Unit  1 Rational Numbers

In Topic B, students extend their understanding of multiplication and division of whole numbers, decimals, and fractions to find the products and quotients of signed numbers.

1. Students begin by conceptualizing multiplication as repeated addition.

They relate multiplication to the Integer Game. Students draw upon their experiences with the Integer Card Game to justify the rules for multiplication of integers. The additive inverse and distributive property are used to show that (−1)(−1) = 1.

1. Students understand division as the process of finding the missing factor of a product. They use this relationship to justify that the rules for dividing signed numbers are consistent with that of multiplication, provided the divisor is not zero. Students extend the integer rules to include all rational numbers, recognizing that every quotient of two integers is a rational number provided the divisor is not zero.

2. In Lesson 13, students realize that the context of a word problem often determines whether the answer should be expressed in the fractional or decimal form of a rational number. They draw upon their previous understanding of equivalent fractions, place value, and powers of ten to convert fractions whose denominators are a product of 2’s and 5’s into decimals.

3. Students use long division to convert any fraction into a decimal that either terminates in zeros or repeats.

4. Students create numerical expressions with rational numbers based on the context of word problems. Properties of operations are used to rewrite expressions in equivalent forms as students multiply and divide rational numbers efficiently without the aid of a calculator

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