Weekly Overview

Weekly Topics

 The focus of this week’s instruction is to deepen students’ understanding of:

  • Multi-Step Ratio Problems
  • Opposite Quantities Combine to Make Zero
  • Using the Number Line to Model the Addition of Integers
  • Understanding Addition of Integers
  • Efficiently Adding Integers and Other Rational Numbers

Materials Needed

  • Equations
  • Expressions
  • Integer Game (See explanation in lesson 2 of this week’s lessons)
  • Number Line
  • Tape Diagram
  • Ratio Table

Standard(s) Covered

7.RP.A.3

  1. Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

  1. Describe situations in which opposite quantities combine to make 0.
  2. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real world contexts.
  3. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference and apply this principle in real-world contexts.
  4. Apply properties of operations as strategies to add and subtract rational numbers.

Representations

Rising eighth grade lesson example

Equation: 3 + 7 = 10

Expression 3 + 7

Additional Terms and Symbols

  • Additive Identity (The additive identity is the number 0.)
  • Additive Inverse (An additive inverse of a number is a number such that the sum of the two numbers is 0.   The additive inverse of a number a is the opposite of a (i.e., -a) because if we add both numbers using the vector approach above, we get a+(-a)=0.)

Familiar Terms and Symbols

  • Absolute Value
  • Commutative Property
  • Equation
  • Expression
  • Integer
  • Inverse
  • Negatives
  • Opposites
  • Positives
  • Rational Numbers