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4 The Real π 9 Number 0 √ 2 Bundle NUMEROUS ACTIVITES & ASSESSMENTS! 8.NS.A.1 8.NS.A.2 5 = 25 √ -5 -4 -3 -2 -1 0 1 2 3 4 5 © Mary Moore, Moore Resources 2015 Real Number System (R) Rational Numbers (Q) Irrational Numbers A rational number may be expressed as a fraction, a terminating decimal, or a repeating decimal. Q stands for the german word quotient. -.44444 = 4 3 9 4 1 = .333... 3 = .75 Any real number that cannot be expressed as a rational number. π = 3.14159265.. . Integers (Z) Z stands for Zahlen (German word for numbers) All whole numbers plus their inverse. Postive numbers, negative numbers and zero. √2 =1.414 2 1356... Z = {....-3, -2, -1, 0, 1, 2, 3.....} -4/4 = -1 so it&isreanal integer, rational -5 -1895 Whole Numbers (W) W = { 0, 1, 2, 3.....} 2.782513 5389... All natural numbers plus 0. All positive counting numbers plus zero 0 is whole, integer, rational, & real Natural (N) Numbers All positive counting numbers. N = { 1, 2, 3, 4, 5.....} atural, whole, n is it so 2 = √4 rational integer, real & © Mary Moore 2014 & 2015 √5 -√5 π √2 √3 Real Number System (R) Rational Numbers (Q) Irrational Numbers Integers (Z) Whole Numbers (W) Natural (N) Numbers © Mary Moore 2014 & 2015 “Real Number System Sorting Task Cover and Directions” I utilize small photo albums I purchased from the dollar store or retail outlets like in this photo. The slots can hold the cards as seen here. When setting up a station, have the album and worksheets laid out for students to complete...or you may do this as a whole group lesson and have the directions on your white board or interactive white board. © Mary Moore, Moore Resources 2015 “Tips, Instructions, Information on this Activity” Directions: This following tasks utilize numbers you print and cut out on card stock or paper. Place the numbers in a Pull aStudents real may number out o bag or envelope and allow students to complete the following tasks that are included. work individuals, in pairs, or in teams. Students choose a number and then write the number on the number line where it belongs in the first task. on the Write the number In the second task, students choose a number and mark which type of Real Number it is on a diagram. Make sure you are conve These tasks may be utilized throughout the year in stations or for review. In this packet, The Number Line task, Diagram task, letter size Real Number chart, and cards are included. out if they are rational o convert decimals to frac Prior to completing this activity with your students they will need to know how rational or irrational. to convert decimals to fractions and fractions to decimals. They will also need to know how to convert square roots to whole numbers if possible. A calculator may Remember the formula: be needed by students to do this activity. The formula for converting a repeating decimal to a fraction is to the right. I’d cover some examples of repeating decimals and how to convert them as seen to the right. Please note that if the decimal is 0.2323... then the students would need to multiply it by 100 to get 100w = 23.2323... and then do the calculations. A HANDOUT IS NOW in this PRODUCT. W = 0.55555….. 10w = 5.555… -‐ w = 0.555…. 9w = 5 w = 5/9 Student will also need to know how to place numbers on a number line or where to approximate their locations..... I suggest this being reviewed also prior to utilizing this activity. For example, √25 = 5, so students would place this on ‘5’ on the number line as in the example in this product. Students will also need to know how to approximate location of irrational numbers on a numit is beacloser group f repeati ber line. For example, 1.42568.... will be placed between 1 and 1.5, itIf would to 1.5othan 1. zeros ‘0’ behind the 1 to I do not wish to inform you on how to teach, yet, I would suggest doing examples first with students and walking them through placing numbers on a number line,After how to convert your numbers, worksheet is and determining where they are in the real number system prior to setting this up as a station. group, to show the answ On the sheeet where students draw numbers and write in their category, you, may wish to review the number system with students. Use the handout and discuss where numbers belong. Also, Check your work and cir I’d allow students to place this in their notebook or have handy when at first doing this task. Students will draw a number and then mark on the sheet where the numbers belong. Sincerely, M Moore © Mary Moore, Moore Resources 2015 Fill out a station sheet o When finished with this 14 repeats 253 repeats Only the 3 repeats Directions: > Simply Divide the numerator by the denominator in the fraction w = 5/9 10w = 5.555… -‐ w = 0.555…. 