Mission 23 Unit 9 6.EE.C.9 · 6.RP.A.3

Tables and Graphs

6.EE.C.9 · Unit 10
Today's objective: Analyze the relationship between dependent and independent variables.
Need a hint?
Re-read the problem and underline the numbers and the question. Pick one representation (model, table, or equation), show your steps, and check that your answer makes sense for the situation.

The school garden club is growing sunflowers for a science fair. They measure the height of one sunflower every week. After week 1 it was 4 cm, week 2 it was 9 cm, week 3 it was 14 cm, and week 4 it was 19 cm. The fair is in week 8. Your team must represent the growth pattern using a table, a graph, and an equation, then predict the sunflower's height at week 8.

Sunflower Growth Over Time Week Height (cm) 0 5 10 15 20 25 30 35 40 1 2 3 4 5 6 7 8 (1, 4) (2, 9) (3, 14) (4, 19) (5, 24)? (6, 29)? (7, 34)? (8, 39)? Known data Predictions

The Problem

How tall will the sunflower be at week 8? Use the data from weeks 1-4 to find the growth pattern. Represent the relationship with a table, a coordinate graph, and an equation. Then use your equation to predict the height at week 8. Explain whether you trust your prediction.

Visual Model: Growth Table and Graph

Week (w) Height (h) cm Change Pattern 1 4 -- start 2 9 +5 5(2)-1=9 3 14 +5 5(3)-1=14 4 19 +5 5(4)-1=19 8 ? +5 each 5(8)-1=39 Constant rate: +5 cm/week

Step-by-Step Investigation Guide

  1. Read and organize the data. Write the week number and height as ordered pairs: (1, 4), (2, 9), (3, 14), (4, 19). Which value is the input (independent)? Which is the output (dependent)?
  2. Find the pattern. Look at the change between each pair of heights: 9-4=5, 14-9=5, 19-14=5. The height increases by 5 cm each week. What does it mean when the change is the same every time?
  3. Write the equation. The rate is +5 per week. Test: h = 5w - 1. Check: 5(1)-1=4, 5(2)-1=9, 5(3)-1=14, 5(4)-1=19. All match! Where does the -1 come from? What would the height be at week 0?
  4. Make the graph. Plot the four known points on a coordinate plane. Draw a line through them. Extend the line to week 8. Does the line go through all four points? What does that confirm?
  5. Predict week 8. Substitute w = 8: h = 5(8) - 1 = 39 cm. Check by reading the graph at w = 8. How confident are you in this prediction? What could make it less accurate?
  6. Reflect on the model. In real life, sunflowers do not grow at a constant rate forever. Discuss when this model might stop working. At what week might the sunflower stop growing? How would the graph change?

Language Support: Key Vocabulary

Table
An organized chart with rows and columns that shows input-output pairs.
Coordinate Graph
A picture that uses a horizontal axis (x) and vertical axis (y) to show points.
Equation
A math sentence with = that shows the rule. Example: h = 5w - 1.
Constant Rate
The same amount of change every time. Here: +5 cm every week.
Predict
Use a pattern or equation to find a value you have not measured yet.
Ordered Pair
Two numbers in parentheses (x, y) that name a point on a graph. Example: (3, 14).
Sentence Frames:

"The table shows that for every 1 week, the height increases by ___ cm."

"The equation h = ___ tells us that at week ___, the height is ___."

"I predict the sunflower will be ___ cm tall at week 8 because ___."

Multiple Representations

Week (w) Height (h) cm Check: 5w - 1
1 4 5(1)-1=4
2 9 5(2)-1=9
3 14 5(3)-1=14
4 19 5(4)-1=19
8 39 5(8)-1=39

See the hero graph above. The four known points form a straight line. The predicted points (dashed gold circles) continue the same pattern. The line goes through (0, -1) if extended backward — but a sunflower cannot have negative height, so the model only works for w=1 and beyond.

In words: "To find the height of the sunflower, multiply the week number by 5, then subtract 1. This works because the sunflower grows 5 cm each week, and at week 1 it was already 4 cm tall (which is 5 times 1 minus 1)."

Team Roles

Facilitator
Read the data aloud. Ask: "What is changing? What stays the same?" Guide the team to build the table first before the graph.
Model Builder
Draw the coordinate graph on graph paper. Label axes (Week on x, Height on y). Plot all known points and extend to week 8.
Precision Checker
Verify the constant change (+5 each week). Check that the equation gives the correct height for all 4 known weeks. Confirm the prediction.
Reporter
Write: "At week 8, the sunflower will be ___ cm because ___." Prepare to show how the table, graph, and equation all agree.

Timed Lab Phases

Ready
Click a phase, then press Start.
03:00
  • Read the scenario and data.
  • Assign roles.
  • Identify: what is the question you need to answer?
  • Checkpoint: Can everyone say the 4 data points?
  • Build the table with week and height columns. Add a "change" column.
  • Find the constant rate (+5 cm/week).
  • Write the equation h = 5w - 1.
  • Draw the coordinate graph.
  • Checkpoint: Do you have all 3 representations started?
  • Use the equation to predict week 8 height.
  • Check: does the graph agree with the equation?
  • Discuss: is 39 cm a reasonable prediction?
  • Checkpoint: Do all 3 representations give the same answer?
  • Reporter: practice showing all 3 representations.
  • Team: discuss when the linear model might stop working.
  • Practice answering the defense questions.
  • Checkpoint: Can the Reporter point to each representation and explain it?

Challenge

Extension: A second sunflower grew 3 cm per week starting at 7 cm. Write its equation. At what week will both sunflowers be the same height? Show this on the graph.
What If...?
  • What if the growth rate slowed to 3 cm/week after week 4? What would the graph look like?
  • What if you only had data from weeks 2 and 4? Could you still find the equation?

Real-Life Connection: Scientists track plant growth to study the effects of sunlight, water, and soil. Tables and graphs help them see patterns and make predictions — just like you did today.

Defense Preparation

  1. How did you find the rule from the data?"We noticed the height increased by ___ each week, so the rate is ___. We tested h = ___ and it matched all 4 data points."
  2. How do the table, graph, and equation connect?"The table shows the numbers, the graph shows the shape, and the equation gives the rule. All three show ___."
  3. Why did you choose a linear equation?"We chose a linear equation because the change is ___ every week, which means the graph is a ___."
  4. When might this prediction be wrong?"The prediction might be wrong after week ___ because in real life ___."
Rubric Quick-Check:
  • Table with at least 5 ordered pairs including the prediction
  • Coordinate graph with labeled axes and a visible pattern line
  • Equation written and verified against all data points
  • Week 8 prediction stated with reasoning
  • Discussion of model limitations

Exit Product

Submit a one-page Lab Report that includes:
  • A completed table (weeks 1-8 with heights)
  • A coordinate graph with labeled axes and plotted points
  • The equation h = 5w - 1 with explanation of what 5 and -1 represent
  • Week 8 prediction with a sentence explaining your confidence
Self-Assessment:
  • I can create a table from a real-world situation
  • I can plot ordered pairs on a coordinate graph
  • I can write an equation that matches a table
  • I can use all three representations to make predictions

Work Space

Table:



Graph:



Equation and Prediction: