Core Connections, Course 2 Checkpoint Materials
[Pages:22]Core Connections, Course 2 Checkpoint Materials
Notes to Students (and their Teachers)
Students master different skills at different speeds. No two students learn exactly the same way at the same time. At some point you will be expected to perform certain skills accurately. Most of the Checkpoint problems incorporate skills that you should have been developing in grades 5 and 6. If you have not mastered these skills yet it does not mean that you will not be successful in this class. However, you may need to do some work outside of class to get caught up on them.
Starting in Chapter 1 and finishing in Chapter 9, there are 9 problems designed as Checkpoint problems. Each one is marked with an icon like the one above and numbered according to the chapter that it is in. After you do each of the Checkpoint problems, check your answers by referring to this section. If your answers are incorrect, you may need some extra practice to develop that skill. The practice sets are keyed to each of the Checkpoint problems in the textbook. Each has the topic clearly labeled, followed by the answers to the corresponding Checkpoint problem and then some completed examples. Next, the complete solution to the Checkpoint problem from the text is given, and there are more problems for you to practice with answers included.
Remember, looking is not the same as doing! You will never become good at any sport by just watching it, and in the same way, reading through the worked examples and understanding the steps is not the same as being able to do the problems yourself. How many of the extra practice problems do you need to try? That is really up to you. Remember that your goal is to be able to do similar problems on your own confidently and accurately. This is your responsibility. You should not expect your teacher to spend time in class going over the solutions to the Checkpoint problem sets. If you are not confident after reading the examples and trying the problems, you should get help outside of class time or talk to your teacher about working with a tutor.
Checkpoint Topics
1. Area and Perimeter of Polygons 2. Multiple Representations of Portions 3. Multiplying Fractions and Decimals 5 Order of Operations 6. Writing and Evaluating Algebraic Expressions 7A. Simplifying Expressions 7B. Displays of Data: Histograms and Box Plots 8. Solving Multi-Step Equations 9. Unit Rates and Proportions
Checkpoints
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1
Checkpoint 1
Problem 1-141
Area and Perimeter of Polygons
Answers to problem 1-141: a. 96 cm2, 40 cm; b. 22 in.2, 25.05 in.; c. 144 cm2, 52 cm; d. 696.67 m2, 114.67 m
Area is the number of square units in a flat region. The formulas to calculate the area of several kinds of polygons are:
RECTANGLE
PARALLELOGRAM
TRAPEZOID
TRIANGLE
h
b
A = bh
h
b
A = bh
b1 h
h
h
b2
A
=
1 2
( b1
+
b2
)
h
b
b
A
=
1 2
bh
Perimeter is the distance around a figure on a flat surface. To calculate the perimeter of a polygon, add together the length of each side.
Example 1: Compute the area and perimeter.
6 feet
5 feet
4 feet 5 feet
6 feet
parallelogram A = bh = 6 ! 4 = 24!feet2 P = 6 + 6 + 5 + 5 = 22!feet
Example 2: Compute the area and perimeter.
7 cm
9 cm 8 cm
6 cm
triangle
A
=
1 2
bh
=
1 2
!6!7
=
21!cm2
P = 6 + 8 + 9 = 23!cm
Now we can go back and solve the original problem.
a. Rectangle: A = bh = 12 ! 8 = 96!cm2 ; P = 8 + 8 + 12 + 12 = 40!cm
b.
Triangle:
A
=
1 2
bh
=
1 2
!11! 4
=
22!in.2 ;
P = 11+ 9.05 + 5 = 25.05!in.
c. Parallelogram: A = bh = 16 ! 9 = 144!cm2 ; P = 16 + 16 + 10 + 10 = 52!cm
d.
Trapezoid:
A P
= =
1221( b+1
2+5b+2
)h
24
= +
1 2
(
25
44.67
+ 44.67 )!10
= 114.67!m
=
696.67
!
m2
;
2
? 2013 CPM Educational Program. All rights reserved.
