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Secondary Mathematics II

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Strand: ALGEBRA - Reasoning With Equations and Inequalities (A.REI)

Solve equations and inequalities in one variable (Standard A.REI.4). Solve systems of equations. Extend the work of systems to include solving systems consisting of one linear and one nonlinear equation (Standard A.REI.7).-
A Linear and Quadratic System

The purpose of this task is to give students the opportunity to make connections between equations and the geometry of their graphs. They must read information from the graph (such as the vertical intercept of the quadratic graph or the slope of the linear one), use that information to construct and solve an equation, then interpret their solution in terms of the graph. -
ALGEBRA - Reasoning With Equations and Inequalities (A.REI) - Sec Math II Core Guide

The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics II - Reasoning with Equations and Inequalities (A.REI) -
Applications of Quadratic Functions

This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review. -
Applications of Quadratic Functions video

This video introduces and explains the topic. -
Braking Distance

The purpose of this task is to give an application arising from a real-world situation in which a quadratic equation arises, and where it is natural to use a graphical method to find an approximate solution and the quadratic formula to find an exact solution -
Completing the square

The goal of this task is to solve quadratic equations with complex roots by completing the square. Students could of course directly use the quadratic formula, but going through the process of completing the square helps reinforce the mathematics behind the quadratic formula. -
Graphing Quadratic Functions

This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review. -
Graphing Quadratic Functions video

This video introduces and explains the topic. -
Introduction to the Materials (Math 2)

Introduction to the Materials in the Mathematics Two of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems. -
Module 3: Solving Quadratics & Other Equations - Student Edition (Math 2)

The Mathematics Vision Project, Secondary Math Two Module 3, Solving Quadratics & Other Equations. The idea that different quadratic forms are useful in graphing is extended in Module 3, Solving Quadratic and Other Equations, when students use different forms of quadratic equations to find the roots or solve quadratic equations of a single variable. -
Module 3: Solving Quadratics & Other Equations - Teacher Edition (Math 2)

The Mathematics Vision Project, Secondary Math Two Module 3, Solving Quadratics & Other Equations. The idea that different quadratic forms are useful in graphing is extended in Module 3, Solving Quadratic and Other Equations, when students use different forms of quadratic equations to find the roots or solve quadratic equations of a single variable. -
Optimization Problems: Boomerangs

This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the constraints and variables mathematically, select appropriate mathematical methods to use, explore the effects of systematically varying the constraints, and interpret and evaluate the data generated and identify the optimum case, checking it for confirmation. -
Proof Without Words: Completing the Square

The act of "completing the square" involves taking half the coefficient of x in the quadratic x2 + ax and adding its square. But many students do not understand why this process works. -
Pythagorean Triples

This task has two separate goals: the first is to solve a pair of equations, one quadratic and the other linear. The second goal is to observe that a point, such as (35,45), that lies on C gives rise to a Pythagorean triple, in this case the triple (3,4,5). -
Quadratic Sequence 1

This task belongs to a series of three tasks that presents students with a sequence of tile figures with the property that the n-th figure in the sequence has f(n) tiles, for some quadratic function f. -
Quadratic Sequence 2

This task belongs to a series of three tasks that has students process a sequence of tile figures with the property that the n-th figure in the sequence has f(n) tiles, for some quadratic function f. -
Solve Quadratic Expressions by Factoring video

This video introduces and explains the concept. -
Solving Quadratic Equations by Completing the Square

This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review. -
Solving Quadratic Equations by Factoring

This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review. -
Solving Quadratic Equations Using the Quadratic Formula video

This video introduces and explains the topic. -
Solving Quadratic Equations: Cutting Corners

This lesson unit is intended to help educators assess how well students are able to solve quadratics in one variable. -
Solving Quadratic Functions by Completing the Square video

This video introduces and explains the topic. -
Sorting Equations and Identities

This lesson unit is intended to help educators assess how well students are able to recognize the differences between equations and identities, as well as substitute numbers into algebraic statements in order to test their validity in special cases. -
Springboard Dive

The problem presents a context where a quadratic function arises. Careful analysis, including graphing, of the function is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square. -
Systems of Non-Linear Equations

This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review. -
Systems of Non-Linear Equations video

This video introduces and explains the topic. -
The Circle and The Line

This task is assessing a simple but important piece of conceptual understanding, namely the correspondence between intersection points of the two graphs and solutions of the system. -
Two Squares are Equal

This classroom task is meant to elicit a variety of different methods of solving a quadratic equation. -
Vertex of a parabola with complex roots

The goal of this Illustrative Mathematics task is to study the relationship between the roots of a quadratic function and its graph. -
Visualizing Completing the Square

The purpose of this task is to help provide geometric intuition for the algebraic process called ''completing the square.''

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE). Send questions or comments to USBE Specialist - Lindsey Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer Throndsen. These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.