Concepts and Processes
Baseline Proficiency Completion Checklist
Student ____________________________ Instructor___________________________
MAT 130/131 Method of Completing Proficiency
and Date Completed
Chapter 3: The Four Fundamental Operations
of Arithmetic
Mental Math ____________________________________
Algorithms ____________________________________
Chapter 4: Number Theory ____________________________________
Chapter 5: Extending the Number System
Modeling Fractions: ____________________________________
Ordering Rational Numbers ____________________________________
Chapter 6: Proportional Reasoning ____________________________________
MAT 132
Chapters 8-10: Geometry
Naming and Classifying 2D and 3D Figures ____________________________________
Transformations and Symmetry ____________________________________
Measurement ____________________________________
Introduction to Baseline Proficiencies
These proficiencies address some of the most fundamental concepts in the course. If you are in the regular Concepts and Processes sequence, you must pass the Chapter 3-6 proficiencies by the end of Math 131 and all the proficiencies by the end of Math 132; if you’re in the intensive sequence, you must pass all the proficiencies by the end of Math 141. When you pass a proficiency, you pass it forever (i.e. if you make a mistake later in the semester on a topic for which you have passed the proficiency, you do not lose your “passed” status on that proficiency). In general, you will first see a proficiency as part of a regular test on the particular material (although in some cases, the proficiencies might be given first as a separate quiz). If you don’t pass the proficiency the first time, you will work to understand your mistakes, and then you can retake the proficiency as either a written or an oral quiz. There is no official limit on how many times you can retake a proficiency until you pass it, but you will need to show that have worked to understand the material between times you retake the proficiency.
Detailed Description of Baseline Proficiencies
Chapter 3: The Four Fundamental Operations of Arithmetic
1. Mental Math: You will be given a list of five arithmetic problems, and for each, you must give a strategy to compute the answer mentally. You must have at least four correct answers and use at least three different strategies.
Example: 26 x 9.
Solution 1: 20 x 9 = 180 and 6 x 9 = 54 so 26 x 9 = 180+54 = 234
Solution 2: 26 x 10 = 260 and 260-26 = 234
Solution 3: 25 x 9 = 225 and 225+9=234
Example: 259 + 47
Solution 1: 250 + 50 = 300 and 9-3=6 and 300+6=306
Solution 2: 59+47 = 60+46 = 106 and 200+106=306
Solution 3: 259 + 41 = 300 and 47-41=6 so 300+6.
2.
Algorithms: You will be given
three questions related to understanding the “standard algorithms” for
addition, subtraction, multiplication, and division (i.e. the ones most
commonly taught in schools in the
Example: In the following problem, explain why the 2 is “carried.”
2
3 9
+ 3 7
1 7
9 3
Example: In the following problem, explain the meaning of the 0.
42
x 22
84
840
924
Chapter 4: Number Theory
To satisfy this proficiency, you must show that you understand the basic concepts of number theory: multiples, factors, and primes. You need to solve four of five problems correctly.
Examples:
Decide whether each of the following numbers is prime or composite: 251, 252, 253, 255, 257.
Factor 7168 into primes.
Chapter 5: Extending the Number System
1. Modeling Fractions
To satisfy this proficiency, you must demonstrate understanding of all three categories of fraction models:
1. Area Models: including fraction factory pieces, pies and pizzas, pattern blocks
2. Length Models: including fraction strips, rulers, cuisenaire rods
3. Discrete Models: including tiles, drawings of dots, etc.
You will be given several problems and you must solve at least one correctly from each type of model.
Examples:
Discrete Model: The rectangle below represents a cover blocking your view of 5/8 of the circles. Draw the missing circles inside the rectangle.
Length Model: The rod below (including all five sections)
has a total of length of a unit.
Shade in the portion of the rod that represents
of a unit.
Area Model: What fraction of the area of the picture below is shaded?
2. Comparing Rational Numbers
To satisfy this proficiency, you must show that you understand the size of rational numbers. You must correctly solve at least four of five designated problems (i.e. over 80% of five or more problems) on topics such as the following:
Placing rational numbers on a number line.
Ordering lists of rational numbers and fractions.
Finding rational numbers between two other decimals.
Identifying rational numbers that
satisfy a specific criterion, e.g. less than 0.5 or more than .
Examples:
Put the following numbers in order from smallest to largest:
Indicate the approximate location of each of the following points on the number line below:
A = 0.903 B= 0.06
Name two fractions, one with a repeating decimal expansion and one with a terminating decimal expansion, that are between 0.6 and 0.7.
Chapter 6: Proportional Reasoning
To satisfy this proficiency, you must solve at least two of three designated problems and demonstrate proportional reasoning.
Examples:
Solve without using algebra or setting up a proportion: On a map, 3/4 of an inch represents 100 miles. How far apart are two cities in real life, if they are 5 inches apart on the map?
At a college, there are 9 women for every 2 men. There are 550 students at the college. How many are men?
A shirt is on sale for 20% off. The sale price is $32. What is the regular price?
Chapters 8-10: Geometry
1. Naming and Classifying 2D and 3D Figures
To satisfy this proficiency, you must answer at least eight of ten questions correctly.
Examples:
Name this figure:
Is this figure a rhombus? Why or why not?
True or false: Some pyramids are cylinders. Explain.
True or false: All squares are rectangles. Explain.
2. Transformations and Symmetry
To satisfy this proficiency, you must answer four of five questions on basic properties of transformations and symmetry.
Examples:
Describe the rotation and reflective symmetries of this star:
What will be the
coordinates of the image of point A if triangle ABC is rotated 180 degrees
about the origin?
B
C
A = (4,1)
3. Measurement
To satisfy this proficiency, you must answer four of five questions related to area, perimeter, and volume.
Examples:
Find the approximate area of a given irregular figure (drawn on a grid).
Draw two rectangles that both have perimeter 20, but that have different areas.
How many 2 x 2 x 2 cubes will fit into a 4 x 6 x 4 box?
Copyright 2005, Debra K. Borkovitz. You may copy or edit this material for non-profit, educational use only.