Core Connections, Course 2
Here are some more to try. Find the area and perimeter of each figure.
9 cm
1.
11 cm
2.
10 in.
12 in. 6 in.
7.2 in.
3. Trapezoid
35 feet
12.7 feet
12.5 feet
20 feet feetfeet
5. Parallelogram
17.8 feet
4. Parallelogram
10.8 cm
10 cm 10.8 cm 16 cm
6.
5 in. 4 in.
12 in.
9 feet 9 feet
4 feet
5 feet
7. Trapezoid
15 cm
8.1 cm
8 cm
9.3 cm
9.9 in.
8.
6.3 m 10 m
6 m
9 cm
6 m
42 feet
9. Parallelogram
18 in.
16 in. 18 in.
29 in.
10.
27 feet
24.5 feet
39.2 feet
Checkpoints
? 2013 CPM Educational Program. All rights reserved.
3
11.
12. Trapezoid
21 in.
2 feet
20 in.
13 in.
32.7 in.
13. Trapezoid
18 feet
19.8 feet
16 feet
14.
16.2 feet
24 in. 5.1 in. 5 in. 3 in. 3.2 in.
32 feet
15. Parallelogram
10 cm
9 cm 10 cm
10 cm
Answers:
1. 99 cm2, 40 cm
3. 343.75 feet2, 85.5 feet
5. 36 feet2, 28 feet
7. 96 cm2, 41.4 cm
9. 464 in.2, 94 in.
11.
14 4
=
3
1 2
feet2
,
30 4
=
7
1 2
feet
13. 400 feet2, 86 feet
15. 90 cm2, 40 cm
16. Trapezoid
2.7 m
0.8 m
0.5 m
4.4 m
1.2 m
2. 36 in.2, 29.2 in. 4. 160 cm2, 53.6 cm 6. 24 in.2, 26.9 in. 8. 18 m2, 22.3 m 10. 514.5 feet2, 108.2 feet 12. 457 in.2, 90.7 in. 14. 7.65 in.2, 13.3 in. 16. 1.78 m2, 9.1 m
4
? 2013 CPM Educational Program. All rights reserved.
Core Connections, Course 2
Checkpoint 2
Problem 2-120
Multiple Representations of Portions
Answers to problem 2-120:
a. 43%,
43 100
,
b.
9 10
,
0.9,
90%
,
c.
39 100
,
0.39
,
d. 64%, 0.64
Portions of a whole may be represented in various ways as represented by this web. Percent means "per hundred" and the place value of a decimal will determine its name. Change a fraction in an equivalent fraction with 100 parts to name it as a percent.
fraction
words or
pictures
decimal
percent
Representations of a Portion
Example 1: Name the given portion as a fraction and as a percent. 0.3
Solution:
The
digit
3
is
in
the
tenths
place
so
0.3
=
three
tenths
=
3 10
.
On a diagram or a hundreds grid, 3 parts out of 10 is equivalent to 30 parts out of 100
so
3 10
=
30 100
=
30% .
Example 2: Name the given portion as a fraction and as a decimal. 35%
Solution:
35% =
35 100
=
thirty-five hundredths = 0.35 ;
35 100
=
7 20
Now we can go back and solve the original problem.
a.
0.43 is forty-three hundredths or
43 100
= 43%
b.
nine tenths is
9 10
=
9 10
!
10 10
=
90 100
=
90% ;
9 10
=
0.9
c.
39%
=
39 100
= ! thirty-nine
hundredths
=
0.39
d.
16 25
=
16 25
!
4 4
=
64 100
=
0.64
=
64%
Checkpoints
? 2013 CPM Educational Program. All rights reserved.
5
Here are some more to try. For each portion of a whole, write it as a percent, fraction, and a decimal.
1. 6%
2. 0.35
3.
1 4
5. 0.16
4.
2 5
6. 87%
7.
13 25
9.
7 50
11. 65%
8. 21% 10. 0.050 12. 3.7%
13.
7 10
15.
