Unit2:RationalsandIrrationals
StudentTrackingSheet
Math9Principles
Name:_________________________
Block:____
What I can do for this unit:
2-1
2-2
After
Practice
After
Review
How I
Did
I can convert rational numbers among their two main forms, fractions
and decimals (terminating or repeating).
I can convert between percent, fraction, and decimal form for rational
numbers.
2-3
I can identify a real number as rational or irrational and, if rational,
write it as a reduced fraction or integer.
2-4
I can prime factor natural numbers, determine whether they are
perfect squares, and if they are evaluate their square root.
2-5
I can evaluate areas and circumferences of circles using radius,
diameter, and π.
Value
Description
Not Yet Meeting Expectations
I just don’t get it.
Minimally Meeting Expectations
Barely got it, I need some prompting to help solve the question.
Meeting Expectations
Got it, I understand the concept without help or prompting.
Exceeding Expectations
Wow, nailed it! I can use this concept to solve problems I may
have not seen in practice. I also get little details that may not
be directly related to this target correct.
Unit 2: Rationals and Irrationals Day 1
Math 9 Principles
2-1: I can convert rational numbers among their two main forms, fractions and decimals
(terminating or repeating).
Find the value of 𝑥 in each pair of equivalent fractions.
1)
3
𝑥
= 63
7
2)
2
3
=
16
𝑥
=
3)
5
6
𝑥
= 48
4)
3
8
=
33
5)
Reduce to lowest terms.
6)
10)
14)
12
18
=
27
7)
=
12
11)
18
15)
=
48
6
4
=
32
8)
=
12)
=
52
16)
14
32
27
=
9)
=
13)
=
42
17)
45
15
10
28
18
24
36
15
51
68
=
=
=
Write the decimal equivalent of each.
18)
22)
26)
30)
1
=
2
19)
3
=
4
23)
4
=
5
27)
7
31)
8
=
1
3
1
5
1
8
=
20)
=
24)
=
28)
32)
2
3
2
5
3
8
=
21)
=
25)
=
29)
33)
1
4
3
5
5
8
=
=
=
𝑥
Write the fractional equivalent of each.
34) 0.3 =
35) 0.45 =
36) 0.225 =
37) 0.5 =
̅̅̅ =
38) 0. ̅12
39) 0. ̅̅̅̅̅
125 =
40) 0. 6̅ =
̅̅̅̅ =
41) 2. 06
42) 0.̅̅̅̅̅̅
081 =
43) 0.7 =
44) 0.55 =
45) 0.075 =
46) 0. 8̅ =
̅̅̅̅ =
47) 0. 27
̅̅̅̅̅ =
48) 0. 018
49) 0.2 =
50) 0.28 =
51) 0.8 =
52) 0.65 =
53) 0.54 =
54) 0.72 =
55) 0.48 =
56) 0.125 =
57) 0.625 =
58) 0.12 =
59) 0.055 =
60) 0.875 =
61) 0.325 =
62) 0. 3̅ =
63) 0. 5̅ =
̅̅̅ =
64) 0. ̅09
̅̅̅ =
65) 0. ̅63
̅̅̅ =
66) 0. ̅60
67) 1.2 =
68) 2.8 =
69) 1.375 =
70) 3.25 =
71) 2.875 =
72) 0. ̅̅̅̅̅
036 =
̅̅̅̅̅ =
73) 0. 108
̅̅̅ =
74) 2. ̅09
75) 0.̅̅̅̅̅
54 =
Unit2:RationalsandIrrationalsDay2
Math9Principles
2-2: I can convert between percent, fraction, and decimal form for rational numbers.
Write the following percentages as fractions in lowest terms.
1) 25% =
2) 85% =
3) 66. 6% =
4) 33% =
5) 33. 3% =
6) 12.5% =
7) 80%
8) 37.5% =
9) 40% =
10) 50% =
11) 55. 5% =
12) 87.5% =
13) 75% =
14) 62.5% =
15) 60% =
Write the following decimals as fractions in lowest terms.
