4.6 Multiplying and Dividing Multi-digit Numbers

Unit Goals

  • Students multiply and divide multi-digit whole numbers using partial products and partial quotients strategies, and apply this understanding to solve multi-step problems using the four operations.

Section A Goals

  • Generate a number or shape pattern that follows a given rule.
  • Identify apparent features of a number pattern that were not explicit in the rule itself.

Section B Goals

  • Multiply a whole number of up to four digits by a one-digit whole number, and 2 two-digit numbers using strategies based on place value and the properties of operations.

Section C Goals

  • Divide numbers of up to four digits by one-digit divisors to find whole-number quotients and remainders, using strategies based on place value, properties of operations, and the relationship between multiplication and division.

Section D Goals

  • Use the four operations to solve problems that involve multi-digit whole numbers and assess the reasonableness of answers.
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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.
  • dividend
    The number being divided. For example, when 37 is divided by 5, we call 37 the dividend. 
  • 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.
  • remainder
    The number left over when we take away as many equal groups as we can from a number. 
  • 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).