Grade 7 Study Guide

Divisibility Rules

• Know divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10.
  • Write the rule.
  • Apply the rule to a number.
  • Find a number given specific information.
• Complete Venn diagrams based on divisibility.

Algebraic Expressions

• Write an algebraic expression for a given sentence.
• Write a sentence for a given algebraic expression (vice versa).
• Know the terms for algebraic expressions.
• Evaluate an expression when given a specific value for the variable. For example, if the expression is $3x + 5$ and $x = 2$, then the value of the expression is $3(2) + 5 = 6 + 5 = 11$.

Expressions from Tables of Values

• Determine the expression (also called relation) given a table of values.
  • Table includes term number and term value.
• Complete a given table given the expression. For example:

To find the missing Term Values, substitute the Term Number (n) into the expression $2n + 1$. So:

• When n = 1, Term Value = $2(1) + 1 = 3$
• When n = 2, Term Value = $2(2) + 1 = 5$
• When n = 3, Term Value = $2(3) + 1 = 7$

Input-Output Tables

• Complete input-output tables.
• Fill in the output values.
• Determine the output expression.
  • Example: If Input (x) is multiplied by 4 to get Output (y), the output expression is $y = 4x$.

Graphing Relations

• Graph the relations from an input and output table.
• Answer questions given a graph.
  • The input values are the x-coordinates and the output values are the y-coordinates.
  • Plot the points (x, y) on the graph and connect them to form a line or curve.
  • Use the graph to find the output value for a given input value, or vice versa.

Algebraic Equations

• Algebraic Equations: Provide the example, given the sentence and vice versa, as well as represent and solve equations using algebra tiles.
  • Write an equation for a given sentence.
  • Write a sentence for a given equation (vice versa).
  • Represent and solve equations using algebra tiles (visual model).