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ESC-20 Certificate of Complete for Mathematics (1)

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Welcome! You are invited to join a meeting: Office Hours. After registering, you will receive a confirmation email about joining the meeting.

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Welcome! You are invited to join a meeting: Office Hours. After registering, you will receive a confirmation email about joining the meeting.

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Check out this Presentation designed by Ashley Armer.

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TSI Readiness Training for Educators: Bridging the Information Gap

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College Prep PD Agenda August 1st, 2025 https://bit.ly/3IKG2s6 College Prep Formula Chart Padlet Welcome and Introductions - Ashley Armer and Robert Ferreiro IHE and District Roll Call (update attendance below) Advisory Committee Update Math Syllabus College Prep Resources (by SLO) Intern…

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CP Assessment Tool for Progress Monitoring

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CP Assessment Tool for Progress Monitoring

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CP Assessment Tool for Progress Monitoring

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CP Assessment Tool for Progress Monitoring

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CP Assessment Tool for Progress Monitoring

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CP Assessment Tool for Progress Monitoring

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With Linked Resources CP Math Supporting Information Document

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With Linked Resources CP Math Supporting Information Document

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Copy of COLLEGE PREP MATH REFERENCE MATERIALS.docx

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College Preparatory Course PEIMS

College Preparatory Course - English Language Arts CP110100
College Preparatory Course - Mathematics CP111200

*PEIMS numbers are the same for Texas College Bridge

College Preparatory Course

House Bill 5 created an opportunity for Alamo Colleges, UTSA, TAMUSA, and several independent school districts within ESC-20, to build a partnership. Together, we have designed the College Preparatory courses for English and Math, which are offered to 12th grade students. In the partnership, professors and K-12 educators collaborated to determine standards, assessments, resources, and professional development to offer the College Preparatory courses in the fall of 2014. If you are interested in building a partnership with Alamo Colleges, UTSA, and TAMUSA, please use the following process:

Download Memorandum of Understanding, add your district logo, then sign and return it to Kristi Booth [email protected] . Ms. Booth will route the MOU through the Alamo Colleges, to TAMUSA, then to UTSA, and back to Alamo Colleges, who will return a fully executed document to you.

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Education Service Center, Region 20 is one of 20 regional education service agencies, within Texas, which assist school districts in improving student performance and increasing the efficiency and effectiveness of school operations. We are a non-regulatory agency; our relationship with school districts is collaborative and supportive. Our clients are our partners.

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College Preparatory Courses for CCMR Accountability

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College Preparatory Courses for CCMR Accountability

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College Preparatory Courses for CCMR Accountability | Texas Education Agency

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In the 2024-2025 school year, TEA is implementing a process to review and approve college preparatory courses that count for college, career and military readiness (CCMR) credit in the public-school accountability system.

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GRADING RUBRIC - Revised College Prep Semester One Exam 11172022

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Updated CP Semester Two Exam Rubric 2024 (1)

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Problems are randomized, allowing students multiple opportunities to get the practice and feedback they need on the road to mastery.

Go beyond right and wrong. As soon as a student submits an answer, they get a detailed age-appropriate explanation.

DeltaMath allows teachers to mix and match problem-sets, control rigor, vary due dates, and, with PLUS or INTEGRAL, create tests and problems of their own.

Use DeltaMath's modules to create high-leverage assignments and track student learning. With DeltaMath PLUS or INTEGRAL, students also get access to help videos. Create and assign tests, assign specific problem-types, even create your own problem.

Learn More

Problems solved with DeltaMath

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Real Numbers - Definition, Examples | What are Real Numbers?

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Real numbers include rational numbers like positive and negative integers, fractions, and irrational numbers. Any number that we can think of, except complex numbers, is a real number. Learn more about the meaning, symbol, types, and properties of real numbers.

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1.2 Identify and use algebraic field properties. Add, subtract, multiply and divide real numbers and manipulate numerical expressions

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1.2 Identify and use algebraic field properties. Add, subtract, multiply and divide real numbers and manipulate numerical expressions

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Explains what "literal" equations are, and demonstrates how to solve them (especially formulas from geometry) for the specified variable.

