Math+Chapter+1

﻿﻿﻿ **Math Chapter 1, Unit 1** **Place Value, Decimals, and Subtraction** ***Super Speed Math will be every Monday, Wendesday, and Friday!!***  Place Value | Comparing and Ordering Whole Numbers | Decimals | Comparing and Ordering Decimals | Adding and Subtracting Mentally | Rounding | Estimating | Adding and Subtracting Decimals | Vocabulary  __**Vocabulary:**__ You can study your vocabulary on Quizlet, which is below. Either study it right on this page, or click on the Quizlet icon to go to the page and play other games to help you study. media type="custom" key="10317802" Back to Top  __**Place Value:**__ ﻿ We will be working with place value through the billions period and to the thousandths (three places AFTER the decimal). Students will identify digits in place value positions through the billions period. Students will write numbers in standard, expanded, and word form. Standard Form Expanded Form Word Form Games Back to Top



 **__Standard Form:__** Standard form is simply writing the number using digits.

346,983,012,673 is written in standard form.

Back to Top | Back to Place Value

 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">**__Expanded Form:__** <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">To write in expanded form, isolate each digit and write the corresponding number of zeroes after it as the original number.For example: 346,983,012,673 would be written as: 300,000,000,000+40,000,000,000+6,000,000,000+900,000,000+80,000,000+10,000+2,000+  <span style="color: #800000; display: block; font-family: 'Courier New',Courier,monospace; font-size: 150%; text-align: justify;">600+70+3 This being said, we would state that the digit 9 in this number has a value of 900,000,000, the digit 7 has a value of 70, and so on. <span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Top | Back To Place Value  <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 26px;">**__Word Form:__** <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">To write in word form, write the number out using words as it is said. <span style="color: #800000; display: block; font-family: 'Courier New',Courier,monospace; font-size: 150%; text-align: justify;">346,983,012,673 would be written as "Three hundred forty-six billion, nine hundred eighty-three million, twelve thousand, six hundred seventy-three" <span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Top | Back to Place Value

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">**__Place Value Games__** <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Place Value Game choose medium to work with numbers through the one billions place. Click on Hard to work with numbers from thousands through the thousandths place. <span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Top | Back to Place Value  <span style="color: #800000; font-family: 'Courier New',Courier,monospace;">__**<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Comparing and Ordering Whole Numbers **__

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Students will compare whole numbers through the billions period using >, <, and = signs. Students will order numbers from least to greatest and greatest to least through the billions period.

<span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Directions and Examples for Comparing and Ordering Whole Numbers <span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Comparing and Ordering Whole Numbers Games <span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Top <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;"> <span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Top | Back to Comparing and Ordering Whole Numbers



__**<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Comparing and Ordering Whole Numbers Games **__

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Compare Whole Numbers game comparing and ordering whole numbers through the billions period. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Compare Decimals game comparing and ordering decimals through the thousandths place.

<span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Top | Back to Comparing and Ordering Whole Numbers

<span style="color: #800000; font-family: 'Courier New',Courier,monospace;"> __**<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 26px;">Decimal Place Value Through Thousandths **__

__**<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">﻿ **__<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Students will identify decimals through the thousandths place. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Students will write decimals through the thousandths place in standard, word, and expanded form.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Standard Form <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Expanded Form <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Word Form <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Games <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Top



<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;"> <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">__**Standard Form**__ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">﻿Like whole numbers, standard form is simply writing the digits. 0.718 is written in standard form as is 345.718. We read the decimal as "and" rather than "point."

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Tutorial on how to read decimals

<span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Decimals | Back to Top

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;"> __<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">**Expanded Form** __ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">For whole numbers, you write the digit with the number of zeroes after it. For decimals, you write the digit with the zeroes before it.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">0.718 would be written as 0.7+0.01+0.008

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">345.718 would be written as 300+40+5+0.7+0.01+0.008

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Think about it...