9w = 5 W = 0.55555….. Converting 0.555... to a fraction Remember the formula: Example .333... 3 1.000 The - 9 pattern repeats 10 over & -9 over 10 - 9 Example 1 3 sure it ybyou onverting fractions to decimals to find >Make Then multiply '10'aifre it iscone repetend create another equation. out if tand hey are rational or irrational. And vice versa, Numerator Subtract your first equation from this convert ecimals to fractions if you can to see if they are one as in the d example. Denominator >rational Solve for 'w'or irrational. > Simply set the repeating decimal > The Denominator is the Write the number on the worksheet where it "bottom" belongs. equal to 'W'. number in the fraction > The simple formula is shown below > The Numerator is n the "top" number Pull a real number out of the pouch with umbers. > There is a formula to handle converting repeating decimals to fractions. ©2015 Mary Moore, M Moore Educational Resources, All rights reserved by author. Distribution on google docs, school websites, is not permitted. Permission to copy for single classroom use only for educational purposes. Electronic distribution limited to single classroom use only. Read the full copyright included with this packet. repeats, European 15.09(09) 09 denotation 120.141414 0.253253... ExampleS 0.33333333... > In the US we use dots and bars, in Europe the repetend may be in parenthesis > Denoted with .... after the decimal or a bar - over the repetend > May be converted to a fraction > The repeated digit sequence is called the repetend or reptend > A repeating decimal continues if it does not end in zero Repeating Decimals Decimal Fraction Fraction Decimal Converting Decimals & Fractions 10w = 3.333... - W = 0.333... Multiply the equation by 10 Subtract the first equation 3 W=9 25 W = 99 99w = 25 99 99 100w = 25.2525... - W = 0.2525... W = 0.2525... 0.252525... 25 0.2525... = 99 Solution Divide both sides by 99 Multiply the equation by 100 Subtract the first equation Set it Equal to W Repeating Decimal Example two ©2015 Mary Moore, M Moore Educational Resources, All rights reserved by author. Distribution on google docs, school websites, is not permitted. Permission to copy for single classroom use only for educational purposes. Electronic distribution limited to single classroom use only. Read the full copyright included with this packet. 3 0.333... = 9 Solution 9w = 3 9 9 W = 0.333... Set it Equal to W Divide both sides by 9 0.33333333... Repeating Decimal Example one 9 W = 99 99w = 9 99 99 100w = 09.0909... - W = 0.0909... W = 0.0909... 0.0909... 9 1 0.0909... = 99 = 11 Solution Divide both sides by 99 Multiply the equation by 100 Subtract the first equation Set it Equal to W Repeating Decimal Example three Converting Repeating Decimals to Fractions Cover page and inside page for small photo album if you wish to set up your station like in the photo with a small album. π .75 √4 = 2 Real Number System Challenge CCSS.Math.Content.8.NS.A.1 -.4444 √5 -4/4 = -1 © Mary Moore, Moore Resources 2015 Directions: Pull a real number out of the pouch with numbers. Remember the formula: W = 0.55555….. 10w = 5.555… -‐ w = 0.555…. 9w = 5 w = 5/9 If it is a group of repeating numbers you’ll need more zeros ‘0’ behind the 1 to multiply by. © Mary Moore, Moore Resources 2015 Write the number on the worksheet where it belongs. Make sure you are converting fractions to decimals to find out if they are rational or irrational. And vice versa, convert decimals to fractions if you can to see if they are rational or irrational. After your worksheet is complete, allow the leader of the group, to show the answers in the back of the album. Check your work and circle any you need to fix. Fix them. Fill out a station sheet on the team players in your group. When finished with this station put your worksheets in your ‘core’ basket. Give the station slip to your teacher. COLOR CODED REAL NUMBER CARDS © Mary Moore, Moore Resources 2015 Real Numbers you may cut out and have students partner together to place in the correct spot on the Real Number Chart. Students can rewrite the numbers in colored pencil. Or you may put them in a bag and let students walk up and draw one out to place in containers labeled with the Real Number System or allow them to place on a poster or number line. There are several options on how you may utilize this resource. A quiz posting or writing the numbers on the chart is also a way to assess student learning. Look for more Real Number Resources in my TpT store. 