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1.2 Identify and use algebraic field properties. Add, subtract, multiply and divide real numbers and manipulate numerical expressions

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1.2 Identify and use algebraic field properties. Add, subtract, multiply and divide real numbers and manipulate numerical expressions

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1.2 Identify and use algebraic field properties. Add, subtract, multiply and divide real numbers and manipulate numerical expressions

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1.2 Identify and use algebraic field properties. Add, subtract, multiply and divide real numbers and manipulate numerical expressions

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Solving for a Variable Jeopardy Template

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How to simplify square roots (review) (article) | Khan Academy

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To simplify a square root: make the number inside the square root as small as possible (but still a whole number):

Example: √12 is simpler as 2√3

Get your calculator and check if you want: they are both the same value!

Here is the rule: when a and b are not negative

And here is how to use it:

Example: simplify √12

12 is 4 times 3:

Use the rule:

And the square root of 4 is 2:

So √12 is simpler as 2√3

Another example:

Example: simplify √8

√8 = √(4×2) = √4 × √2 = 2√2

(Because the square root of 4 is 2)

And another:

Example: simplify √18

√18 = √(9 × 2) = √9 × √2 = 3√2

It often helps to factor the numbers (into prime numbers is best):

Example: simplify √6 × √15

First we can combine the two numbers:

Then we factor them:

√(6 × 15) = √(2 × 3 × 3 × 5)

Then we see two 3s, and decide to "pull them out":

√(2 × 3 × 3 × 5) = √(3 × 3) × √(2 × 5) = 3√10

Fractions

There is a similar rule for fractions:

Example: simplify √30 / √10

First we can combine the two numbers:

Then simplify:

Some Harder Examples

See if you can follow the steps:

Example: simplify 2√12 + 9√3

First simplify 2√12:

Now both terms have √3, we can add them:

4√3 + 9√3 = (4+9)√3 = 13√3

Surds

Note: a root we can't simplify further is called a Surd. So √3 is a surd. But √4 = 2 is not a surd.

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Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.

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Do you feel confused when asked to simplify a square root that is not a perfect square? It can be tricky, but I'm going to break it down for you and you will be simplifying these babies in no time!

What You'll Find on This Page:

Analyzing a Perfect Square

Before we dive into analyzing any square roots, you will want to make sure that you know the perfect squares through 10 and some of the perfect cubes.

I've created a table of perfect square roots and cubes! Download this document and have it by your side as your study square roots and radicals.

Here we are asked to simplify the square root of 4.

You probably already know the answer to this problem, but let's break it down and think about how we come up with the answer.

We first have to think of "what number squared is 4?

That answer is 2, right? Let's write it like this:

We know that anytime we take the square root of a number squared, our answer is that base number. So....

There are so many properties in math that allow us to solve problems. I'm going to introduce you to a property in Algebra called the "Product Property of Radicals".

But first, I want you to think about this...

If I have the number 6, is it okay to express this number as 3 times 2?

That works, right? Both sides of the equation are equal because 3 times 2 equals 6.

This property works the same way! Check it out!

Product Property of Radicals

**If n is even, then x and y must both be nonnegative**

So, I know these technical properties are difficult to understand. Let's take a look at this property using numbers.

Product Property of Radicals (Using Numbers)

Now we are going to use this property and our knowledge of square and square roots to simplify a non-perfect square root!

Simplifying the Square Root of 18

Since 18 is not a perfect square, we must simplify this expression by rewriting it as a product of 2 square roots. We want to rewrite this so that one of the factors is a perfect square.

Let's first think of the factors for 18.

Now, we need to see if any of these factors are a perfect square.

Since 9 is a perfect square, we will rewrite this square root using its factors of 9 and 2.

Did you notice how we rewrote the square root of 18 as the product of 2 factors, and one of them was a perfect square?

This allowed us to take the square root of the perfect square (which results in a whole number) and then we must leave the square root of 2, as the square root of 2 because it cannot be simplified any further.

