Instructions for the ELL Math Online course

Table of Contents

In this Math course we will go ONLINE and use many lessons from Khan Academy. However, we will not be doing every lesson and exercise. Students in this course will follow the lesson links BELOW. (one after another). There are also links to other lessons outside Khan academy and hand out pages.

In Khan academy, if you feel like you know the practice, then you can try the links called EXERCISE. You must get five questions correct in a row to get Mastery and points - do NOT go on until you get mastery. If you have problems you can review the video AND talk to the teacher to help you.

Once you get mastery then come back to THIS PAGE and go to the next link.

Note: to Open Notebook files use this site -
You can also open Notebook files online


Unit 6 - Statistics

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Reading and interpreting data

This tutorial is less about statistics and more about interpreting data--whether it is presented as a table, pictograph, bar graph or line graph. Good for someone new to these ideas. For a student in high school or college looking to learn statistics, it might make sense to skip (although it might not hurt either).

Lesson 1
Intro to statistics - graph vocabulary, trends
p. 172, 173 ABE
parts of a graph worksheet
ex 1. __
Trends vocab - Terms page

Lesson 2 - Line Graphs
Parts of a line Graph -

Reading Line Graphs

Reading line charts 1

Lesson 3 - Data from Tables and Tallies
constructing line graphs with tables
Constructing Line Graphs

Reading tables 1

Reading tables 2

Reading tables 2

Lesson 4 - Bar Graphs
Parts of a Bar Graph -

Parts of a Bar Graph - __

from a table

Reading bar charts 1

Creating bar charts 1

Creating bar charts 1

Reading bar charts 2

Reading bar charts 2

Reading bar charts 3

Reading bar charts 3

Lesson 5 - Horizontal bar Graphs

Lesson 6 - Double bar graphs

Lesson 7 _pictographs

Stats Can:

Reading pictographs 1

Reading pictographs 2

Reading Bar Graphs

Lesson 8 - Circle graphs
Stats Can:

Reading Pie Graphs (Circle Graphs)

Lesson 9 - Histograms


Lesson 10 - Stem and leaf plots
Stem and leaf plot 1.
2. __
videos on:
3. __

Reading stem and leaf plots

Reading stem and leaf plots

Lesson 11: Data Choices

Finding the Mean

Median Mode and Mean






Triangles on the Net.doc






Section5 _Review.notebook

transversal_extend.notebook - Transversals

Points, lines, and planesexternal image segments-and-angles-60x60.png?9This topic introduces the basic conceptual tools that underpin our journey through Euclidean geometry. These include the ideas of points, lines, line segments, rays, and planes.SUBSCRIBE

Introduction to Euclidean geometry

Roughly 2400 years ago, Euclid of Alexandria wrote Elements which served as the world's geometry textbook until recently. Studied by Abraham Lincoln in order to sharpen his mind and truly appreciate mathematical deduction, it is still the basis of what we consider a first year course in geometry. This tutorial gives a bit of this background and then lays the conceptual foundation of points, lines, circles and planes that we will use as we journey through the world of Euclid.

Euclid as the Father of Geometry

Language and Notation of Basic Geometry

Lines, Line Segments, and Rays

Recognizing rays lines and line segments

Specifying planes in three dimensions

Points, lines, and planes

Language and Notation of the Circle

The Golden Ratio

Identifying Rays

Measuring segments

Most of what we call "lines" in everyday life are really line segments from a mathematical point of view. This exercise makes you a bit more familiar with line segments by giving you some practice measuring and comparing them. Have fun!

Measuring segments

Measuring segments

Congruent segments

Congruent segments

Algebraically determining segment length

In this tutorial, you'll flex both your algebra and geometry muscles at the same time. You'll do this by applying the right amount of spray tan (which is needed for properly flexing any muscle) and then solve problems about line segments using algebra!

Segment addition

Segment addition

Algebraic midpoint of a segment exercise

Midpoint of a segment

Khan Academy Lessons

Angles and intersecting linesexternal image parallel-and-perpendicular-lines-60x60.png?9This topic continues our journey through the world of Euclid by helping us understand angles and how they can relate to each other.SUBSCRIBE

Angle basics and measurement

This tutorial will define what an angle is and help us think about how to measure them. If you're new to angles, this is a great place to start.

