Algebra 1. Discussion Based Assessment Prompts

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1 Algebra 1 Discussion Based Assessment Prompts

2 DBA Rubric DiscussionBased Assessment Meets Expectations (85%89%) Exceeds Expectations (90%100%) Goals: Build relationships Demonstrate competency Demonstrate higher order thinking Ensure academic Integrity Shows mastery of competencies by... easily recalling key facts and ideas accurately explaining Important concepts correctly using associated vocabulary providing specific examples to demonstrate understanding demonstrating higherorder thinking skills by applying and evaluating knowledge In addition to meeting expectations, shows expert mastery of competencies by... describing concepts in great de tail when asked by instructor, making connections between the competency topic and other aspects of the course offering ideas about how the competency content is important in a larger context (possible realworld application) reflecting on personal growth and learning

3 Module 1 Discussion Prompts 1. Explain the difference between algebraic expressions and equations. 2. Consider the expression One student says the answer is 2 and another says it is 6. Which student is correct? Explain what went wrong with the student who made a mistake. 3. Translate the following and explain where these examples could be found in real world. a) 6 less than a number b) 2 times the quotient of a number and two c) 4 times the difference of a number and 8 4. Explain how the algebraic properties are applied in the steps to solving equations and use them to solve 1/2x + 4 = What is the length of time a loan will last if it has a rate of 0.02, a principal of $500, and it accrued $60 of interest? Interest = Principal * Rate * Time. How would you reduce the time of the loan?

4 Module 2 Competency Students will demonstrate an understanding of inequalities by applying graphical and analytic methods to analyze and solve inequalities involving one or two variables.

5 Module 2 Discussion Prompts 1. What does it mean isolate the variable when given an equation? 2. When a variable drops out of the equation, what are the two possible solutions that you can get when you try to solve and what do they mean? Give an example of your own what each answer would look like. 3. Explain why absolute value equations have more than one solution. Create an absolute value equation with no solution and explain why it does not have one. 4. Do you think inequalities or equations are used more in everyday life? Justify your answer. In your answer include literal equations. How is solving a literal equation different from a one- or two-step equation? 5. Compare the process of solving an equation and an inequality. What are the differences and the similarities?

6 Module 3 Competency Students will demonstrate an understanding of linear functions by applying graphical and analytic methods to analyze and solve problems modeled by linear equations.

7 Module 3 Discussion Prompts 1. Explain the difference between function and relation and the relationship between the domain and the range of a function. 2. Explain the difference in solving a function when given the following information: f(x) = 2 and f(2). 3. What are the key features for a linear function, and how can you use those features to sketch graphs? Explain them through examples of your own. 4. Explain a real-world scenario where you would get a negative slope when you graphed the relationship. 5. Explain whether the line of best fit can or cannot be a predictor. What are the limitations?

8 Module 4 Competency Students will demonstrate an understanding of exponential functions by applying analytical and graphical methods to simplify, solve and analyze problems involving exponents.

9 Module 4 Discussion Prompts 1. Explain the properties of exponents with examples of your own. 2. Summarize how to rewrite a rational power as a radical term. Provide an example of your own. 3. Why are radicals simplified before adding and subtracting? Explain your reasoning by adding sqrt27 and sqrt3. 4. Compare and contrast through tables and graphs the linear and exponential functions. 5. Give an example to an Arithmetic and a Geometric Sequence. What are the differences between each? Which functions are these sequences related to? Explain your reasoning.

10 Module 5 Competency Students will demonstrate an understanding of systems of equations by applying graphical and analytic methods to analyze and solve systems of equations in two variables.

11 Module 5 Discussion Prompts 1. What are the different methods solving systems of equations? 2. How is solving systems of equations different from and similar to solving just one equation? 3. Explain with examples of your own when it is best to use substitution, elimination and graphing to a system of equations. 4. Explain how using systems of equations would help you find a better deal on a cell phone plan, a cable or satellite company or buying a car? 5. Give an example of a real-world problem that you would use a system of equations to solve. (Please do not use any of the options listed before.)

12 Module 6 Competency Students will demonstrate an understanding of statistical analysis of univariate and bivariate data sets through analytical analysis and visual representations of data sets.

13 Module 6 Discussion Prompts 1. What are the steps of the Statistical Process and how are they used in the real world? 2. What is the difference between categorical and quantitative data? Give examples of each of your own for each. Also decide whether the following example are categorical and quantitative data and explain how you know it. a) Colors of phone cover b) Weight of different phones c) Types of dogs d) Temperatures in the U.S. cities 3. Explain the difference between correlation and causation and what makes causation difficulty to prove? 4. Design a Statistical Process for finding how satisfied the students are in the cafeteria of the school with the quality of the food. 5. From the activity that you did in this module, explain whether the line of best fit can or cannot be a predictor. What are the limitations?

14 Module 7 Competency Students will demonstrate an understanding of polynomial functions and numeric properties by applying analytic methods to simplify, perform arithmetic operations, and solve problems by factoring involving polynomial functions.

15 Module 7 Discussion Prompts 1. What is standard form of a polynomial and what are like terms? Provide examples of your own. 2. Explain the difference between vertical and horizontal methods used to combine or simplify polynomials. 3. Explain the difference in the final product of (a + b)^2 and (a b)^2. 4. Explain why there is no middle term in the final product of (a b)(a + b) 5. From the activity that you did in this module, how do you think the graphs of polynomials differ from the graphs of linear equations?

16 Module 8 Competency Students will demonstrate an understanding of polynomial functions and numeric properties by applying analytic methods to simplify, perform arithmetic operations, and solve problems by factoring involving polynomial functions.

17 Module 8 Discussion Prompts 1. What is factoring? 2. Explain the relationship between factoring and multiplying polynomials. 3. Factor x^2-25 and x^2-10x How would you identify a perfect square trinomial? Give an example. 5. Design a rectangular pool using polynomial expressions and determine the area of the land the pool will cover.

18 Module 9 Competency Students will demonstrate an understanding of quadratic functions by applying graphical and analytic methods to analyze and solve problems modeled by quadratic equations.

19 Module 9 Discussion Prompts 1. What is the graph of a quadratic equation? 2. What is the relationship between the solution to a quadratic equation and the graph o f a quadratic equation? 3. How many possible solutions can you get from solving a quadratic equation and why does it vary? 4. Explain the relationship of c value of a quadratic equation and the b value of a liner equation. 5. Explain a real-life scenario for a quadratic function.

Algebra 1, Quarter 3, Unit 3.1. Line of Best Fit. Overview

Algebra 1, Quarter 3, Unit 3.1 Line of Best Fit Overview Number of instructional days 6 (1 day assessment) (1 day = 45 minutes) Content to be learned Analyze scatter plots and construct the line of best