Use this original formative assessment after graphing practice. Students read values, compare changes, and distinguish a pattern from a causal explanation. Materials: the graphs or data below, paper, and a calculator if appropriate. Prerequisites: axes, units, line graphs, bar charts, and scatterplots.
Graph data and accessible alternative
The three datasets are simulated. The tables provide the complete values for students who use a screen reader or need a text alternative.
Graph preparation: construct the three graphs from the data tables below, then answer the questions. Use a line graph for A, bars for B, and a scatterplot for C. No external image is required.
Graph A: time (days)
Height (cm)
0
0
2
4
4
7
6
9
8
10
Graph B: condition
Germinated seeds out of 20
A
8
B
14
C
11
Graph C: leaf length (cm)
Leaf width (cm)
3
1.5
4
2.0
5
2.1
6
3.0
7
3.2
8
4.0
Questions
In graph A, which variable is on each axis, and what are its units?
How tall is the seedling on day 4?
Which two-day interval shows the greatest increase? Calculate that interval’s average increase per day.
What is the average increase per day over the entire day 0–8 record? Does that mean the seedling increased by the same amount every day?
In graph B, calculate the germination percentage for each condition.
By how many percentage points does B exceed A? What additional design information is needed before claiming a treatment caused the difference?
In graph C, describe the association. Would joining points in collection order clarify it?
Does graph C establish that increased leaf length causes increased width? Explain.
Answer explanations
Horizontal: time in days. Vertical: height in centimeters. Axis placement does not by itself prove a causal relationship.
7 cm, read at day 4.
Day 0–2: (4 − 0) ÷ (2 − 0) = 2 cm per day, the largest interval average.
(10 − 0) ÷ (8 − 0) = 1.25 cm per day. This overall average does not imply a constant daily rate; the interval increases differ, and no daily values between the plotted times were measured in the dataset.
A: 8/20 = 40%; B: 14/20 = 70%; C: 11/20 = 55%.
70 − 40 = 30 percentage points. Need treatment definitions, comparable conditions, independent replication, and the assignment method to evaluate a causal interpretation.
Longer leaves tend to be wider. Joining independent leaf measurements in arbitrary collection order would imply an order that the data do not have.
No. This observational association does not identify a mechanism or rule out other influences.
Teaching notes: Award credit for supported reasoning and units, not a memorized phrase. Ask students to correct one misleading statement after review. Provide large-print graphs, oral explanation, or table-based access as needed. These explanations apply only to the new questions above; the former embedded quiz and placeholder are replaced.