Graph Number Patterns Grade 5

Graph Number Patterns Grade 5

Mr. Alonzo

Objective

5.4(C) generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph.

5.8(C) graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real‐world problems, including those generated by number patterns or found in an input‐output table.

Vocabulary

• Independent Variable (INPUT) - is always the X. The problem always tells you what to put for the X.

• Dependent Variable (OUTPUT) - is always the Y.

• Ordered Pair-Two numbers written in parentheses like this:

  (12,5)

  Which can be used to show the position on a graph, where the "x" (horizontal) value is first, and the "y" (vertical) value is second.

• Equations - Since the Dependent Variable (The Y) "depends" on what you put for the Independent Variable (The X) equations look like this

   $y=x+5$  OR  $y=5x$  
  

Displaying Number Patterns on the Coordinate Plane.

When Alice completes each level in her favorite video game, she wins 2 extra lives. How can you display this number patterns on the coordinate grid?

FIRST Step 1: Create an Input/Output Table as pictured to the right.

When creating this Table YOU put the input numbers because the problem tells you what to put.

Multiple Choice

After completing level 2, how many extra lives does Alice have?

• $2$

• $3$

• $4$

• $6$

Multiple Choice

After completing level 3, how many extra lives does Alice have?

•  $5$ 

• $3$

• $4$

• $6$

Multiple Choice

After completing level 4, how many extra lives does Alice have?

•  $8$ 

•  $5$ 

•  $7$ 

• $6$

Step 2: Create the Equation!

• Equations are either adding or multiplying.

• You must find out what you do the the Input (The X) to make it the output (The Y)

• In this example the equation is  $y=2x$  

• For example if you plug in 4 for the X  $8=2\left(4\right)$  

Open Ended

Step 3: Using your equation and your Input/Output Table.

Write the related pairs of data as ordered pairs. The input is the x-coordinate and the output is the y-coordinate.

Level 2:

Level 3:

Level 4:

Step 4: Plot the ordered pairs in the coordinate grid.

Level 1: (1, 2)

Level 2: (2, 4)

Level 3: (3, 6)

Level 4: (4, 8)

Another Example

• Here is the problem "Multiply the number of nickels by 5 to find the number of pennies that equal the value."

• The "Input" in a pattern is the X-value also known as the independent variable.

• The "Output" in a pattern is the Y-value also known as the dependent variable.

Multiple Choice

Using the Table and Graph determine what equation represents the pattern of Pennies to Nickles.

• $y=5x$

• $y=x+5$

• $x=5y$

• $x=y+5$

Open Ended

Given the Rule "Add 5 to the input", What would be the output for each of the input's listed?

Multiple Choice

Which equation best represents the rule "Add 5 to the input"?

• $y=x+5$
  

• $y=5x$

• $x=5y$

• $x=y+5$

Open Ended

The rule for a pattern is add 4 to the input. What would the equation be? Explain how you can use the the Steps to write ordered pairs that represent the pattern.

Open Ended

Write five ordered pairs that represent the pattern rule multiply input by 3.

Multiple Choice

Ted gets a $10 allowance every week and saves $6 of it. He makes a graph to show his savings, where the x-coordinate represents the number of weeks and the y-coordinate represents the number of dollars saved. Which of the following ordered pairs could be on the graph?

• $\left(6,\ 60\right)$
  

• $\left(36,\ 6\right)$

• $\left(1,\ 60\right)$

• $\left(6,\ 36\right)$

Multiple Choice

Tina owns a flower shop. The table shows the prices for different numbers of flowers. She makes a graph that compares number of flowers to total price. Which ordered pair should NOT be on the graph?

• $\left(8,\ 12\right)$
  

• $\left(6,\ 4\right)$

• $\left(6,\ 9\right)$

• $\left(10,\ 15\right)$

Multiple Choice

Steve mixes 4 cups grape juice with 3 cups ginger ale to make a punch. Steve makes a graph to compare the amounts of juice needed for several batches. Which ordered pairs could be on the graph?

• $\left(4,\ 3\right),\ \left(5,\ 4\right),\ \left(6,\ 5\right)$
  

• $\left(3,\ 4\right),\ \left(5,\ 6\right),\ \left(6,\ 7\right)$

• $\left(4,\ 3\right),\ \left(8,\ 6\right),\ \left(12,\ 9\right)$

• $\left(3,\ 4\right),\ \left(8,\ 6\right),\ \left(12,\ 9\right)$

Multiple Choice

Rob is making a fruit punch for a party. He adds 4 cups of pineapple juice for every cup of orange juice. Which ordered pair shows how many cups of pineapple juice he needs for 3 cups of orange juice?

• $\left(4,\ 8\right)$

• $\left(1,\ 2\right)$

• $\left(3,\ 12\right)$

• $\left(3,\ 4\right)$