Here is what you wrote and published on the Internet.

• https://myedme.com/logincome-into-the-milky-way/
• MY BABY BUNNY BODY LANGUAGE

Leap Day Math!!

Imad is making covers for the throw pillows on a sofa. For each pillow cover, he needs 3/16 yard of print fabric and 3/8 yard of solid fabric. What is the total amount of fabric Imad needs for each pillow cover?

How much fabric would he need for 2 pillows?

Imad is baking chocolate chip cookies and oatmeal cookies. He needs 1-1/4 cup of sugar for the chocolate chip cookies, and 1/8 cups for the oatmeal cookies. How much sugar does he need altogether?

Imad saved seven quarters and 25 pennies. What is the total value of Imad’s large savings?

Imad is printing his first book. The paper is 8-1/2 inches wide. He makes the left border 1 1/2 inches and the right border 1 1/2 inches. How wide is the print area on the sheet of paper?

Imad prints a picture of his bunny. The picture is 8 inches wide. The picture frame is 1 5/8 inches wide on each side. How wide will the picture and frame be?

More fraction practice: https://docs.google.com/document/d/1GQ4npYfDnOiQsO911JZWIT5LvrT0Mgwa/edit#

You can keep practicing your skills in fun ways. First, you can use this book to practice reading.

• https://myedme.com/loginelectricity-is-elementary-e-book/

Need fraction reminders?

Here are the steps we talked about last week.

This may help too. It shows how different denominators have different lengths.

When you need a break!

This website shows you how we train machines to think like people. The big idea is is called “Artificial Intelligence” which some people say by the initials A.I. (What are your initials?) This version of AI is called AI for Oceans. Click “Try Now” to start and “Continue” to move through the stages.

I taught this at the GMU Engineering Conference 13 days ago. If you have questions, you can text me or we can talk about them soon!

Check out this picture of the day showing the Milky Way!

• https://www.smithsonianmag.com/photocontest/photo-of-the-day/2020-02-03/the-milky-way-as-seen-from-devils-tower-wy/

And, you can use this game to keep your multiplication skills fresh.

Play the fraction game one time to practice your mixed numbers and fractions greater.

Math Strategies

• Read the question carefully and keep rereading it.
• If necessary, draw your own picture

Here are word problems you can practice. Grab a piece of paper so you can write down your work!

• Problem Set 1: https://docs.google.com/document/d/18bhavSjNATjhzeQUQzwAjZCszBbwFOsL/edit#
• Problem Set 2 (more fractions): https://docs.google.com/document/d/1GQ4npYfDnOiQsO911JZWIT5LvrT0Mgwa/edit#
• https://myedme.com/loginwhole-number-problems/
• https://myedme.com/loginfraction-problems/
• Problems for showing strategies

New Science Materials

Remember that the Earth orbits around the sun to create seasons. The Earth spins so we feel day when we face the sun and night when we face away from the sun. The moon orbits around the Earth every 29 days. The gravity from the moon creates tides because the oceans are pulled toward the moon.

One quick fact: The moon does not create light. But, the moon does reflect the Sun’s light.

Lunar eclipse means moon is covered. In this video, the moon is behind the Earth.

Solar eclipse means the Sun is covered. In this video, the moon is between the Sun and the Earth. (Remember how we used our thumb to cover up the lamp.) Here are two videos about solar eclipse from 2017.

Materials from Previous Weeks

Think about what will happen this week. Is there a test or multiple tests you want help studying? You can send me that information here.

Here is a wide variety of practice. Try to do 3 before the end of the weekend:

1. Social Studies paragraph: Choose a person or culture below and write a paragraph that explains what you know about their importance in Virginia history.
   1. People: George Washington, Thomas Jefferson, Patrick Henry, and James Lafayette
   2. Cultures: European (English, Scots-Irish, German) immigrants, Africans, and American Indians
      • (You can upload a file below.)
2. Science Graphic Organizer: Many other kids I help confuse what causes seasons and what causes day/night. I am hoping that you can create a drawing that helps explain these two concepts for other kids.
3. Math Practice: Let’s practice 2-digit x 2-digit multiplication this week. Use the game we used here to check the answers to these 10 questions. (If you need other practice use the box above.)
   1. 15 x 40
   2. 60 x 25
   3. 78 x 10
   4. 34 x 35
   5. 62 x 13
   6. 58 x 29
   7. 44 x 44
   8. 39 x 27
   9. 37 x 18
   10. 36 x 29
4. Reading Practice: You can read 2-3 chapters of the Electricity is Elementary book and answer the questions. Choose whatever seems most interesting to you!

You can upload paragraphs and pictures here:

Materials from Previous Weeks

It’s been an exciting start to the year! You have already mastered:

• Division using partial divisors
• Multiplying 2-digit numbers using the box method
• Reading about space and all the terms that accompany space
• Already Completed: Writing a project about black holes!

Comic Book Explanations

Use the comic books to write a paragraph. You don’t need to add new details, but be sure to use words that show what you see. Comics use pictures to share information, you will use words!

If you want to share your paragraphs, you can upload them here.

Use these links to find the tools and games we have used:

1. Building an airplane: Using the instructions
2. Saturday Activities: https://myedme.com/loginsaturday-school/
3. The Electricity is Elementary e-book is here: https://myedme.com/loginelectricity-is-elementary-e-book/
4. The Multiplication/Factors game is here: https://myedme.com/loginmultiplication/
5. CNN reporting breaking news about black holes: https://www.cnn.com/2019/11/28/asia/china-black-hole-discovery-intl-hnk-scli-scn/index.html
6. If you get free brain time, follow these instructions to make paper airplanes that we found go the furthest: https://myedme.com/loginbuilding-an-amazing-airplane

Here is the area model we use to explore multiplication quickly.

If you want to think more about area and perimeter, play this game. It’s pretty fun!

Decimals are simply fractions written using a different strategy. Instead of writing denominators all the time. Decimals tell you the denominator by their place value. Tenths mean a denominator of 10. Hundredths mean a denominator of 100.

This interface is designed to show decimal multiplication, but first play with it to show decimals like 0.8, 1.8, and 0.8 + 1.0. Then, use it to see how each column is equal to tenths, but each square is equal to hundredths because 0.1 x 0.1 = 0.01. (You know this because a 10% tax on a dime is one penny.)

Sources of Energy

First things first, the Sun is the most important energy source for all life on earth. The Sun is a key ingredient when plants make energy through photosynthesis. Photosynthesis allows plants to make their own food, and we will discuss it more in another chapter. The sun can also create electricity through solar panels. The sun provides energy in the forms of heat and light. Without the sun, life on earth would not exist! That is why the sun is the most important energy source.

There are different types of energy across the Earth. Plant energy is easy to eat, but hard to use in power plants. We use different types of energy for different purposes! For example, there are many types of energies that power cars and electrical plants. Energy can be created from coal, oil, water, natural gas, and wind. Now, I bet you are thinking, how does oil create energy? Or even wind? Well, we use oil to make gasoline that makes cars go! And perhaps, you’ve driven by a farm or a hilly area on a road trip, and came across these gigantic, white-colored windmills! Well these gigantic windmills are actually called wind turbines. Wind turns a wind turbine and this rotation is used to generate electricity. Coal and natural gas are also used to produce electricity.

Sources of energy are put into two groups: nonrenewable and renewable. 

Nonrenewable means cannot be renewed quickly. Nonrenewable sources are used faster than they can be replaced. This means that their supply is limited. Coal, natural gas, and oil are some examples of nonrenewable energies. These three sources of energy are also known as fossil fuels. Fossil fuels are made from fossils of plants and animals that died millions of years ago. They were alive millions and millions of years ago. Back then, they gained energy and now that energy is stored as coal, gas and oil. It takes millions of years to make this type of energy, so we cannot replace the coal, gas and oil that we use.

Renewable means can be renewed quickly. Renewable sources are unlimited or very common on our planet. For example, the sun creates a tremendous amount of energy every moment and will burn for billions of years. We call this solar energy. Read on to the text box to learn how the sun and water come together to make electricity. 

