Author:
Ashley Hatz
Subject:
Educational Technology, Mathematics
Material Type:
Activity/Lab, Assessment
Level:
High School
Tags:
Language:
English

# Stem Integrated Modules

## Overview

There are three weeks of online, stem-integrated modules. The first week is on Linear Equations, the second is Systems of Equations, and the third is Quadratic Equations. There is a teacher document that explains standards, links, and the order that everything is supposed to be viewed in. There is also a student checklist with links that provides the order in which students should be viewing the material.

# Ashley Hatz

## Information:

For: High School Algebra Classroom

How the modules should be used:

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Standards From:

Next Generation Science Standards - Illinois

International Society for Technology in Education

Common Core State Standards Initiative - Illinois

## Contents:

Module 1: Solving Linear Equations

Module 2:  Systems of Equations

# Solving Linear Equations

## Teacher Version

Standards:

Science/Engineering

5-PS1-3- Make observations and measurements to identify materials basked on their properties.

MS-ETS1-3- Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each that can be combined into a new solution to better meet the criteria for success.

MS-ETS1-4- Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved.

Technology:

EMPOWERED LEARNER 1C- Students use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways.

CREATIVE COMMUNICATOR 6C- Students communicate complex ideas clearly and effectively by creating or using a variety of digital objects such as visualizations, models, or simulations.

Mathematics:

CCSS.MATH.CONTENT.HSA.REI.A1- Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

CCSS.MATH.CONTENT.HSA.REI.B3- Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

CCSS.MATH.CONTENT.HSA.CED.A.1- Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

CCSS.MATH.CONTENT.HSA.CED.A.4- Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.

CCSS.MATH.CONTENT.HS.SSE.A.1- Interpret expressions that represent a quantity in terms of its context.

CCSS.MATH.PRACTICE.MP2-Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP4-Model with mathematics.

CCSS.MATH.PRACTICE.MP6-Attend to precision.

Daily Outline:

Day 1: SOLVING ONE-STEP AND TWO-STEP EQUATIONS

• (10 minutes) Students should complete the warmup problems in the form of a Google Quiz titled Inverse Operations. They will be asked to identify the inverse operations that will solve the assigned equations.
• (20 minutes) Students will then need to watch the narrated PowerPoint presentation that goes over an introduction to solving linear equations.
• (10 minutes) Students will then need to play an individual Kahoot review game that will go over solving one and two step equations.
• (10 minutes) Students will then complete the review questions in the google doc that go over solving one and two step equations.

Day 2: SOLVING GENERAL EQUATIONS WITH CONSTANTS AND VARIABLES ON BOTH SIDES

• (20 minutes) Students should follow along with this Khan Academy video that introduces solving equations with constants and variables on both sides.
• (30 minutes) After the video, students will complete the rest of their review questions from the document on Day 1.

Day 3: FRACTIONS AND DECIMALS

• (15 minutes) Students will follow through a Powerpoint presentation that shows them how to solve equations with fractions and decimals.
• (20 minutes) Students will then watch a Youtube video that shows them another way of solving equations with fractions and decimals.
• (15 minutes) Students will then complete Google Doc review questions on solving equations with fractions and decimals.

Day 4: TRANSLATING WORD PROBLEMS

• (20 minutes) Students will follow along with the emaze presentation that introduces translating word problems.
• (20 minutes) Students will then create a FlipGrid explaining a word problem that they have created on their own that is 50-75 seconds long. They need to explain the problem they have created, the equation that is created from the word problem, and how to solve and verify their solution.
• (10 minutes) Students will then take a look at their boat challenge for Day 5 and start to come up with their own ideas.

Day 5: LAB DAY

• (40 minutes) Students will complete the Boat Challenge that they should have already started brainstorming for.
• (10 minutes) Students will then complete an exit slip on whether they think the lab would have been different if they built with cardboard instead of aluminum foil.

# Systems of Equations

## Teacher Version

Standards:

Science:

HS-PSI-7- 7.        Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction.

Technology:

EMPOWERED LEARNER 1C- Students use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways.

Mathematics:

CCSS.MATH.CONTENT.8.EE.C.7- Solve linear equations in one variable.

CCSS.MATH.CONTENT.8.EE.C.8- Analyze and solve pairs of simultaneous linear equations.

