A brief refresher on the Cartesian plane includes how points are written in (x, y) format and oriented to the axes, and which directions are positive and negative. Then students learn about what it means for a relation to be a function and how to determine domain and range of a set of data points.

This task presents a real world application of finite geometric series. The context can lead into several interesting follow-up questions and projects. Many drugs only become effective after the amount in the body builds up to a certain level. This can be modeled very well with geometric series.

This unit of four lessons highlights different aspects of students’ understanding and use of patterns as they analyze relationships and make predictions, as discussed in the Algebra Standard. In this cluster of activities, students use two interactive math applets (both catalogued separately) to learn about repeating and growing patterns. In the first part, students explore a two-square pattern unit and in the second part, students investigate repeating patterns with pattern units of three, four, and five squares. In Part 3, students analyze repeating patterns of colored cubes and lastly in Part 4, students create growing patterns of colored cubes and compare them to repeating patterns.

In this lesson, students will each find the volume of a cylinder (an actual can), using already explored formulas, and then create on paper a rectangular prism that has the same volume. Since this exercise is for a "real" company, they are challenged to minimize the surface area of their prism. Through class discussion, students compare the two formulas for volume, and the relation between volume and surface area. Included here are student questions, assessment ideas, and activity pages.

This lesson plan introduces the game Deep Sea Duel, which develops students' operation skills and strategic thinking, and can be played online or with cards. After playing several variations of the game, students attempt to identify a winning strategy and compare the game to other familiar games. Variations include whole numbers, decimals, fractions, exponents, and words. The lesson includes printable cards and a student worksheet, questions for student discussion and teacher reflection, assessment options, and extensions. The online game and the cited article are cataloged separately.

The primary purpose of this task is to illustrate certain aspects of the mathematics described in the A.SSE.1. The task has students look for structure in algebraic expressions related to a context, and asks them to relate that structure to the context. In particular, it is worth emphasizing that the task requires no algebraic manipulation from the students.

This lesson shows how to understand square roots. [Developmental Math playlist: Lesson 42 of 196]

This lesson uses a series of related arithmetic experiences to prompt students to generalize into more abstract ideas. In particular, students explore arithmetic statements leading to a result that is the factoring pattern for the difference of two squares. An excellent teaching idea on how to help students walk the bridge from arithmetic to algebra.

This task does not actually require that the student solve the system but that they recognize the pairs of linear equations in two variables that would be used to solve the system. This is an important step in the process of solving systems.

This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.

" Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems."

In this math meets health science activity, learners observe a model of exponential decay, and how kidneys filter blood. Learners will calculate the amount of a drug in the body over a period of time. Then, they will make and analyze the graphical representation of this exponential function. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

Students act as Mars exploratory rover engineers, designing, building and displaying their edible rovers to a design review. To begin, they evaluate rover equipment and material options to determine which parts might fit in their given NASA budget. With provided parts and material lists, teams analyze their design options and use their findings to design their rovers.

This task asks students to use inverse operations to solve the equations for the unknown variable, or for the designated variable if there is more than one. Two of the equations are of physical significance and are examples of Ohm's Law and Newton's Law of Universal Gravitation.

The purpose of this task is to directly address a common misconception held by many students who are learning to solve equations. Because a frequent strategy for solving an equation with fractions is to multiply both sides by a common denominator (so all the coefficients are integers), students often forget why this is an "allowable" move in an equation and try to apply the same strategy when they see an expression.

This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure. The problem aligns with A-SSE.2 because it requires students to see the factored form as a product of sums, to which the distributive law can be applied.

In this unit, students use online pan balances to study equality, order of operations, numerical and variable expressions, and other key algebraic concepts. Lessons focus on balancing shapes to study equality and equivalence; balancing algebraic understanding, to explore simplifying expressions; and balancing algebra, to determine if algebraic expressions are equal.

The rules of Krypto are amazingly simpleäóîcombine five numbers using the standard arithmetic operations to create a target number. Finding a solution to one of the more than 3 million possible combinations can be quite a challenge, but learners love it. This game helps to develop number sense, computational skill, and an understanding of the order of operations. Play this game online or use a deck of Krypto cards.