Minds On
Equations in everyday situations
Describe some everyday situations where you could use an equation.
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Sample responses: I could use an equation if I had a budget and wanted to know how many of specific things I could buy.
I could also use an equation if I wanted to calculate how much paint I needed to decorate my room.
I could use an equation to calculate how much space a new garden would take up.
I could use an equation to figure out the volume- how much I could pour into a container.
What real-life situation might be described by the equation: 2x + 10= 22?
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I bought 2 plants and something else for $10, and altogether I spent $22. I want to figure out how much each plant cost.
I had some toonies and a $10 bill, and altogether I had $22. How many toonies did I have?
In a class with 22 students, we had one group of 10, and then some partners (groups of 2). How many groups of 2 were there?
Action
Ball drop versus bounce
Develop the following math model:
When a ball is dropped at height h, how high does it come back up in relation to the height it was dropped?
Is there a pattern or formula that will give you the bounce height when you know the drop height?
You can use objects such as a meter stick, a ball, a digital app, or other materials in order to help support your thinking.
Use the Process of Mathematical Modelling chart to plan how you will predict, plan, analyze, model, and assess the mathematical investigation.
Press Process of Mathematical Modelling to discover the steps needed.
Make predictions and assumptions about the mathematical situation.
Create questions that will guide what wants to be discovered during the math investigation.
Think about the many ways that mathematics can be used to enable us to better understand the situation.
Create a model to test theories (for example, test the drop at 10 different heights).
Reassess the model and decide if it works or needs changing. (How are results observed?)
Record your observations and numbers through a method of choice, incorporating other math strategies previously learned.
Present your findings (chart, graph, diagram, detailed description, etc.)
Use your findings to justify your original question(s).
Consolidation
Reflecting on mathematical findings
Reflect on the mathematical process that was followed, and record your ideas using a voice recorder, speech-to-text, or writing tool.
- What is important about this process?
- In what way are assumptions key to developing an effective model?
- To what extent was your model helpful?
- What ideas would you add to the process?
Where would an experiment like this be useful? Who would conduct a similar investigation in real-life?
What variables can be changed (for example, size or type of the ball)? How do you think it might change the investigation?
Find a real-life investigation where data is collected over a period of time (for example, weather patterns in a certain area). How is this data presented? What observations can be made? What predictions do you notice?
Record your thinking using a method of your choice.
Reflection
As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.
I feel...
Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.
When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.