2.) = 7.) Find the unit rate of 6 miles in 20 minutes. 4.) 6 8 = 8.) Put in simplified exponential form (8 3 )(8 6 )

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Warm Up Do you remember how to... 1.) 3 + 9 = Wobble Chairs: Braden, Weston, & Avalon 6.) Put 3,400,000 in scientific notation? 2.) 2 + 8 = 7.

1 Warm Up Do you remember how to... 1.) = Wobble Chairs: Braden, Weston, & Avalon 6.) Put 3,400,000 in scientific notation? 2.) = 7.) Find the unit rate of 6 miles in 20 minutes. 3.) 2 17 = 4.) 6 8 = 8.) Put in simplified exponential form (8 3 )(8 6 ) 5.) ( 3)( 4)( 10) = 1

Content Objective: I can determine to which number set(s) a number belongs. 7.1.1.1 I can recognize when a calculator is giving me a repeating decimal. 7.1.1.2 I can use division to create a rational number.

2 Content Objective: I can determine to which number set(s) a number belongs I can recognize when a calculator is giving me a repeating decimal I can use division to create a rational number. I can recognize that electronic devices chop off (truncate) or round numbers when calculating Assignment: 4.1A Due Quiz 4.1 & Vocab Quiz after lesson 4.1B Lesson 4.1A 2

3 Lesson 4.1A Number Sets Rational Numbers I can determine to which number set(s) (natural, whole, integer, or rational) a number belongs I can recognize when a calculator is giving me a repeating decimal I can use division to create a rational number I can recognize that electronic devices chop off or round numbers when calculating. The word rational does not have the word ratio in it by accident. Rational numbers are numbers that can be written as a ratio of two integers (or in other words can be written as a fraction). Remember that a fraction is a hidden division problem, so division can be used to change any fraction into a decimal number. Use a calculator to change the following fractions into decimals. 1a.) 1 / 8 = 1b.) 6 / 25 = 1c.) 81 / 600,000 = Each of the fractions above can be converted (changed) into decimals that have an end. These types of decimals are called terminating decimals. We will need cell phones that have calculator apps and regular calculators for this exercise. If you don't have a cell phone with a calculator app get a calculator and pair up with another student who has a cell phone (make a trio if you need to). Use the calculator and cell phone to change the fractions into decimals. Record all the digits that are being displayed by the device. Calculator Cell Phone (Vertically) Cell Phone (Horizontally) 2a.) 1 / 3 = 2b.) 5 / 6 = 2c.) 7 / 9 = 2d.) 8 / 11 = 2e.) 5 / 7 = What did you notice? Each of the fractions above can be converted to decimals that repeat a pattern you could put a bar over and never end. These types of decimals are called repeating decimals. Write each fraction as a repeating decimal. 3a.) 1 / 3 = 3b.) 5 / 6 = 3c.) 7 / 9 = 3d.) 8 / 11 = 3e.) 5 / 7 = Because calculators cannot display decimals that continue forever they are programmed to either round the decimal or truncate the decimal (chop off part of the decimal). You need to be able to recognize which one a calculator is doing. 3

4 Lesson 4.1A Number Sets Rational Numbers I can determine to which number set(s) (natural, whole, integer, or rational) a number belongs I can recognize when a calculator is giving me a repeating decimal I can use division to create a rational number I can recognize that electronic devices chop off or round numbers when calculating. The word rational does not have the word ratio in it by accident. Rational numbers are numbers that can be written as a ratio of two integers (or in other words can be written as a fraction). Remember that a fraction is a hidden division problem, so division can be used to change any fraction into a decimal number. Use a calculator to change the following fractions into decimals a.) 1 / 8 = 1b.) 6 / 25 = 1c.) 81 / 600,000 = Each of the fractions above can be converted (changed) into decimals that have an end. These types of decimals are called terminating decimals. We will need cell phones that have calculator aps and regular calculators for this exercise. If you don't have a cell phone with a calculator ap get a calculator and pair up with another student who has a cell phone (make a trio if you need to). Use the calculator and cell phone to change the fractions into decimals. Record all the digits that are being displayed by the device. Calculator Cell Phone (Vertically) Cell Phone (Horizontally) 2a.) 1 / 3 = 2b.) 5 / 6 = 2c.) 7 / 9 = 2d.) 8 / 11 = 2e.) 5 / 7 = What did you notice? Each of the fractions above can be converted to decimals that repeat a pattern you could put a bar over and never end. These types of decimals are called repeating decimals. Write each fraction as a repeating decimal. 3a.) 1 / 3 = 3b.) 5 / 6 = 3c.) 7 / 9 = 3d.) 8 / 11 = 3e.) 5 / 7 = Because calculators cannot display decimals that continue forever they are programmed to either round the decimal or truncate the decimal (chop off part of the decimal). You need to be able to recognize which one a calculator is doing. 4