Angle basics

Measuring angles in degrees

Using a protractor

Measuring angles

Measuring angles

Acute right and obtuse angles

Angle types

Vertical, adjacent and linearly paired angles

Exploring angle pairs

Angles between intersecting and parallel lines

Welcome. I'd like to introduce you to Mr. Angle. Nice to meet you. So nice to meet you. This tutorial introduces us to angles. It includes how we measure them, how angles relate to each other and properties of angles created from various types of intersecting lines. Mr. Angle is actually far more fun than you might initially presume him to be.

Introduction to vertical angles

Vertical angles

Using algebra to find the measures of vertical angles

Vertical angles 2

Proof-Vertical Angles are Equal

Angles Formed by Parallel Lines and Transversals

Identifying Parallel and Perpendicular Lines

Figuring out angles between transversal and parallel lines

Congruent angles

Parallel lines 1

Using algebra to find measures of angles formed from transversal

Parallel lines 2

CA Geometry: Deducing Angle Measures

Angles with triangles and polygons

Do the angles in a triangle always add up to the same thing? Would I ask it if they didn't? What do we know about the angles of a triangle if two of the sides are congruent (an isosceles triangle) or all three are congruent (an equilateral)? This tutorial is the place to find out.

Proof - Sum of Measures of Angles in a Triangle are 180

Triangle Angle Example 1

Triangle Angle Example 2

Triangle Angle Example 3

Challenging Triangle Angle Problem

Proof - Corresponding Angle Equivalence Implies Parallel Lines

Finding more angles

Angles 1

Angles 2

Sum of Interior Angles of a Polygon

Angles of a polygon

Sum of the exterior angles of convex polygon

Complementary and supplementary angles

In this tutorial we'll look at the most famous types of angle-pairs--complementary and supplementary angles. This aren't particularly deep concepts, but you'll find they do come in handy!

Complementary and supplementary angles

Complementary and supplementary angles

Example using algebra to find measure of complementary angles

Example using algebra to find measure of supplementary angles

Angle addition postulate

Perimeter and area of rectangles

How long of a fence do you need? How big is your house? How big is your waistline? What's your hat size? These are fundamentally important questions that need to be answered! This is a tutorial to give you the basics of what perimeter, circumference (really the perimeter of a circle) and area are and then applies the ideas to triangles, rectangles and circles. This is more of review for students who are going through the main geometry narrative and can be skipped if yo u remember it from grade-school.

Perimeter and Area Basics

Area and Perimeter

Perimeter of a Polygon

Perimeter of a shape

Perimeter 1

Finding dimensions given perimeter

Area 1

Finding dimensions given area

Perimeter and area of triangles

You first learned about perimeter and area when you were in grade school. In this tutorial, we will revisit those ideas with a more mathy lense. We will use our prior knowledge of congruence to really start to prove some neat (and useful) results (including some that will be useful in our study of similarity).

Perimeter and Area Basics

Triangle Area Proofs

Area of triangles

Interesting Perimeter and Area Problems

Area of Diagonal Generated Triangles of Rectangle are Equal

Area of an equilateral triangle

Area of shaded region made from equilateral triangles

Shaded areas

Challenging Perimeter Problem

Circumference and area of circles

Circles are everywhere. How can we measure how big they are? Well, we could think about the distance around the circle (circumference). Another option would be to think about how much space it takes up on our paper (area). Have fun!

Circles: Radius, Diameter and Circumference

Parts of a Circle

Radius diameter and circumference

Area of a Circle

Area of a circle

Volume of a box or rectangular prism

Volume measures how much 3-dimensional "space" an object takes up. We'll see in this tutorial that it is an extension of length (1-D) or area (2-D) to three dimensions!

How we measure volume

Measuring volume with unit cubes

Volume with unit cubes

Measuring volume as area times length

Volume of a rectangular prism or box examples

Volume 1

Volume word problem example

Volume word problems

Volume and surface area

Tired of perimeter and area and now want to measure 3-D space-take-upness. Well you've found the right tutorial. Enjoy!

Solid Geometry Volume

Cylinder Volume and Surface Area

Volume of a Sphere

Solid geometry

Unit 4A - Measurement Standards

Metric System Length - Khan

Metric System Perimeter

Area of a Square in Metric worksheet

Metric System - volume - solid and liquid

Metric System - Fluid Volume -Khan

Metric System - weight and mass -Khan

Which Measurements to Use

Assignment - Measurement

Unit 4B - Measurement Conversions

Measurements of Time
Time Word Problems

Converting Metric Distances
Unit conversion: ordering metric distances
Math » 5th grade (U.S.) » Measurement and data » Unit conversionWe're asked to arrange the following measurements in order from smallest to largest.
Converting Metric Volumes

