Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 9:
Homework

Problem H1

The number line shown below has seven points labeled with numbers or letters. The line is not drawn to scale.

Name the lettered point or points that could possibly represent the following:

 a. c • d b. d c c. c - d d. c + d

Problem H2

Given three rational numbers, a, b, and c, you know that:

a > 1
0 < b < 1
0 < c < 2

Fill in the blanks with the symbols <, =, >, or ? so that each sentence will be true. Use ? to indicate that you do not have enough information to ascertain the relationship.

a.

 a • b ? = > < a

b.

 b • c ? = > < b

c.

 a • b • c ? = > < b

d.

 a b ? = > < a

e.

 a c ? = > < a

f.

 b c ? = > < b

g.

 b b ? = > < b

h.

 b2 ? = > < b

 <

See solutions for
an explanation of

 ?

 ?

 >

 ?

 ?

 >

 <

 Problem H3 A clearance sale offers an additional 50% off items that are already reduced by 20%. Explain why this is not the same as 70% off the original price.

 Pick a specific dollar amount that is easy to calculate; for example, \$100.   Close Tip Pick a specific dollar amount that is easy to calculate; for example, \$100.

 Fibonacci Bracelets You can make "bracelets" using Fibonacci-like sequences of numbers. Here's how: Choose any pair of one-digit numbers. Make a Fibonacci-like sequence by recording only the units digit of the sum of these numbers and subsequent number pairs. For example, the sequence starting (1,3) makes the following pattern: 1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2, 1, 3, . . . Eventually the sequence repeats (in the example above, after the number 2). At this point, attach the last digit in the sequence to the first digit, thus making a bracelet of digits. <--- 1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, 2, ---> Note that sequences starting with any clockwise consecutive pair of numbers in the circle will make the same bracelet. Thus (3,4), (7,1), (1,8), etc. will result in the same bracelet. You should note, however, that although the pair (1,3) is in this bracelet, the pair (3,1) is not.

 Problem H4 Assuming that you can start the sequence with any two one-digit numbers, how many different bracelets are possible?

This activity requires careful organization of information. The method of organization you choose is directly related to the amount of time required to answer the question.   Close Tip