Scientists Take Notes! Often you will learn about two terms at the same time because they are related but opposite. Here is one way to take notes when you have this situation.

Scientists Write! Grab a piece of paper and write three things that will be in this book:

Writing paragraphs advice: This last sentence is your topic sentence. The other three details will form your paragraph’s body. Then, write a final sentence that ties all your ideas together. The paragraph introduces an idea, explains it and summarizes it.

Energy is not Created or Destroyed

It’s crazy when you first hear it! Energy is not created when we turn on a light or start a fire. This energy was already stored in a power plant or inside a piece of wood. Then, we did something that changed the stored energy into energy we use. This big idea is called the Law of Conservation of Energy. The Law of Conservation of Energy states that energy cannot be created or destroyed. It can only change between different forms. This law means that energy can change forms many times but it is never truly created or lost. That’s a big idea!

Here are some examples that show what the Law of Conservation of Energy means:

• We do not create energy when we burn gasoline in cars. We are actually turning the energy stored in gasoline into heat and energy that moves the car. (And, you remember that gasoline got this energy from plants that stored the solar energy millions of years ago).
• A water wheel does not create energy. It takes energy from moving water and changes it to energy that rotates an axle.
• A spark starts a fire that releases chemical energy stored in a log. Even though the fireplace “creates” heat, it is simply releasing stored energy in the burning material. The heat and the light are the new forms of energy created by fire.
• You get energy from food. This energy is then stored all over your body. Your muscles use this energy to turn pages in your favorite book and your brain uses this energy to help you think about what you just read.

Energy Changes Forms

You will need to explain how energy changes to do work. For example, energy from the sun powers a toy car with a solar panel. Energy from fossil fuels can power an airplane’s motor. Energy from a waterfall can turn a wheel in Hoover Dam that makes electricity. The big idea in each example is converting energy into work that is useful for us.

Energy is not only converted by machines, you now know that you do it every second of every day! Our bodies convert energy often. Our bodies store chemical energy from the food we eat.  Our brains use electrical energy to signal our hands to hold a book. Our brains even use electrical energy to tell our eyes to blink even though we do not think about it! Because our bodies are always using energy, we need to constantly add energy to our bodies. That’s why we eat!

Solar Energy Powers the Water Cycle

Solar energy is an important part of the water cycle. The water cycle describes how water moves from the Earth, into the air, and back to the Earth’s surface. It is powered by heat from the sun. Without the sun, there would be no water cycle. The sun heats the water up and makes some of the water evaporate. When water evaporates it turns into a gas that goes up in the air. Eventually it gets so high that it can form clouds. When water is a gas it is called steam or water vapor. This water can condense back into water or even freeze into ice when it is high in the sky. It weighs so little that is able to float (for a while) because the sun is heating the Earth which continues to push air upward.

Water in clouds can eventually fall back to Earth as rain or snow. Water sticks to other water very easily. In clouds, tiny drops of water connect with other drops of water and get bigger and bigger. When they get too big, they will start to fall back to earth. If this water immediately runs into a river, lake or ocean, it is still in the water cycle. If this water is immediately absorbed by a plant’s roots, then it helps the plant make energy (more on that next chapter!). If that water falls in your mouth, it is delicious!

Think about the energy that this process takes! The sun is warming water on earth, which makes it move. As water drops get higher, they gain the potential energy to fall back to earth. When the drops get big enough, they fall back to earth. The energy from falling rain can move pebbles and dirt as water runs into streams. And, the energy stored in water can be used by plants to grow tall, make seeds, and sink roots deep into the earth. All this energy starts with the sun and is transformed over and over again. It’s a great example of how energy changes forms but never is destroyed!

Humans use water’s energy. Smart!

Humans have figured out that energy from the water cycle can be used to produce electricity. Hydropower is creating energy (such as electricity) from moving water. When water is released from a reservoir, which is a large lake that stores water, it enters a turbine. The turbine spins the water. The turbine is connected to a generator, so when the turbine spins the generator produces electricity. Hydropower uses energy to create work. That work is making electricity. Hydropower uses moving water, which we consider to be renewable (remember “renewable” from chapter 1?). Why is moving water renewed? Because the water cycle allows water to circulate across the earth all the time. The water cycle is an endless, recharging cycle, which makes hydropower a renewable energy source. 