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">10 has 1 zero. 10ths are 1 place after the decimal place and have one zero. So, to write 7 tenths, write one zero then the 7 (like writing 70 backwards) and put the decimal after the zero. It will look like 0.7.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">100 has 2 zeroes. 100ths are 2 places after the decimal place and have 2 zeroes. So, to write 1 hundredth, write two zeroes then the 1 (like writing 100 backwards). As always, place the decimal after the first zero. It will look like 0.01

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">1,000 has 3 zeroes. 1,000ths are 3 places after the decimal place and have 3 zeroes. So, to write 8 thousandths, write three zeroes then the 8 (like writing 8,000 backwards), then place the decimal after the first zero. It will look like 0.008.

<span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Decimals | Back to Top

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;"> <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">__**Word Form**__ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">﻿Word form is the same as it is for whole numbers. Remember, the decimal is read as "and" when there are whole numbers before the decimal.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">0.718 is written as seven hundred eighteen thousandths.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">345.718 is written as three hundred forty-five and seven hundred eighteen thousandths.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">You may find it easiest to follow the following pattern if you are going from word form to standard form. We will use eighty and six hundred seven thousandths as our example.


 * 1) <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px; line-height: 29px;">When you read a decimal, you read the decimal point as "and." Place the decimal point on your paper.
 * 2) <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Look at the word form. We see that eighty is written before the word "and." Write 80 before the decimal point. Your paper should now look like 80..
 * 3) <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Look at the words after the word "and." we see six hundred seven thousandths. Write 607 after the decimal. It should look like this 80.607. We know that this is correct because the last digit is three places after the decimal point, and thousandths are three places after the decimal point.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Top | Back to Decimals

 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">__**Decimal Games**__

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Decimal Practice an easy to follow explanation of decimal place value followed by a review game <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Word form to Standard Form explanation of thousandths followed by a game requiring you to transfer word form to standard form to the thousandths place without numbers to the left of the decimal. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Word to Standard Form II explanation of how to read and write decimals with whole numbers to the left. This is followed by a game requiring you to transfer from word to standard form. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Identifying Specific Place Value Explanation and game for identifying specific place values in decimals. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Decimals of the Carribbean Shoot the ship with the standard form that matches the given word form.

<span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Top | Back to Decimals

<span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;"> <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">__**Comparing and Ordering Decimals**__

<span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Games

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">﻿Comparing and ordering decimals is easy! Just like when you compare whole numbers, line up your numbers up and down making sure the decimal point lines up. If your decimal point lines up, then all the other place value spaces should line up. Start at the place furthest to the left and compare, then go down the line until you have your numbers in order or have decided whether the answer is > < or

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<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Least to Greatest practice putting decimals in order from least to greatest <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Comparing Decimals use > < or = to make each statement true <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Ordering Decimals put the decimals in order. Be sure to choose thousandths!

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;"> __**<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Adding and Subtracting Mentally **__

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__<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Commutative Property of Addition __ __<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">Associative Property of Addition __ __<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">Compatible Numbers __ __<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">Compensation __ __<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">Games __ __<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">Back to Top __

__**<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">﻿ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Commutative Property of Addition **__

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">The commutative property of addition says that we can add a series of numbers in any order that we want and we will still get the same answer. That is why 2+3 is the same as 3+2. Both equal 5. 10+34+26=70; 10+26+34=70, 26+34+10=70, etc.

