Name ________________________________
Math 131
Spring 04
Test 3 Group
Part I: Baseline Proficiency Questions
For each question, include a brief, “convince a skeptic” explanation of your answer.
A. Modeling Fractions (Baseline Proficiency 4)
1. If the purple Cuisinaire Rod represents ,
what does the orange Cuisinaire Rod represent?
2. What fraction of the area of the picture below is shaded?
3. The dots below represent .
Below, draw a picture of dots that represents (assuming each dot has the same value as it
does in the above picture).
B. Comparing Rational Numbers (Baseline Proficiencies 5 and 7):
4. Put the following numbers in order from smallest to largest:
5. Circle all the numbers below that are greater than 1/2:
6/13 3/5 8/9 12/4 9/12 .06
.828 .0788 .502 2/7 3/8 5/8
6,7. Indicate the approximate location of each of the following points on the number line below (counts as two problems):
A = 0.903 B= 0.06 C = 11/8 D = 3/5
8. Name two fractions, one with a repeating decimal expansion and one with a terminating decimal expansion, that are between 0.6 and 0.7.
C: Using Zero Correctly (Baseline Proficiency 9)
As with all questions, be sure to explain your answer in a way that can convince a skeptic that you’re correct (counts as two problems)
9,10a. =
b. =
c.
=
Problem 1 Scoring:
Sections A, B, and C count as Problem 1 (there are 10 questions in this section):
Level 5: Perfect score
Level 4: 9 or more correct
Level 3: 7 or more correct
Level 2: 5 or more correct
Level 1: 3 or more correct
Score for Problem 1 ___
D. Operations
(Baseline Proficiency 6 has 3 parts):
Note: If you use algorithms to do these problems, you must justify why they work. It’s best if you draw pictures to explain why your answers are correct.
1. Fill in each box below with a natural number so that the final addition problem is correct (i.e. find two fractions whose difference is 2/3, one of which has denominator 6):
2
6 3
2. Find .
3. Find .
4. What is ?
5. What is
E: Estimation (Baseline Proficiency 8)
6. Which of the following is closest to 0.02+0.004653?
a. b.
c.
d.
7. The decimal point has been omitted from the number below, which is a rounded off solution to 32.674 x 0.092345. Insert the decimal point in the correct place.
3 0 1 7 2 8 0 5 3
8. Which of the
following is closest to ?
a. 0.03 b. 0.3 c. 3 d. 30 e. 300
9. Which of the following points (A, B, C, D or
E) is closest to ?
A B
C D E
0 1 2
10. Which of points (on the number line in the
last problem) is closest to ?
Problem 2 Scoring:
Sections D and E count as Problem 2. There are 10 questions.
Level 5: Perfect score
Level 4: 9 or more correct
Level 3: 7 or more correct
Level 2: 5 or more correct
Level 1: 3 or more correct
Score for Problem 2 ___
Part 2: Problems
Choose one of the problems below. You may use manipulatives and a sheet of notes. These problems may be used to the baseline proficiency for problem solving.
Tile Problem
There are some red, yellow, green, blue, orange, purple, and pink tiles on the table. All of the following clues are true:
There are fewer than 50 tiles on the table.
No two colors have the same number of tiles on the table.
The number of red tiles is less than the number of green tiles and is also less than the number of yellow tiles.
The number of red, yellow, and green tiles together equals the number of pink tiles.
of the total tiles are blue.
The number of pink tiles is the number of blue tiles.
The number of yellow tiles is the number of purple tiles.
a) How many tiles of each color are on the table? Explain how to convince a skeptic that you are correct.
Red: ___________ Yellow: ___________ Green: ___________ Blue: ___________
Purple:________
b) Find all additional solutions, if you are allowed to use up to 100 tiles. Convince a skeptic that you have found all such solutions.
Scoring Guide
Level 5 -- Solves all parts of the problem with superb justification
Level
4 Solves part a with excellent justification or
solves a with some justification and solves part of b
Level
3 Solves part a with at least some justification
Level
2 Makes significant progress
Level 1 -- Makes some progress.
Level 0 -- Doesn’t make progress
Score ___________
B. Fill in the Blanks:
For the following problems, you are allowed to select six different numbers from the natural numbers from 1 to 20 (start fresh with each problem).
a. Fill in the boxes below to make the answer as small as possible.
6
b. Convince a skeptic that your answer in part a really is the smallest possible.
c. Fill in the boxes below to make the answer as big as possible.
6
d. Convince a skeptic that your answer really is the biggest possible.
Scoring Guide
Level 5 -- Solves all parts of the problem with superb justification
Level
4 Solves parts a and b with some justification
or is close to solving a and b, but includes generally excellent justification
(that maybe misses a case)
Level
3 Very close to solving a and b or solves one
part and does good work on the other
Level
2 Makes significant progress
Level 1 -- Makes some progress.
Level 0 -- Doesn’t make progress
Score ___________
C. Fun With Decimals
a. Using the base ten blocks, as
we did in class, with the large cube equal to 1, describe how to represent
0.243, 0.203 and . You can invent smaller pieces to describe the
last number.
b. Using the base ten blocks in your explanation, explain why the following are true:
c. Repeat part b, but multiply the original numbers by 100, not by 10.
d. List five different fractions that are in simplified form that have denominator 9. Do the same for denominators 99 and 999. Find the decimal expansion of each fraction. What patterns do you notice?
e. Here is a method to write as a fraction:
Start
with
Subtract