Scientists Write! This time you will create an argument. First, choose your argument by circling your point of view:

Solar energy powers the water cycle.          Solar energy does not power the water cycle.

Write your paragraph defending your argument and upload it here.

Here are two videos with more counting practice. Let me know if you really like one of these!

And, here is a reminder about how to round to the nearest ten whenever you want!

One last thing, here is a space shuttle countdown!

You have a goal to achieve a certain score on this test. We will work with you to identify what you personally need to be successful, and then we will make a plan that works with your schedule to master all these topics by your chosen test day. We know it may be a while since you were successful in math, but together we will master these topics. If you need anything at any time, email us (edMe@myedme.com). We are here to make sure you are successful!

edMe Learning

There are four key topics in Unit 0:

• 0.1  Recognize place value and names for numbers
• 0.2  Perform operations with whole numbers
• 0.3  Round whole numbers and estimation with whole numbers
• 0.4 Solve application problems by adding, subtracting, multiplying, or dividing whole numbers

The key to this unit is understanding numbers. If you can put these numbers on a number line, then you already have a strong foundation.

(If you can divide 2,000 by 40 in your head, you are probably ready for Unit 1. If not, we are happy you can use these fun resources!!)

Choose “Game” in this interactive and play a couple quick games to get familiar again with thinking about hundreds, tens and ones. It shouldn’t take long and you may even have fun!

Quick Walk down Number Name Lane (Unit 0.1)

These number names help us explain numbers like 330,000,050 (“330 million and 50”).

Each digit in the millions and thousands can be said on its own. 600,000 is “six hundred thousand”. 70,000 is “seventy thousand.” And, 8,000 is “eight thousand.” Altogether it is 678,000.

Numbers that have zeroes take more careful consideration. Because there are more place values than numbers in the description it is easy to make a mistake. For example, you know “three hundred five” is 305 but may need to take more time to write “eight hundred twenty thousand, seventy five.” It’s easy to incorrectly write the numbers in order, 8275, but it just takes an extra second to use the place value words to correctly write: 820,075.

You can click on this picture to have even more real-world numbers to practice. The U.S. population here is “three hundred thirty million, eighty-five thousand, and two hundred thirty seven.” How would you say the world population? How about Mexico’s population?

You can write any number in words, and should be able to write the number described in words.

8 Problems about Number Names

Using Whole Numbers

Many people need a refresher on these types of number facts.

Here are the same facts presented in a way that is easier to skip count.

The facts with 1, 2, 3, and 5 are generally used, so you can focus more on the facts with 6, 7, 8, and 9 if you need some practice.

This rewarding game will help you practice multiplication, division, and factoring. Knowing the factors will help you identify the “Greatest Common Factor” (you write all the factors of each number then choose the greatest number that is common to both lists). Practice by playing!

Practice Whole Number Math

Rounding Numbers (Unit 0.3)

The key idea is to move the number to the closest allowed number. For example, when rounding 584 to the nearest ten 580 is closer to 584 than 590, so we round to 580. If you needed to round 584 to the nearest hundred, then 600 is closer than 500.

This video has hysterical birds that flap but do not move. And it emphasizes this rounding idea using the term “midpoint”.

This Khan Academy video covers this ground well too. (#youcanlearnanything)

When you estimate with numbers, round them first then solve the problem. This will quickly give you an answer near the exact answer.

Rounding Numbers Practice

Progress Check

Practice: This worksheet has addition of whole numbers, fractions and decimals. Click here when you are ready to check your answers.

Problem Solving

These word-problem sequences give you immediate right/wrong feedback, and we will give you strategy feedback via email within 24 hours.

• Playing Music questions
• Running Races questions
• Bake Sale questions

If it feels like you need more practice with these types of questions, we have hundreds of questions to support you. Let’s start with these questions to see where we are.

Basic Geometry for Problem Solving

You will see some questions about solving for the area and perimeter of shapes. Area is the space a shape covers. Perimeter is the distance around. This short video explains this difference in an example.

