The purpose of this task is to investigate the meaning of the …
The purpose of this task is to investigate the meaning of the definition of function in a real-world context where the question of whether there is more than one output for a given input arises naturally. In more advanced courses this task could be used to investigate the question of whether a function has an inverse.
In this activity, students will choose a math topic that they have …
In this activity, students will choose a math topic that they have learned about in the year and plan and film a video about using that topic in a real life way. For example a student could choose fractions and make a video about using a recipe. Students will present their film as part of the assessment.
This task can be implemented in a variety of ways. For a …
This task can be implemented in a variety of ways. For a class with previous exposure to properties of perpendicular bisectors, part (a) could be a quick exercise in geometric constructions, and an application of the result. Alternatively, this could be part of an introduction to perpendicular bisectors, culminating in a full proof that the three perpendicular bisectors are concurrent at the circumcenter of the triangle, an essentially complete proof of which is found in the solution below.
This is a simple exercise in creating equations from a situation with …
This is a simple exercise in creating equations from a situation with many variables. By giving three different scenarios, the problem requires students to keep going back to the definitions of the variables, thus emphasizing the importance of defining variables when you write an equation. In order to reinforce this aspect of the problem, the variables have not been given names that remind the student of what they stand for. The emphasis here is on setting up equations, not solving them.
This task is part of a series presenting important foundational geometric results …
This task is part of a series presenting important foundational geometric results and constructions which are fundamental for more elaborate arguments. They are presented without a real world context so as to see the important hypotheses and logical steps involved as clearly as possible.
This task is designed to get at a common student confusion between …
This task is designed to get at a common student confusion between the independent and dependent variables. This confusion often arises in situations like (b), where students are asked to solve an equation involving a function, and confuse that operation with evaluating the function.
An introductory lesson to polygons and circles and their properties. This lesson will …
An introductory lesson to polygons and circles and their properties. This lesson will help them connect basic geometric principles to real-world examples, recognizing their significance. Students will also learn how to use many Google tools for Education.Image Credit: "All the possible polygons!" by aldoaldoz, CC BY-NC-SA 2.0, from Flickr
In this task students construct and compare linear and exponential functions and …
In this task students construct and compare linear and exponential functions and find where the two functions intersect. One purpose of this task is to demonstrate that exponential functions grow faster than linear functions even if the linear function has a higher initial value and even if we increase the slope of the line. This task could be used as an introduction to this idea.
This task compares the usefulness of different forms of a quadratic expression. …
This task compares the usefulness of different forms of a quadratic expression. Students have to choose which form most easily provides information about the maximum value, the zeros and the vertical intercept of a quadratic expression in the context of a real world situation. Rather than just manipulating one form into the other, students can make sense out of the structure of the expressions.
In this video segment from Cyberchase, the CyberSquad breaks down an action …
In this video segment from Cyberchase, the CyberSquad breaks down an action into a series of steps in order to program a robot to do what they need it to do.
This lesson series is designed to teach students how to prove parallelograms …
This lesson series is designed to teach students how to prove parallelograms by slope, distance and midpoints. Students will have a performance assessment where they give their shape a personality and bring their shape to life. They will then prove mathematically that their shape is, indeed, a paralellogram by each of the methods described.
This question provides students with an opportunity to see expressions as constructed …
This question provides students with an opportunity to see expressions as constructed out of a sequence of operations: first taking the square root of n, then dividing the result of that operation into s. Students studying statistics encounter the expression in this question as the standard deviation of a sampling distribution with samples of size n when the distribution from which the sample is taken has standard deviation s.
This task has some aspects of a mathematical modeling problem (SMP 4) …
This task has some aspects of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). Students are given all the relevant information on the nutritional labels, but they have to figure out how to use this information. They have to come up with the idea that they can set up two equations in two unknowns to solve the problem.
This tasks is an example of a mathematical modeling problem (SMP 4) …
This tasks is an example of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). Students are only told that there are two ingredients in the pasta and they have a picture of the box. It might even be better to just show the picture of the box, or to bring in the box and ask the students to pose the question themselves.
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