19 20
17. 0.23
14. 0.66 16. 20% 18. 1.0
19. 135%
20.
77 100
Answers:
1.
6 100
=
3 50
,
0.06
3. 25%, 0.25
5.
16%,
16 100
=
4 25
7. 52%, 0.52
9. 14%, 0.14
11.
13 20
,
0.65
13. 70%, 0.7
15. 95%, 0.95
17.
23%,
23 100
19.
135 100
=
1
35 100
=1
7 20
, 1.35
2.
35%,
35 100
=
7 20
4. 40%, 0.4
6.
87 100
,
0.87
8.
21 100
,
0.21
10.
5%,
5 100
=
1 20
12.
37 1000
,
0.037
14.
66%,
66 100
=
33 50
16.
20 100
=
1 5
,
0.2
18.
100%,
100 100
=
1 1
20. 77%, 0.77
6
? 2013 CPM Educational Program. All rights reserved.
Core Connections, Course 2
Checkpoint 3
Problem 3-110
Multiplying Fractions and Decimals
Answers to problem 3-110:
a.
9 20
,
b.
1 5
,
c.
4
2 9
,
d.
7
1 5
,
e. 12.308,
f. 0.000208
To multiply fractions, multiply the numerators and then multiply the denominators. To multiply mixed numbers, change each mixed number to a fraction greater than one before multiplying. In both cases, simplify by looking for factors than make "one."
To multiply decimals, multiply as with whole numbers. In the product, the number of decimal places is equal to the total number of decimal places in the multiplied numbers. Sometimes zeros need to be added to place the decimal point.
Example 1: Multiply
3 8
!
4 5
Solution:
3 8
!
4 5
"
3!4 8!5
"
3! 4 2! 4 !5
"
3 10
Example 2:
Multiply
3
1 3
!
2
1 2
Solution:
3
1 3
!
2
1 2
"
10 3
!
5 2
"
10!5 3!2
"
5! 2 !5 3! 2
"
25 3
or
8
1 3
Note that we are simplifying using Giant Ones but no longer drawing the Giant One.
Example 3: Multiply 12.5 ! 0.36
Solution:
(one decimal place)
(two decimal places)
(three decimal places)
Now we can go back and solve the original problem.
a.
2 3
!
2 5
"
2!2 3!5
"
4 15
c.
2
1 3
!
2
1 2
"
7 3
!
5 2
"
7!5 3!2
"
35 6
or
5
5 6
e.
b.
7 10
!
2 7
"
7!2 5! 2 ! 7
"
1 5
d.
1
1 3
!2
1 6
"
4 3
!
13 6
"
2! 2 !13 3! 2 !3
"
26 9
or
2
8 9
f.
Checkpoints
? 2013 CPM Educational Program. All rights reserved.
7
Here are some more to try. Multiply the fractions and decimals below.
1. 0.08 ! 4.7
2. 0.21! 3.42
3.
4 7
!
1 2
4.
5 6
!
3 8
5.
8 9
!
3 4
7. 3.07 ! 5.4
6.
7 10
!
3 4
8. 6.57 ! 2.8
9.
5 6
!
3 20
10. 2.9 ! 0.056
11.
6 7
!
4 9
12.
3
1 7
!1
2 5
13.
2 3
!
5 9
14.
3 5
!
9 13
15. 2.34 ! 2.7
16.
2
1 3
!4
4 5
17.
4
3 5
!
1 2
19. 0.235 ! 0.43
18.
3 8
!
5 9
20. 421! 0.00005
Answers: 1. 0.376
3.
2 7
5.
2 3
7. 16.578
9.
1 8
11.
8 21
13.
10 27
15. 6.318
17.
2
3 10
19. 0.10105
2. 0.7182
4.
5 16
6.
21 40
8. 18.396
10. 0.1624
12.
4
2 5
14.
27 65
16.
11
1 5
18.
5 24
20. 0.02105
8
? 2013 CPM Educational Program. All rights reserved.
Core Connections, Course 2
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