Geometry-Based Questions

The NOVA Math Placement test covers foundational math concepts. Some of this practice will feel too basic, but it’s intent is to provide simple examples of harder concepts. For example, it’s easy to remember to align the ones when adding 18 + 7, but we all know it’s easy to make mistakes when adding 32.6 + 0.36.

This practice will highlight the underlying concepts. Some of this conceptual texts comes from a forthcoming book that explains math concepts to parents. If you have questions about the concepts, use the comment sections and we will respond to use as quickly as possible.

In the first unit, there are lots of fluencies. Math fluencies mean fast and accurate computations. You will want to practice the Fluency sets until you can solve them quickly and with confidence.

Here are the links to the practice for each unit:

• Unit 0 – Operations with Whole Numbers
• Unit 1 – Operations with Positive Fractions
• Unit 2 – Operations with Positive Decimals and Percents
• Unit 3 – Algebra Basics

Some topics feel so foreign because it’s hard to remember a time when “5 x 7” looked like your teacher forgot how to write “+”. We have many (all?) multiplication facts memorized, but your child is just starting this journey.

There are three big phases to understanding multiplication:

1. Initial understanding of the multiplication process based on skip counting.
2. Using multiplicative thinking to solve problems about equal groups, areas, and arrays.
3. Final mastery of the multiplication facts.

Beginning in Kindergarten your child has started skip counting. In fact, skip counting by 2s will be a key skill that will help unlock many multiplication ideas. Encourage your child to use their fingers to count the number of skips (and don’t forget the first number!). Children love to show how smart they are. At this stage, your student can fluently tell you facts like 1 x 8 = 8 and 7 x 1 = 7. Encourage them to show off!

As they begin to investigate other rows in the multiplication table, teachers introduce different multiplication ideas. Here are the three types of problems your child will master this year:

1. Equal groups. For example, Eva bought 5 bags of apples, and each bag has 8 apples. How many apples did she buy?
2. Areas. What is the total area of a rectangle that is 6 inches wide and 10 inches long?
3. Arrays. Mr. Atu’s classroom has 5 rows of desks. Each row has 7 desks. How many desks are in Mr. Atu’s classroom?

These applications help students know “why do we have to learn this?!” In addition, well-designed problems will help students practice facts involving 2s, 5s, and 10s.

Examples of three types of multiplication situation.

Interactive games like this one help students become fast and accurate with multiplication.

By the end of grade 3, states require students to memorize all the facts in the 10×10 or 12×12 multiplication table. With practice and lots of self-testing, students can master all these facts.

Keep working hard for Friday’s quiz! It will have questions on both the big ideas: calculating areas (integrals) and finding rates of change (derivatives) with a mix of natural logs, exponential functions and u-substitution.

Using Fundamental Theorem of Calculus & U-substitution with Integrals

Using the Power Rule Backwards

This video is the foundational piece for using the power rule backwards to solve integrals. You can use the power rule like normal to check your answers.

Review: Overview of Derivative and Anti-Derivative

Integral of one Term

Solving e^u

Trig Function Integrals

Review: Finding Integrals with Anti-Derivative

Previous Videos

Big picture explanation

This video is good at explaining these ideas conceptually.

Derivatives of Natural Logs

Derivatives of Log Properties

Derivatives of e^x

Derivatives of ln, logs, and e^x

Derivatives of Units 5 & 6 in One Summary

Proofs of ln and e^x Derivatives

Review of Limits: If finding limits seems challenging, you can always review this video.

Heart of Calculus: Applications of Derivatives & Integrals

Mean Value Theorem (formal definition):

Contrasting Average Value and Average Rate of Change

Watch by Sunday:

Mean Value Theorem (informal definition):

Implicit Differentiation is the key to understanding Related Rates problems. Please review both these videos and write down questions with timestamps (like, 8:02) that we can review Sunday.

Optimization Practice

If you can’t solve these questions, then please review the four videos below.

• An airplane is flying in a horizontal, straight-line path. The speed of the airplane is 100 meters per second, and its altitude is 1000 meters. What is the rate of change of the angle of elevation, , when the horizontal distance from a reference point P on the ground is 2,000 meter?
• A ball is expanding at a rate of 0.25 inches per minute. How is the volume changing?
• A cylinder is increasing its height at 2 centimeters per minute. How is its volume changing?

