Remember, terminology that may seem routine to us, as mathematical experts, can appear intimidating to students.Īt this point, students should have experience with x-intercepts. You must also explain in what format you expect students to provide answers and/or solution sets. They should know that solving a quadratic equation means you are finding the roots or the x-intercepts. Students need to know that the roots and zeros of a quadratic equation are the x-intercepts. If students encounter all of these words without any preparation, it may feel quite intimidating! Take the time to explain to students what each word means and how students will receive prompts. Students may be asked for solutions, solution sets, roots, zeros, and x-intercepts. It is important as a teacher of mathematics to present information clearly and expose students to the various prompts they may see. ![]() Return to the Table of Contents What Does it Mean to Solve a Quadratic Equation? Then, discuss which differences are universal to all linear equations and quadratic equations. Allow groups a moment to present their findings to the class. You may assign students jobs or require each student to come up with a certain number of characteristics. Give students a set length of time to determine characteristics of the graph that are the same or different. Give each table a different pair of graphs, one linear and one quadratic. Separate students into groups of three or four. □ Teaching TipĬomparing and contrasting are great opportunities to encourage conversation in class! Talking about math helps even successful math students improve their abilities to communicate mathematical ideas. Of course, students can easily recognize this shape is like the letter “U.” However, “parabola” is the keyword to repeat as this is what students will hear and see in future courses.Īgain, using the correct verbiage will increase the likelihood that students will recall the correct information at the correct time. For example, the quadratic equation is shaped like a parabola. It is important to use terminology students will continue to use in future courses. It takes time and repetition for students to connect the image of the graph with the equation of the graph.īased on the level of your students, you can choose how in-depth you want to make your comparison of linear and quadratic equations. It is important to include visuals of the equations when beginning the study of quadratic equations. Can have two x-intercepts (zero, one, or two). ![]() Depending on the experience of your students, you may choose to keep examples very simple and obvious or to include examples in different forms. You can show your students examples and non-examples of quadratic equations. The quadratic may not contain x^3 or any x with an exponent above 2. Your students may not know what “degree” means, so you will need to explain that all quadratics contain an x^2 term. In a quadratic equation, the degree is 2, so a \neq 0. Return to the Table of Contents What is a Quadratic Equation?īegin by presenting quadratic equations in standard form: Teaching students to reflect on their own learning helps them to be responsible for their own understanding of the material. Help students evaluate their progress using in-class practice, homework problems, or quizzes. ![]() Let students evaluate whether or not they can achieve learning goals. Take time in class to allow students to reflect on their learning. Students should know the end goal of every math problem, class discussion, and homework assignment. Clarity and organization give students confidence about what they are doing and give students purpose behind assignments and tasks in class. You decide what verbiage your students walk away with by how you present the information. If someone asked your students what they are learning, what would they say? Would they say “We are solving equations with x^2 with a long equation?” or “We are solving quadratic formulas?” Keeping the terminology clear and consistent throughout the unit will help students to retain information. Students should know what they are expected to learn and what they will be assessed on. “I can solve quadratic equations using multiple methods, including factoring and the quadratic formula” “I can use answer questions about real world events using quadratic equations” ![]() “I can solve quadratic equations using factoring” “I can solve quadratic equations using the quadratic formula”
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