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Unlock the Power of Math with Real-World Calculus and Statistics

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Introduction to exponents | Pre-Algebra | Khan Academy

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Algebra: Linear equations 1 | Linear equations | Algebra I | Khan Academy

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Math 8 Reference Guide aka Online Math Textbook

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Math 8 Reference Guide aka Online Math Textbook

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Scientific Notation Calculator (to check your work)

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Scientific Notation Calculator (to check your work)

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Scientific Notation (also called Standard Form in Britain) is a special way of writing numbers:

Like this:

Or this:

It makes it easy to use big and small values.

OK, How Does it Work?

Example: 700

Why is 700 written as 7 × 10² in Scientific Notation ?

Both 700 and have the same value, just shown in different ways.

Example: 4,900,000,000

1,000,000,000 = 10 ⁹ ,
so 4,900,000,000 = in Scientific Notation

The number is written in two parts:

Just the digits, with the decimal point placed after the first digit, followed by

× 10 to a power that puts the decimal point where it should be
(i.e. it shows how many places to move the decimal point).

In this example, 5326.6 is written as 5.3266 × 10³,
because 5326.6 = 5.3266 × 1000 = 5.3266 × 10 ³

Try It Yourself

Enter a number and see it in Scientific Notation:

Now try to use Scientific Notation yourself:

images/sci-notation-num.js

Other Ways of Writing It
3.1 × 10^8
We can use the ^ symbol (above the 6 on a keyboard), as it is easy to type.

3 × 10^4 = 3 × 10 × 10 × 10 × 10 = 30,000

Calculators often use "E" or "e" like this:

Example: 3.12E4 is the same as 3.12 × 10⁴

How to Do it
To figure out the power of 10, think "how many places do I move the decimal point?"
Example: 0.0055 is written 5.5 × 10⁻³

Because 0.0055 = 5.5 × 0.001 = 5.5 × 10⁻³

Example: 3.2 is written 3.2 × 10⁰

We didn't have to move the decimal point at all, so the power is

But it is now in Scientific Notation

Check!

After putting the number in Scientific Notation, just check that:

The "digits" part is between 1 and 10 (it can be 1, but never 10)

The "power" part shows exactly how many places to move the decimal point

Why Use It?

Because it makes it easier when dealing with very big or very small numbers, which are common in Scientific and Engineering work.

Example: it is easier to write (and read) 1.3 × 10⁻⁹ than 0.0000000013

It can also make calculations easier, as in this example:

Example: a tiny space inside a computer chip has been measured to be 0.00000256m wide, 0.00000014m long and 0.000275m high.
What is its volume?
Let's first convert the three lengths into scientific notation:

Then multiply the digits together (ignoring the ×10s):

2.56 × 1.4 × 2.75 = 9.856

Last, multiply the ×10s:

10⁻⁶ × 10⁻⁷ × 10⁻⁴ = 10⁻¹⁷ (easier than it looks, just add −6, −4 and −7 together)

The result is 9.856×10⁻¹⁷ m³

It is used a lot in Science:

Example: Suns, Moons and Planets

The Sun has a Mass of 1.988 × 10 ³⁰ kg.

Easier than writing 1,988,000,000,000,000,000,000,000,000,000 kg
(and that number gives a false sense of many digits of accuracy.)

It can also save space! Here is what happens when you double on each square of a chess board:

Values are rounded off, so 53,6870,912 is shown as just 5×10 ⁸

That last value, shown as 9×10 ¹⁸ is actually 9,223,372,036,854,775,808

Engineering Notation

Engineering Notation is like Scientific Notation, except that we only use powers of ten that are multiples of 3 (such as 10 ³, 10⁻³, 10 ¹² etc).

Examples:

Notice that the "digits" part can now be between 1 and 1,000 (it can be 1, but never 1,000).

The advantage is that we can replace the ×10s with Metric Numbers. So we can use standard words (such as thousand or million), prefixes (such as kilo, mega) or the symbol (k, M, etc)

Example: 19,300 meters is written 19.3 × 10³ m, or 19.3 km

Example: 0.00012 seconds is written 120 × 10⁻⁶ s, or 120 microseconds

1340, 1341, 1342, 1344, 1345, 5077, 5078, 5079, 1343, 1346, 1347, 5080

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Scientific Notation (also called Standard Form in Britain) is a special way of writing numbers: Like this: Or this: It makes it easy to use big and small values. Why is 700 written as 7 × 102 in Scientific Notation ? Both 700 and have the same value, just shown in different ways.

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In our analytical age, being able to interpret and create graphs is a highly useful skill. Math Games helps children master this skill, and encourages them to have fun in the process with our popular, curriculum-based games!

Our engaging online games can be played virtually anywhere and for free. They are available in apps for your phone or tablet, or can be played online without downloading any software. We also offer free math worksheets for offline use! Kids can use these tools to practice:

Understanding Venn diagrams and interpreting picture graphs, tally charts and tables

Interpreting and creating bar graphs, pictographs, and line plots

Graphing images and mapping decimal and fractional distances

Finding coordinates, interpreting histograms and graphing lines

Our games are tailored to a range of grade and ability levels. See how easy and enjoyable our resources are to use by clicking on a skill above to get started!

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math games practice graphing free math games practice common core standards

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Find Math games to practice every skill.

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Click below to learn how CVEU is working to keep quality educators at our school. Our student's deserve the best!

Sign up to receive communication from your teachers' union about how you can help support your students' educators.

Use this form to update your contact information as well.

Attend a School Board Meeting

Want to learn more about important issues and decisions that affect your student's education? The next CAVA School Board meetings begin on December 6th!

All board meetings have the same meeting location: https://zoom.us/j/3446279195

​

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Click below to learn how CVEU is working to keep quality educators at our school. Our student's deserve the best! Sign up to receive communication from your teachers' union about how you can help support your students' educators. Use this form to update your contact information as well.

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www.desmos.com

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Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math.

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What is California Virtual Educators United (CVEU)?

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What is California Virtual Educators United (CVEU)?

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Sign up here to subscribe to the newsletter and keep up to date on what is happening in CVEU.

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Parent Contact Information

Hello Parents!

California Virtual Educators United (CVEU) is the teacher's union for California Virtual Academies (CAVA). Teachers have come together this school year to fight for smaller student to teacher ratios, resources for students, safe in person events, and more time outside of the classroom to support our students.

We want to connect with you. We want to hear from you about what issues matter most and keep you informed on our progress toward those goals. Please complete the form to receive a newsletter written by CAVA teachers to keep you updated on what is happening at our school, helpful hints, and invitations to important virtual school meetings, including school board meetings.

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Hello Parents! California Virtual Educators United (CVEU) is the teacher's union for California Virtual Academies (CAVA). We are advocates for your student(s). We are bargaining for smaller student to teacher ratios, resources for students, safe in person events, and more time outside of the classroom to support our students.

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Check out the family support matrix. This has a breakdown of all the various contact numbers and emails within CAVA!

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On-your-own troubleshooting:
1. Clear cache and check cookies settings in chrome
2. Log out of the OLMS and then log back in
3. Restart your computer
4. If none of these steps resolves your tech issues then you need to call tech support or submit a web form to get tech support:
Call: 866-512-2273
General online troubleshooting: https://www.help.k12.com
Webform Submit a Help Case: https://www.help.k12.com/s/submit-a-case

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https://chrome.google.com/webstore/category/ext/22-accessibility

Find extensions to help you customize Chrome and make school stuff more easy to access!

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Small programs that add new features to your browser and personalize your browsing experience.

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Introduction to negative exponents | Exponent expressions and equations | Algebra I | Khan Academy

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Multiplying & dividing powers (integer exponents) | Mathematics I | High School Math | Khan Academy

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One-step addition and subtraction equations

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One-step addition and subtraction equations

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How to solve one-step equations | Linear equations | Algebra I | Khan Academy

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One-step addition & subtraction equations: fractions & decimals

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One-step addition & subtraction equations: fractions & decimals

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How to solve one-step equations with fractions and decimals | 6th grade | Khan Academy

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One-step multiplication & division equations: fractions & decimals

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One-step multiplication & division equations: fractions & decimals

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How to solve one-step multiplication and division equations with fractions and decimals

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How to Solve One-Step Equations (Multiplication and Division) | Math with Mr. J

