Download Real Numbers

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
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