Let's take a look at another example.

Simplifying the Negative Square Root of 125

Notice that 125 is not a perfect square, and there is a negative sign outside of the radical.

The negative sign outside of the radical means that our answer will be negative, but we don't really have to worry about that until the end.

Our first job is to think of the factors of 125. In particular, we want one of those factors to be a perfect square.

It works out perfect that the main factors for 125 is 5 and 25. 25 is a perfect square and this allows us to continue simplifying this square root!

Now we can rewrite the square root like this:

So, how are you doing? This isn't such a bad process when you think of simplifying in terms of perfect squares!

Let's take a look at one more example. This one is a little different!

Simplifying The Product of the Square Root of 8 and Square Root of 3

This problem is a little different in that it is written as a product of two square roots.

First we want to see if either one of the factors is a perfect square.

Unfortunately, 8 nor 3 are perfect squares, so we need to see if there is another way to simplify.

We know from the Product Property of Radicals that we can multiply 8 times 3 and write it as one square root, like this:

I hope this helps you to simplify square roots. We will continue simplifying square roots by simplifying square roots of algebraic expressions.

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Learn How to Simplify a Square Root in 2 Easy Steps

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Learning how to simplify a square root can be broken down into 2 easy steps. First think of the factors and determine if one of those factors is a perfect square.

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2.1 Solve problems using equations and inequalities

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2.1 Solve problems using equations and inequalities

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1,100 possible mastery points

About this unit

There are lots of strategies we can use to solve equations. Let's explore some different ways to solve equations and inequalities. We'll also see what it takes for an equation to have no solution, or infinite solutions.

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Solving equations & inequalities | Algebra 1 | Math | Khan Academy

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There are lots of strategies we can use to solve equations. Let's explore some different ways to solve equations and inequalities. We'll also see what it takes for an equation to have no solution, or infinite solutions.

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2.2 Simplify and evaluate numerical and algebraic expressions with integer exponents using Laws of Exponents

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2.2 Simplify and evaluate numerical and algebraic expressions with integer exponents using Laws of Exponents

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01 - Simplify Expressions w/ Exponents in Algebra (Quotients of Monomials) - Part 1

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2.2 Simplify and evaluate numerical and algebraic expressions with integer exponents using Laws of Exponents

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2.2 Simplify and evaluate numerical and algebraic expressions with integer exponents using Laws of Exponents

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01 - Simplifying Algebraic Expressions that Involve Sums and Differences, Part 1

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3.1 Plot ordered pairs (integrate with other concepts)

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3.1 Plot ordered pairs (integrate with other concepts)

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Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

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3.1 Plot ordered pairs (integrate with other concepts)

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3.1 Plot ordered pairs (integrate with other concepts)

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Plotting ordered pairs on a coordinate plane is like a treasure hunt! The first number tells us how many steps to hop right or left on the x-axis. The second number guides us up or down on the y-axis. So, for (6, -8), we hop 6 steps right and 8 steps down. Voila, we've found our treasure! Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

Plot the ordered pair 6, comma negative 8 into the coordinate plane. So this is a coordinate plane right over here. The horizontal axis here, this is the x-axis. The vertical axis here is the y-axis. And the convention, when we get an ordered pair like this, is that the first coordinate is the x-coordinate, and the second coordinate is the y-coordinate. So they're telling us that we have an x-coordinate of 6. That means we count up 6 on the x-axis. So let's count up 1. I could even write it down-- 1, and then we have 2. That's right there. Then we have 3. Then we have 4. Then we have 5. And then we've moved up 6 along the x-axis. We started at the origin, at 0, 0. That's the origin. And we moved 6 to the right. That's this part right over here. Now, our y-coordinate is negative 8. That means we move down 8 in the vertical direction. So we can see it right over here. So this right here, I'll just do that every two. So this is down 1. This right here is negative 2, negative 3. This right here is negative 4, negative 5, negative 6, negative 7, negative 8. So we move to the right 6, and then we move down 8. We move to the right 6, and then we move down 1, 2, 3, 4, 5, 6, 7, and 8. And we are right over there. So that is the point , 6 negative 8. You could also look at it this way. The x-coordinate is 6. So you move 6 there. And so we're going to be along this line right over here. And then you can go, and then the y-coordinate is negative 8. So you go down to negative 8. And you say, we're going to be along this line over here. And the place that they intersect is this coordinate. The easiest way I'd like to think of it, move 6 to the right, move along the x-axis, and then move along in the vertical direction along the y-axis. So you go down 8.

