Grade 6 - Unit 1 Patterns

Grade 6 Math Patterns Study Guide

Vocabulary

·      A variable is a symbol that can stand for any one of a set of numbers or other objects (Example: 3 x o = 4           …    o is the variable used to represent 10).

·      Numbers, symbols, and operators (+, -, x, ÷) grouped together that show the value of something is an expression. (Example: 3 x o can be used to represent the pattern in a t-table).

·      An equation is similar to an expression, but it shows that two things are equal. (Example: 3 x o = 4).

·      Coordinates: A group of numbers used to indicate the position of a point, line, or plane. Example: (5, 7).

·      In an Ordered Pair: The first number tells the horizontal distance from the origin (x axis). The second number tells the vertical distance from the origin (y axis) – REMEMEBER: you crawl, then stand.

·      The Commutative Property of Addition is the rule that states: when we add two numbers their order does not affect the sum: (e.g., 5 + 4 = 9 is the same as 4 + 5 = 9)

·      The Commutative Property of Multiplication is a rule that states: when we multiply two numbers their order does not affect the product (e.g., 4 x 5 = 20 is the same as 5 x 4 = 20)

·      When each side of the equation is changed in the same way, the values remain equal. This is called the preservation of equality.

1) Represent and describe patterns and relationships, using graphs and tables.

• Input/output machines, T-tables, and line-graphs.

2) Know how to plot coordinates on a graph and use coordinates to describe the location of a point on a graph. 

• Remember: X axis is always first and Y axis is second in an ordered pair (3, 2).

3) Identify pattern rules from rows of patterns, figure patterns, tables, and graphs. Extend these patterns. 

• The pattern rule for a row of numbers, or just the input or output side of a table, like 2, 3, 4, 5, 6, would be “Start at 2, add 1 each time.”
• The pattern rule relating the input to the output would be: “Multiply the input by 3 each time.”

4) Demonstrate an understanding of relationships within tables to solve problems for patterns using expression (see the September 16^th problem).

·      Example: Find the pattern relating the input to the output in a machine, and create an expression to describe the pattern (F – 4). Use this expression to find the output for an input of 12 (12-4 = 8).

5) Know how to solve and create an equation (a x 4 = 8) and an expression (4n, 4 x n) using letter variables.

6) Know how to balance an equation by representing the same value with different equations (example: 5 + 4 = 9 or 4 + 5 = 9 or 5 + 4 = 9, etc). Know how to apply the preservation of equality to these equations (see the September 25^th problem).