__**<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 20px;">﻿ **__

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media type="custom" key="10454938" <span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Top | Back to Adding and Subtracting Mentally __**<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Associative Property of Addition **__ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">This is pretty similar to the commutative property of addition. Because I can add my numbers in any order, I can also group them any way I want and still get the same answer. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Using the example from above, 10+34+26, I can add 10+34 to get 44 then add 44+26 to get 70, or I can add 34+26 to get 60, and 60+10 is 70, etc. media type="custom" key="10454920" align="center"

<span style="color: #800000; display: block; font-family: 'Courier New',Courier,monospace; font-size: 150%; text-align: left;">Back to Top | Back to Adding and Subtracting Mentally <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">﻿__**Compatible Numbers**__ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Compatible numbers are numbers that are easy to compute. Usually, when we have a series of numbers to add, we try and find numbers that will add to a multiple of 10. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">For example, in 10+34+26, I can see that 34+26 will equal 50, a multiple of 10. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Example 2: 1,800+300+3,700 I can see that 300+3,700 will equal 4,000, a multiple of 10. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Remembering your 10 facts will help with addition: <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">10+0=10  <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">9+1=10  <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">8+2=10  <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">7+3=10  <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">6+4=10  <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">5+5=10 <span style="color: #800000; display: block; font-family: 'Courier New',Courier,monospace; font-size: 150%; text-align: left;">We can do the same for subtraction when we are subtracting two numbers that may not be easy to subtract mentally. Instead of finding pairs of numbers to add to 10, we can subtract to 0. Example: If I had to subtract 369-199 mentally, I would have to regroup in the 10s place. Instead, I can subtract 30 from 199 to get 169. It is much easier to do 369-169 and get 200. Because I took 30 away from 199, I still have to subtract 30. 200-30=170.

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">When you find numbers with these combinations in the same place value, you have found compatible numbers! See Examples from our book above. <span style="color: #800000; display: block; font-family: 'Courier New',Courier,monospace; font-size: 150%; text-align: left;">Back to Top | Back to Adding and Subtracting Mentally <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;"> **__<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">Compensation __** <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Compensation allows me to take from one number and add it to another using compatible numbers. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Example: 1,800+300+3,700 <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Because I know my compatible numbers, I know that if I added 1,800+200 I would have 2,000. Where can I get 200 from? <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">I can go next door to my 300, and take 200. This leaves me with 1,800+200+100. 1,800+200=2,000. I can then add 2,000+100+3,700. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">I could also go to 3,700 and take 200. This leaves me with 1,800+200+3,500. 1,800+200=2,000. I can then add 2,000+3,500+300. See Rikki's example in example A above. <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Top | Back to Adding and Subtracting Mentally


 * __<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;"> <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">﻿Games __**

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Sumbler Be quick! Use your mental math skills to choose numbers that add to specific sums


 * __<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 26px;">Rounding __**

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%; line-height: 29px;"> Games <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%; line-height: 29px;">Back to Top

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media type="youtube" key="3afU6JQG15I" height="315" width="420" <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">**__Games__** media type="custom" key="10591278" align="center"

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<span style="display: block; line-height: 0px; overflow-x: hidden; overflow-y: hidden; text-align: center;"> <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%; line-height: 29px;">Back to Top | Back to Rounding

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%; line-height: 29px;"> __**<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%; line-height: 29px;">﻿Estimating **__

<span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Games <span style="font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Top

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Estimating is easy! For whole numbers, simply find the place furthest to the left in each number and round to that place value then add or subtract! Easy, right?

<span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">For decimals, round to the nearest whole number. That means find the ones place then took to the tenths and round. Easy!


 * <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 200%;">﻿__Games__ **

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media type="custom" key="10591610" <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Back to Estimating | Back to Top <span style="color: #800000; font-family: 'Courier New',Courier,monospace;"> <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 26px; line-height: 39px;">__**Adding and Subtracting Decimals**__ <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%; line-height: 39px;">Games <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%; line-height: 39px;">Back to Top <span style="color: #800000; font-family: 'Courier New',Courier,monospace; font-size: 150%;">Adding and subtracting decimals is just like adding and subtracting any other number. Just like whole numbers, you have to line up each place value. The easiest way to do this is to simply line up the decimal points. If you do this, all of the other place values will automatically line up on their own :) media type="youtube" key="V6pZyY6mM3g" height="315" width="420" align="center"

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