Expressions with Rational Numbers and Solving Problems with Rational Numbers

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

7

Overview

The purpose of this video lesson is to help students make sense of expressions, and reason about their position on the number line— whether the number is positive or negative, which of two numbers is larger, or whether two expressions represent the same number. They work through common misconceptions that can arise about expressions involving variables. They also reason about expressions in a and b, given the positions of a and b on a number line without a given scale. This helps develop the idea that the letters in an algebraic expression can be thought of as numbers, even if you don't know the value of a.

Students connect ideas about rational number arithmetic and the interpretation of negative quantities, such as negative time or negative rates of change. They solve problems with rational numbers in various contexts by making tables or numerical calculations. As students reason about the meaning of negative quantities, they engage in MP2.

 

This resource includes the Expressions with Rational Numbers and Solving Problems with Rational Numbers lesson printout and a Practice Problems handout.

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.

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.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

PD
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