Unit OverviewMany important arithmetic problems involve breaking a whole number into equalized pieces or finding a number into which a given number will divide evenly. Solving problems like these involves finding factors and multiples. For example:
-A class of 30 students is to be divided into equal-sized teams for a school competition. What team sizes are possible? -Taniya and Jeremiah want to go to the art museum together the next time they both have a day off from work. Taniya has a day off every fourth day. Jeremiah has a day off every fifth day. they both had the day off today. In how many days will they be able to go to the museum together? Solving grouping and repeated-action problems like those above depends on finding factors and multiples of whole numbers. Realizing that some numbers are rich in factors, while other numbers have very few factors, is essential for effective problem solving. While the focus of this Unit is on the multiplicative structure of numbers, the Distributive Property is introduced to illustrate the additive and multiplicative structure of numbers. That is, numbers can be written as a product of factors or as a sum of terms. The Order of Operations convention is introduced so that students can work with numerical expressions that contain parenthesis and more than one operation. A primary goal of this Unit is to help students learn some new and useful strategies for finding factors and multiples of whole numbers. They can apply these strategies to gain familiarity with prime and composite numbers and to solve real-life problems. Common multiples and common factors are at the heart of many major mathematical ideas that are developed in middle grades. For example, common factors and multiples are the building blocks for equivalent fractions, which in turn provide a foundation for operations with fractions and proportional reasoning.
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