4.5 Multiplicative Comparison and Measurement

Unit Goals

  • Students interpret, represent, and solve multiplicative comparison problems using an understanding of the relationship between multiplication and division. They use this thinking to convert units of measure within a given system from larger to smaller units.

Section A Goals

  • Analyze, describe, and represent multiplicative comparison situations.
  • Solve one-step and two-step problems involving multiplicative comparison.

Section B Goals

  • Convert from larger units to smaller units within a given system of measurement.
  • Solve multi-step problems involving multiplicative comparison and measurement.
  • Understand the relative sizes of kilometers, meters and centimeters, liters and milliliters, kilograms and grams, and pounds and ounces.

Section C Goals

  • Solve multi-step problems involving multiplicative comparison and measurement.
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Glossary Entries

  • common denominator
    The same denominator in two or more fractions. For instance, \(\frac{1}{4}\) and \(\frac{5}{4}\) have a common denominator.

  • composite number
    A whole number with more than 1 factor pair.

  • denominator
    The bottom part of a fraction that tells how many equal parts the whole was partitioned into.

  • equivalent fractions
    Fractions that have the same size and describe the same point on the number line. For example, \(\frac{1}{2}\) and \(\frac{2}{4}\) are equivalent fractions.

  • factor pair of a whole number
    A pair of whole numbers that multiply to result in that number. For example, 5 and 4 are a factor pair of 20.

  • mixed number
    A number expressed as a whole number and a fraction less than 1. 

  • multiple of a number
    The result of multiplying that number by a whole number. For example, 18 is a multiple of 3, because it is a result of multiplying 3 by 6.

  • numerator

    The top part of a fraction that tells how many of the equal parts are being described.

  • prime number
    A whole number that is greater than 1 and has exactly one factor pair: the number itself and 1.

  • rounding

    A formal way to say which number a given number is closer to. For example, for 182, the number 180 is the closest multiple of ten and 200 is the closest multiple of a hundred. We can round 182 to 180 (if rounding to the nearest ten) or 200 (if rounding to the nearest hundred).