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Solving equations with the distributive property | Linear equations | Algebra I | Khan Academy

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Multi-step equations review (article) | 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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Introduction to solving an equation with variables on both sides 

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Introduction to solving an equation with variables on both sides 

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Introduction to solving an equation with variables on both sides | Algebra I | Khan Academy

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Number of solutions to linear equations | Linear equations | Algebra I | Khan Academy

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Solving Equations - Identities & Contradictions

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Classifying Equations Contradiction Conditional and Identity

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x- and y-intercepts 2 | Linear equations and functions | 8th grade | Khan Academy

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Introduction to slope | Algebra I | Khan Academy

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Finding the slope of a line from its graph | Algebra I | Khan Academy

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How to visually identify proportional relationships using graphs | 7th grade | Khan Academy

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Slope-intercept form | Algebra I | Khan Academy

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We're asked to convert these linear equations into slope-intercept form and then graph them on a single coordinate plane. We have our coordinate plane over here. And just as a bit of a review, slope-intercept form is a form y is equal to mx plus b, where m is the slope and b is the intercept. That's why it's called slope-intercept form. So we just have to algebraically manipulate these equations into this form. So let's start with line A, so start with a line A. So line A, it's in standard form right now, it's 4x plus 2y is equal to negative 8. The first thing I'd like to do is get rid of this 4x from the left-hand side, and the best way to do that is to subtract 4x from both sides of this equation. So let me subtract 4x from both sides. The left hand side of the equation, these two 4x's cancel out, and I'm just left with 2y is equal to. And on the right-hand side I have negative 4x minus is 8, or negative 8 minus 4, however you want to do it. Now we're almost at slope-intercept form. We just have to get rid of this 2, and the best way to do that that I can think of is divide both sides of this equation by 2. So let's divide both sides by 2. So we divide the left-hand side by 2 and then divide the right-hand side by 2. You have to divide every term by 2. And then we are left with y is equal to negative 4 divided by 2 is negative 2x. Negative 8 divided by 2 is negative 4, negative 2x minus 4. So this is line A, let me graph it right now. So line A, its y-intercept is negative 4. So the point 0, negative 4 on this graph. If x is equal to 0, y is going to be equal to negative 4, you can just substitute that in the graph. So 0, 1, 2, 3, 4. That's the point 0, negative 4. That's the y-intercept for line A. And then the slope is negative 2x. So that means that if I change x by positive 1 that y goes down by negative 2. So let's do that. So if I go over one in the positive direction, I have to go down 2, that's what a negative slope's going to do, negative 2 slope. If I go over 2, I'm going to have to go down 4. If I go back negative 1, so if I go in the x direction negative 1, that means in the y direction I go positive two, because two divided by negative one is still negative two, so I go over here. If I go back 2, I'm going to go up 4. Let me just do that. Back 2 and then up 4. So this line is going to look like this. Do my best to draw it, that's a decent job. That is line A right there. All right, let's do line B. So line B, they say 4x is equal to negative 8, and you might be saying hey, how do I get that into slope-intercept form, I don't see a y. And the answer is you won't be able to because you this can't be put into slope-intercept form, but we can simplify it. So let's divide both sides of this equation by 4. So you divide both sides of this equation by 4. And you get x is equal to negative 2. So this just means, I don't care what your y is, x is just always going to be equal to negative 2. So x is equal to negative 2 is right there, negative 1, negative 2, and x is just always going to be equal to negative 2 in both directions. And this is the x-axis, that's the y-axis, I forgot to label them. Now let's do this last character, 2y is equal to negative eight. So line C, we have 2y is equal to negative 8. We can divide both sides of this equation by 2, and we get y is equal to negative 4. So you might say hey, Sal, that doesn't look like this form, slope-intercept form, but it is. It's just that the slope is 0. We can rewrite this as y is equal to 0x minus 4, where the y-intercept is negative 4 and the slope is 0. So if you move an arbitrary amount in the x direction, the y is not going to change, it's just going to stay at negative 4. Let me do a little bit neater. y is just going to stay at negative 4. Or you can just interpret it as y is equal to negative 4 no matter what x is. So then we are done.

