New Jersey: ASK6
Mathematics
Third Edition
by Jonathan D. Kantrowitz and Ralph R. Kantrowitz
Edited by Philip W. Sedelnik
Item Code
•
QXP 3007
•
Copyright © 2010
Queue, Inc • 80 Hathaway Drive • Stratford CT 06615
Phone 800 232 2224 • Fax 800 775 2729
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Table of Contents
Chapter One
Number and Numerical Operations ............................................1
Lesson 1: Number Sense ............................................................................1
Lesson 2: Money ........................................................................................10
Lesson 3: Magnitude of Numbers ..............................................................15
Benchmark Quiz #1 ....................................................................................20
Lesson 4: Ratios and Proportions ..............................................................21
Lesson 5: Percents ....................................................................................26
Lesson 6: Equivalent Whole Numbers, Fractions, and Decimals ..............30
Lesson 7: Primes, Factors, and Multiples ..................................................36
Lesson 8: Comparing and Ordering Numbers............................................43
Benchmark Quiz #2 ....................................................................................49
Lesson 9: Operations ................................................................................51
Lesson 10: Methods of Computation..........................................................56
Benchmark Quiz #3 ....................................................................................67
Lesson 11: Division ....................................................................................69
Lesson 12: Selecting Computational Methods ..........................................78
Lesson 13: Squares and Cubes ................................................................81
Lesson 14: Reasonableness of Computations ..........................................84
Lesson 15: Relationships and Properties of Operations ............................87
Lesson 16: Order of Operations ................................................................90
Lesson 17: Estimation Strategies ..............................................................94
Lesson 18: Appropriateness of Estimations ..............................................98
Lesson 19: Accuracy of Estimates ..........................................................100
Benchmark Quiz #4 ..................................................................................103
Chapter Two
Geometry and Measurement ..................................................106
Lesson 20: Lines and Angles ..................................................................106
Lesson 21: Polygons and Circles ............................................................112
Lesson 22: Similar Figures ......................................................................122
Lesson 23: Congruent Figures ................................................................126
Lesson 24: Three-Dimensional Shapes ..................................................131
Lesson 25: Projections ............................................................................136
Lesson 26: Nets........................................................................................142
Benchmark Quiz #5 ..................................................................................148
Lesson 27: Transformations ....................................................................154
Lesson 28: Geometry in Everyday Life ....................................................160
Lesson 29: Coordinate Grids....................................................................166
Lesson 30: Units of Measure....................................................................172
Lesson 31: Scales and Proportions..........................................................176
Benchmark Quiz #6 ..................................................................................180
Lesson 32: Conversion Units....................................................................182
Lesson 33: Equivalent Measures ............................................................186
Benchmark Quiz #7 ..................................................................................190
Lesson 34: Measuring Angles ..................................................................191
Lesson 35: Perimeter and Area................................................................195
Lesson 36: Surface Area and Volume ......................................................203
Lesson 37: Area and Perimeter Relationships ........................................211
Lesson 38: Approximating Measures ......................................................215
Benchmark Quiz #8 ..................................................................................218
Chapter Three
Patterns and Algebra ..............................................................220
Lesson 39: Number Patterns....................................................................220
Lesson 40: Graphs of Functions ..............................................................230
Lesson 41: Modeling ................................................................................238
Lesson 42: Graphing Information ............................................................243
Benchmark Quiz #9 ..................................................................................248
Lesson 43: Solving Equations ..................................................................252
Lesson 44: Properties of Operations........................................................256
Lesson 45: Evaluating ..............................................................................260
Lesson 46: Inequalities ............................................................................263
Benchmark Quiz #10 ................................................................................266
Chapter Four
Data Analysis, Probability, and Discrete Mathematics ............268
Lesson 47: Collecting and Displaying Data..............................................268
Lesson 48: Data Analysis ........................................................................283
Lesson 49: Probability ..............................................................................290
Lesson 50: Determining Probabilities ......................................................295
Lesson 51: Compound Events ................................................................299
Benchmark Quiz #11 ................................................................................303
Lesson 52: Concepts of Probability..........................................................306
Lesson 53: Multiple Outcomes ................................................................309
Lesson 54: Combinations and Permutations............................................317
Benchmark Quiz #12 ................................................................................325
Lesson 55: Strategies and Directions ......................................................328
Lesson 56: Vertex-Edge Graphs ..............................................................331
Lesson 33
4.2.6.D.4 Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile).
