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5.06 Number patterns

Lesson

Data in tables

When we see a table of data, often there is a relationship between the information in one column and the information in the other column. We can look for any relationships and then use this to find other values. For example, when a group of sixth-grade runners raced against third-grade runners, their times were adjusted to make it fair. Their times are written in the table below.

Actual times versus adjusted times (secs)
ACTUAL ADJUSTED
35 43
37 45
48 56
54 62

 

In Video 1, we will see how to look up information in this table and calculate an adjusted time for a runner whose actual time was $40$40 secs.

 

Data on a graph

This time we will look at data on a graph and see how two pieces of information are related to each other. We do that by looking at the corresponding values on the vertical and horizontal axes. Let's compare your age to your sister's age and see what happens as your sister gets $1$1 year older each year. You don't have a sister? That's okay, just imagine someone else in the example. 

 

Writing a rule

Now we can write a rule to describe one set of data to another. We identify the rule and then use variables, or letters, to write it in a shorter way. Let's write a rule using variables for our previous example that tells us how old you are based on your sister's age.

Information Variable
Your age $y$y
Your sister's age $x$x

Let's see how we do this.

 

Writing it a different way

We looked at how to calculate your age, once we knew your sister's age. What if we wanted to write the rule in a different way? This time we will work out your sister's age if we know your age. How do you think our rule, or equation, might change?

Let's have a look in our last video.

 

Practice questions

Question 4

A catering company uses the following table to work out how many sandwiches are required to feed a certain number of people.

Fill in the blanks:

Number of People Sandwiches
$1$1 $5$5
$2$2 $10$10
$3$3 $15$15
$4$4 $20$20
$5$5 $25$25
    • For each person, the caterer needs to make $\editable{}$ sandwiches.
    • For $6$6 people, the caterer would need to make $\editable{}$ sandwiches.

Question 5

Consider the pattern shown on this line graph:

Loading Graph...

  1. If the pattern continues on, the next point marked on the line will be $\left(\editable{},\editable{}\right)$(,).

  2. Fill in the table with the points from the graph, and the one you just found (the first one is filled in for you):

    $x$x-value $y$y-value
    $0$0 $0$0
    $\editable{}$ $\editable{}$
    $\editable{}$ $\editable{}$
    $\editable{}$ $\editable{}$
  3. Choose all statements that correctly describe this pattern:

    The rule is $x=y\div4$x=y÷​4

    A

    The rule is $y=4\times x$y=4×x

    B

    The rule is $y=x\div4$y=x÷​4

    C

    As $x$x increases $y$y increases.

    D

    The rule is $x=y\div4$x=y÷​4

    A

    The rule is $y=4\times x$y=4×x

    B

    The rule is $y=x\div4$y=x÷​4

    C

    As $x$x increases $y$y increases.

    D

Question 6

Consider the pattern shown on this dot plot:

Loading Graph...

  1. If the pattern continues on, the next point marked on the line will be $\left(\editable{},\editable{}\right)$(,).

  2. Fill in the table with the points from the graph, and the one you just found (the first one is filled in for you):

    $x$x-value $y$y-value
    $0$0 $0$0
    $\editable{}$ $\editable{}$
    $\editable{}$ $\editable{}$
    $\editable{}$ $\editable{}$
  3. Choose all statements that correctly describe this pattern:

    The rule is $x=y\div2$x=y÷​2

    A

    The rule is $y=x\div2$y=x÷​2

    B

    As $x$x increases $y$y increases.

    C

    The rule is $y=2\times x$y=2×x

    D

    The rule is $x=y\div2$x=y÷​2

    A

    The rule is $y=x\div2$y=x÷​2

    B

    As $x$x increases $y$y increases.

    C

    The rule is $y=2\times x$y=2×x

    D

Outcomes

6.EE.C.9

Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

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