4 2.7825... 9 √4 -√2 25 7 5.9815... 9 π 3 3 1 2 -1895 √16 1 3 1.222... 4 1 4 1.9805... 2 -2 -√49 1 7 √64 0.25 0.35 3 π -√9 -5 4 4 1 4 0 √2 √9 5 9 0 √2 -4895 2 9 √25 3 23 1.444... 4 -√4 -13 1 -√2 14 2.9805... 2 -4 -√81 1 15 3 17 √49 0.15 0.65 © 2015 Mary Moore, MMoore Educational Resources, All Rights Reserved. TpT Store ~Moore Resources REAL NUMBER CARDS © Mary Moore, Moore Resources 2015 Real Numbers you may cut out and have students partner together to place in the correct spot on the Real Number Chart. Students can rewrite the numbers in colored pencil. Or you may put them in a bag and let students walk up and draw one out to place in containers labeled with the Real Number System or allow them to place on a poster. There are several options on how you may utilize this resource. A quiz posting or writing the numbers on the chart is also a way to assess student learning. Look for more Real Number Resources in my TpT store. 4 2.7825... 9 √4 -√2 25 7 5.9815... 9 π 3 3 1 2 -1895 √16 1 3 1.222... 4 1 4 1.9805... 2 -2 -√49 1 7 √64 0.25 0.35 3 π -√9 -5 4 9 1 4 0 √2 √9 5 9 0 √2 -4895 2 9 √25 3 23 1.444... 4 -√4 -13 1 -4 2.9805... -√81 -√2 14 2 1 15 3 17 √49 0.15 0.65 © 2015 Mary Moore, MMoore Educational Resources, All Rights Reserved. TpT Store ~Moore Resources © Mary Moore, Moore Resources 2015 2nd Set of Number Cards 1 2.6325... 9 √121 0 √5 π -√25 -10 8 8 1 5 -√5 13 45 11 7.9815... 9 1 8 √9 -√2 13 4.9805... 7 2 3 √36 6 4.222... 14 -7 -√64 11 √81 0.34 0.27 0 √2 -101 8 9 √144 2 16 4.444... 5 1 -4 6.9805... 6 -√81 8 2 11 √11 0.45 0.15 6 π -√144 -1 5 5 1 16 8 9 -795 © 2015 Mary Moore, MMoore Educational Resources, All Rights Reserved. TpT Store ~Moore Resources © Mary Moore, Moore Resources 2015 2nd Set of Number Cards B&W 1 2.6325... 9 √121 0 √5 -√5 45 11 7.9815... 9 √9 π -√144 -1 5 5 1 16 √36 6 7 4.222... 14 2 -7 4.9805... 13 -√64 3 1 11 √81 0.34 0.27 8 π -√25 -10 8 8 1 5 -795 -√2 6 13 2 6 8 9 0 √2 8 9 6.9805... 16 1 8 -101 √144 2 4.444... 5 -4 -√81 11 √11 0.45 0.15 © 2015 Mary Moore, MMoore Educational Resources, All Rights Reserved. TpT Store ~Moore Resources LARGER REAL NUMBER CARDS Real Numbers you may cut out and have students partner together to place in the correct spot on the Real Number Chart. Students can rewrite the numbers in colored pencil. Or you may put them in a bag and let students walk up and draw one out to place in containers labeled with the Real Number System or allow them to place on a poster or number line. There are several options on how you may utilize this resource. A quiz posting or writing the numbers on the chart is also a way to assess student learning. Look for more Real Number Resources in my TpT store. 4 2.7825... 9 √4 π -√9 -5 4 9 1 4 -√2 4 25 1 3 0 √2 5 9 3 1 2 1.9805... 7 √64 0.25 0.35 -2 -√49 1.222... -0.5 125 √16 1 4 -1895 © 2015 Mary Moore, MMoore Educational Resources, All Rights Reserved. TpT Store ~Moore Resources NAME:___________________________________________________ Date:_________________________ Sorting Real Numbers on the Number Line Directions: Choose a number from the bag. Place the number on the number line where it belongs. Write the number and it’s equivalent if necessary on the number line like the example. 5 = 5 √2 Example: -5 -4 -3 -2 -1 0 1 2 3 4 5 0 0 0 0 © Mary Moore, Moore Resources 2015 © Mary Moore, Moore Resources 2015 Core:________________ The Number You Chose Goes Here Natural Number Whole Number Integer Rational Number Irrational Number Real Number Directions: Choose a number from the bag. Write the number in the first column. Mark an x in each column of the number set the number you chose belongs to. Name:______________________________________________________________________________ Date:________________________________________ Name:__________________________________________ Date:___________________ Real Number Test. Place an X in each box that describes each number. There may be an X in more than one box. 3 /3 √12 2.11111… -2.5 π -(-123) 2 1 ⅙ 8.63741… 0 √64 54 /6 - √64 0.5 8 /4 -20 © Mary Moore, Moore Resources 2015 0.5 -15 6.181818… 18 -25 √36 Natural Whole Integer Rational Irrational Name:__________________________________________ Date:___________________ Real Number Test. Place an X in each box that describes each number. There may be an X in more than one box. 3 /3 Natural √12 X Whole X Integer X X -2.5 π 2 1 ⅙ X X X X X X X X X X X 8.63741… 0 √2 54 /6 - √64 X /4 -12 X X X X X X 0.5 15 6.181818… 18 -25 √36 © Mary Moore, Moore Resources 2015 X X X X X X X X X X X X X X X Irrational X X X X 0.5 8 X X 2.11111… -(-12) Rational X X X X X X X X X X X X Real Number System Foldable In my class all students made a foldable based on the real number system. The next 2 pages contain photos of the foldable. This is a very simple foldable to make. All you need are colored paper or construction paper and glue. I used one regular piece to contain all the smaller pieces of paper which I folded over to label and then inside make notations. I suggest utilizing Magenta/Pink paper for Irrational numbers - Red paper for Natural Numbers - Orange paper for Whole Numbers - Blue paper for Integers - and Green paper for Rational numbers so that the foldable colors match with the poster and students associate the colors and numbers to their classification. You may also use plain white paper to make the foldable and utilize colored pencils to write the information in the foldable. Please understand this one is not color coded like the poster in this packet due to the resources at the time this foldable was made. These photos are to provide guidance and a resource for you and your students. OR USE THE PRINT OUTS FOR THIS IN THIS PACKAGE - ALL FOLDABLE PAGES ARE PRINTABLE IN THE FOLDABLE PRODUCT © Mary Moore, Moore Resources 2015 © Mary Moore, Moore Resources 2015 Real Number System 24 Challenge by Mary Moore Included: 72 Task Cards, Recording Sheets (sample one to explain to students how to mark their answer, color recording sheet, & black & white sheet), and Answer Keys for Task Cards are at the end of each set. Use as a station. Set 1 - Set I, Easier problems to Solve, 24 Task Cards & Answer Key Set 2 - Set II, Harder level problems to Solve, 24 Task Cards & Answer Key Set 3 - Set III, Harder (with a few easier problems) level problems to Solve, 24 Task Cards & Answer Key Directions: Print tasks on colored paper & cut out the task cards. Handout to each student a recording sheet “Let’s Play 24” Place the cards on a table. Let students choose a card to solve and write the answer in the appropriate box. Depending on your class you may wish to model solving one first and writing in the answer to demonstrate what to do. After they solve their problem, they write the solution in the box that cooresponds on their recording sheet. Problem 1 will be written in box 1, problem 5 in box 5, etc. After they solve a problem have them get up, place it in the pile and then get another card.....OR if you do not wish them to get up and down, group the studens and give each group a set of task cards to work on together. Or set it up as a station activity and let students rotate through stations that day. *** You may also put the task cards in a small photo album or make it a flip book for students to work through and record their answers. OTHER USES: Use the task cards as starter problems. Cut out one or two and let students do them as a starter for the day prior to class begnning. Use in stations, as a review, or even as homework. Cut apart and send home for homework or use a sheet for classwork or as a quiz. There are numerous ways you may use this resource. At the end of this bundle is a sheet with the same problems in the task cards you may use as an assessment if you wish. Or just print one sheet and let that be a quiz. I hope you enjoy this activity. Standards US Common Core Standards Listed.... CCSS.8.NS.A.1, 8.NS.A.2 © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources EXAMPLE - Blank Recording Sheets following this page Name:__________________________________ Date:__________________ Class:____________ Let’s Play 24 Real Number System 1. 2. 4. 7. 8. c a 5. 3. 