GeoGebra

Maths and science

Autor:Mihai Mihai
1. Physics – Speed and Time GraphMathematical idea: linear functions and graphs. Problem: A car moves at a constant speed of 20 m/s. GeoGebra ActivityCreate a distance-time graph. Steps
  1. Open GeoGebra Graphing Calculator.
  2. Insert the function:
  1. Set x-axis as time (seconds).
  2. Set y-axis as distance (meters).
  3. Observe the graph.
Tasks
  1. Find the distance traveled in 5 seconds.
  2. Find the distance traveled in 12 seconds.
  3. Determine if the graph is increasing or decreasing.
  4. Explain what the slope represents.
Questions
  1. What happens to the distance when time increases?
  2. Why is the graph a straight line?
  3. What would happen if the speed doubled?
2. Chemistry – Temperature and Reaction RateMathematical idea: coordinate systems and data analysis. ProblemThe reaction rate increases with temperature. GeoGebra ActivityCreate a scatter plot. Data
  • (10,2)
  • (20,4)
  • (30,7)
  • (40,11)
  • (50,16)
Steps
  1. Insert all points into GeoGebra.
  2. Use the Spreadsheet or Point tool.
  3. Analyze the trend of the graph.
  4. Connect the points.
Tasks
  1. Identify the temperature with the highest reaction rate.
  2. Describe how the reaction changes.
  3. Estimate the reaction rate at 60°C.
  4. Determine whether the relationship is linear.
Questions
  1. Why does temperature affect reaction rate?
  2. Which point represents the fastest reaction?
  3. Is the graph increasing or decreasing?
3. Biology – Population GrowthMathematical idea: exponential growth. ProblemA bacteria population doubles every hour. GeoGebra Activity Create a population growth graph. Steps
  1. Insert the function into GeoGebra.
  2. Set x-axis as time (hours).
  3. Set y-axis as number of bacteria.
  4. Observe how the graph changes.
Tasks
  1. Find the population after 3 hours.
  2. Find the population after 6 hours.
  3. Compare the growth between hours 2 and 5.
  4. Explain why the graph rises quickly.
Questions
  1. What type of graph is this?
  2. Why does the population increase rapidly?
  3. What happens after many hours?
4. Physics – Projectile MotionMathematical idea: quadratic functions. ProblemA ball is thrown upward. GeoGebra ActivityCreate the trajectory graph. Steps
  1. Insert the function into GeoGebra.
  2. Observe the parabola.
  3. Find the maximum point.
  4. Determine where the graph intersects the x-axis.
Tasks
  1. Find the maximum height.
  2. Determine when the ball reaches the ground.
  3. Identify the axis of symmetry.
  4. Explain why the graph is a parabola.
Questions
  1. What does the highest point represent?
  2. Why does the graph curve downward?
  3. What happens if the initial force increases?
5. Chemistry – pH ScaleMathematical idea: logarithmic relationships. ProblemThe pH scale measures acidity. GeoGebra ActivityCreate a pH number line. Steps
  1. Draw a horizontal axis from 0 to 14.
  2. Mark:
    • Acidic: 0–6
    • Neutral: 7
    • Basic: 8–14
  3. Place sample substances on the scale.
Tasks
  1. Identify acidic substances.
  2. Identify basic substances.
  3. Compare pH 3 and pH 6.
  4. Explain what pH 7 means.
Questions
  1. Which substances are most acidic?
  2. Why is the pH scale mathematical?
  3. What happens when pH increases?
6. Biology – Heart Rate InvestigationMathematical idea: statistics and averages. ProblemMeasure heart rate before and after exercise. GeoGebra ActivityCreate a bar chart. Data Example
  • Student 1: 70 → 110
  • Student 2: 72 → 120
  • Student 3: 68 → 115
  • Student 4: 75 → 125
Steps
  1. Insert the data into GeoGebra Spreadsheet.
  2. Create a bar chart.
  3. Compare the values.
  4. Calculate the average heart rate.
Tasks
  1. Find the highest heart rate.
  2. Find the average before exercise.
  3. Find the average after exercise.
  4. Explain how exercise affects heart rate.
Questions
  1. Why does heart rate increase?
  2. Which student had the largest increase?
  3. Why are averages useful in biology?

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