Math 5 _ 2011

Unit 1 Test ReviewMath 5 _ 2011

Welcome! This will be a review for your first math unit test in Math 5.1Math ReviewMath JournalPencilQuiet SpaceThink Time

These are the things you will need for this math review. The most important thing is time to think about the math. You can do the simple addition and multiplication problems. It is knowing when and how to use them that you need to figure out. Are you ready? Lets begin!2Number System

The number system that we use is based on 10 digits. Our mathematics operations are based on these 10 digits and various symbols that give us direction on how to manipulate these digits to create values or numbers. These digits are well known to you. Im sure you could guess them. Here is your chance to!

Write them in your journal before they pop up on the screen!

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Number System

Did you guess correctly? Im sure you did. These are the 10 digits that create all the values in our number system.Oh wait! Thats only 9. Can you tell me which one is missing?Ill give you a hint. It is a digit that is needed to help make more numbers.4

Number System

Did you guess it? If you said zero. You were right!

These 10 digits create every conceivable number to represent a value. How they are placed or arranged together determines how large or small that value is compared to other values. Lets take a look to see how that works.5

Number SystemThree hundred forty-twoOne thousand seven hundred fifty-six

When we say or write numbers, we group them together so that each number holds its own place value.Here are two examples. 342 and 1756.You write the words just the same as you say the numbers. Now I want you to give it a try.

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Number SystemThree hundred forty-two

One thousand seven hundred fifty-six

Can you write these numbers in word form?

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Number SystemThree hundred forty-two

Eight hundred ninety-seven

One thousand, seven hundred fifty-six

Four thousand, two hundred thirty

How did you do? Lets keep practicing.

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Number SystemFive hundred and twelve

One thousand, six hundred (or sometimes expressed as sixteen hundred)

Two million, eight hundred thousand, and sixty - oneThree hundred thousand, seven hundred and seventy-two

Three thousand four hundred and thirteen

Write these numbers in digit form.9

Number SystemFive hundred and twelve512One thousand, six hundred (or sometimes expressed as sixteen hundred)1,600Two million, eight hundred thousand, and sixty one2,800,061Three hundred thousand, seven hundred and seventy-two300,772

Three thousand four hundred and thirteen3,413

Did it get easier? Im sure it did. I have a real challenge for you now!10Place Value Challenge!

Take a look at this number. Do you think you could read this one on your own? Im sure you can do it!11Place Value Challenge!

This is how you say it (read it with me)

Two hundred ten billion, one hundred twenty three million, four hundred fifty-six thousand, seven hundred eighty nine.

Do you see the typo in this chart?12Place Value Challenge!

eighty-nine

Thats right. It reads eight nine but it should say eighty nine!

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Number System

Fact FamiliesFact FamiliesWere still talking about how numbers work together in a number system. Fact Families help to show the relationship between and among numbers. These are fact families. Can you tell how they are related? Write your equations and then we will check your answers.

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Number System

Fact FamiliesThe numbers 6, 8, and 48 are related to each other through multiplication and division. That makes them a fact family.

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Number System

The numbers 2, 9, 11 are related through addition and subtraction. That makes them a fact family.

16Fractions

1 Pizza

My favorite way to talk about fractions is over a slice of pizza. Too bad this is a virtual lecture! We could order in!

Here we start with a whole pizza. No matter how many slices we will make out of this pizza to share with friends it will always be only ONE pizza.17Fractions

1 Pizzawith two slices

When we begin to cut our pizza, we are making slices to share with friends. This would be make two halves. Each would represent of the pizza, but we would still only have ONE pizza altogether.18Fractions

1 Pizzawith four slices

Now we are really slicing things up! We still only have ONE pizza but there are four slices or four friends can share four REALLY slices of pizza. Each slice represents (one-fourth) of the pizza. If we were to cut each of these pieces in 1/2 , how many pizza slices would we have and what would the fraction be?19

Fractions

1 Pizzawith eight1/8 slices

Yep! If we cut each of these slices into two pieces we would make 8 slices altogether. So, our one pizza could be shared with 8 friends. Hey, looks like someone started without us. 1/8 of the pizza is gone already! Lets dig in!20Fractions

one-halfone-fourthone-eighthone-sixteenth

As we begin to cut or divide items equally, we create a fraction. A fraction is really a division problem. A fraction can be represented easily in a picture to show how fractions with different numbers are actually showing the same division problem. They are said to be equivalent or the same or equal. Lets take a look. Here we have four different division problems or four different fractions. All of them are equal to one whole as long as all the pieces are there. If one is missing, then we have a fraction. If we were looking at only one section in each of these figures, we would call the fraction, , , 1/8, 1/16.21Fractions

1/4

Lets keeping digging in for more. In this example, we have one piece colored. We could say that is . Three pieces are missing. What fraction would that make? 22Fractions

1/43/4

1-4+3-4=4-4

If you said , the you got the idea!Adding these two together and you will get 4 over 4 or 4/4 which is the same as one whole! Lets look at another example.23Fractions

1/43/42/86/8

The area shaded in green in our new figure is 2/8. What fraction represents the area that is missing? 6/8!If you add these two together, you would still get one whole because the fraction would be 8 over 8 or 8/8.

