This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
A+ Click is an interactive collection of more than 3700 math problems …
A+ Click is an interactive collection of more than 3700 math problems and answers for K-1 K-12 school program. It defines the personal level of math knowledge. You move up into the next level if you give 5 correct answers in a row. Practice makes perfect.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
This is a task from the Illustrative Mathematics website that is one …
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
In this seminar you will learn about the absolute value of numbers. …
In this seminar you will learn about the absolute value of numbers. You will learn how taking the absolute value affects both positive and negative numbers. You will use the techniques learned in this seminar to verify solutions to various other types of problems involving absolute value as you move forward. When looking at absolute value, you will identify how it can change a solution and the compare the difference that it makes in equations when there are multiple negative signs.StandardsCC.2.1.HS.F.2Apply properties of rational and irrational numbers to solve real world or mathematical problemsLearning TargetI can find the absolute value of a given number or numbers.Habits of MindPersistingCritical Thinking SkillAnalyze/evaluateAcademic/Concept VocabularyAbsolute valueNegativeNumber linePositive
In this video, we explore some concepts fundamental to algebra. To streamline …
In this video, we explore some concepts fundamental to algebra. To streamline the discussion of relationships between physical quantities, we introduce variables, functions, composition, and inverse. By thinking about the concept of an inverse function, we obtain our first glimpse of the imaginary root (i.e. square-root of -1) and the complex plane.
A work in progress, CK-12's Algebra I Second Edition is a clear …
A work in progress, CK-12's Algebra I Second Edition is a clear presentation of algebra for the high school student. Topics include: Equations and Functions, Real Numbers, Equations of Lines, Solving Systems of Equations and Quadratic Equations.
CK-12's Texas Instruments Algebra I Student Edition Flexbook allows students to better …
CK-12's Texas Instruments Algebra I Student Edition Flexbook allows students to better utilize a graphing calculator in understanding the fundamental concepts of algebra.
CK-12's Texas Instruments Algebra I Teacher's Edition Flexbook allows an Instructor to …
CK-12's Texas Instruments Algebra I Teacher's Edition Flexbook allows an Instructor to teach students to better utilize a graphing calculator in understanding the fundamental concepts of algebra.
CK-12 Foundation's Algebra I Teacher's Edition FlexBook complements CK-12's Algebra I Student …
CK-12 Foundation's Algebra I Teacher's Edition FlexBook complements CK-12's Algebra I Student Edition. The solution and assessment guides are available upon request.
CK-12 Foundation's Basic Algebra FlexBook is an introduction to the algebraic topics …
CK-12 Foundation's Basic Algebra FlexBook is an introduction to the algebraic topics of functions, equations, and graphs for middle-school and high-school students.
National Board Certified teacher Marlo Warburton introduces a fresh approach to teaching …
National Board Certified teacher Marlo Warburton introduces a fresh approach to teaching the notoriously difficult "mixture" word problems for Algebra I. Using an in-class demonstration and incorporating basic physics principles of weight and distance, Ms. Warburton helps her students visualize, solve -- and even enjoy! -- these challenging problems.
This resource provides an explanation of two number/magic puzzles that can be …
This resource provides an explanation of two number/magic puzzles that can be demystified and explained by using algebra. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.
In this four part series, we visit the classrooms of two partner …
In this four part series, we visit the classrooms of two partner teachers who plan all their lessons together but have totally different styles inside the classroom. See the same lesson unfold in each class, the class structures used by each teacher, and the group work formats used by each.
In this four part series, we visit the classrooms of two partner …
In this four part series, we visit the classrooms of two partner teachers who plan all their lessons together but have totally different styles inside the classroom. See the same lesson unfold in each class, the class structures used by each teacher, and the group work formats used by each.
In this four part series, we visit the classrooms of two partner …
In this four part series, we visit the classrooms of two partner teachers who plan all their lessons together but have totally different styles inside the classroom. See the same lesson unfold in each class, the class structures used by each teacher, and the group work formats used by each.
