Minds On

Plotting additional patterns on graphs

The following graph examines how far a car has travelled by measuring distance vs. time. Examine the graph then answer the following questions. Record your thoughts using a method of your choice.

A line graph measuring distance vs. time. Title reads, Road Trip. The X-axis is labeled Time (mins) and starts at 0, increasing by 30 each time. The y-axis is labeled Distance travelled (km) and starts at 0, increasing by 50 each time. The first point on the graph is 30, 50, the second point is 60, 100, etc..

Consider the following. Record answers to the following questions in a method of your choice.

  1. How far had the car travelled after two hours?
  2. What is the pattern rule?
  3. How might the graph look if it showed another car that started 100km closer?

Press ‘Answer’ to reveal the answers and check your work.

  1. In two hours, they had travelled 200 km.
  2. The pattern rule is every hour × 100 km.
  3. The first point would be plotted at (0, 100). If the car travelled at the same rate (100 km every hour) then the line would go on the same angle (slope) and would be parallel (run alongside) the first line.

Action

Elements of a graph

A graph has many necessary elements that need to be included. There must be a title, labels for each axis, and a proper scale.

Explore the following video to deepen your understanding about graphing.

The following is a diagram showing the different elements in a line graph.

This is a line graph that is labelled with 5 main elements: title, x-axis, y-axis, labels and scale. The title of this graph is “Average Temperatures in Toronto.” The x-axis is a line going horizontal at the bottom of the graph. This axis is labelled with the 12 months of the year starting with January. The y-axis is a line going vertical on the left of the graph. This is labelled with the temperature from negative 5 to 25 degrees Celsius. The scale for the y-axis is every tick mark (interval) is 5 degrees Celsius.

Select one of the problems below, and show your work using a method of your choice.

You will create a table of values, a graph, and write the pattern rule.

Problem one

A delivery driver receives $15 an hour, works eight hours a day, and receives an extra five dollars at the end of each day as a tip. Predict how many days it will take to make $400.

Press ‘Answer’ to reveal the answers and check your work.

If a driver makes $15 an hour × eight hours a day = $120 a day + $5 = $125

Day Total Money Made ($)
1 125
2 250
3 375
4 500

This is a line graph titled “Total Money Made by the Driver.” The x-axis is labelled with each day from 0 to 4. The y-axis is labelled with money made in dollars from 125 to 625 dollars. The amount of dollars between each of the tick marks (intervals) on the y-axis is 125 dollars. The line plotted on this graph matches the table of values provided just before this line graph.

Pattern rule: day × $125.

It will take 4 days to make $400. They will have $100 extra!

Problem two

In the Rocky Mountains it snows 50 cm per week for 12 weeks. Predict what week there will be 600 cm of snow.

Press ‘Answer’ to reveal the answers and check your work.

Week Amount of Snow (cm)
1 50
2 100
3 150
4 200
5 250
6 300
7 350
8 400
9 450
10 500
11 550
12 600

This is a line graph titled “Snow in the Rocky Mountains.” The x-axis is labelled with each week from 0 to 12. The y-axis is labelled with amount of snow in centimetres from 100 to 700 centimetres. The amount of dollars between each of the tick marks (intervals) on the y-axis is 100 centimetres. The line plotted on this graph matches the table of values provided just before this line graph.

Pattern rule: week × 50 cm

There will be snow during the 12th week.

Consolidation

Variety of patterns

Name a variety of ways to represent a pattern and explain which way is easiest for you to determine and extend the patterns. Record your thinking using a method of your choice.

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

I feel...

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.