1. No category

Name———————————————————————— Lesson
2.1
Date —————————————
Practice A
For use with the lesson “Use Inductive Reasoning”
Sketch the next figure in the pattern.
1.
3.
2.
4.
5.
Lesson 2.1
6.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
7.
The first four objects in a pattern are shown. How many squares are there
in the next object?
8.
9.
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Name———————————————————————— Date —————————————
Practice A continued
Lesson
2.1
For use with the lesson “Use Inductive Reasoning”
Describe a pattern in the numbers. Write the next number in the pattern.
10. 5, 10, 15, 20, . . .
11. 26, 23, 20, 17, 14, . . .
12. 2, 6, 18, 54, . . .
13. 32, 16, 8, 4, . . .
14. 212, 28, 24, 0, . . .
15. 3, 29, 27, 281, . . .
Complete the conjecture based on the pattern you observe in the
specific cases.
16. Use the following products of odd integers to complete the conjecture about the
Conjecture The product of any two odd integers is    ?   .
17. Complete the following table. Then complete the conjecture that follows.
Pair of odd numbers
1, 3
Sum of the numbers
divided by 2
3, 5
113
2
7, 9
9, 11
315
}
​     
​ 
Average of numbers
5, 7
​ }
   
​ 
2
2
Conjecture The average of any two consecutive odd whole numbers is    ?   .
Show the conjecture is false by finding a counterexample.
18. The average of any two consecutive even numbers is an even number.
19. Any four-sided polygon is a square.
20. The square of any integer is a positive integer.
21. Evaporation You are performing an experiment to explore the effects of surface area on evaporation. Each day you record the
depth (in millimeters) of the water in the bowl pictured. The table
below shows your results.
Day
Water level (mm)
0
1
2
3
4
5
180
169
158
147
136
125
a. Predict the height of the water surface in the bowl on day 6.
b. Based on these results, make a conjecture about how the surface area of a body
of water affects the rate of change of its depth by evaporation.
2-8
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Lesson 2.1
product of any two odd numbers: 1 3 3 5 3, 1 3 5 5 5, 3 3 3 5 9, 3 3 5 5 15,
5 3 1 5 5, 5 3 5 5 25, 5 3 7 5 35, 7 3 1 5 7, 7 3 3 5 21, 7 3 7 5 49
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Answers for Chapter 2
Lesson 2.1 Use Inductive
Reasoning
Teaching Guide
front and a 0 between the 8 and 1; 99,980,001;
9,999,800,001
2. 111,105; 222,210; 333,315; Pattern: the first
three numbers are a multiple of 111 and the last
three numbers are a multiple of 105. Increase both
by one multiple each time; 444,420; 555,525
3. 9; 1089, 110,889; (Pattern: a 1 is placed at the
beginning of the number and an extra 8 is placed
in front of the 9); 11,108,889; 1,111,088,889
21. a. 114 mm b. conjecture: The rate of change
of depth of a body of water is not affected by the
surface area.
Practice Level B
1.
2.
113
224
100
200
0
2.
3
3.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
5.
300
557
400
9
6
13
500
18
600
24
9 12 15 18 21 24 27 30
1
3
6.
8. 9 9. 15
7.
446
7. add 2 to the numerator and 1 to the
9
denominator; }
​ 7 ​
0.0
4.
335
6. add consecutive integers to each term, starting
with 2; 24
4 6
Practice Level A
1.
4.
5. add 111 to each term; 557
Technology Activity
1. about 25.68
3.
answers
1. 81; 9801; 998,001; Pattern: place a 9 in
Reasoning and Proof
0.2
3
4
0.4
0.6
5
5
0.8
7
6
1.0
9
7
1.2
1.4
8. subtract 1 from the numerator and 1 from the
3
denominator; ​ }4 ​
0.70
3
4
4
5
5
6
0.75
0.80
6 7
7 8
0.85
0.90
0.95
9. subtract 3 from each term; 29
10. add 5 to previous term; 25 11. subtract 3
from previous term; 11 12. multiply previous
term by 3; 162 13. divide previous term by 2; 2
14. add 4 to previous term; 4 15. multiply
previous term by 23; 243 16. an odd integer
17.
3, 5
5, 7
7, 9
9, 11
315
517
719
9 1 11
4
6
8
10
​ }
   
​  }
​  2   
​  }
​  2   
 
​ }
​  2   
​ 
2
29
26
210 28
26
0
23
24
22
3
0
2
4
10. square numbers; 25
1
0
4
3
9
6
16
25
9 12 15 18 21 24 27 30
11. double the number and add 1; 47
2 5
0
11
23
47
5 10 15 20 25 30 35 40 45 50
12. prime numbers; 13
1
2 3
5
7
3
5
7
9
11
13
11
13
15
the even number between the consecutive odd
numbers.
2
13. 16 14. 20 15. Sample answer: ​ } ​5 0.5
4
214
18. Sample answer: ​ }
   
​ 5 3, 3 is not even.
2
16. Sample answer: 5 2 7 5 22
19. Sample answer:
is not a square.
20. Sample answer: 02 is not a positive integer.
22
17. Sample answer: ​ }
   ​ 
52
22 1 1
Î
}
1
1 1 1
18. Sample answer: ​ ​ } ​ ​ 5 }
​ 2 ​, }
​ 2 ​> }
​ 4 ​
4
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