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Patterns, Functions, and Algebra
 
Session 9 Part A Part B Part C Homework
 
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Session 9:
Homework

Problem H1

Solution  

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

Solution  

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

 show answers

 

 

<

See solutions for
an explanation of
each answer.

 

?

 

?

 

>

 

?

 

?

 

>

 

<

hide answers


 

Problem H3

Solution  

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.


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Pick a specific dollar amount that is easy to calculate; for example, $100.   Close Tip

 
 

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.


Take it Further

Problem H4

Solution

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
 

Suggested Reading:

For more about the Fibonacci series in nature, see Renaissance: Numbers in Nature at www.learner.org/exhibits/renaissance/fibonacci/.

Kilpatrick, J.; Swafford, J.; and Findell, B., ed. (2001). Adding It Up: Helping Children Learn Mathematics. A Report of the National Research Council. Washington, D.C.: National Academy Press. Reproduced with permission from the publisher. © 2001 by National Academy Press. All rights reserved.

Download PDF File:
Adding It Up: Helping Children Learn Mathematics
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