2340 Exam 1 Study Guide (Spring 2022)

Page 1: Numeration Systems

• Whole Numbers, Decimals, Integers

  • Place value in various bases (5, 6, 2, 8, etc.)

  • Conversion between base ten and other bases

  • Number sequences in various bases

  • Operations in Different Bases

    • Addition, subtraction, multiplication only

    • Drawing operations is essential

    • Understanding the meaning of each place in base ten

    • Expanded forms of numbers

    • Properties of addition and multiplication

    • Order of operations

  • Whole Number Operations

    • Addition and subtraction (base ten models, expanded forms)

    • Multiplication (partial products, area models)

    • Division (partial quotients, scaffold method)

  • Decimal Concepts

    • Representations of tenths and hundredths (base ten blocks, decimal paper)

    • Number lines based on base ten

    • Rounding with number lines

    • Expanded forms of numbers

  • Decimal Operations

    • Addition, subtraction, multiplication, division

    • Drawing operations on decimal paper

    • Representation with counters

  • Absolute Value

  • Integer Operations

    • Addition, subtraction, multiplication, division

    • Representing operations with counter diagrams

Page 2: Fractions and Short Answer Problems

• Understanding Fractions

  • Definition of fractions (measurement interpretation)

• Comparison and Equivalence of Fractions

  • Reasoning strategies to compare fractions

  • Equivalent fractions using models

• Fraction Operations

  • Addition and Subtraction

    • Importance of common denominators

  • Multiplication

    • Area models for visualization

  • Division

    • "How many groups?" perspective and common denominator strategy

• Base-Ten Blocks

  • Draw a whole number (1,524) using base-ten blocks

  • Alternative representation and explanation of part (a)

Page 3: Rounding Problems

• Rounding Demonstrations

  • Draw marked number lines to demonstrate rounding

    • a. Round 653,079 to the nearest ten-thousand

    • b. Round 12.07519 to the nearest hundredth

    • c. Round 503.982 to the nearest tenth

Page 4: Additional Problems

• Identifying Decimal Numbers

  • Find a decimal between -3.06 and -3.07 using a base-ten frame number line

• Measurement Perspective of Fractions

  • Describe the shaded region of the rectangle in terms of fraction

  • Convert this fraction to a decimal

  • Explain the relationship between the model and decimal value

• Problem Solving with Fractions

  • a. Determine fraction of doughnuts with frosting and sprinkles

  • b. Calculate the amount of lemonade Dwight sold; compare with Jim's sales

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