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Unit 0 Practice

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.

\Large 0, -3, \frac{3}{2}, 4, 4.6, 4.09, -1.75

(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!!)

Quick Walk down Number Lane (Unit 0.1)

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

place values for millions, thousands, hundreds, tens and ones.

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.”

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?

The world population is “seven billion, six hundred and fourteen million, nine hundred and seventy-nine thousand and forty nine.” While Mexico has the tenth most people with one hundred twenty seven million, three hundred eighteen thousand and one hundred twelve people at 9:50am on December 3, 2019.

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

Rounding Numbers

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.

584 on a number line from 0-600. Shows that 584 is closer to 600 than 500.
It’s easy to see that 584 is closer to 600 than 500. You will also want to be able to think that 4 is closer to 0 than 10, so 584 rounded to the nearest ten is 580.

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.

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

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NOVA Math Placement Practice

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.

Link to NOVA's free resources

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:

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Remembering when multiplication was new

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.

5 groups of 4 apples have 20 total apples
This array uses shelves to organize the “rows”. There are 3 shelves with 10 books for a total of 30 books.
The area model is a great way to learn multiplication and practice multiplication of decimals and fractions. Here the rectangle is 10 inches wide and 2 inches long, so it’s area is 20 square inches.

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.

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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.

\lim_{h \to 0} \frac{f(x + c) - f(c)}{h}

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
\lim_{x \to 1-} f(x) = \lim_{x \to 1+} f(x)

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.

These were problems; they seemed better in the group test. But, look through those questions while covering up the answers. Do you feel comfortable with these questions now?

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

f(x) = x^2, then f'(x) = 2x

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

h(x) = (3x-7)x^2, then h'(x) = (3)(x^2)+(3x-7)(2x)

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:

\frac{(5x-4)}{x^2} or \frac{sin(x)}{cos(x)}

These functions have derivatives using one rule:

\frac{(5x-4)}{x^2} -> \frac{5(x^2)-(5x-4)(2x)}{(x^4)}

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

h(x) = (2x-9)^2, then h'(x) = 2(2x-9)*(2)

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?

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.

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John’s Entertainment

These first videos update what is happening at Christchruch School. This first video includes Jack Taylor, class of 1974.

Here are videos that share the research at the University of Georgia.

These are more entertaining. This channel is dedicated to videos about hunting waterfowl across North America.

This channel focuses on rural antiques across the country.

If you can’t find anything, you can tell Mom to text me or type a comment below. Happy birthday!

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Salma Supports

Here are some new art resources that you can use to read for information while learning about types of art you may not see in your classes.

Please click on the link below and read each section under the “Contents” heading. This 1993 exhibit introduces some of the plastic qualities of African works of art, along with a basic orientation regarding the artworks’ function and significance in their culture. When you have finished reading, return to the homepage and click on the “Art of the African Mask” link at the bottom of the page to view the collection. This exhibit will introduce you to a few different types of traditional African masks. Please note that the term mask refers to the entire costume, and what most students traditionally consider the mask – which is actually the headpiece – often sits atop the head rather than on the face.

Art Contest information we discussed last time

Now that we are getting close to a season with less intense academics I want to start getting back to the art topics we started with in the beginning. Today, please look at the six art contests listed here and bring notes that describe: What art is due, When is it due, One thing you like about the contest, One thing you do not like:

Here is a seventh contest. This one is STEAM because it has science you know with art and engineering. If you have time answer the questions about this contest too:

Whenever you could use extra resources, just let me know! I am here to help you meet your goals.


We talked some about this, but I wanted to add a little bit more context to our discussion. Long-term goals are inspirational. They are big, grand and represent the best version of yourself. That said, it’s had to know if you are meeting or falling behind meeting your long-term goals. That is why you want to write 1 or 2 long-term goals, then write a few short-term “SMART” goals that work toward your long-term goal.

So, your way to stay inspired and motivated is:

  1. Write 1-2 long-term goals.
  2. Write a few SMART goals (Maybe one for each subject or a couple that focus on study processes you know work for you.)


I worked with the people at Khan Academy and I know they value proportional relationships as much as any topic in mathematics. Proportions show relationships that exist continuously (e.g., when you drive 55 miles per hour, your distance traveled changes proportionally). The fundamental idea behind proportions are ratios. Ratios are in recipes (2 cups of water for each 1 cup of rice; there are 3 girls for every 2 boys, etc.).

If you feel like some practice on ratios would be helpful, Khan Academy has a series of videos. (Make sure you actively listen to the videos by having pencil and paper out and working through the examples with him!)

This video connects ratios and proportions with examples.

This video might be the most important because it helps unlock math word problems you will see. If you have any questions, you can send them to me in the comments section below. Thanks!

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Youssef Strategies and Self-Checks

A couple fun challenges to help your brain stay fresh while it continues to digest all your holiday meals.

  1. This page shows how to make the best paper airplane. Follow these directions step by step and you will have success!
  2. This game is like the Multiplication Game, but for proper and improper fractions!
  3. Here is a link to new Science readings about energy. Try to write the sentences and paragraph the page describes.

Here are previous highlights from our work together!

I am so glad you took the writing assignment seriously. I typed up your first paragraph here:

then moon has a rocky surface it orbits the earth. then moon is a sign of night is coming soon. there is moon phases there is a crescent moon, a waning, 2 waxing, 2 gibbons, 2 quarter, 2 full, and a new moon.

Math practice for decimal multiplication.

Multiplication practice for factors:

Fraction exploration:

Here is another version of your paragraph that adds more detail about what the moon looks like and where it is.