In this four part series, we visit the classrooms of two partner …
In this four part series, we visit the classrooms of two partner teachers who plan all their lessons together but have totally different styles inside the classroom. See the same lesson unfold in each class, the class structures used by each teacher, and the group work formats used by each.
Use tiles to represent variables and constants, learn how to represent and …
Use tiles to represent variables and constants, learn how to represent and solve algebra problems. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra.
This lesson is about trying to get students to make connections between …
This lesson is about trying to get students to make connections between ideas about equations, inequalities, and expressions. The lesson is designed to give students opportunities to use mathematical vocabulary for a purpose to describe, discuss, and work with these symbol strings.The idea is for students to start gathering global information by looking at the whole number string rather than thinking only about individual procedures or steps. Hopefully students will begin to see the symbol strings as mathematical objects with their own unique set of attributes. (7th Grade Math)
Students learn about linear programming (also called linear optimization) to solve engineering …
Students learn about linear programming (also called linear optimization) to solve engineering design problems. As they work through a word problem as a class, they learn about the ideas of constraints, feasibility and optimization related to graphing linear equalities. Then they apply this information to solve two practice engineering design problems related to optimizing materials and cost by graphing inequalities, determining coordinates and equations from their graphs, and solving their equations. It is suggested that students conduct the associated activity, Optimizing Pencils in a Tray, before this lesson, although either order is acceptable.
This final lesson in the unit culminates with the Go Public phase …
This final lesson in the unit culminates with the Go Public phase of the legacy cycle. In the associated activities, students use linear models to depict Hooke's law as well as Ohm's law. To conclude the lesson, students apply they have learned throughout the unit to answer the grand challenge question in a writing assignment.
Use your knowledge of rectangle areas to calculate the missing measurement of …
Use your knowledge of rectangle areas to calculate the missing measurement of these composite diagrams. Find the value of the question marks in the diagrams. All of the shapes are rectangles but are not drawn to scale.
Build rectangles of various sizes and relate multiplication to area. Discover new …
Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying large numbers. Use the game screen to test your problem solving strategies!
This is a challenge based activity in which students use augmented reality …
This is a challenge based activity in which students use augmented reality and trial and error in order to determine how changes to a quadratic equation affect the shape of a parabola. Students use the Geogebra AR app to manipulate equations and change the parabola to fit around a physical object.
This is a challenge based activity in which students use augmented reality …
This is a challenge based activity in which students use augmented reality and trial and error in order to determine how changes to a quadratic equation affect the shape of a parabola. Students use the Geogebra AR app to manipulate equations and change the parabola to fit around a physical object.
This lesson unit is intended to help teachers assess how well students …
This lesson unit is intended to help teachers assess how well students are able to create and solve linear equations. In particular, the lesson will help you identify and help students who have the following difficulties: solving equations with one variable and solving linear equations in more than one way.
Many students are motivated by real world applications of mathematics, and most …
Many students are motivated by real world applications of mathematics, and most students are familiar with the term CGI from watching movies and playing video games. This particular activity ties matrix multiplication to CGI (Computer Generated Imagery). It has been used successfully with high school students in an Algebra II course who had just learned how to do matrix multiplication, middle school and high school students (some of whom were seeing matrix multiplication for the first time) attending a special Math Day on a university campus, and with College Algebra students (during a unit about matrices).
This is a complete, full-year Algebra 1 course with tons of interactivity …
This is a complete, full-year Algebra 1 course with tons of interactivity included in every lesson. Some lessons include videos, and all include interactives and newly added inline questions. Inline questions offer instant, per-answer feedback to help you learn by knowing why your answers are correct or incorrect. Every lesson also has specifically chosen 'Related Modalities' that teach the same concept in different ways. Related Modalities may be additional videos, interactives, or study guides (often written by students themselves). You can choose to use the resources directly embedded within the Algebra 1 FlexBook® 2.0 lessons, or learn Algebra your way by using the Related Modalities that are most effective for you!
