Learning Resource Type

Classroom Resource

Multiplying Rational Numbers

Subject Area

Mathematics

Grade(s)

7

Overview

The purpose of this lesson is to develop the rules for multiplying two negative numbers. Students use the familiar fact that distance = velocity x time to make sense of this rule. They interpret negative time as the time before a chosen starting time and then determine the position of an object moving with a negative velocity at a negative time. An object moving with a negative velocity is moving from right to left along the number line. At a negative time, it has not yet reached its starting point of zero, so it is to the right of zero, and therefore its position is positive. So a negative velocity times a negative time gives a positive position. When students connect reasoning about quantities with abstract properties of numbers.

    Mathematics (2019) Grade(s): 7

    MA19.7.4

    Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.

    Unpacked Content

    UP:MA19.7.4

    Vocabulary

    • Integers
    • Rational numbers
    • Additive inverses
    • opposite quantities
    • Absolute value
    • Terminating decimals
    • Repeating decimals

    Knowledge

    Students know:
    • a number and its opposite have a sum of 0.
    • A number and its opposite are called additive inverses.
    • Strategies for adding and subtracting two or more numbers.
    • Absolute value represents distance on a number line, therefore it is always non-negative.
    • Strategies for multiplying signed numbers.
    • Every quotient of integers (with non-zero divisor) is a rational number.
    • If p and q are integers, then -(p/q) = (-p)/q = p/(-q).
    • The decimal form of a rational number terminates or eventually repeats.

    Skills

    Students are able to:
    • add rational numbers.
    • Subtract rational numbers.
    • Represent addition and subtraction on a number line diagram.
    • Describe situations in which opposite quantities combine to make 0.
    • Find the opposite of a number.
    • Interpret sums of rational numbers by describing real-world contexts.
    • Show that the distance between two rational numbers on the number line is the absolute value of their difference.
    • Use absolute value in real-world contexts involving distances.
    • Multiply and divide rational numbers.
    • Convert a rational number to a decimal using long division.

    Understanding

    Students understand that:
    • finding sums and differences of rational numbers (negative and positive) involves determining direction and distance on the number line.
    • Subtraction of rational numbers is the same as adding the additive inverse, p - q = p + (-q).
    • If a factor is multiplied by a number greater than one, the answer is larger than that factor.
    • If a factor is multiplied by a number between 0 and 1, the answer is smaller than that factor.
    • Multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers.
    • Integers can be divided, provided that the divisor is not zero.
    Link to Resource

    CR Resource Type

    Audio/Video

    Resource Provider

    PBS
    Accessibility
    License

    License Type

    PD
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