The moon has a white rocky surface. It orbits the Earth, and is much smaller than earth. In fact, the moon is about one quarter the size of the Earth. Like most things in the universe, half of the moon is exposed to sunlight. Because the moon is white with almost no atmosphere, it reflects the sunlight and we call this light “moonlight”-even though the light is from the Sun! When we look up at the moon on earth, we see 2 waxing, 2 gibbons, 2 quarter moons. We also see a full, bright moon and a new, dark moon every lunar cycle (lunar cycle means the time it takes the moon to revolve around the Earth.

More details about what the moon is and what it looks like

In your argument essay, use some of these ideas to add a paragraph that adds a description of the foam bullets. Make sure you answer these questions:

  1. How do the foam bullets feel?
  2. What do the foam bullets look like?
  3. How do the foam bullets travel through the air?

Writing Checklist

  • Did I write my “i” and “t” correctly?
  • Does each sentence start with a capital letter?
  • Do I have some words in this paper that describe what things look like?
  • Do I use “and” twice in a sentence that should be broken into 2 sentences?

Moon Landing Simulator

This simulator is design to show you about the gravity and atmosphere on the moon.

You can send me information through Google docs, your Mom can email (, or you can write a comment below. The first thing we need to share is a complete list of the topics on Wednesday’s test.

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Younes Goals & Study Support

  1. Here is a link to new Science readings about energy. Try to write the sentences and paragraph the page describes.
  2. You and your brother have this fun activity, but read it yourself so your plane can be better! This page shows how to make the best paper airplane. Follow these directions step by step and you will have success!
  3. Last activity for the weekend: Talk with your mom to have 3 study goals this week. I am giving you one. (You two decide one more.)
    • Study Goal 1: I will have every book I need Monday night, Tuesday night, Wednesday night and Thursday night.
    • Study Goal 2: __________________________________ .
    • Study Goal 3: __________________________________ .

I know you are smart and dedicated enough to do well with these classes. If you want to send me any information you need help studying, you can upload it to Google docs, your Mom can email (

In the meantime, here is a tool to practice multiplying with decimals.

Here are previous highlights from our work together!

Here are some study aids that will help you prepare for Wednesday’s Science test. We can help you be successful on this test. On Monday, please bring home a list of topics on Wednesday’s test. If you need to ask the teacher, that’s ok. He will be happy to know that you are focused on doing well on this test.

You can send me information through Google docs, your Mom can email (, or you can write a comment below. The first thing we need to share is a complete list of the topics on Wednesday’s test.

Here is the multiplication game.

Flashcards are a great study tool when you have to memorize between 5 and 15 things.

And, here is a video about the Scientific Method. You should write down definitions to these words on flashcards: Observation, Inference, Scientific Method, Evidence, and Data.

Play this video on loop so it repeats while you make your flashcards. It explains three big ideas:

  1. Earth rotates causing night & day
  2. Earth is slightly tilted which causes Summer and Winter.
  3. Earth rotates around the Sun in 1 year.


Saturn and Jupiter are huge! Uranus and Neptune are pretty big too. All 4 planets are primarily made of gas. That’s funny and you can remember the last 4 planets are gassy!

The inside 4 planets are rocky. We talked about Mercury having the shortest year and it’s the second hottest. Venus is the hottest and closer to the Sun than Earth. Mars is the fourth planet.

Your memory aid is a great one. Stick with it. Here is another “Planet Song” you can use while you study the order of the planets.

Space Scientists

The universe was first studied by Greeks in 300 B.C. Two scientists were Aristotle and Ptolemy. These two scientists believed the Earth was in the center of the universe.

In 1500s and 1600s new scientists named Copernicus and Galileo used new scientific tools, like telescopes, to figure out that the Sun is the center of the universe.

Remember old scientists thought the Earth was the center of the universe, and there names were Aristotle and Ptolemy. Newer scientists, named Copernicus and Galileo, understood the Sun is the center of the solar system.


If weather is on your test, this video from an expert at the Weather Channel describes weather maps and how weather works. All in 4 minutes! If you do not know any of these words, write them on a piece of paper and ask your parents.

Plate Tectonics

If you do need to know about the Ring of Fire and plate tectonics, here is a 2-minute video that explains these big ideas.

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Christ Church

You can use this interface to check out by credit card. Simply add the items to your cart and then click Cart to check out.

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Personalized Bible Gifts

We personalize a bible by focusing on 20 passages that you choose and we can bring the reading level down to your child’s level if you are interested. You can check out by adding one or both products below to your cart and then check out above.

Here are our top 20 selections that may help you decide:

  1. Creation and the fall (Genesis 1-3)
  2. Noah’s Ark (Genesis 6.9–9.17)
  3. Moses and the burning bush (Exodus 3.1–15)
  4. The Exodus (Exodus 14.1–31)
  5. David and Goliath (1 Samuel 17.1–58)
  6. The Ten Commandments (Deuteronomy 5.1–22)
  7. Entering the Promised Land (Joshua 3)
  8. God chooses David and David kills Goliath (1 Samuel 16-17)
  9. Isaiah’s prophecies about a Messiah (Isiah 7.10-17)
  1. The Birth of Jesus (Luke 2.1–7 and Matthew 2.1–12)
  2. The Good Samaritan and Mary, Martha, & Jesus (Luke 10.25–42)
  3. The Crucifixion and Resurrection of Jesus (Mark 15.20–41; Matthew 28.1–21)
  4. Jesus feeds the five thousand (Mark 6.31–44)
  5. Jesus turns water into wine (John 2.1–11)
  6. The Sermon on the Mount (Matthew 5.1–7.29)
  7. The parable of the prodigal son (Luke 15.11–32)
  8. The parable of the rich man and Lazarus (Luke 16.19–31)
  9. The last supper (Mark 14.12–.26)
  10. The resurrection (Matthew 28.1–15)
  11. The Holy Spirit is sent to the disciples (Acts 2.1–13)

Still have questions? Email us at