This lesson unit is intended to help teachers assess how well students …
This lesson unit is intended to help teachers assess how well students are able to classify solutions to a pair of linear equations by considering their graphical representations. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using substitution to complete a table of values for a linear equation; identifying a linear equation from a given table of values; and graphing and solving linear equations.
The foundation of this lesson is constructing, communicating, and evaluating student-generated tables …
The foundation of this lesson is constructing, communicating, and evaluating student-generated tables while making comparisons between three different financial plans. Students are given three different DVD rental plans and asked to analyze each one to see if they could determine when the 3 different DVD plans cost the same amount of money, if ever. (7th/8th Grade Math)
A brief refresher on the Cartesian plane includes how points are written …
A brief refresher on the Cartesian plane includes how points are written in (x, y) format and oriented to the axes, and which directions are positive and negative. Then students learn about what it means for a relation to be a function and how to determine domain and range of a set of data points.
Do you have a big decimals test coming up? Or are you …
Do you have a big decimals test coming up? Or are you studying for your standardized math test? This site is both fun and helpful! On this site you can review the following topics: place values of decimals, how to read decimals, expanded notation for decimals, and how to convert fractions into decimals. On this site you can also review how to add, subtract, multiply, and divide decimals. You will also learn about terminating and repeating decimals.
Ana Donevska Todorova Humboldt Universitハt zu Berlin Mathematisch-Naturwissenschaftliche Fakultハt II Institut f゚r …
Ana Donevska Todorova Humboldt Universitハt zu Berlin Mathematisch-Naturwissenschaftliche Fakultハt II Institut f゚r Mathematik, Didaktik der Mathematik ??? ?????????? ?????? ???????? ?? ???????????? ????? ? ????
This purpose of this task is to help students see two different …
This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.
This lesson unit is intended to help assess how well students are …
This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units.
Learn about graphing polynomials. The shape of the curve changes as the …
Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.
Khan Academy video tutorial. Solving one and two step equations-this is made …
Khan Academy video tutorial. Solving one and two step equations-this is made slightly more difficult than the Simple Equations tutorial by adding constants to the variable term.
Gallery OverviewAllow students who have a clear understanding of the content thus …
Gallery OverviewAllow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then use this time to provide additional help to students who need review of the unit's concepts or to assist students who may have fallen behind on work.Gallery DescriptionsKeep It BalancedStudents will use reasoning to complete some equations to make them true.Equation SortStudents will sort equations into three groups: equations with one solution, equations with many solutions, and equations with no solutionsOn the Number LineStudents will use a number line to identify numbers that make an equation or inequality true.How Many Colors?Students will write and solve an equation to find the number of different colored blocks in a box.Value of sStudents will use a property of equality to solve an equation with large numbers.Marbles in a CupStudents are given information about the weight of a cup with two different amounts of marbles in it. They use this information to find the weight of the cup.When Is It True?Students will use what they know about 0 and 1 to decide when a certain equation is true.
The purpose of this task is to directly address a common misconception …
The purpose of this task is to directly address a common misconception held by many students who are learning to solve equations. Because a frequent strategy for solving an equation with fractions is to multiply both sides by a common denominator (so all the coefficients are integers), students often forget why this is an "allowable" move in an equation and try to apply the same strategy when they see an expression.
