use this tool, I am impressed by how interactive in is and how well it presents mathematical content. Something that always impresses me about Desmos is the visualization of a mathematical concept and how they can make mathematics fun. I will absolutely be using this activity, and other activities like it in my own classroom.

To use this activity as formative assessment, I would use the assessment tools within the activity. Throughout the activity, there are questions that act as a check for understanding.