16) 0.6 =
17) 0.625 =
18) 0.75 =
19) 1. 3 =
20) 0. 8 =
21) 0.375 =
22) 0.25
23) 0.875 =
24) 3.4 =
25) 2.75 =
26) 5.6 =
27) 5. 6 =
28) 0. 207 =
29) 0. 03 =
30) 1. 45 =
Fill in the missing portions of the chart with equivalent answers. All fractions must be in lowest
terms. Use improper fractions if appropriate.
#
Percent
Decimal
Fraction
31)
7
9
32)
3
5
33)
2
7
8
4
3
5
2
1
4
34)
0.625
35)
0. 3
36)
0. 27
37)
1
33 %
3
38)
575%
39)
1
11 %
9
40)
1
37 %
2
41)
1. 6
42)
0.875
43)
44)
45)
155. 5%
Unit2:RationalsandIrrationalsDay3
Math9Principles
2-3: I can identify a real number as rational or irrational and, if rational, write it as a reduced
fraction or integer.
If the number is rational, write it as an integer or fraction in lowest terms. Otherwise write
irrational.
1)
√20
2)
0. 2
3)
0. 4
4)
√160
5)
√576
6)
0. 06
7)
80%
8)
37.5%
9)
40%
10) 0. 12
11) 0.2121121112 …
12) 0.06
13) √0.25
16)
5
14)
7
15)
17)
4
18)
3 ∙8
19) √0.64
20) 0. 45
21) √291
22) √441
23) √0.0324
24)
25) √0.4
26) √0.04
27) √0.001
28) 0. 63
29)
30)
0. 1
12
Unit2:RationalsandIrrationalsDay4
Math9Principles
2-4: I can prime factor natural numbers, determine whether they are perfect squares, and if
they are evaluate their square root.
Test to see if each number below is divisible by any of 2, 3, 4, 5, 6, 9, or 10.
Specify which ones are factors for each number.
1)
2025
2)
120
3)
1215
4)
432
5)
2736
6)
9600
7)
51285
8)
3574
9)
95232
Prime factor each number and determine whether it is a perfect square. If it is, state the square
root. No Calculators!
10) 2304
11) 1152
12) 1764
13) 3328
14) 8400
15) 32 400
16) 5292
17) 360 000
18) 676
19) 4332
20) 900
21) 84100
Unit 2: Rationals and Irrationals Day 5
Math 9 Principles
2-5: I can evaluate areas and circumferences of circles using radius, diameter, and π.
Complete each row of this char for circles without using a calculator.
No decimals, fractions only.
#
Radius
1)
5
2)
2
5
Diameter
3)
14
4)
0.6
5)
1
4
Circumference
6)
18𝜋
7)
2𝜋
3
Area
8)
16𝜋
9)
36𝜋
10)
9𝜋
16
9𝜋
2
11)
12)
5
4
13) What is the area of a pizza with a diameter of 12 inches?
14) What is the area of a circle with a circumference of 50𝜋?
15) A Ferris wheel has a radius of 60 feet. What is its circumference?
16) What is the diameter and circumference of a plate that has an area of 64𝜋?
17) The spray from a spinning lawn sprinkler makes a circle with a 32’ radius. What is the
circumference and area of the circle?
1
18) What is the area of a CD with a radius of 2 4 "?
19) Gears on a bicycle are just circles in shape. One gear has a diameter of 6”, and a
smaller one has a diameter of 3”. How much bigger is the circumference of the larger
one compared to the smaller one?