6. d b 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Name:__________________________________ Date:__________________ Class:____________ Let’s Play 24 1. Real Number System 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Name:__________________________________ Date:__________________ Class:____________ Let’s Play 24 1. Real Number System 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 1 - Tier One Problems (easier problems) 1 Choose an answer to the problem 2 Choose an answer to the problem What is 2.333... in fraction form? What is 1.333... in fraction form? a) 2 1/3 a) 7/9 b) 2 2/3 b) 3/9 c) 2/9 c) 12/9 d) 2 6/9 d) 3/9 3 Choose an answer to the problem 4 Choose an answer to the problem What type of number is 2? What type of number is -5? a) whole number a) whole number b) irrational number b) integer c) integer c) irrational number d) natural number d) natural number © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 1 - Tier One Problems (easier problems) 5 Choose an answer to the problem What is 4/9 in decimal form? 6 Choose an answer to the problem Fractions are in the set of integers. a) 4.44444..... b) 0.9999.... a) True c) 0.4444.... b) False d) 0.40404... 7 Choose an answer to the problem Determine if the numbers x and y are rational or irrational. x = √16 y = √2 8 Choose an answer to the problem 0 is an integer. a) True b) False a) x and y are irrational b) x and y are rational c) x is irrational y is irrational d) x is rational y is irrational © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 1 - Tier One Problems (easier problems) 9 Choose an answer to the problem 10 Choose an answer to the problem 1 is a whole number. -4 is what kind of number? a) True a) natural, whole, integer, rational b) False b) whole, integer, rational c) integer, irrational, whole d) integer and rational 11 Choose an answer to the problem 12 Choose an answer to the problem What type of number is √16? What type of number is √2? a) whole number a) whole number b) irrational number b) irrational number c) integer c) integer d) natural number d) natural number © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 1 - Tier One Problems (easier problems) 13 Choose an answer to the problem What is 5/9 in decimal form? 14 Choose an answer to the problem Decimals are in the set of rational numbers. a) 5.5555... b) 0.9999.... a) True c) 0.555.... b) False d) 0.50505... 15 Choose an answer to the problem Determine if the numbers x and y are rational or irrational. x = √25 y = √5 16 Choose an answer to the problem 0 is a natural number. a) True b) False a) x and y are irrational b) x and y are rational c) x is irrational y is irrational d) x is rational y is irrational © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 1 - Tier One Problems (easier problems) 17 Choose an answer to the problem 1.236512145... is irrational. a) True b) False 18 Choose an answer to the problem 25 is what kind of number? a) natural, whole, integer, rational b) whole, integer, rational c) integer, irrational, whole d) integer and rational 19 Choose an answer to the problem 20 Choose an answer to the problem What type of number is π ? What type of number is √4? a) whole number a) whole number b) irrational number b) irrational number c) integer c) integer d) natural number d) natural number © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 1 - Tier One Problems (easier problems) 21 Choose an answer to the problem What is 2/9 in decimal form? 22 Choose an answer to the problem Fractions are in the set of whole numbers. a) 0.222... b) 2.9999.... c) 2.222.... a) True b) False d) 0.20202... 23 Choose an answer to the problem Determine if the numbers x and y are rational or irrational. x = √5 y = √3 24 Choose an answer to the problem 1/3 is an integer. a) True b) False a) x and y are irrational b) x and y are rational c) x is irrational y is rational d) x is rational y is irrational © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 1 - Tier One Problems ANSWER KEY 1. a13. c 2. c14. a 3. d15. d 4. b16. b 5. c17. a 6. b18. a 7. d19. b 8. a20. d 9. a21. a 10. d22. b 11. d23. a 12. b24. b © 2015 Mary Moore, MMoore Educational Resources. All rights reserved Set 2 - Tier TWO Problems (harder problems) 1 Choose an answer to the problem What is 0.25 in fraction form? a) 2/10 2 Choose an answer to the problem What type of numbers are x and y? x = -5 y = 15 b) 25/10 a) x and y are irrational c) 1/4 b) x is irrational