Study Session for Unit Test on Quadratics

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Objective

SWBAT prepare for the upcoming unit test by demonstrating understanding of unit learning objectives by completing practice problems individually and in small groups

Big Idea

Students work on the important executive function skill of progress monitoring by identifying areas of need and working on those types of problems to be active participants in studying for a unit test!

Lesson Author

Jason Colombino

Salem, MA

Grade Level

Ninth grade

Subjects

Math

Algebra

linear models

modeling

Geometry

Standards

HSA-SSE.B.3a

Factor a quadratic expression to reveal the zeros of the function it defines.

HSA-SSE.B.3b

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

HSA-REI.B.3

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

HSA-REI.B.4a

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)<sup>2</sup> = q that has the same solutions. Derive the quadratic formula from this form.

HSA-REI.B.4b

Solve quadratic equations by inspection (e.g., for x<sup>2</sup> = 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.

HSF-IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

HSF-IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*

HSF-IF.B.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*

HSF-IF.C.7a

Graph linear and quadratic functions and show intercepts, maxima, and minima.

HSF-IF.C.8

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

HSF-IF.C.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.

HSF-BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Study Guide - Group Work and Class Review

90 minutes

This is a review class for an upcoming unit test on linear functions.

There are a number of ways to organize study sessions. I still find that most ninth graders benefit from having a study guide generated for them (in terms of cognitive development, the task of making a study guide and picking out relevant notes, etc. is a worthy, but overwhelming task for them!).

So I have a study guide that is split into two sections (which fits nicely into 2 45 minute classes or 1 90 minute class - which I am currently teaching). I arrange students into groups and like to mix up the ability level when preparing for tests. The reason for heterogeneous grouping is I find that the students that can complete the problems with relative ease benefit from having to explain or teach specific problems to students who are struggling more with the skills and concepts covered in the unit.

I like to assign a group of problems, and then reconvene the class to review the questions. As students are working on the problems in groups, I typically assign one problem that each group has to focus on and will have to review to the class.

We continue the cycle of group work, class review as we complete the study guide.

I like to complete the odd problems in class and then assign the even problems for homework - as a note, the study guide follows the type of questions found on the unit test, and there are two of each type of problem found on the test (for example, item 1 on the test should correlate to items 1 and 2 on the study guide).

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