CCSS.MATH.CONTENT.HSA.REI.B.3- Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

CCSS.MATH.CONTENT.HSA.REI.C.5- Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

CCSS.MATH.CONTENT.HSA.REI.C.6- Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

CCSS.MATH.CONTENT.HSA.REI.C.8-(+) Represent a system of linear equations as a single matrix equation in a vector variable.

CCSS.MATH.CONTENT.HSA.REI.D.10- Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

CCSS.MATH.PRACTICE.MP2-Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP4-Model with mathematics.

CCSS.MATH.PRACTICE.MP6-Attend to precision.

Daily Outline:

Day 1:CREATING SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES

• (20 minutes) Students will read through an article about applying linear systems in reality.
• (30 minutes) Students will complete a worksheet that guides them through creating systems of equations. This is provided by a Google Doc.

Day 2: SOLVING SYSTEMS GRAPHICALLY

• (15 minutes) Students will watch a Youtube video introducing systems of equations being solved graphically. They should follow along and take notes.
• (35 minutes) Students will complete the alpine slide activity which guides them through creating a system of equations and solving it.

Day 3: SOLVING SYSTEMS BY COMBINATION

• (30 minutes) Students will follow along with the Emaze presentation based on the combination method. This includes watching a video at the end of the presentation that shows another example of this method.
• (20 minutes) Students will fill out their exit slip for the day in this Google Forms. It asks questions about applying the method to their life.

Day 4: SOLVING SYSTEMS BY SUBSTITUTION

• (10 minutes) Students will complete the warmup for solving systems by substitution. It includes prior knowledge from past lessons.
• (20 minutes) Students will follow along with a Youtube video about solving systems using substitution. Students will take notes.
• (20 minutes) Students will complete the substitution activity provided in the Google Doc below.

Day 5: LAB DAY

• (5 minutes) Students will watch a video I have created to show them how to set up a matrix from a system of equations.
• (10 minutes) Students will watch the Youtube video about balancing chemical equations using linear algebra.
• (35 minutes) Students will complete the Google Doc that will assess their application skills using linear algebra and matrices to solve systems of equations.

# Module 3:

## Teacher Version

Standards:

Technology:

EMPOWERED LEARNER 1C- Students use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways.

CREATIVE COMMUNICATOR 6C- Students communicate complex ideas clearly and effectively by creating or using a variety of digital objects such as visualizations, models, or simulations.

Mathematics:

CCSS.MATH.CONTENT.HSA.REI.B.4- Solve quadratic equations in one variable.

CCSS.MATH.CONTENT.HSA.REI.B.4.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.

CCSS.MATH.CONTENT.HSA.REI.B.4.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.

CCSS.MATH.CONTENT.HSA.CED.A.1- Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

CCSS.MATH.CONTENT.HSA.SSE.B.3.A- Factor a quadratic expression to reveal the zeros of the function it defines.

CCSS.MATH.PRACTICE.MP2-Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP4-Model with mathematics.

CCSS.MATH.PRACTICE.MP6-Attend to precision.

Daily Outline:

• (30 minutes) Students will follow along with the Powerpoint presentation that introduces them to solving quadratic equations with the quadratic formula.
• (5 minutes) Students will watch a Youtube video that plays a song to help students memorize the quadratic formula.
• (15 minutes) Students will complete a Google Forms exit slip over the quadratic formula.

Day 2: SQUARE ROOTS METHOD

• (20 minutes) Students will follow a Khan Academy Youtube video that will show an example of solving quadratic equations using the square root method.
• (30 minutes) Students will follow the Emaze presentation that will show them how to use the square root method and when to use it.

Day 3: COMPLETING THE SQUARE

• (10 minutes) Students will read the article about how and when to use the complete the square method.
• (10 minutes) Students will watch a video of me giving an example of using the complete the square method.
• (15 minutes) Students will complete the Kahoot Review Game that will assess their knowledge of using completing the square.
• (15 minutes) Students will complete the exit slip for completing the square.

Day 4: FACTORING AND ZERO PRODUCT PROPERTY

• (35 minutes) Students will follow along with the Emaze presentation that will introduce the factoring method and the zero product property.
• (15 minutes) Students will complete the exit slip for the day.

Day 5: Applications Day

• (10 minutes) Students will watch the Youtube video that will go through an example that is like the quadratic applications they will work on next.
• (40 minutes) Complete the Quadratics Application worksheet in the Google Doc.