and y is rational d) 2/4 c) x is whole and y is natural d) x is an integer and y is natural 3 Choose an answer to the problem 4 Choose an answer to the problem Which set of real numbers only contain integers? Which set of real numbers only contain natural numbers? a) { 2/10, 1/4, 0, -4 } a) { 7, 2, 0, -4 } b) { 2/9, 2, 0, -3 } b) { 8/2, 25/5, 4, 250 } c) { 8/9, 2, 1, -7 } c) { 7/9, 3, 0, 2 } d) { -2, 0, 10/2, 6 } d) { 8/2, 25/5, 0, 250 } © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 2 - Tier TWO Problems (harder problems) 5 Choose an answer to the problem What is 2.25 in fraction form? a) 2 2/10 6 Choose an answer to the problem What type of numbers are x and y? x = 10/5 y = 1/4 b) 2 25/10 a) x is natural and y is rational c) 2 1/4 b) x is irrational and y is rational d) 2 2/4 c) x is whole and y is natural d) x is an integer and y is natural 7 Choose an answer to the problem 8 Choose an answer to the problem Which set of real numbers only contain whole numbers? Which set of real numbers only contain integers? a) { 2/10, 1/4, 0, -4 } a) { 7, 2.22.., 0, -4 } b) { 2/9, 2, 0, -3 } b) { -4, 25/5, 4, -250 } c) { 8/9, 2, 1, -7 } c) { 7/9, 3, 0, 2 } d) { 5, 0, 15, 6 } d) { 8/2, 25/5, 0, 250/9 } © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 2 - Tier TWO Problems (harder problems) 9 Choose an answer to the problem What is 0.77... in fraction form? 10 Choose an answer to the problem What type of numbers are x and y? x = 0.35 y = -235 a) 7/9 b) 77/10 c) 7/10 d) 77/9 a) x is natural and y is rational b) x is irrational and y is rational c) x is rational and y is an integer d) x is an integer and y is whole 11 Choose an answer to the problem 12 Choose an answer to the problem Which set of real numbers only contain whole numbers? Which set of real numbers only contain natural numbers? a) { 7/9, 1/4, 0, -4 } a) { 9, 4.22.., 0, -4 } b) { 3/9, 2, 0, -3 } b) { 3, 28, 4, 250 } c) { 18/9, 2, 1, 7 } c) { 7/9, 3, 0, 2 } d) { 5/9, 0, 10/2, 6 } d) { 8/2, 25/5, 0, 250/9 } © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 2 - Tier TWO Problems (harder problems) 13 Choose an answer to the problem What is 105/15 in decimal form? 14 Choose an answer to the problem What type of numbers are x and y? x = 105/15 y = 8/4 a) 7.150 b) 7.01 c) 7.0 d) 7.253 a) x is natural and y is rational b) x is irrational and y is rational c) x is whole and y is natural d) x is natural and y is natural 15 Choose an answer to the problem 16 Choose an answer to the problem This set only contains natural numbers { 20/10, 8/4, 0, -4 }. This set only contains integers a) True a) True b) False b) False { 18/9, 25/5, 0, -4 }. © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 2 - Tier TWO Problems (harder problems) 17 Choose an answer to the problem What type of number is 22/7? a) rational 18 Choose an answer to the problem What type of numbers are x and y? x = 7 y = 8/4 b) whole a) x is natural and y is irrational c) irrational b) x is irrational and y is rational d) integer c) x is whole and y is irrational d) x is natural and y is natural 19 Choose an answer to the problem What two numbers will √5 be between on a number line? a) 2.01 and 2.24 b) 2.3 and 3.25 c) 2.1 and 2.156 d) 1.9 and 2.0 20 Choose an answer to the problem Which two numbers will -105/15 be between on a number line? a) -6.5 and -5.52 b) -8.225 and -7.5 c) -7.9 and -6.9 d) -8 and -7.10 © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 2 - Tier TWO Problems (harder problems) 21 Choose an answer to the problem 22 Choose an answer to the problem Which two numbers will -8.25 be between on a number line? What type of numbers are x and y? x = -5 y = 2 a) -9.1 and -8.5 a) x is an integer and y is natural b) -7.56 and -8.0 b) x is irrational and y is rational c) -7.46 and -8.15 c) x is whole and y is natural d) -8.45 and -8.1 d) x is natural and y is natural 23 Choose an answer to the problem 24 Choose an answer to the problem What two numbers will √2 be between on a number line? What type of number is 1.2323232323232323? a) 1.42 and 1.56 a) integer, whole, natural b) 1.40 and 1.42 b) irrational, whole, real c) 1.30 and 1.40 c) rational, whole, integer d) 1.00 and 1.40 d) rational © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 2 - Tier TWO Problems ANSWER KEY 1. c13. c 2. d14. d 3. d15. b 4. b16. a 5. c17. c 6. a18. d 7. d19. a 8. b20. c 9. a21. d 10. c22. a 