The Exponents and Radicals module is separated into two parts -- exponents …
The Exponents and Radicals module is separated into two parts -- exponents and radicals. Each part has two subtopics. Each subtopic has a video lecture page and a practice assignment. The video lecture page includes guided notes in pdf form and videos that follow the guided notes. There are also Word document versions of the notes in the "files" section of this course for instructor convenience. Each video lecture page also includes supplemental YouTube videos which are optional for students and may be used if further instruction is needed. The practice assignment is a set of exercises in Derivita that correspond to the skills covered in the video lecture.There are also two review assignments in this module -- one for exponents and one for radicals. These assignments cover everything from that part of the module, rather than being broken up into parts like the practice assignments. So there are a total of six assignments in the module and instructors can choose which assignments are most appropriate for their students' needs.This work, by Madilyn Marshall, is licensed under a Creative Commons Attribution 4.0 International License.CC-BY
The Factoring module is separated into two parts -- factoring numbers and …
The Factoring module is separated into two parts -- factoring numbers and factoring algebraic expressions. Each part has subtopics. Each subtopic has a video lecture and a practice assignment. The video lecture page includes guided notes in pdf form and videos that follow the guided notes. Each video lecture page also includes supplemental YouTube videos which are optional for students and may be used if further instruction is needed. The practice assignment is a set of exercises in Derivita that correspond to the skills covered in the video lecture.This work, by Magdalene (Maxie) Inigo, is licensed under a Creative Commons Attribution 4.0 International License.Links to an external site.CC-BY
In this video segment from Cyberchase, Harry has a fixed budget for …
In this video segment from Cyberchase, Harry has a fixed budget for clothing, so he must figure out what combination of jackets and pants he can buy with $100.
This task is the second in a series of three tasks that …
This task is the second in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.
Khan Academy tutorial video that uses Excel spreadsheet and actual income data …
Khan Academy tutorial video that uses Excel spreadsheet and actual income data to predict annual income and expresses why lines and models are useful and interesting.
Students learn about four forms of equations: direct variation, slope-intercept form, standard …
Students learn about four forms of equations: direct variation, slope-intercept form, standard form and point-slope form. They graph and complete problem sets for each, converting from one form of equation to another, and learning the benefits and uses of each.
The Fraction module is separated into five pages. Each page except the …
The Fraction module is separated into five pages. Each page except the first page has videos and lecture notes. At the end of the entire module are review problems. The review problems are a set of exercises in Derivita that correspond to the skills covered in the lecture pages and the videos.The instructors can choose to assign the practice problems based on their students' needs.This work was created by Kathryn Kozak, and it is licensed under a Creative Commons Attribution 4.0 International License.CC-BY
This lesson unit is intended to help you assess how well students …
This lesson unit is intended to help you assess how well students working with square numbers are able to: choose an appropriate, systematic way to collect and organize data, examining the data for patterns; describe and explain findings clearly and effectively; generalize using numerical, geometrical, graphical and/or algebraic structure; and explain why certain results are possible/impossible, moving towards a proof.
Students will calculate the glide slope ratio and angle of paper airplanes …
Students will calculate the glide slope ratio and angle of paper airplanes they have created. They will make claims about the type of airplane and support claims with evidence and reasoning from their class data.
In Module 4, students extend what they already know about unit rates …
In Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs. Students understand the connections between proportional relationships, lines, and linear equations in this module. Students learn to apply the skills they acquired in Grades 6 and 7, with respect to symbolic notation and properties of equality to transcribe and solve equations in one variable and then in two variables.
Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.
Students learn about an important characteristic of lines: their slopes. Slope can …
Students learn about an important characteristic of lines: their slopes. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero or undefined. Students get an explanation of when and how these different types of slope occur. Finally, they learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another.
Rebecca Davis sets up a coordinate plane on the floor of her …
Rebecca Davis sets up a coordinate plane on the floor of her classroom. Groups of 3 or 4 students are assigned equations in slope-intercept form and graph them using their bodies on the giant coordinate plane. As extensions, Ms. Davis changes the slope or y-intercept of the original equation and makes the activity into a race.
This exploration can be done in class near the beginning of a …
This exploration can be done in class near the beginning of a unit on graphing parabolas. Students need to be familiar with intercepts, and need to know what the vertex is.
This problem asks the students to represent a sequence of operations using …
This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.
Si definisce monomio un'espressione letterale nella quale non compare l'operazione di addizione …
Si definisce monomio un'espressione letterale nella quale non compare l'operazione di addizione algebrica. Il monomio è formato da una parte letterale è un coefficiente numerico.Due o più monomi sono simili quando hanno la stessa parte letterale.
In this activity, students write and solve a system of two linear …
In this activity, students write and solve a system of two linear equations to explore the numerical and graphical meaning of "solution." The activity closes by asking students to apply what they've learned to similar situations.