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Converting to slope-intercept form (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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- [Voiceover] As we start to graph lines, we might notice that they're differences between lines. For example, this pink or this magenta line here, it looks steeper than this blue line. And what we'll see is this notion of steepness, how steep a line is, how quickly does it increase or how quickly does it decrease, is a really useful idea in mathematics. So ideally, we'd be able to assign a number to each of these lines or to any lines that describes how steep it is, how quickly does it increase or decrease? So what's a reasonable way to do that? What's a reasonable way to assign a number to these lines that describe their steepness? Well one way to think about it, could say well, how much does a line increase in the vertical direction for a given increase in the horizontal direction? So let's write this down. So let's say if we an increase increase, in vertical, in vertical, for a given increase in horizontal for a given increase a given increase in horizontal. So, how can this give us a value? Well let's look at that magenta line again. Now let's just start at an arbituary point in that magenta line. But I'll start at a point where it's going to be easy for me to figure out what point we're at. So if we were to start right here, and if I were to increase in the horizontal direction by one. So I move one to the right. To get back on the line, how much do I have to increase in the vertical direction? Well I have to increase in the vertical direction by two. By two. So at least for this magenta line, it looks like our increase in vertical is two, whenever we have an increase in one in the horizontal direction. Let's see, does that still work if I were to start here, instead of increasing the horizontal direction by one, if I were increase in the horizontal direction... So let's increase by three. So now, I've gone plus three in the horizontal direction, then to get back on the line, how much do I have to increase in the vertical direction? I have to increase by one, two, three, four, five, six I have to increase by six. So plus six. So when I increase by three in the horizontal direction, I increase by six in the vertical. We were just saying, hey, let's just measure how much to we increase in vertical for a given increase in the horizontal? Well two over one is just two and that's the same thing as six over three. So no matter where I start on this line, no matter where I start on this line, if I take and if I increase in the horizontal direction by a given amount, I'm going to increase twice as much twice as much in the vertical direction. Twice as much in the vertical direction. So this notion of this increase in vertical divided by increase in horizontal, this is what mathematicians use to describe the steepness of lines. And this is called the slope. So this is called the slope of a line. And you're probably familiar with the notion of the word slope being used for a ski slope, and that's because a ski slope has a certain inclination. It could have a steep slope or a shallow slope. So slope is a measure for how steep something is. And the convention is, is we measure the increase in vertical for a given in increase in horizontal. So six two over one is equal to six over three is equal to two, this is equal to the slope of this magenta line. So let me write this down. So this slope right over here, the slope of that line, is going to be equal to two. And one way to interpret that, for whatever amount you increase in the horizontal direction, you're going to increase twice as much in the vertical direction. Now what about this blue line here? What would be the slope of the blue line? Well, let me rewrite another way that you'll typically see the definition of slope. And this is just the convention that mathematicians have defined for slope but it's a valuable one. What is are is our change in vertical for a given change in horizontal? And I'll introduce a new notation for you. So, change in vertical, and in this coordinate, the vertical is our Y coordinate. divided by our change in horizontal. And X is our horizontal coordinate in this coordinate plane right over here. So wait, you said change in but then you drew this triangle. Well this is the Greek letter delta. This is the Greek letter delta. And it's a math symbol used to represent change in. So that's delta, delta. And it literally means, change in Y, change in Y, divided by change in X, change in X. So if we want to find the slope of the blue line, we just have to say, well how much does Y change for a given change in X? So, the slope of the blue line. So let's see, let me do it this way. Let's just start at some point here. And let's say my X changes by two so my delta X is equal to positive two. What's my delta Y going to be? What's going to be my change in Y? Well, if I go by the right by two, to get back on the line, I'll have to increase my Y by two. So my change in Y is also going to be plus two. So the slope of this blue line, the slope of the blue line, which is change in Y over change in X. We just saw that when our change in X is positive two, our change in Y is also positive two. So our slope is two divided by two, which is equal to one. Which tells us however much we increase in X, we're going to increase the same amount in Y. We see that, we increase one in X, we increase one in Y. Increase one in X, increase one in Y. >From any point on the line, that's going to be true. You increase three in X, you're going to increase three in Y. It's actually true the other way. If you decrease one in X, you're going to decrease one in Y. If you decrease two in X, you're going to decrease two in Y. And that makes sense from the math of it as well Because if you're change in X is negative two, that's what we did right over here, our change is X is negative two, we went two back, then your change in Y is going to be negative two as well. Your change in Y is going to be negative two, and negative two divided by negative two, is positive one, which is your slope again.

