MATH 210, Study Guide for Midterm Test 1

9/28/2012

Test coverage

1. Place Value and Models for Arithmetic
   1. Counting. Whole Numbers. Decimal, Egyptian and Roman Numerals (1.1)
   2. Place Value. Place Value Systems with Bases Other than Ten (1.2)
   3. Addition (1.3)
   4. Subtracton (1.4)
   5. Multiplication (1.5)
   6. Division (1.6)
2. Mental Math and Word Problems
   1. Mental Math (2.1)
   2. Word Problems (2.2, 2.3)
3. Algorithms
   1. Addition (2.1)
   2. Subtraction (3.2)
   3. Multiplication (3.3)
   4. Long Division by One-Digit Numbers (3.4)

Key concepts (review them as you prepare for the test)

• Whole numbers. Set model, measurement model. The number line (for whole numbers)
• Numerals, digits, place value system
• Arithmetic operations (addition, subtraction, multiplication, division with remainder)
• Formal definitions: Subtraction (part-whole/missing addend), Multiplication (repeated addition) and Division (missing factor)
• Properties of arithmetic operations: "any-order" (commutative, associative), identity (additive/multiplicative), distributive
• Terminology for arithmetic operations: addends, sum, minuend, subtrahend, difference, factors, product, dividend, divisor, quotient, remainder
• Proper use of the equal sign (p. 18)
• Techniques for addition: number bonds, tens combinations, adding doubles, compensation, using place value ("left-to-right")
• Three interpretations of subtraction: take-away, part-whole, comparison
• Techniques for subtraction: counting up, counting down, regrouping, compensation, using place value ("left-to-right")
• Techniques for multiplication: regrouping, compensation, using place-value
• Two interpretations of division: partitive and measurement
• The Quotient-Remainder Theorem
• Bar diagrams used to solve word problems
• Teacher's solutions (p. 55)
• Addition algorithm: rebundling and carrying
• Subtraction algorithm: unbundling (borrowing), carrying, regrouping across zero
• Multiplication algorithm: rebundling, carrying
• Lattice algorithms: addition and multiplication
• Long division algorithm: partitive and measurement interpretations

Key types of questions (look for these types in the homework and quiz questions)

• Conversion from decimal to Egyptian, Roman systems and back. Conversion between different bases of the place value system.
• Demonstrate and explain the use of place-value system (find largest/smallest number, values of different digits in numerals ... )
• Identify arithmetic properties and thinking strategies used in computations (commutative, associative, multiplicative/additive identity, various techniques ... )
• Use various models (bundle, chip, or measurement) to illustrate arithmetic operations
• Perform mental math calculations, present teacher's solutions
• Apply and explain the use of arithmetic algorithms
• Solve word problems, use bar diagrams technique, give step-by-step solutions
• Make up word problems to match with different interpretations of arithmetic operations
• Illustrate different interpretations of arithmetic operations (part-whole, take-away, partitive/measurement ... )
• Give visual "proofs" of arithmetic properties (commutative, associative ... )

Check solutions to Quizzes and Homework Problems posted on the main page.