Unit 2: Rationals and Irrationals Key
Math 9 Principles
2-1:
1) 27
3
13) 8
2) 24
3) 40
8
2
14) 13 15) 3
25)0.8 26)0.125
125
2
27
18
6
37)33
11
8
65)
3
3
7) 5
9
8) 4
9) 4
10)
16
7
51
28)0.625
3
7
29)0.875
11
3
8
3
11
7
4
4
23
38) 37 39) 10 40) 20 41) 40 42) 9
12
14
5
64)
3
6)2
16) 68 17)0.5 18)0. 3̅ 19)0. 6̅ 20)0.25 21)0.75
1
49) 50 50) 25 51) 25 52) 8
63) 5
2
5) 3
27)0.375
68
35) 999 36) 3
4) 88
66)
13
4
5
53)8
67)
54) 25 55) 200 56) 8
23
8
3
11) 2
12)
12
5
22)0.2 23)0.4 24)0.6
3
9
2
1
9
1
7
4
1
7
30) 10 31) 20 32) 40 33) 2
3
43) 11 44) 111 45) 5
13
1
5
57) 40 58) 3
59) 9
46) 25 47) 5
1
4
3
13)
4
11
25) 4
17
2
2) 20
5
8
28
26) 5
33
3) 3
14)
3
5
17
3
15)
27)
5
3
5
23
28) 111
16)
1
35) 33. 3̅, 3
34) 62.5%, 8
2
3
41)166. 6̅%, 1 𝑜𝑟
1
6
68) 111 69) 37 70) 11 71) 11
1
4) 100 5) 3
5
3
4
6) 8
5
8
17)
3
4
16
30) 11
18)
1
29) 33
3
7) 5
19)
2
8) 8
4
3
20)
1
9) 5
8
9
5
10) 2
3
8
21)
22)
11) 9
1
4
23)
31) 77. 7̅%, 0. 7̅ 32)60%, 0.6
7
8
7
12) 8
24)
17
5
33) 287.5%, 2.875
̅̅̅%, 3 37) 0. 3̅, 1 38) 5.75, 5 3 𝑜𝑟 23 39)0. 1̅, 1 40)0.375, 3
36) 27. ̅27
11
3
4
4
9
8
42)87.5%,
7
8
5
9
43)460%, 4.6 44)225%, 2.25 45)1. 5̅, 1 𝑜𝑟
14
9
2-3:
2
9
3)
2
3
1) irrational
2)
11) irrational
12) 50 13) 2
22) 21
23) 50 24) irrational
3
4) irrational
1
8
14) 3
9
5) 24
8
15) 5
9
16) 4
25) irrational
6)
2
33
17)
11
5
1
26) 5
7)
4
5
8)
18) 5
3
8
9)
4
19) 5
27) irrational
2
5
10)
4
33
5
20) 11 21) irrational
7
1
28) 11 29) 3
7
30) 2
2-4:
1) 3,5,9
2) 2,3,4,5,6,10 3) 3,5,9
4) 2,3,4,6,9
5) 2,3,4,6,9
6) 2,3,4,5,6,10 7) 3,5
8) 2
9)2,3,4,6
10)48 11)not a p.c
12) 42 13) not a p.c 14)not a p.c
15) 180
16)not a p.c
17) 600
18) 26 19) not a p.c 20) 30 21) 290
2-5:
1) 10, 10𝜋, 25𝜋
1 2 𝜋
4 4
4𝜋
2) 5 , 5 𝜋, 25
3
3) 7, 14𝜋, 49𝜋 4) 10 ,
3 3 3𝜋
2
7) 3 , 3 , 9
8)4, 8, 8𝜋
9) 6, 12, 12𝜋
10) 4 , 2 ,
14) 625𝜋
15) 120𝜋
16) 𝑑 = 16, 𝐶 = 16𝜋
3𝜋 9𝜋
,
5 100
1 𝜋 𝜋
5) 8 , 4 , 64
9 9 81𝜋
16
11) 4 , 2 ,
19)𝐶1 = 6𝜋, 𝐶2 = 3𝜋. The larger gear is 2 times bigger than the smaller gear
6)9, 18, 81𝜋
5 5𝜋 25𝜋
,
4 64
12) 8 ,
17) 𝐶 = 64𝜋, 𝐴 = 1024𝜋
13
48) 20
20
60) 11 61) 11 62) 33
2-2:
1)
4
34) 33
18) 𝐴 =
13) 36𝜋
81𝜋
16