11. c23. b 12. b24. d © 2015 Mary Moore, MMoore Educational Resources. All rights reserved Set 3 - Tier THREE Problems 1 Choose an answer to the problem What is 0.252525.... in fraction form? 2 Choose an answer to the problem What type of numbers are x and y? x = -0.2525... y = 5.1834... a) 25/100 b) 25/10 c) 25/99 d) 25/9 a) x and y are irrational b) x is irrational and y is rational c) x is whole and y is natural d) x is rational and y is irrational 3 Choose an answer to the problem 4 Choose an answer to the problem Which set of real numbers only contain natural numbers? What type of number is 256.232323? a) { 7, 2, 0, -4 } a) integer b) { 8/2, -25/5, 4, 250 } b) irrational c) { 7/9, 3, 0, 2 } c) rational d) { 8/2, 25/5, 18, 250 } d) all of the above © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 3 - Tier THREE Problems 5 Choose an answer to the problem 6 Choose an answer to the problem What is 0.126126.... in fraction form? What type of numbers are x and y? x = -98.2525... y = 8952 a) 126/100 a) x and y are irrational b) 126/9 b) x is irrational and y is rational c) 126/999 c) x is whole and y is natural d) 126/99 d) x is rational and y is natural 7 Choose an answer to the problem Which set of real numbers only contain integers? 8 Choose an answer to the problem 256.232323 is irrational. a) True a) { 7, 2.55, 0, -4 } b) False b) { 8/2, 25/5, -4, 250 } c) { 7/9, 3, 0, 2 } d) { 8/2, 25/9, 0, 250 } © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 3 - Tier THREE Problems 9 Choose an answer to the problem What is 0.858585.... in fraction form? 10 Choose an answer to the problem 1256.353535 is rational. a) True a) 85/100 b) False b) 858/99 c) 85/9 d) 85/99 11 Choose an answer to the problem Which set of real numbers only contain natural numbers? 12 Choose an answer to the problem What type of number is -895? a) integer a) { 156, 28, 0, -47 } b) { 8/2, 250/50, 0, 250 } c) { 14, 2789, 4, 250 } b) irrational c) rational d) all of the above d) { 156, 28, 18.5, -47 } © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 3 - Tier THREE Problems 13 Choose an answer to the problem 14 Choose an answer to the problem What is 0.12461246.... in fraction form? What type of numbers are x and y? x= 0 y=2 a) 1246/10000 a) x and y are irrational b) 1246/9 b) x is irrational and y is rational c) 1246/9999 c) x is whole and y is irrational d) 1246/99 d) x and y are whole 15 Choose an answer to the problem 16 Choose an answer to the problem What type of number is 3? 125.23614598..... is irrational. a) whole, natural, irrational a) True b) natural, whole, integer b) False c) natural, whole, irrational d) whole and rational only © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 3 - Tier THREE Problems 17 Choose an answer to the problem 18 Choose an answer to the problem What type of number is π ? 187,256 is a natural number. a) rational, irrational a) True b) irrational, whole b) False c) irrational only d) irrational, natural 19 Choose an answer to the problem What type of number is -278956 ? 20 Choose an answer to the problem What type of number is 895? a) natural a) rational, irrational, integer b) irrational, whole c) rational, integer b) whole c) integer d) all of the above d) irrational, natural © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 3 - Tier THREE Problems 21 Choose an answer to the problem 22 Choose an answer to the problem What is 0.181818.... in fraction form? What type of numbers are x and y? x = 0 y = 1/2 a) 1818/10000 a) x and y are natural b) 18/9 b) x is natural and y is rational c) 18/999 c) x is whole and y is irrational d) 18/99 d) x is whole and y is rational 23 Choose an answer to the problem 24 Choose an answer to the problem What type of number is 397? 0 is irrational. a) natural, whole, integer a) True b) natural, whole, irrational b) False c) natural, whole, irrational d) whole and rational only © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Set 3 - Tier THREE Problems ANSWER KEY 1. c13. c 2. d14. d 3. d15. b 4. c16. a 5. c17. c 6. d18. a 7. b19. c 8. b20. d 9. d21. d 10. a22. d 11. c23. a 12. a24. b © 2015 Mary Moore, MMoore Educational Resources. All rights reserved Name:___________________________________________________ Date:______________________ Real Number System Assessment Answer each question. Circle the correct answer to the problem. 