Now, and 2/8 are considered equivalent fractions. Can you see why? They are the exact same amount of pizza! It just depends on how many slices I cut it into to begin with that makes the difference. The total number of original slices will always be the bottom number. That is the number you know you started with when you are working with an equation. The top number is some part of the total. It just depends on what your are talking about! You have to pay attention to the question! Watch out for that in word problems!

24Fractions

1/43/42/86/81-4x2-2=2-8

We have learned through our fact families that multiplication and division are inverse operations. They can create the values using the same set of numbers. Fractions are really a division problem so to compare these two figures we would use multiplication. What would I do to the fraction to get the fraction 2/8 ? Whatever I multiple to the top number I have to multiply to the bottom number. That keeps the fractions balanced. In this example, I would multiply by 2. That makes sense because I have actually doubled the amount of pizza I can share with friends by creating more equal slices. Do you see how division and multiplication complement each other?

25Fractions

1/43/42/86/83-4x6-8=

Now lets use this same example to show how these fractions are equivalent. We can determine if fractions are equivalent by using a method called cross multiplying. It is so easy and tells us right away if these fractions are talking about the same division problem or same amount of pizza that is missing out of each pie!

26Fractions

1/43/42/86/83-4x6-8=24

I will multiply 3 x 8 and my answer is 24.

27Fractions

1/43/42/86/83-4x6-8=2424

I check to see what my product is for 4 and 6. It is 24 also. That means that these two fractions are equivalent. They are related to the same division problem. So I can change them by using multiplication or reduce them by using division. When you reduce a fraction, you are putting it into the most simplest of terms or the smallest fraction that you can make. It really helps to understand things better when you just keep it simple.

28Fractions

Now its your turn. Look at the new figure on our screen.What fraction is created by the area shaded in green?What fraction is created by the missing pieces?What fraction do you created when you add these two together?

Is the new figure equivalent to the other two fraction problems?Can you reduce the new figures fractions into lowest terms?

Work this out in your journal and we will check your answers.29Fractions

1/43/4

4/1612/16

In our new figure, there are 16 slices altogether. So, 16 will be the bottom number.

The area shaded in green can be represented in the fraction 4/16.The missing pieces are shown in the fraction 12/16.

What fraction is created when you add these two together? 16/16 of course!

Are these fractions equivalent to and ? They sure are? How do you know? If you cross multiplied, you can check your answers to be sure.Another method is to ask yourself the questionWhat would I have to do to my fraction to get 4/16 and my fraction to get 12/16? Multiply by 4!30RoundingTensHundredsThousands562831720346356223255508501

Lets move onto the topic of rounding. When you round a number you are simply choosing to use a value that is closest to the one that you need.Using a number line can help you make that decision.If a two-digit number ends in a number greater than 5 (6, 7, 8, 9), the number is rounded to the higher ten.If a two-digit number ends in a number less than 5 (0, 1, 2, 3, 4), the number is rounded to the lower ten.If a two-digit number ends in 5, the number is in the middle of the two tens. We choose to say that 5 is rounded to the higher ten. Because, of course, who doesnt want more of something if you are going to round off lets saythe number of candies your friend shares with you at lunch?

Lets try each one of these and see if you can guess the right answer before I display it. Write the answer in your journal and then we will check it.

31RoundingTensHundredsThousands562831720603001800346356223305006000255508501306009000

Did you notice that 34 and 25 round to the same number?When you are rounding you are really just estimating a number. You are giving a guess as to the amount. You are not expected to be exact. It is okay to be off by a few tens, hundreds, or thousands depending on what you are rounding up to. When you estimate you are rounding. When you are roundingyou are estimating!

When someone asks you to estimate how many there might be of something, then you use rounding to figure out that kind of problem. Lets look at an example.32Rounding / Estimating

= 5050 x 10 = 500

If I wanted to know how many jellybeans are in my jar, I could do two things. I could sit and count each one and then I would know exactly how many are in my jar, but I dont REALLY need to know that kind of information. I just need an estimate. So, my second choice is to guess the number jellybeans in my jar or to estimate. I know it takes 10 scoops to fill up my jar. How many jellybeans are in each scoop? Well, I scoop up some jellybeans and I count. There are 47. Ill round that number up to 50. Then, I can multiply 50 x 10 to find my answer to the number of jellybeans in my jar! There are 500 jellybeans in my jar. Now, that would have been a long time of counting each jellybean one by one.33Rounding / Estimating Challenge

Why dont you try to estimate the number of cereal pieces in your favorite cereal?

Use a similar method and try it out on your own. If you are brave and have a lot of time on your hands, you could actually count them out and see if your estimation was correct!34Teachers CornerIf you need additional help with any concepts from this unit of study, check out these website links. Many have practice sheets, demonstration videos, and extended examples.

Place Value

Fact Family

Fractions

Rounding

Estimation

Weve covered quite a bit of material for your first unit test in math. These are some additional website links that will give you the extra practice you might need for help with your review. All you have to do is click on them to take you to the sites! They will be the pdf document I sent in your email.35Unit 1 Test ReviewMath 5 _ 2011

This has been a review for your first unit test in Math 5. If you have any further questions after you study some more on your own, please give me a call! I will talk to you soon!36