Converting Metric Weights

Converting to Smaller Units


Unit 7 - Exponents and Scientific Notation

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Intro to Exponents

Exponents Lesson

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Exponents 2

mod2_2B_varexp.pdf 6 MB
variables and Expenonents

multiplying exponents

dividing exponents


Small Numbers – Powers of Ten.doc

Exponential Growth

Brackets and Exponents

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Scientific Notation Introduction Activity.doc

scino_large.pdf - with large numbers
scino_small.pdf - with small numbers

Scientific Notation Internet Hunt.doc

scino_review.pdf - scientific Notation review

Khan Academy Lessons - Exponents and scientific Notation

The world of exponents

Addition was nice. Multiplication was cooler. In the mood for a new operation that grows numbers even faster? Ever felt like expressing repeated multiplication with less writing? Ever wanted to describe how most things in the universe grow and shrink? Well, exponents are your answer! This tutorial covers everything from basic exponents to negative and fractional ones. It assumes you remember your multiplication, negative numbers and fractions.

Introduction to exponents

Raising a number to the 0th and 1st power

Powers of 1 and -1

Powers of fractions

Powers of zero

Exponent example 1

Exponent example 2

Positive and zero exponents

Exponent properties

Tired of hairy exponent expressions? Feel compelled to clean them up? Well, this tutorial might just give you the tools you need. If you know a bit about exponents, you'll learn a ton more in this tutorial as you learn about the rules for simplifying exponents.

Patterns in zeros exercise

Patterns in zeros

Exponent Rules Part 1

Exponent Rules Part 2

Exponent Properties Involving Quotients

Exponent rules

Negative and fractional exponents

It's normally a bad idea to hang around with negative people or do negative things, but we think it's OK to associate with negative exponents. And fractional exponents are even more fun. This idea will open up entirely new vistas to your mathematical life.

Negative exponents

Negative Exponent Intuition

Zero, Negative, and Fractional Exponents

Negative exponents

Basic fractional exponents

Negative fractional exponent examples

Negative fractional exponent examples 2

Fractional exponents

Fractional exponents with numerators other than 1

Fractional exponents 2

Scientific notation

Scientists and engineers often have to deal with super huge (like 6,000,000,000,000,000,000,000) and super small numbers (like 0.0000000000532) . How can they do this without tiring their hands out? How can they look at a number and understand how large or small it is without counting the digits? The answer is to use scientific notation. If you come to this tutorial with a basic understanding of positive and negative exponents, it should leave you with a new appreciation for representing really huge and really small numbers!

Introduction to scientific notation

Scientific Notation

Scientific notation intuition

Scientific Notation Examples

Scientific Notation I

Scientific Notation Example 2

Scientific notation

Orders of magnitude

When people want to think about the general size of things but not worry about the exact number, they tend to think in terms of "orders of magnitude". This allows us to analyze and make comparisons between numbers very quickly, which allows us to make decisions about them quickly as well.

Orders of magnitude exercise example 1

Orders of magnitude exercise example 2

Orders of magnitude

Computing with scientific notation

You already understand what scientific notation is. Now you'll actually use it to compute values and solve real-world problems.

Multiplying in Scientific Notation

Multiplying in scientific notation example

Dividing in scientific notation example

Multiplying and dividing in scientific notation

Multiplying and dividing scientific notation

Simplifying a complicated expression into scientific notation

Calculating red blood cells in the body using scientific notation

Computing in scientific notation

Old Lessons

REVIEW Lessons

Khan Academy

Comparing decimals

Regrouping decimals

Adding and subtracting decimals

Multiplying decimals

Dividing decimals


- Numbers and Basic Operations
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Addition with carrying

You're somewhat familar with adding, say, 17+12 or 21+32, but what happens for 13+19? Essentially, what happens when I max out the "ones place". In this tutorial, we'll introduce you to the powerful tool of carrying and why it works.

Subtraction with borrowing (regrouping)

You can subtract 21 from 45, but are a bit perplexed trying to subtract 26 from 45 (how do you subtract the 6 in 26 from the 5 in 45). This tutorial is your answer. You'll see that we can essentially "regroup" the value in a number from one place to another to solve your problem. This is also often called borrowing (although it is like "borrowing" sugar from your neighbor in that you never give it back).

Addition and subtraction word problems

You feel comfortable with adding and subtracting multi-digit numbers. Now you can apply some of your skills to solve problems that arise in the real world (often called "word problems").

