Page 173 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

• Students might want to examine why stops are closer together in some areas. They might also look at how long it takes a bus to start and stop, collect data as to how far students are willing to walk to a bus stop, and so on.
2. Have students identify possible assumptions; for example, who gets picked up by the bus first and dropped off last, or the importance of shorter wait times at certain times of the day.
3. Have students identify what they think is important to consider. For example, they may want to determine the cost of constructing each bus stop and other considerations for working within a fixed budget.
D2.4 Process of Mathematical Modelling
determine ways to display and analyse the data in order to create a mathematical model to answer the original question of interest, taking into account the nature of the data, the context, and the assumptions made
Teacher supports
Examples
• displaying and analysing the data in order to create a mathematical model:
o Plastic waste contributes to the pollution of Earth’s ecosystems. How does the proportion
of plastic that ends up in recycling compare to the proportion that ends up in the garbage?
▪ creating the mathematical model may involve calculating the average mass of the
plastic waste in a recycling bin and a garbage bin and determining its percentage relative to the mass of other recyclables and other garbage in the same bin for different locations and for different times; it may also involve using this average to calculate the total amount of plastic in recycling and in the garbage for the entire population of interest
▪ displaying the data may involve representing it as a proportion of plastic in recycling to plastic in the garbage using a circle graph, or as a multiple bar graph to show a comparison of various locations or different times or seasons
▪ analysing the data may involve comparing the percentages and the actual amounts of plastic being recycled and being placed in the garbage at various locations or at different times or seasons
o Is there a relationship between the mass of a vehicle and its fuel efficiency or energy consumption?
▪ displaying data collected on the mass of a vehicle and its fuel efficiency or energy consumption may involve using a scatter plot
▪ analysing the data may include:
• describing the relationship between the mass of a vehicle and its fuel
efficiency or energy consumption by examining the scatter plot and 172