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.
Glossary Entries
- common denominatorThe same denominator in two or more fractions. For instance, \(\frac{1}{4}\) and \(\frac{5}{4}\) have a common denominator.
- composite numberA whole number with more than 1 factor pair.
- denominatorThe bottom part of a fraction that tells how many equal parts the whole was partitioned into.
- dividendThe number being divided. For example, when 37 is divided by 5, we call 37 the dividend.
- equivalent fractionsFractions 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 numberA pair of whole numbers that multiply to result in that number. For example, 5 and 4 are a factor pair of 20.
- mixed numberA number expressed as a whole number and a fraction less than 1.
- multiple of a numberThe 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 numberA whole number that is greater than 1 and has exactly one factor pair: the number itself and 1.
- remainderThe 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).