Common Core High School Algebra Teaching and Learning Resources
Domain: CED: Creating Equations
Select the cluster for resources on this page:
CED-A: Create equations that describe numbers or
relationships
Standards:
- 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.
- CED-A.2. Create equations in two or more variables to
represent relationships between quantities; graph equations on
coordinate axes with labels and scales.
- CED-A.3. Represent constraints by equations or
inequalities, and by systems of equations and/or inequalities, and
interpret solutions as viable or nonviable options in a modeling
context. For example, represent inequalities describing
nutritional and cost constraints on combinations of different foods.
- 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.
Technology-enhanced investigations:
Mathwords.com: Math Dictionary:
Key vocabulary for this domain. Use with CED-A:
Concord Consortium STEM resources: Mathematics: Each of the
following includes an applet, student activity, teacher lesson plan, and
student assessment.
- Linear Equations: Ski Slope:
Learn about the numeric representation of the
slope of a line, including using rise and run to graph lines
with a given slope. Aligns with standard CED-A.2.
- y= mx + b:
Learn to graph a line using its slope and y-intercept, or to identify the slope
and y-intercept from a linear equation written in slope-intercept form.
Aligns with standard CED-A.2, and REI-D.10.
- Linear Equations: Points, Intercepts, and Slopes, Oh My!:
Students learn to graph lines using the x- and y-intercepts of
equations, as well as how to graph a line when given an equation
in point-slope form. Aligns with standard CED-A.2, and
REI-D.10.
- Linear Equations: Word Problems:
Learn to apply linear equations and their graphs to real-world
problems. Write an equation based on a word problem, and graph
the line described by your equation. Relate the equation and the
line to the situation described in words. Aligns
with CED-A.2 and REI-D.10.
- Solving Systems of Equations:
Two linear equations, with two variables, are presented and
students use graphs to solve the system of equations. Students
graph the lines and solve the problem using the graphs.
Aligns with CED-A.2 and REI-C.6.
- Systems of Equations: Word Problems 1:
Students explore two real-life scenarios that involve solving
systems of equations. The first situation involves mixing
chemicals to create a new solution while the second situation
involves cost and revenue for a bake sale. Aligns with
CED-A.2 and REI-C.6.
- Systems of Equations: Word Problems 2:
Students explore two new scenarios that involve solving systems
of equations. The first situation involves the travel time for a
round trip on an airplane, while the second situation involves
calculating the numbers of students and adults attending a high
school musical. Aligns with CED-A.2 and REI-C.6.
HOT: DadsWorksheets.com:
Online slope calculator for graphing two points on a coordinate plane and
showing the slope-intercept equation, including the rise and run, on the
coordinate axes. Interactively change slope,
intercepts, rise over run or more for reverse calculations. It includes math content to explain the
theory. This is a great tool to explore linear equations in
slope-intercept form. Aligns with CED-A.2.
Imagine Learning Classroom (formerly LearnZillion) subscription needed:
- Lesson set:
Solve
problems with
equations and inequalities in one variable: This is a series of six
video lessons that also include guided practice on this topic.
Videos demonstrate how to create and solve: 1. linear
inequalities, 2. quadratic equations, 3. quadratic inequalities, 4.
rational equations by expressing relationships as unit rates, 5. simple
exponential functions by examining exponential growth and decay
problems, and 6. exponential equations by using a table of values.
Aligns with standard CED-A.1.
- Lesson set:
Create equations in two
or more variables to represent relationships between quantities
(non-linear functions): This is a series of five video lessons that
also include guided practice on this topic. Videos demonstrate how
to create an equation for a geometric sequence involving exponential
growth or decay by making a table and drawing a graph; how to represent
solutions and constraints to systems of linear inequalities by graphing;
how to solve problems involving quadratic functions by using a table of
values; and how to create an equation for a simple rational function by
using a graph and a table of values. Aligns with standard CED-A.2.
- Lesson set:
Represent constraints
by equations or inequalities, and by systems of equations and/or
inequalities: This is a series of four video lessons that also
include guided practice on this topic. Aligns with standard
CED-A.3.
MathsIsFun.com: Explore multiple types of graphs with
Make Your Own
Graphs. Select a Function Grapher and Calculator (also graphs
polar forms), an Equation Grapher (e.g., great for conics), and more.
