Math Portfolio

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Mathematics Portfolio



All resources were obtained from class EDBE 8F83


● Intermediate/Senior Teaching Mathematics ●

Daniel Van Oosten March 10, 2016

ORBIT INTEGERS A computer game that provides student with practice in addition and subtraction of negative and positive integers. The game allows students to race alien spaceships by correctly answering the provided addition and subtraction question. Having the fewest incorrect answers and in record time, the better chance a student will have at winning the race! You can access ORBIT INTEGERS by clicking the link below: http://www.arcademics.com/games/orbit-integers/orbit-integers.html You will also find ORBIT INTEGERS and many other games hosted by arcedemics! ORBIT INTEGERS is an online game that is FREE! A very effective tool for practicing integers! Games, like Orbit Integers, have the ability to provide immediate feedback for students which separates them from a traditional textbook. Immediate feedback is supportive for academic improvement because the consequences don’t limit a student’s attempt. Rather, students can try again at the task, with already having prior experience, in hopes of improving their skills.


Figure 1 Once a session is completed, Orbit Integers provides you with immediate feedback (Figure 1). This screen will show students where they ranked among their peers, their question accuracy, missed questions and equations completed per minute. Orbit Integers is geared towards grade 7 students because it aligns with the Ontario Curriculum expectations in regards to the Number Sense and Numeration strand. An overall expectation that the game aligns with is, “solving problems involving whole numbers, decimal numbers, fractions, and integers, using a variety of computational strategies.” A specific expectation that the game aligns with is, “add and subtract integers, issuing a variety of tools.” Positives • Exciting, engaging, motivating, fun and competitive • Mental math development • Immediate feedback • Play with friends – compete • Supports instrumental understanding

Negatives • Losing the race may demoralize students • Not teacher controlled/friendly • Must have an account on Arcedemics Plus in order to track student achievement

SLOPE-INTERCEPT GAME An online math game where students are given a series of math questions regarding slope and intercepts to help their character score baskets in a basketball game. The main objective of the game is to have students answer questions correctly in order to have a chance to shoot the ball in the basket. You can access the game hosted by MATH-PLAY by clicking the link below: http://www.math-play.com/slope-intercept-game.html Slope-Intercept basketball is a free fun-filled game with a basketball twist! As seen in Figure 2, the slope-intercept game is a multiple choice setup with 4 answers to choose from. The game is essentially a 10question quiz on intercepts and slope with the opportunity to shoot 3-point basketball shots. If students get the right answer, they can shoot the basketball, but if students get the ‘wrong’ answer, then they are given the buzzer noise and automatically miss their shot. After 10 questions you are given immediate feedback in the form of a report card.

As

Figure 2


The game aligns with the Ontario Curriculum expectations for the Grade 9 Academic course MPM1D in the analytic geometry unit.

Overall Expectations. • Determine, through investigation, the properties of the slope and the y-intercept of a linear relation Specific Expectations. • Express the equation of a line in the form y = mx + b, given the form Ax + By + C = 0 • Identify, through investigation with technology, the geometric significance of m and b in the equation y=mx+b; • Determine, through investigation, various formulas for the slope of a line segment or a line. • • • •

Positives Positive reinforcement Constant and instant feedback Promotes self-regulation Can see progress and reflect on past questions

Downfalls • Teacher is unable to keep track of student achievement • Negative reinforcement – buzzer sound – when the answer is wrong • Negative remarks, ex. Use your brain! • No tracking sheet for teachers to see student progress

Polynomial and Rational Functions Course: Grade 12 University Advanced Functions (MHF4U) Unit: Polynomial Functions Big Ideas, Overall Expectations, Specific Expectations obtained from: Ontario Ministry of Education. (2007). The Ontario curriculum for grades 11 and 12: Mathematics. https://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf

Overall Expectations 1.

identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions

Specific Expectations 1.1

recognize a polynomial expression (i.e., a series of terms where each term is the product of a constant and a power of x with a nonnegative integral exponent, such as x – 5x + 2x – 1); recognize the equation of a polynomial function, give reasons why it is a function, and identify linear and quadratic functions as examples of polynomial functions


1.4

distinguish polynomial functions from sinusoidal and exponential functions [e.g., f(x) = sin x, g(x) = 2x ], and compare and contrast the graphs of various polynomial functions with the graphs of other types of functions

The Polynomial and Relational Function unit has a key component in relating the graph of the function to the equation of the function. So, Example 1 provides students with the opportunity to visualize how a polynomial function translates onto a graph. See below.

