This resource is an introduction to polynomial vocabulary and naming of polynomials. It includes an interactive presentation using Pear Deck and a note taking sheet for students.

This resource was developed as a part of the Creating Lessons Using Transformative Technology - Platteville Public Schools OER grant.

Students learn about four forms of equations: direct variation, slope-intercept form, standard form and point-slope form. They graph and complete problem sets for each, converting from one form of equation to another, and learning the benefits and uses of each.

This task shows three equivalent expressions and requires that students understand the structure and purpose of each one. This is a critical aspect of Seeing Structure in Expressions. 
The primary purpose of this task is to assess students' knowledge of certain aspects of the mathematics described in the High School domain A-SSE: Seeing Structure in Expressions. Specifically, standard A-SSE.3 reads A-SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
The Standards avoid the term "simplify" as there isn't always an obvious simplest form. The emphasis instead is on, "purposeful transformation of expressions into equivalent forms that are suitable for the purpose at hand." This task shows three equivalent expressions and requires that students understand the structure and purpose of each one. This is a critical aspect of Seeing Structure in Expressions. 
Mathematically this task:
• Prompts students to analyze three equivalent quadratic expressions • Allows students to focus on the structure of the expressions without focusing on the procedural skill of factoring or expanding the expressions • Gives a real-world context for students to interpret the properties of quadratic expressions • Requires students to look for and make use of structure (MP.7)
In the classroom: • Offers students and teachers an opportunity to see an assessment-type task with two response types • Allows teachers to target specific student misunderstandings for reteaching • With follow-up questions, teachers can prompt students to share their thinking about the concepts in this task

Mathematical goals
This lesson unit is intended to help you assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation. In particular, the lesson will help you identify and help students who have the following difficulties:
Understanding how the factored form of the function can identify a graph's roots.Understanding how the completed square form of the function can identify a graph's maximum or minimum point.Understanding how the standard form of the function can identify a graph's intercept.

Before the lesson, students work individually on an assessment task that is designed to reveal their current understandings and difficulties. You then review their work and create questions for students to answer in order to improve their solutions.After a whole-class interactive introduction, students work in pairs on a collaborative discussion task in which they match quadratic graphs to their algebraic representation. As they do this, they begin to link different algebraic forms of a quadratic function to particular properties of its graph.At the end of the lesson there is a whole-class discussion.In a follow-up lesson students attempt to improve their original response to the assessment task.
Materials required
Each individual student will need two copies of the Quadratic Functions assessment task and a mini-whiteboard, pen, and eraser.Each pair of students will need Domino Cards 1 and Domino Cards 2, cut into ten ‘dominoes'.
Time needed
15 minutes before the lesson, a 95-minute lesson (or two shorter lessons), and 10 minutes in a follow-up lesson. Timings are approximate and will depend on the needs of the class.

Lesson objective: Apply knowledge of ways to name numbers. 
This lesson provides an opportunity for students to apply their knowledge and understanding of naming numbers to a mathematical situation. Students are asked to help the teacher complete her set of game cards by coming up with equivalent names for numbers. 
Key Concept students will use: 
Representing a whole number in different ways (including base ten numerals, number-names, and expanded form) does not change its value.
Skills students will use:
Understand that the three digits of a three-digit number represent the amount of hundreds, tens, and ones (Grade 2, Unit 6)Write three-digit numbers in expanded formWrite three-digit numbers in word formWrite three-digit numbers in standard form
Students engage in Mathematical Practice 7 (Look for and make use of structure) as they look for patterns in the way we name numbers to name numbers they have not seen before. 

Prepared with pre-algebra or algebra 1 classes in mind, this module leads students through the process of graphing data and finding a line of best fit while exploring the characteristics of linear equations in algebraic and graphic formats. Then, these topics are connected to real-world experiences in which people use linear functions. During the module, students use these scientific concepts to solve the following hypothetical challenge: You are a new researcher in a lab, and your boss has just given you your first task to analyze a set of data. It being your first assignment, you ask an undergraduate student working in your lab to help you figure it out. She responds that you must determine what the data represents and then find an equation that models the data. You believe that you will be able to determine what the data represents on your own, but you ask for further help modeling the data. In response, she says she is not completely sure how to do it, but gives a list of equations that may fit the data. This module is built around the legacy cycle, a format that incorporates educational research feindings on how people best learn.