1) What is 0.25 in fraction form? a) 2/10 b) 25/10 c) 1/4 d) 2/4 3) Which set of real numbers only contain integers? a) { 2/10, 1/4, 0, -4 } b) { 2/9, 2, 0, -3 } c) { 8/9, 2, 1, -7 } d) { -2, 0, 15, 6 } 5) What is 2.333... in fraction form? a) 2 1/3 b) 2 2/3 c) 2/9 d) 2 6/9 7) What type of number is 2? a) whole number b) irrational number c) integer d) natural number 9) This set only contains natural numbers { 20/10, 8/4, 0, -4 }. a) True b) False 2) What type of numbers are x and y? x = -5 y = 15 a) x and y are irrational b) x is irrational and y is rational c) x is whole and y is natural d) x is an integer and y is natural 4) Which set of real numbers only contain natural numbers? a) { 7, 2, 0, -4 } b) { 8/2, 25/5, 4, 250 } c) { 7/9, 3, 0, 2 } d) { 8/2, 25/5, 0, 250 } 6) What is 1.333... in fraction form? a) 7/9 b) 3/9 c) 12/9 d) 3/9 8) What type of number is -5? a) whole number b) integer c) irrational number d) natural number 10) This set only contains integers { 18/9, 25/5, 0, -4 }. a) True b) False © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Name:___________________________________________________ Date:______________________ Real Number System Assessment Answer each question. Circle the correct answer to the problem. What two numbers will √5 be between 11) on a number line? a) 2.01 and 2.24 b) 2.0 and 3.25 c) 2.1 and 2.156 d) 1.9 and 2.0 Which two numbers will -8.25 be 13) between on a number line? a) -9.1 and -8.5 b) -7.56 and -8.1 c) -7.46 and -8.35 d) -8.45 and -8.1 15) What two numbers will √2 be between on a number line? a) 1.42 and 1.56 b) 1.40 and 1.42 c) 1.30 and 1.40 d) 1.00 and 1.40 1 is a whole number. 17) a) True b) False What is 5/9 in decimal form? 19) a) 5.5555... b) 0.9999.... c) 0.555.... d) 0.50505... 12) Which two numbers will -105/15 be between on a number line? a) -6.5 and -5.52 b) -8.225 and -7.5 c) -7.9 and -6.9 d) -8 and -7.10 14) What type of numbers are x and y? x = -5 y = 2 a) x is an integer and y is natural b) x is irrational and y is rational c) x is whole and y is natural d) x is natural and y is natural 16) What type of number is 1.2323232323232323? a) integer, whole, natural b) irrational, whole, real c) rational, whole, integer d) rational 18) -4 is what kind of number? a) natural, whole, integer, rational b) whole, integer, rational c) integer, irrational, whole d) integer and rational 20) Decimals are in the set of rational numbers. a) True b) False © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Real Number System Assessment ANSWER KEY 1) c 11) a 2) d 12) c 3) d 13) d 4) b 14) a 5) a 15) b 6) c 16) d 7) d 17) a 8) b 18) d 9) b 19) c 10) a 20) a © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources The formula for converting a decimal to a fraction W = 0.555555.... 10w = 5.555... - w = 0.555... 9w = 5 w = 5/9 W = 0.525252.... 100w = 52.5252... - w = 0.5252... 99w = 52 w = 52/99 If the decimal does not have a whole number then use this formula. Move the decimal one place to the right as in the example to the left and set it equal to 10w. (If you multiply .555... by 10 you’ll get 5.555....) Subtract 1w = .555 from 10w = 5.555... to get rid of everything after the decimal point. Now you end up with 9w = 5. Solve the one step equation for ‘w’. Your answer is 5/9 which is the fractional equivalent of 0.5555.... If the decimal has a repeating pattern. Move the decimal however many places to the right as in the example to the left and set it equal to however many ‘places’ you had to move it to get a whole number in front of the decimal. (If you multiply .5252... by 100 you’ll get 52.5252...) Subtract 1w = .5252... from 100w = 52.5252... to get rid of everything after the decimal point. Now you end up with 99w = 52. Solve the one step equation for ‘w’. Your answer is 52/99 which is the fractional equivalent of 0.525252.... © 2015 Mary Moore, MMoore Educational Resources. All rights reserved TpT Moore-Resources Thank you for taking time to download and purchase one of my teaching resources. “Real Number System Bundle” It means a lot to me to know there are other teachers and guardians using items I have created to educate our future generation. After you use this product. For more products my Teachers Pay Teachers store at: http://www.teacherspayteachers.com/Store/Moore-Resources Other products you may like.... 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