Equivalent Measures
Remember what you have learned about estimating the values of
numbers. Estimating is very important when converting between metric
and customary units. Although it is relatively simple to convert kilometers
to meters, you need to understand how to convert kilometers to miles as
well. The list below shows some basic conversions between the two
different systems of measurements. The ≈ sign means “approximately
equal to.” All of these relationships are estimates, not exact calculations.
1
1
1
1
km ≈ 0.6 mile
inch ≈ 2.5 centimeters
foot ≈ 30 cm
meter ≈ 3.25 feet
Example 1:
Laquisha ran a 10 km race to raise money for a charity. About how many
miles are in 10 km?
Step 1: Find the approximate conversion factor.
1 km ≈ 0.6 mile
Step 2: Use the conversion factor to set up a proportion.
1/10 = .6/?
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Step 3: Solve the proportion.
Since 1 x 10 = 10, the second ratio is greater than the first by a factor of
10. So, multiply the denominator by 10 to find the missing value.
0.6 x 10 = 6
Laquisha ran about 6 miles in her race.
Example 2:
Rowena is 5.5 feet tall. About how many centimeters is that?
Step 1: Find the approximate conversion factor.
1 foot ≈ 30 cm
Step 2: Use the conversion factor to set up a proportion.
1/30 = 5.5/?
Step 3: Solve the proportion.
Since 1 x 5.5 = 5.5, the second ratio is greater than the first by a factor of
5.5. So, multiply the denominator by 5.5 to find the missing value.
30 x 5.5 = 165
Rowena is about 165 cm tall.
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Example 3:
Ned found a worm in his back yard that was 7.5 cm long. About how many
inches long is the worm?
Step 1: Find the approximate conversion factor.
1 inch ≈ 2.5 cm
For this problem, since we start with centimeters, it is best to reverse this
approximation.
2.5 cm ≈ 1 inch
Step 2: Use the conversion factor to set up a proportion.
2.5 = 7.5
1
x
Step 3: Solve the proportion.
Cross-multiply to find the ratio.
2.5x = 1 x 7.5
2.5x = 7.5
x=3
x = 3, so the worm must be 3 inches long.
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Practice
Solve the following:
1.
1.2 miles ≈ _____ kilometers
2.
5 centimeters ≈ _____ inches
3.
60 centimeters ≈ _____ feet
4.
6.5 feet ≈ _____ meters
5.
8 meters ≈ _____ feet
6.
8 inches ≈ _____ centimeters
7.
8 feet ≈ _____ centimeters
8.
8 kilometers ≈ _____ miles
9.
1 yard ≈ _____ centimeters ≈ _____ meters
10. A sign in France said the speed limit was 100 km/hour. That is the same as
A.
B.
C.
D.
160 m.p.h.
100 m.p.h.
66 m.p.h.
60 m.p.h.
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Benchmark Quiz #7
1.
60 inches = _________ ft
2.
2 yards = _________ in
3.
10 pounds = _________ ounces
4.
2,000 centimeters = _________ meters
5.
4 gallons = ________ quarts
6.
10 inches equal about _____
centimeters.
a.
b.
c.
d.
7.
3.5
2.5
35
25
2 kilometers equal about _______
miles.
a.
c.
c.
d.
8.
a.
b.
c.
d.
9.
.6
6
1.2
12
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1 kilogram equals about _______
pounds.
1 gallon equals about ________
liters.
a.
b.
c.
d.
190
.22
2.2
.45
4.5
4
1
.4
.1
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