Activity Instructions A fun and collaborative matching activity allows students to apply their knowledge on Polynomial and Rational functions. The activity provides students with several functions and several corresponding graphs. The idea of the activity is for students to match the function to the correct graph, and by doing so, create a math word. When students find a word that aligns with their math literacy, then they know they have successfully completed the matching activity. Students will then use their math word to identify their boxed letters. These letters are part of a word jumble which involves the entire class. Students will then collaborate as a team to solve the final math phrase. Below you will see an example of a matching polynomial activity which is only a piece of the puzzle.


Why the Activity Works! I like the concept of the polynomial matching activity because it is a great universal formative assessment tool that can be used after any function-to-graphing lesson. Teachers can see if students understand how to relate the equation to its corresponding graph by checking if students completed their math word. Also, students develop their math literacy by completing and comparing words that they have discovered throughout the activity. I like the setup to the activity because it parallels, in a way, the functionality of a working business. Students complete their individual task, just as workers do, as part of a cog in a larger machine. Each student does their part in the activity to solve the final project, just like workers add their individual expertise to help complete a project. Also, it gives students a sense of belonging because they know that without their completed work, the final project would be difficult to solve.

Trigonometric Ratios and the Sine and Cosine Law Course: Grade 11 University level Mathematics (MCR3U) Strand: Trigonometric Ratios Big Ideas, Overall Expectations, Specific Expectations obtained from: Ontario Ministry of Education. (2007). The Ontario curriculum for grades 11 and 12: Mathematics. https://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf

Overall Expectations 1) Determine the values of the trigonometric ratios for angles less than 360째; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law and the cosine law Specific Expectations 1.6) Pose problems involving right angles and oblique triangles in two-dimensional settings, and solve these and other such problems using the primary trigonometric ratios, cosine law


1.7) Pose problems involving right angles and oblique triangles in three-dimensional settings, and solve these and other such problems using the primary trigonometric ratios, cosine law Students Mathematical Process • • •

Students must select the appropriate formulas, tools and computational strategies to solve the given equations Students will develop, apply, and compare problem solving strategies used to solve the given real world application problems and deepen their mathematical understanding Students will communicate their mathematical thinking in writing, orally, and visually using precise mathematical vocabulary

The Trigonometric Ratios activity involves 4 parts and in each part you are successful you will receive letters to your word jumble. Right triangles and Oblique triangles are 2 topics covered in the activity and students must demonstrate their knowledge by applying and utilizing the proper formula to solve the problem. Below is an example question from the activity.

Part 4: Presenting your findings Students were given a scenario where they had to use the sine law and cosine law to reach a conclusion. What’s unique about the activity is that part 4 involved the individual student and their partner. The scenario was about my partner and myself, which was awesome! The photo below shows my groups answer to our unique scenario.


After solving the problem on chart paper, groups were given the opportunity to share their solution with the class. Activity Positives • • • • • • •

The teacher can place students into groups to ensure that each group consists of students with a range of abilities. This will create a positive learning environment, and encourage peer tutoring and collaboration You can create original word problems and make it unique to each group This activity caters to both instrumental and relational understanding and it is best utilized as review practice, after learning these concepts in class The word scramble promotes math literacy Students develop their math terminology to explain their thought process during the activity and presentation Students are able to apply their knowledge and understanding of the concepts by drawing representative diagrams Students get to collaborate and develop their teamwork skills

Number Sense & Algebra - Buying Juice Problem Course: Grade 9 Applied Mathematics Unit: Number Sense and Algebra Overall Expectations •

Solve problems involving proportional reasoning

Specific Expectations •

Make comparisons using unit rates

Solve problems involving rations, rates and directly proportional relationships in various contexts

The Problem You walk into a store and are craving an Iced Tea. There are two options; a can for $1.47 + tax and a box for $1.12 + tax. You know that both are recyclable in St. Catharine’s so you make the conclusion that your ecological footprint will be just as big regardless of your purchase. You then sit there and try to find out which is this better bang for your buck. What conclusion do you come to and what is the unit price for both?


Positives • Diverse question with a simple, yet very valuable concept • The problem stems student future thinking skills about wasting money • Juice can and juice box are both recyclable! • Environmentally conscience • Teacher can easily differentiate the problem by simplifying prices or taking away the tax • Easily modifiable and accommodating

I believe this juice buying problem will challenge the students ability to problem solve, critically think and reason. The students have a variety of ways to approach the problem by finding the price per 1mL, the price per 100mL, the volume you get for 1cent, or 1 dollar, or the students can equate the same price and find the volume that each would have. I like how there are a number of ways to approach it and therefore a number of ways for students to explore! This problem is a real-world scenario that happens frequently at the grocery store for example. When students see the value of their learning, they may be motivated to solve the problem. This also gives a context for learning, which I believe is extremely important. The teacher can choose to differentiate the activity by removing the tax portion to the question, or can complicate the question further by adding packages or boxes of multiple cans.


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