This activity is a culmnating assessment of students' abilities to describe a …
This activity is a culmnating assessment of students' abilities to describe a linear function in words, in an equation, in a table, in a graph, identify a solution, and explain the solution.
This lesson unit is intended to help teahcers assess how well students …
This lesson unit is intended to help teahcers assess how well students are able to interpret speed as the slope of a linear graph and translate between the equation of a line and its graphical representation.
Students practice using algebraic expressions by recording data from a video segment …
Students practice using algebraic expressions by recording data from a video segment in which two staircases ascend at different rates. They record the patterns in two-column tables, draw line graphs and write simple algebraic relations.
This is a supplemental activity sheet for Mathematics in the Modern World. …
This is a supplemental activity sheet for Mathematics in the Modern World. This will assist the teachers in mastering the concepts of translating mathematical phrases into symbols. This will also enable the students to establish mastery of the learning content.
Repeated motion is present everywhere in nature. Learn how to 'make waves' …
Repeated motion is present everywhere in nature. Learn how to 'make waves' with your own movements using a motion detector to plot your position as a function of time, and try to duplicate wave patterns presented in the activity. Investigate the concept of distance versus time graphs and see how your own movement can be represented on a graph.
Students are introduced to classroom routines and expectations, and complete a full …
Students are introduced to classroom routines and expectations, and complete a full mathematics lesson. The class discusses how to clearly present work to classmates. Key ConceptsStudents match a numerical expression to its corresponding description in words. Students interpret parentheses and brackets in numerical expressions and they construct viable arguments and critique the reasoning of others. Students learn to use the exponent 2 to represent squaring.Goals and Learning ObjectivesDescribe the classroom routines and expectations.Collaborate with a partner.Critique a partner’s reasoning.Connect a numerical expression to its corresponding word description.Learn to use an exponent of 2 to represent squaring.
Equations and Inequalities Type of Unit: Concept Prior Knowledge Students should be …
Equations and Inequalities
Type of Unit: Concept
Prior Knowledge
Students should be able to:
Add, subtract, multiply, and divide with whole numbers, fractions, and decimals. Use the symbols <, >, and =. Evaluate expressions for specific values of their variables. Identify when two expressions are equivalent. Simplify expressions using the distributive property and by combining like terms. Use ratio and rate reasoning to solve real-world problems. Order rational numbers. Represent rational numbers on a number line.
Lesson Flow
In the exploratory lesson, students use a balance scale to find a counterfeit coin that weighs less than the genuine coins. Then continuing with a balance scale, students write mathematical equations and inequalities, identify numbers that are, or are not, solutions to an equation or an inequality, and learn how to use the addition and multiplication properties of equality to solve equations. Students then learn how to use equations to solve word problems, including word problems that can be solved by writing a proportion. Finally, students connect inequalities and their graphs to real-world situations.
Lesson OverviewStudents apply the addition property of equality to solve equations. They …
Lesson OverviewStudents apply the addition property of equality to solve equations. They are introduced to this property using a balance scale.Key ConceptsUp until this lesson, students have been solving equations informally. They used guess and check and reasoned about the quantities on either side of the equation in order to solve the equation.In this lesson, students are introduced to the addition property of equality. As equations become more and more complicated, students will need to rely on formal methods for solving them. This property states that the same quantity can be added to both sides of an equation and the new equation will be equivalent to the original equation. That means the new equation will have the same solutions as the original equation.To solve an equation such as x + 6 = 15, –6 can be added to both sides to get the resulting equation x = 9. However, since adding a negative number has not been introduced yet, students will consider both adding and subtracting a number (which is the equivalent of adding a negative number) from both sides to be an application of the addition property of equality.Students will apply the addition property of equality to an equation with the goal of getting the variable alone on one side of the equation and a number on the other.Goals and Learning ObjectivesUse the addition property of equality to keep a scale balanced.Use the addition property of equality to solve equations of the form x + p = q for cases in which p, q, and x are all non-negative rational numbers.
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