Though written in the format of a lesson, this resource is more valuable as a source of information on two different ideas -- equity in mathematics and applications of the Pythagorean Theorem. In the first part of the lesson, students share thoughts about careers and gender roles. Then they read an article that discusses the long history of discrimination against women in mathematics and science. In the second part of the lesson they work in groups to apply and prove the Pythagorean Theorem in several real-world contexts. Discussion questions, suggestions for homework and assessment, lesson extensions, and interdisciplinary connections are included.

The purpose of this task is to give students additional practice with writing proportionality statements about similar triangles. Students will generate a new proof of the Pythagorean theorem that is based on similar triangles, rather than area. They will also explore a geometric way of representing the geometric mean between two numbers. Students may have previously worked with the geometric mean algebraically in the task Geometric Meanies found in the Mathematics Vision Project, Secondary Mathematics I course.

The purpose of this task is to develop a strategy for solving quadratic inequalities and extend this strategy to higher-degree polynomials when the factors are known. The context of the task gives students an opportunity to engage in mathematical modeling: students will use mathematical models, in this case quadratic and cubic inequalities, to model various contextualized situations. The solutions to the inequalities then have to be interpreted in terms of what they mean in the situations. That is, the solutions for x in the inequalities are not the answers to the questions being asked in the situations—rather they provide information from which those questions can be answered. Students will have to keep track of the meaning of the variables as they work through these problems.

This task allows students to extend their work with symmetries of quadrilaterals and practice making conjectures about geometric figures that are based on reasoning with the definitions of reflection and rotation. The work of this task will be revisited in Mathematics II, where students will be asked to create formal proofs for the conjectures they are making in this task about the properties of different types of quadrilaterals. Therefore, while this is classified as a practice understanding task, the mathematics students should be practicing is making and justifying conjectures about geometric figures based on the definitions of rigid-motion transformations, rather than practicing knowledge about the specific properties of different types of quadrilaterals. Whatever properties about sides, angles and diagonals of quadrilaterals students surface is sufficient for this task.

The purpose of this task is to solidify and extend student thinking about quadratic functions to include those with a maximum point. Students will use the graph of the function to discuss the domain and range of a continuous quadratic function in addition to identifying the maximum value and finding the intervals on which the function is increasing and decreasing.

This task provides opportunities for students to become fluent converting between exponential and radical representations of expressions, as well as using the rules of exponents to simplify exponential and radical expressions.

Students are figuring out what rational exponents are. The mathematics task is intended to be a problem or question that encourages the use of mathematical practices. The dialogue is meant to show how students might engage in the mathematical practices as they work on the task.

This lesson unit is intended to help you assess how well students reason about the properties of rational and irrational numbers. In particular, this unit aims to help you identify and assist students who have difficulties in: ? Finding irrational and rational numbers to exemplify general statements. ? Reasoning with properties of rational and irrational numbers.

The purpose of this task is for students to practice graphing absolute value functions and determine a process for writing them as piecewise-defined functions. To become more precise in their language, students will extend their knowledge of linear absolute value to other functions. Understanding where the piecewise function changes (based on sign change of function within the absolute value) is key. Students will also practice graphing with transformations.

Students will analyze and explain precisely the process of solving an equation. Through repeated reasoning, students develop fluency in writing, interpreting, and translating between various forms of linear equations and inequalities and make conjectures about the form that a linear equation might take in a solution to a problem.

The purpose of this task is for students to find relationships between sine and cosine using their knowledge of right triangles, complementary angles, and the Pythagorean theorem. The focus of this task is on Part II where students reason about conjectures. Emphasis in the discussion should be placed on questions related to the complementary relationship between sine and cosine as well as the Pythagorean identity.

Resources for Transforming Functions to include polynomials, absolute value, exponential and logarithmic functions. A special thank you to the original author Wendi Hinson for allowing her resource to be remixed.  

I remixed the original unit by pulling out and using the notes and removing all unit numbers. I loved the notes!

The purpose of this task is to solidify student understanding of quadratic functions by giving another opportunity to create a quadratic model for a context. This task introduces the idea that quadratic functions are models for the sum of a linear function, which obviously creates a linear rate of change. Again, students have the opportunity to use algebraic, numeric, and graphical representations to model a story context with a visual model.

Students are using geometric transformations to help them find the corresponding sides of similar figures in order to use their proportionality. The mathematics task is intended to be a problem or question that encourages the use of mathematical practices. The dialogue is meant to show how students might engage in the mathematical practices as they work on the task.

Students will solve radical equations with an index of two. These equations may include extraneous solutions. Activity should take about an hour for students to complete. Please not this resource does not completely cover standard M2.A.REI.A.2.