5 9(1)= 9(2)= 9(3)= 9(4)= 9(5)= 9(6)= 9(7)= 9(8) = 9(9)= 9(10)= 5

$Natural Start at 1 and go up by ones Whole Start at 0 and go up by ones Integer Start at 0 and go up or down by ones Rational Can be written as a fraction (includes terminating decimals and repeating$

6 4.) Decide what each of the following calculators are doing to the rational numbers. 4a.) 4b.) 4c.) 4d.) Round or Truncate Round or Truncate Round or Truncate Round or Truncate A number belongs to a number set if you can get to the number by using the descriptions below. Numbers may belong to more than one number set. Natural Start at 1 and go up by ones Whole Start at 0 and go up by ones Integer Start at 0 and go up or down by ones Rational Can be written as a fraction (includes terminating decimals and repeating decimals) Start on the left side the first box you check, check all boxes that follow. Nobody Wants Insane Rats. To which number set(s) does each of the following numbers belong? For example, 0 belongs to the whole, integers, and rationals. 5.) 50 6.) ) 3 / 4 8.) 82 Circle all the number sets (natural, whole, integers, and rational) for which the statement is always true for every number in the set. 9.) If you add two numbers in this set together, the sum must be greater than either of the numbers with which you started. 10.) If you add two numbers in this set together, the sum must be greater than or equal to ) If you multiply three numbers in this set together, the product will be the same no matter the order in which you multiply them. 12.) If you multiply three numbers in this set together, the product might be a negative number. 13.) If you add two numbers in this set, you get a number in the same set. 14.) If you subtract two numbers in this set, you get a number in the same set. 6

15.) The Venn diagram to the right shows the relationship between the set of odd numbers and the set of natural numbers. In each section of the diagram, fill in at least three more numbers. 16.

Include at least three numbers in each section of the diagram. integers whole numbers 18a.

7 15.) The Venn diagram to the right shows the relationship between the set of odd numbers and the set of natural numbers. In each section of the diagram, fill in at least three more numbers. 16.) Which two sets could this Venn diagram represent? Choose from: Natural Whole Integer Rational 17.) Draw a Venn diagram that shows the relationship between the integers and the whole numbers. Include at least three numbers in each section of the diagram. integers whole numbers 18a.) Work with a partner to create a diagram with four concentric circles (circles having a common center) representing the natural numbers, whole numbers, integers, and rational numbers. Include sample numbers in each area of your diagram. Rationals Integers Whole Natural 18b.) Can you think of number that cannot be in any of the circles? 7

8 Anika, Haley, and Antonio created number puzzles. Each student thought of a number and then gave clues so that the others could guess the secret number. Use your understanding of number sets to solve their number puzzles. For problems 19 21, the secret number lies between 10 and ) Puzzle 1: My number is not a natural number. My number is odd. If you add 3 to my number, the sum is a natural number. Remember, odd numbers are numbers that are not divisible by 2. 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ) Puzzle 2: My number is a whole number. My number is a multiple of 3. My number divided by 2 is an integer. 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ) Puzzle 3: My number squared is smaller than my number itself. My number multiplied by 4 is an integer. My number multiplied by 10 is larger than 7. (Hint: Look at all numbers between 10 and 10, not just the integers between 10 and 10.) 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Find a number for which the statement is true. If no number can be found, write none. 22.) Find a whole number that is not a natural number. 23.) Find a rational number that is not a whole number. 24.) Find an integer that is not a natural number. 25.) Find an integer that is not a whole number. 26.) Find an integer that is not a rational number. 27.) If a number belongs to the set of whole numbers, to which other sets must it also belong? 8

Integers and Rational Numbers

Integers and Rational Numbers A A Family Letter: Integers Dear Family, The student will be learning about integers and how these numbers relate to the coordinate plane. The set of integers includes the set of whole numbers (0, 1,,,...)