Algebra I Professional Development. Quadratics. Module 6. Outcome Participants will experience a rigorous Algebra I concept task. CCSS Domains on Quadratics. Algebra - Seeing Structure in Expressions Algebra – Reasoning with Equations and Inequalities Functions – Interpreting Functions
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a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
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.
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
c. Graph polynomial functions, identifying zeros when suitable
a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Share, Discuss, and Analyze:
How do we make the mathematics accessible to all students?
How can the four access strategies:
be more explicitly embedded in the lesson?
Read through the lesson and discuss how the TTLP was used to design it.
Module 8 Protocol
How will this activity support the academic language development for your students?
What questions can you ask to engage students with this activity?
How will you use this with your students?
What do you need to modify or add?
Why is this activity important?
When else can you use this activity with future lessons?
Module 9 Protocol
y is always x squared
Take the cards out of your envelope and spread them out on your table.
Match together the verbal descriptions, tabular representations, graphs, and symbolic representation.
In a small group, discuss what helped you to identify the members of each set?
Each group will then share one set of four representations and explain how they identified the members of that set.
How does this activity enrich the students’ understanding of different quadratic representations?
How might you use a similar type activity in a different unit of study?
Each group will receive one of the comparing graphs sheet.
Each member of the group will be receiving a blank transparency, a different colored marker, and a piece of graph paper.
Each person in the group will graph one of the equations on a transparency—your group will have a total of five different graphs.
Now that your group has graphed each equation, layer your transparencies.
What do you notice?
What is causing this to happen?
Generate two more equations which illustrate that you know what is causing the changes to occur.