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Intro to slope | Algebra (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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Solving unit rates problem | Ratios, proportions, units, and rates | Pre-Algebra | Khan Academy

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Slope and rate of change | Graphing lines and slope | Algebra Basics | Khan Academy

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Introduction to point-slope form | Algebra I | Khan Academy

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Writing equations in all forms | Algebra I | Khan Academy

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Graphing a line given point and slope | Linear equations & graphs | Algebra I | Khan Academy

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Graph from slope-intercept equation example | Algebra I | Khan Academy

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Write an equation in slope-intercept form from a graph

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Write an equation in slope-intercept form from a graph

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Slope-intercept equation from a graph examples | Algebra I | Khan Academy

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Class Math - Trolls, Tolls, and Systems of Equations

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Number of solutions to a system graphically

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Number of solutions to a system graphically

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Analyzing solutions to linear systems graphically 2 | Algebra II | Khan Academy

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Solving systems of equations by elimination | Algebra Basics | Khan Academy

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Solving linear systems by substitution | Algebra Basics | Khan Academy

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Systems of equations word problems example 1 | Algebra I | Khan Academy

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Monterey Institute for Technology and Education

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Linear equation word problem: sugary drinks

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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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Domain and range of a relation | Functions and their graphs | Algebra II | Khan Academy

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What is a function? | Functions and their graphs | Algebra II | Khan Academy

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Relations and functions | Functions and their graphs | Algebra II | Khan Academy

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Difference between equations and functions | Functions and their graphs | Algebra II | Khan Academy

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Algebra 1 - Interpreting Graphs of Functions

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Learn Functions – Understand In 7 Minutes

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How to Submit Overdue Notes for Quarter 1

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How to Submit Overdue Notes for Quarter 1

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Option 1: Go to the playback room and watch a recording of a class that covers one of the week's assigned lessons (usually my first slide is a slide of important notes for the day).

Option 2: Go back to one of the assigned lessons for that week and take notes as you go through the lesson, then

submit.

Semester 1: Quarter 1

Week 1: 8/18-8/22

Lessons: Readiness Checkpoint - 1.02

Week 2: 8.25-8.29

Lessons: 1.03-1.08

Week 3: 9.2-9.5

Lessons: 1.09-1.12

Week 4: 9.8-9.12

Lessons: 1.14-2.02

Week 5: 9.15-9.19

Lessons: 2.04-2.10

Week 6: 9.22-9.26

Lessons: 2.11-2.14

Week 7: 9.29-10.3

Lessons: 3.01-3.05

Week 8: 10.6-10.10

Lessons: 3.07-3.09

Week 9: 10.14-10.17

Lessons: 3.10-3.12

Final due date for any late submissions of Quarter 1 work is  11:59pm on Friday, October 24th!

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How to Submit Overdue Notes from Quarter 2

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How to Submit Overdue Notes from Quarter 2

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Option 1: Go to the playback room and watch a recording of a class that covers one of the week's assigned lessons.

Option 2: Go back to one of the assigned lessons for that week and take notes as you go through the lesson, then

submit.

Semester 1: Quarter 2

Week 10: 10/20-10/24  Lessons: 3.10-4.03

Week 11: 10/27-10/31  Lessons: 4.05 -4.08

Week 12: 11/3-11/7  Lessons: 4.09 - 5.02

Week 13: 11/10-11/14  Lessons: 5.03-5.07

Week 14: 11/17-11/20  Lessons: 5.09-5.11

Week 15: 12/1-12/5 Lessons: 6.01-6.05

Week 16: 12/8-12/12 Lessons: 6.06-6.10

Week 17: 12/15- 12/19 Lessons: 6.11-6.15

Final due date for any late submissions of Quarter 2 work is  11:59pm on Sunday, January 18th!

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Scientific notation examples | Pre-Algebra | Khan Academy