You can begin by exploring linear and quadratic graphs. Aligns
with CED-A.2.
MIT BLOSSOMS: Video lessons with additional teacher
and learner resources. Descriptions are from the video summaries.
-
Free Fall: "This video lesson is an example of "teaching for
understanding" in lieu of providing students with formulas for
determining the height of a dropped (or projected) object at any
time during its fall. The concept presented here of creating a
chart to organize and analyze data collected in a simple
experiment is broadly useful." Aligns with Algebra
standard CED-A.2 and Function standards IF-B.6, IF-C.7.a, and
LE-A.1.a.
-
The Quadratic Equation: It’s Hip to Be Squared: "The lesson begins with three
quadratics and their graphs (three parabolas): y = x2 -
2x + (0 or 1 or 2). The prerequisite or co-requisite is some working
experience with algebra, like factoring x2 -2x into
x(x-2). The objective is to connect four things: the formula for
y, the graph of y (a parabola), the roots of y and the minimum
or maximum of y." Aligns with Algebra standards SSE-B.3.a,
CED-A.2, and REI-B.4.b and Function standards IF-B.4, IF-C.7.a,
IF-C.8.a, BF-B.3.
-
The Power of Exponentials, Big and Small:
"Exponential growth is keenly applicable to a variety of
different fields ranging from cell growth in biology, nuclear
chain reactions in physics to computational complexity in
computer science. In this lesson, through various examples and
activities, [the presenters] have tried to compare exponential
growth to polynomial growth and to develop an insight about how
quickly the number can grow or decay in exponentials."
Aligns with Algebra standards SSE-B.3.c and CED-A.2 and Function
standards IF-A.3, IF-C.7.(a, c, e), IF-C.8.b, and LE-A.1.(a, c).
-
Selfish Drivers: The Braess Paradox and Traffic Planning:
"The idea of this lesson is to introduce, in a simplified
manner, the so-called Braess Paradox by providing simple
examples to clarify that the addition of some new roads to a
network does not always lead to an improvement in the liquidity
of the traffic; in some cases it might even increase the time
required to get from one point to another if all drivers are
selfish. The educational objectives for this lesson can be
summarized as follows: providing a practical application of
mathematics; indicating the importance of scientific research;
training the students on methods of counting and surveying all
the possibilities in a given problem; and introducing Nash
Equilibrium and Braess Paradox in a simplified manner by visual
examples." Aligns with CED-A.3 and REI-C.6.
Ohio Resource Center on YouTube:
Tutorials for High School Mathematics.
Select the following:
OnlineMathLearning.com: Types of
Algebra Word Problems and How to Solve Them Among those are complete explanations and how to's
for age, average, coin, consecutive integer, distance, fraction, geometry,
interest, lever, mixture, number sequences, ratio, proportion, symbol, and
work problems.
YouTube video lessons. Use the following with CED-A.4:
Wolfram Demonstrations Project:
Download the free Wolfram CDF player to interact with the following
manipulatives:
- US Common Core State Standard Math HSA-CED.A.1:
20 manipulatives. Among those: Maximizing area of
rectangle with fixed perimeter (uses a quadratic), carbon dating
(uses an exponential), and more.
- US Common Core State Standard Math HSA-CED.A.2:
26 manipulatives. Among those: Finding the linear function
rule, finding a pattern (linear equations), linear function
game, slope and equations of lines through points, and more.
- US Common Core State Standard Math HSA-CED.A.3:
10 manipulatives. Among those: Graphing systems of
inequalities, graph of inequalities, the greatest fenced area
along a barn, a word problem about boats, and more.
- US Common Core State Standard Math HSA-CED.A.4:
2 manipulatives: The Wire problem and Maximizing the area of
some geometric figures of fixed perimeter.
Thinking Mathematics:
Purplemath:
Translating Word
Problems: Keywords and Worked Examples Following this are sections with
explanations and examples of typical word problems that learners
encounter, including the following:
Purplemath:
Variation Equations: Direct, Joint, and
Inverse Variation including word problems
YouTube video lessons for solving algebra word problems. The presenter
translates the word problem into the algebraic equation, discusses the
problem, shows diagrams as needed, and presents the solution. He is
very detailed--excellent how-to videos. Students: For a learning
experience, pause the video after the problem is presented, then solve.