Multi-digit multiplication

You know your multiplication tables and are ready to learn how to multiply *any* number (actually, any whole number). Imagine the possibilities! This tutorial will make you unstoppable.

Loooong division!

You know your multiplication tables and are getting the hang of basic division. In this tutorial, we will journey into the world of loooong division (sometimes, referred to as "long division", but that's not as much fun to say). After this tutorial, you'll be able to divide any whole number by any other. The fun will not stop!


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- Unit 3 Lesson A

Khan Academy

Conceptualizing decimals and place notation -lessons

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  1. Decimal Place Value
  2. Decimal Place Value 2
  3. Expanding out a decimal by place value
  4. Writing a decimal to represent a quantity
  5. Writing and interpreting decimals - Exercise
  6. Comparing place values in decimals
  7. Comparing decimal place value - Exercise
  8. Using money to understand decimal place value
  9. Money and decimal place value intuition - Exercise

Regrouping decimals

Let's explore how we can regroup and redistribute value among the various place values in a decimal number.

Decimals on a number line

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Let's think about where decimals are on a number line. It will help us understand what decimals represent in general!

Comparing decimals

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Let's test our understanding of decimals by comparing them to one another!

- Unit 3 Lesson B

Adding and subtracting decimals

You get the general idea of decimal is and what the digits in different places represent (place value). Now you're ready to do something with the decimals. Adding and subtracting is a good place to start. This will allow you to add your family's expenses to figure out if your little brother is laundering money (perhaps literally). Have fun!

- Unit 3 Lesson F

Khan Academy

Multiplying decimals

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The real world is seldom about whole numbers. If you precisely measure anything, you're likely to get a decimal. If you don't know how to multiply these decimals, then you won't be able to do all the powerful things that multiplication can do in the real world (figure out your commission as a robot possum salesperson, determining how much shag carpet you need for your secret lair, etc.).

Dividing decimals

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You can add, subtract and multiply decimals. You know you'd feel a bit empty if you couldn't divide them as well. But something more powerful is going to happen. If you are like us, you never quite liked those pesky remainders when dividing whole numbers. Well, those pesky remainders better watch out because they are going to be divided too!!!! Ah ha ha ha ha!!!!!

RATES with decimals

Finding Unit Prices
Finding Unit Rates
Rate Problems

Khan Academy

Converting between fractions and decimals

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Both fractions and decimals are desperate to capture that little part of our heart that desires to express non-whole numbers. But must we commit? Can't we have business in the front and party in the back (younger people should look up the word "mullet" to see a hair-style worth considering for your next trip to the barber)? Can't it look like a pump, but feel like a sneaker? Well, if 18-wheelers can turn into self-righteous robots, then why can't decimals and fractions turn into each other?

Estimating and rounding with decimals

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Laziness is usually considered a bad thing. But sometimes, it is useful to be lazy in a smart way. Why do a big, hairy calculation if you just need a rough estimate? Why keep track of 2.345609 when you only need 2.35? This tutorial will get you comfortable with sometimes being a little rough with numbers. By being able to round and estimate them, it'll only add one more tool to your toolkit.

Significant figures

There is a strong temptation in life to appear precise, even when you are aren't accurate. If you precisely measure one dimension of a carpet to be 3.256 meters and eyeball the other dimensional to be "roughly 2 meters", can you really claim that the area is 6.512 square meters (3.256 x 2)? Isn't that a little misleading? This tutorial gets us thinking about conundrum and gives us the best practices that scientists and engineers use to not mislead each other.

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Moving the decimal to multiply and divide by 10

In our decimal number system, as we move places to the left, the place values increase by a factor of 10 (likewise, they decrease by a factor of 10 as we move rightward). This idea gets direct application when we multiply or divide a decimal number by 10 because it has the effect of shifting every place value one to the right or left (sometime seen as moving the decimal point).

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Unit 2 - Working with Numbers, Factors, and Multiples

- Unit 2 Lesson A - counting, number lines, sets, types of numbers

- Divisibility of Numbers

Whether you are trying to impress your dog's friends (who are obsessed with figuring out number divisibility) or quickly factor a number, it can be very useful to tell whether a number is divisible by another. This tutorial walks through some of the more standard divisibility methods and describes why they work.

- Unit 2 Lesson B and Activity - Factors

Divisibility and factors

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In this tutorial, we'll begin to think about the numbers that "make up" the number. This will be useful throughout our study of math. Whether we are adding fractions, exploring mystical number patterns, or breaking computer codes, factoring numbers are key! Eye of the tiger!

