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