New Overview

Previous Overview: There are five practice worksheets ready now: Limits, Power Rule, Product Rule, Quotient Rule, and Chain Rule. After you finish each sheet, you can click these links after you work through the worksheets for Limits Worksheet Answers, Power Rule Answers, Product Rule Answers, Quotient Rule Answers, and the Chain Rule Answers.

Tuesday we will talk though this limit definition of the derivative one more time. We are going to highlight examples of f(x) and how the structure shows that we are finding f‘(x) at a certain point. I want to talk about the concept so the fluency makes more sense.

You are seeing this definition where f(c) is already solved, so f(c) equals a number like, 1000. Then, we see the structure of the function because f(x + c) is never solved. It just shows how f(x) works. Here are the solution steps we will dive deeply into.

The remainder of this page has definitions and tools that we will review up until the test on Thursday.

Tools/Definitions from the Last Quiz

Definition of a continuous function.

• Functions have limits if the left and right limits go to the same place

limit of a piece-wise function

When you have time for a 10-minute video. Here is another voice (Sal Khan!) to help make the piece-wise/continuity/approaching ideas make more sense.

The limit is critical in calculus because it gives us access to the idea of how we can find the rate of change at one point. For most of the next month you will find the rate of change of a graph at one point. You will think about the rate of change as a tangent line to the graph and you will use this limit definition. Be sure to actively take notes during this video to think about how you can identify the function and point where you are finding the rate of change.

Power Rule: The rule we use all the time when we have polynomials (but not rational functions). Here is the simplest example:

Product rule: This may require some memorization, but what is the derivative of (f(x))(g(x))?

We say something like “Derivative of the first times the second plus the derivative of second times the first.”

Because we now have the quotient rule, I am going to encourage us to keep this idea of derivative of one times the other. The product rule has the sum of these two types. The quotient rule has the difference of these two types (and a denominator).

Quotient Rule: For rationale functions we can’t use the Power Rule and the Chain Rule is too complicated. We use this rule for functions like:

These functions have derivatives using one rule:

Chain rule to calculate a derivative: This may require some memorization, but what is the derivative of (f(g(x))?

Because the function on the inside is 2x-9 and the function on the outside is ( )². The derivative of the outside function is 2( ). Power Rule!! The derivative of the inside function is 2. That means altogether we get 2(2x-9)x2.

Derivatives of sinusodial function: What is the derivative of sin? (If you memorize one, then you know the derivative of cos is similar but has a different sign.)

Integration is Antidifferentiation

Indefinite integral (antidifferentiation): Using the power rule, product rule, and chain rule backwards requires the persistence to check your work over and over again. (Also, remember the last 2 problems we did emphasizing adding in the constant term “+c”)

Bigger Problems

Find the critical points of a function: This is why we take derivatives. The process is to take the derivative and set it equal to 0.

Write the intervals over which the function is increasing or decreasing: Another reason to take the derivative. If the derivative is positive, then the rate of change is positive. If the derivative is negative, then the rate of change is?

Horizontal asymptote of a graph: You can solve these with limits if you are interested in extremely large or extremely negative values. In the middle of a function, you use critical points. Question: Given a function, how will you find the local minimum and local maximum values?

Online Tools

• How functions work: https://www.geogebra.org/m/rmqjtbxS
• Slope Fields: https://homepages.bluffton.edu/~nesterd/apps/slopefields.html

Topics you memorized for the quiz

• Power Rule
• Product Rule
• Chain Rule
• derivative of sin
• derivative of cos
• derivative of e^x
• antiderivative using power rule (If f'(x)=6x, what is f(x)?)

Today let’s go over any of the topics/explanations that you think are troubling. Then, let’s discuss the homework problems that do not seem possible. Note that the calculator is not available but you can quickly sketch graphs by plotting points and calculating critical points.

Word Problems

Scroll through this video to find related rates word problems which use implicit differentiation to solve word problems you will see throughout this semester.