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4.03 Compare and graph two patterns

Lesson

Are you ready?

Do you remember how to continue number patterns? Let's try this problem to practice.

Look at the following Input/Output table and then fill in the blank:

Input Output
$40$40 $45$45
$80$80 $85$85
$120$120 $125$125
$160$160 $165$165
$200$200 $205$205
  1. Each output is $\editable{}$ more than the input.

  2. Which of the following best describes the pattern above?

    Add $8$8

    A

    Add $5$5

    B

Learn

This video looks at how we can plot points from a table of ordered pairs.

Apply

Question 1

Think about the two patterns:

Pattern $A$A: start at $0$0 and add $2$2 each time

Pattern $B$B: start at $0$0 and add $4$4 each time

  1. Use the patterns to complete the table:

    Position 1st 2nd 3rd 4th
    Pattern $A$A $0$0 $\editable{}$ $\editable{}$ $\editable{}$
    Pattern $B$B $0$0 $\editable{}$ $\editable{}$ $\editable{}$
  2. Plot Pattern $A$A on the coordinate plane as a set of ordered pairs, where the $x$x-value is the position of a value in the pattern.

    Loading Graph...

  3. Plot Pattern $B$B on the coordinate plane as a set of ordered pairs, where the $x$x-value is the position of a value in the pattern.

    Loading Graph...

  4. How can we describe the relationship between Pattern $A$A and Pattern $B$B?

    The values in Pattern $A$A are $2$2 more than the values in Pattern $B$B.

    A

    The values in Pattern $A$A are double the values in Pattern $B$B.

    B

    The values in Pattern $A$A are half the values in Pattern $B$B.

    C

    The values in Pattern $A$A are $2$2 less than the values in Pattern $B$B.

    D

Learn

This video looks at how we can compare number patterns and find a relationship between them.

Apply

Question 2

Two patterns are plotted on the coordinate plane, with the $x$x-values representing the position in the pattern.

Pattern $P$P is represented by the filled points, and Pattern $Q$Q is represented by the hollow points.

Loading Graph...

  1. Which relationship describes the two patterns?

    The values in Pattern $P$P are $2$2 more than the values in Pattern $Q$Q.

    A

    The values in Pattern $P$P are half the values in Pattern $Q$Q.

    B

    The values in Pattern $P$P are $2$2 less than the values in Pattern $Q$Q.

    C

    The values in Pattern $P$P are double the values in Pattern $Q$Q.

    D
  2. Which pattern is increasing at a faster rate?

    Pattern $P$P

    A

    Pattern $Q$Q

    B

    They are increasing at the same rate.

    C
  3. Which pattern has a greater starting value?

    Pattern $P$P

    A

    Pattern $Q$Q

    B

    They have the same starting value.

    C

 

Remember!

When plotting points onto the coordinate plane, the $x$x-value is the value along the horizontal axis and the $y$y-value is the value along the vertical axis.

Outcomes

MA.5.AR.3.1

Given a numerical pattern, identify and write a rule that can describe the pattern as an expression.

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