Graphing Points: Real-World Data Stories

Lesson 1 of 1

In this lesson:

• Plot and interpret points in real-world contexts
• Read coordinates from existing graphs
• Connect rules, tables, and graphs

Learning Objectives for This Lesson

1. Plot ordered pairs in a real-world context
2. Read coordinates of a point from a graph
3. Interpret each coordinate's meaning in context
4. Generate ordered pairs from a rule
5. Use a graph to answer questions
6. Plot pairs that follow a given rule

What Can a Graph Tell Us?

You already know how to plot points on the coordinate plane.

• (3, 5) — move 3 right, then 5 up
• But what does that point mean?

Today every point will carry a real-world story.

Labels Give a Graph Its Meaning

The same three points mean nothing without labels.

Every Point Tells a Real-World Story

• The x-coordinate tells the input quantity
• The y-coordinate tells the output quantity
• Together, they make a statement about the situation

Example: On a "Cups Sold vs. Dollars Earned" graph, the point (3, 6) means selling 3 cups earns $6.

Lemonade Stand: Building the Table

Each cup of lemonade costs $2. Fill in the earnings:

Lemonade Stand: Plotting the Points

• (3, 6) means selling 3 cups earns $6
• (5, 10) means selling 5 cups earns $10

Your Turn: Complete the Plant Table

A plant grows 3 cm each week.

Fill in the blanks, then plot.

What Does This Point Mean?

The point (5, 15) is on the plant-growth graph.

• The x-coordinate 5 means week 5
• The y-coordinate 15 means 15 centimeters tall

Sentence: After 5 weeks, the plant is 15 cm tall.

From Plotting to Reading Graphs

So far, we built graphs from tables.

But in the real world, you often see a graph first — and need to pull information out of it.

Next: reading coordinates from existing graphs.

Reading Points: Trace Down and Left

Trace from the point straight down to the x-axis and straight left to the y-axis.

Reading the Savings Account: Forward Lookup

Question: What was the balance at Week 4?

• Find on the x-axis
• Trace up to the plotted point
• Trace left to the y-axis →

Answer: The balance at Week 4 was $25.

Reading the Savings Account: Reverse Lookup

Question: When was the balance $25?

• Find on the y-axis
• Trace right to the plotted point
• Trace down to the x-axis →

Answer: The balance was $25 at Week 4.

Your Turn: Temperature During the Day

• What was the temperature at 11 AM (hour 3)?
• At what time was the temperature highest?
• Between which two hours did it drop?

Temperature Graph Answers and Key Takeaway

• At 11 AM (hour 3): 72 degrees
• Highest at hour 4 (noon): 75 degrees
• Temperature dropped between hours 4 and 5

Three Ways to Show One Pattern

We have plotted data and read from graphs. Now let's connect three representations:

• Rule — words or a formula
• Table — organized numbers
• Graph — visual picture

They all describe the same relationship.

Cookie Rule: From Words to Table

Rule: 4 cookies per box.

Cookie Rule: Points on the Graph

The points form a straight line through the origin.

Extend the Pattern Beyond the Table

If , what is ?

• Rule says:
• The point (7, 28) continues the line

Where would (7, 28) land on the graph?

Think about this, then advance.

Second Baker Offers a Different Deal

Rule: 2 cookies per box, plus 6 free.

Two Rules on One Graph

• Both lines cross at (3, 12)
• For 3 boxes, both bakers give 12 cookies

Which Baker Gives You More Cookies?

• Fewer than 3 boxes: Baker 2 wins (free samples help)
• More than 3 boxes: Baker 1 wins (4 per box adds up)

Which baker for a 6-box order?

Practice: Plot, Read, and Interpret

1. A car travels 50 miles per hour. Table for hours 1-4, then plot.
2. Savings graph: how much did the balance grow from Week 1 to Week 3?
3. Rule: . Table for to 4, then plot.

Answers to the Three Practice Problems

1. (1, 50), (2, 100), (3, 150), (4, 200) — steep line
2. Week 1 = $10, Week 3 = $20 → increase of $10
3. (0, 2), (1, 5), (2, 8), (3, 11), (4, 14) — line from (0, 2)

Key Takeaways and Common Mistakes

✓ Every labeled point is a real-world fact
✓ Read graphs by tracing down and left
✓ Rule, table, graph show one pattern

first — hallway then elevator
Count from zero at the origin
Read both axis labels first

Preview of What Comes Next in Math

• Grade 6 extends the plane to all four quadrants
• Today's skills transfer directly to negative values
• You will connect graphing to ratio tables

Great work today!