Grade 6 - Patterns Review

Solving Equations

100

Solve for g:

4g = 12

g = 3

200

Solve for p:

17 = p + 9

p = 8

300

Solve for e:

13 = 28 - e

e = 15

400

Solve for r:

5 + 4 + r = 12 - 2

r = 1

500

Solve for n:

6n - 11 = 7

n = 3

Function Machine

100

Function (rule): x2 - 6

Input (x): 0, 1, 5, 10, 14

Output (y): -6, -4, 4, 14, 22

200

Function (rule): /4 + 1

Input (x): 16, 8, 0, 40, 100

Output (y): 5, 3, 1, 11, 26

300

Function: y = x + 7

Input (x): 0, 1, 2, 3, 4

Output (y): 7, 8, 9, 10, 11

400

Function: y = 2x - 2

Input (x): 5, 2, 7, 10, 0

Output (y): 8, 2, 12, 18, -2

500

Function: y = x/2 - 6

Input (x): 6, 24, 100, 66, 15

Output (y): -3, 6, 44, 27, 1.5

Vocabulary

100

What is a variable?  How do we write a variable in algebra?

A variable is an unknown value / number.  We usually use a letter to represent a variable (x, y, n, etc.)

200

What is the difference between an expression and an equation.  Give an example of each.

An equation has an equals sign (=).  It has a left side and a right side.  An expression does not have an equals sign.

Expression: 4x - 2          Equation: x + 5 = 21         

300

What does RPR stand for?  What is an RPR?  Give an example.

Recursive Pattern Rule

It is the description of a pattern using words.

Ex: start a 5, add 3 each time

400

What does EPR stand for?  What is an EPR?  Give an example.

Explicit Pattern Rule

An equation that can be used to determine any value in a pattern through substitution.

y = 2x       or      y = x - 9

500

Which two operations allow for the "Preservation of Equality", and which two don't?

Yes: multiplication (x) and addition (+)

No: division (/) and subtraction (-)

Shifted Times Tables

100

Determine the TIMES TABLE shown in the (y) column:

x         y

1         6 

2        12

3        18

4        24

5        30

Times Table: 6

200

Determine the TIMES TABLE shown in the (y) column:

Determine the SHIFT up/down:

x         y

1         0 

2         3

3         6

4         9

5        12

Times Table: 3

Shift: down 3

300

Determine the TIMES TABLE shown in the (y) column:

Determine the SHIFT up/down:

x         y

1         9 

2        11

3        13

4        15

5        17

Times Table: 2

Shift: up 7

400

Determine the TIMES TABLE shown in the (y) column:

Determine the SHIFT up/down:

What goes in the blank?

x         y

1        -7 

2        -3

3         1

4         5

5        __

Times Table: 4

Shift: down 11

Blank: 9

500

Fill in the Blanks:

x         y

1        -2 

2        __

3         4

4        __

5        10

Blank 1: 1

Blank 2: 7