Use the video to check your solution method:
Khan Academy video lessons and practice problems:
Systems of Equations Word Problems
Additional YouTube video lessons:
- Distance = Rate x
Time (Airplanes traveling in opposite directions)
- Coins (coins
consisting of dimes and nickels)
- Rate of Work
Problems (How much time does it take to complete the job if two
people or things work together?)
- Interest
Word Problems
(Use Interest = Principal x Rate: Money was invested, part at one rate
and part at another rate. The total interest in one year is
provided. How much was invested at each rate?)
Multiple Choice:
CK-12: Algebra: Video examples, practice problems
online, and real world
applications. The following align with CED-A.2:
MathsIsFun.com: Tutorials on equations. Examples are shown.
Learners then complete 10 multiple choice problems in each section.
Aligns with CED-A.2:
Constructed-response:
Achieve the Core:
Quadratic Equations Mini-Assessment
(pdf or Word docx)
can be used to evaluate students' understanding of algebra standards REI-B.4 and CED-A.1 in order to prepare to teach this material or to check for
student ability to demonstrate understanding and apply these concepts.
West Texas A & M University: Virtual Math Lab: Intermediate Algebra:
Tutorial 16: Equations of Lines. Use with CED-A.1.
Khan Academy:
HSA-A-CED
includes HSA-CED.A.1, HSA-CED.A.2, HSA-CED.A.3 and HSA-CED.A.4 Common Core aligned problems.
Also see the following practice questions with videos to use with CED-A.2:
Algebra Lab:
Consortium for Mathematics and Its Applications (COMAP):
Mathematical
Modeling Handbook (Sample). This sample mathematical modeling module
aligns to Common Core Standards. It contains teacher guidance for implementation and student questions
to complete during their investigation:
- The module For the Birds aligns to number and
quantity standards Q-A.1 and Q-A.2, and algebra standard CED-A.4.
WisWeb:
HTML5 Applets:
-
Click on the title
Guess the functions on the list of applets. Learners are shown the graph of a
linear equation and then determine and write the equation
(formula) of it. Use this
HTML5 applet with standard CED-A..
Performance tasks:
Illustrative Mathematics:
Algebra:
Inside Mathematics: MARS Tasks:
-
Number Towers: Learners form and solve equations obtained from a
number pattern. This task aligns with algebra standards CED-A.2
and CED-A.3.
-
Expressions: Learners work with algebraic expressions for areas and
perimeters of parallelograms and trapezoids. This task aligns with
standard CED-A.4.
-
Sorting Functions (pdf) or see all MARS Tasks: Functions &
Relations: Course 1 Algebra: Scroll down the page to select
Sorting Functions: Learners match graphs of four functions with
their equations, tables, and rules. This task aligns with function
standard IF-C.7 and algebra standard CED-A.2.
Mathematics Assessment Project:
Standards: High School: Algebra:
Mathematics Vision Project,
Secondary 1 Student Edition:
-
Getting Ready Module:
This module contains 10 classroom tasks. Task 5: Cafeteria
Actions and Reactions aligns to algebra standard CED-A.1; Task 6:
Elvira’s Equations and Task 7: Solving Equations, Literally align with
CED-A.4.
- Module 1: Systems of Equations and Inequalities:
This module contains 10 classroom tasks. Standards addressed include REI-C.5, REI-C.6, REI-D.12, and CED-A.2, CED-A.3,
and CED-A.4.
- Task 2: Too Big or Not Too Big, That is the Question;
Task 3: Some of One, None of the Other; Task 4: Pampering and Feeding
Time align with CED-A.2;
- Task 1: Pet Sitters; Task 4: Pampering
and Feeding Time; Task 5: All for One, One for All, parts 1 & 2;
and Task 9: Food for Fido and Fluffy align with CED-A.3.
- Module 4: Features of Functions:
This module contains nine classroom tasks. Task 4: Water Park;
Task 5: Pooling it Together; and Task 6: Interpreting Functions align
with CED-A.4.
NCTM's Reasoning and Sense Making Task Library: Over the Hill includes the task overview, teacher notes for its use, and student activity sheet. Aligns with function standard BF-A.1b, algebra standards CED-A.2, REI-C.6,
and mathematical practice standards 1, 4, 5, and 7.
Back to top
Common Core Math:
Intro | HS Algebra Domain:
SSE | APR | CED | REI |
Comments?
Are you finding resources at CT4ME of value?