The purpose of this task is for students to select 2 numbers …
The purpose of this task is for students to select 2 numbers from a set of 3 that sum to 9. The task can be completed for sums equaling any number. Teachers may choose to ask students to write the simple equations they select.
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.
The purpose of this task is to have students add mixed numbers …
The purpose of this task is to have students add mixed numbers with like denominators. This task illustrates the different kinds of solution approaches students might take to such a task.
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.
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.
The purpose of this task is to help students see that when …
The purpose of this task is to help students see that when you have a context that can be modeled with a ratio and associated unit rate, there is almost always another ratio with its associated unit rate (the only exception is when one of the quantities is zero), and to encourage students to flexibly choose either unit rate depending on the question at hand.
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.
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 asks students to find the amount of two ingredients in …
This task asks students to find the amount of two ingredients in a pasta blend. The task provides all the information necessary to solve the problem by setting up two linear equations in two unknowns.
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.
The purpose of the task is to show students a situation where …
The purpose of the task is to show students a situation where squaring both sides of an equation can result in an equation with more solutions than the original one. The reason for this is that it is possible to have two unequal numbers whose squares are equal.
In this number tracing activity students create a rainbow number line. This …
In this number tracing activity students create a rainbow number line. This can be a colorful tool with a personal connection to the student that may be used as a reference. It can serve as a visual and motor reminder when reading and writing numbers because the student went through the tracing motion.
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