- Unit 2 - Lesson C - Prime and Composite Numbers

Prime numbers have been studied by mathematicians and mystics for ages (seriously). They are both basic and mysterious. The more you explore them, the more you will realize that the universe is a fascinating place. This tutorial will introduce you to the magical world of prime numbers.

- Unit 2 Lesson D - Factor Trees

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You know what prime numbers are and how to identify them. In this tutorial, we'll see that *all* positive whole numbers can be broken down into products of prime numbers (In some way, prime numbers are the "atoms" of the number world that can be multiplied to create any other number). Besides being a fascinating idea, it is also extremely useful. Prime factorization can be used to decrypt encrypted information!

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Least common multiple

Life is good, but it can always get better. Just imagine being able to find the smallest number that is a multiple of two other numbers! Other than making your life more fulfilling, it will allow you to do incredible things like adding fractions.

Greatest common divisor

You know how to find factors of a number. But what about factors that are common to two numbers? Even better, imagine the largest factors that are common to two numbers. I know. Too exciting!

For the Teacher - - Unit 2 Lesson Plans link

Unit 3 - Percents

- meaning of percent, decimals to percent, percent to decimals

Khan Academy

Intro to percentages

At least 50% of the math that you end up doing in your real life will involve percentages. We're not really sure about that figure, but it sounds authoritative. Anyway, unless you've watched this tutorial, you're really in no position to argue otherwise. As you'll see "percent" literally means "per cent" or "per hundred". It's a pseudo-decimally thing that our society likes to use even though decimals or fractions alone would have done the trick. Either way, we're 100% sure you'll find this useful.

Percent word problems

Whether you're calculating a tip at your favorite restaurant or figuring out how many decades you'll be paying your student debt because of the interest, percents will show up again and again and again in your life. This tutorial will expose you to some of these problems before they show up in your actual life so you can handle them with ease (kind of like a vaccine for the brain). Enjoy.

- Lesson B

- Lesson C Method 2

Other Pecent Conversions

  1. Another percent word problem
  2. Percent word problems
  3. Percent word problems 1 example 2)
  4. Solving percent problems 2
  5. Solving percent problems 3
  6. Percentage word problems 1 - Exercise

Unit 4 - Ratios and proportion

Unit Plan [for teachers and instructors]

This is a lesson about ratios - exercise pages are on the "assignments page"

Here are some internet lessons about ratios
Ratios Lesson Online
Thinking Box lessons and practice online
Math Playground Online Lessons

Khan Academy

Ratios and proportions

Would you rather go to a college with a high teacher-to-student ratio or a low one? What about the ratio of girls-to-boys? What is the ratio of eggs to butter in your favorite dessert? Ratios show up EVERYWHERE in life. This tutorial introduces you to what they (and proportions) are and how to make good use of them!

Scale Drawing -

Scale drawings

Equivalent Ratios

Cross multiply Problems

Writing and Interpreting Decimals

Place Notation

Let's think about where decimals are on a number line. It will help us understand what decimals represent in general!

Decimals on a number line

Decimals on the number line 1

Decimals and fractions on a number line

Decimals on the number line 2

Placing positive and negative decimals on a number line

Decimals on the number line 3

Let's test our understanding of decimals by comparing them to one another!

Comparing decimals example 1

Comparing decimals example 2

Comparing decimals 1

Comparing decimals: difference in largest place value

Comparing decimals: place value difference

Comparing decimals 2

Comparing decimals: ordering from least to greatest

Comparing decimals: ordering from smallest to biggest

Ordering decimals

Review - Number System and Place Value

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- Unit 3 Lesson A

Conceptualizing decimals and place notation -lessons

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- Writing Numbers in English

- Writing and Comparing Numbers Advanced

Time conversions

Time - Khan Academy Exercises

Unit conversion: minutes to hoursMath » 5th grade (U.S.) » Measurement and data » Unit conversionHow many hours are in 549 minutes? ... Then you have 4 hours, which is 240 minutes. 5 hours is 300 minutes. 6 hours is 360 minutes. 7 hours,Converting between units of timeMath » 4th grade (U.S.) » Measurement and data » Unit conversionLet's convert between hours, minutes, and seconds. ... Well, it would be the same exact idea. 60 minutesper hour, if I have 2 hours, ...Multi-step word problem with fractions and units of timeMath » 7th grade (U.S.) » Fractions and decimals » Multi-step word problemsI'll just write min for short-- divided by 60 minutes per hour gives us 300 divided by 60 is 5 hours.