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Plotting a point (ordered pair) (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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3.1 Plot ordered pairs (integrate with other concepts)

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3.1 Plot ordered pairs (integrate with other concepts)

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IXL | Graph points on a coordinate plane | 6th grade math

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Improve your math knowledge with free questions in “Graph points on a coordinate plane” and thousands of other math skills.

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3.2 Define a function and use function notation. Determine if a function exists given multiple representations

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3.2 Define a function and use function notation. Determine if a function exists given multiple representations

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How To Determine Whether The Relation Is A Function

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A relation is a function if it relates every element in its domain to one and only one element in the range.

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3.2 Define a function and use function notation. Determine if a function exists given multiple representations

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3.2 Define a function and use function notation. Determine if a function exists given multiple representations

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How do you evaluate equations and functions?

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To evaluate an equation at a given value, you plug that value in for the specified variable; then simplify to find the value of the other variable.

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3.2 Define a function and use function notation. Determine if a function exists given multiple representations

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3.2 Define a function and use function notation. Determine if a function exists given multiple representations

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3.2 Define a function and use function notation. Determine if a function exists given multiple representations

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3.2 Define a function and use function notation. Determine if a function exists given multiple representations

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Students explore the definition of a function by playing an interactive game called “Club Function.” The goal of the game is to be in the club! With students each assigned to be either a zebra or a rhinoceros, they group themselves according to the “rules” of the club function. After two minutes, st…

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3.5 Write, model and evaluate a function using function notation given a problem situation

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3.5 Write, model and evaluate a function using function notation given a problem situation

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Finding Specific Function Values (Verbal/Symbolic) | Texas Gateway

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Given a verbal and symbolic representations of a function, the student will find specific function values.

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3.5 Write, model and evaluate a function using function notation given a problem situation

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3.5 Write, model and evaluate a function using function notation given a problem situation

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What does a line look like when it is linear?, What does a line look like that is non-linear?, What does it mean when a line is constant?, What would a graph look like if you were told a person speeds up, stays constant and then has to stop because of some kind of obstacle?

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3.6 Identify domain, range and intercepts of functions

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3.6 Identify domain, range and intercepts of functions

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MGAlgU1 - Algebra Math unit 1  Domain and Range

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3.6 Identify domain, range and intercepts of functions

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3.6 Identify domain, range and intercepts of functions

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3.6 Identify domain, range and intercepts of functions

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4.1 Graph linear equations & linear inequalities in two variables

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4.1 Graph linear equations & linear inequalities in two variables

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4.1 Graph linear equations & linear inequalities in two variables

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4.1 Graph linear equations & linear inequalities in two variables

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Oops. Something went wrong. Please try again. | Khan Academy

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Uh oh, it looks like we ran into an error. You need to refresh. If this problem persists, tell us.

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4.1 Graph linear equations & linear inequalities in two variables

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4.1 Graph linear equations & linear inequalities in two variables

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4.1 Graph linear equations & linear inequalities in two variables

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4.1 Graph linear equations & linear inequalities in two variables

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Multiple representations of y-intercepts (Tables, Graphs)

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4.2 Find the slope of a line & write its equation

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4.2 Find the slope of a line & write its equation

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4.2 Find the slope of a line & write its equation

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5.1 Define absolute value, including form and notation

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5.1 Define absolute value, including form and notation

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Graphing absolute value functions (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Semester Two Grading Rubric with Solutions

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Semester Two Grading Rubric with Solutions