Big Idea:

Mathematical Modelling relating to choosing Daily Physical Activity (DPA) activities

Expectations:

Algebra

• C4. apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations

Physical and Health Education

• B2. demonstrate an understanding of the importance of being physically active, and apply physical fitness concepts and practices that contribute to healthy, active living

  • B2.3 assess a specific component of their health-related fitness by noting physical responses during various physical activities, and monitor changes over time

Social-Emotional Learning (SEL) Skills in Mathematics and the Mathematical Processes

• A1. Throughout this grade, in order to promote a positive identity as a math learner, to foster well-being and the ability to learn, build resilience, and thrive, students will apply, to the best of their ability, a variety of social-emotional learning skills to support their use of the mathematical processes and their learning in connection with the expectations in the other five strands of the mathematics curriculum.

In this lesson, to the best of their ability, students will learn to think critically and creatively as they apply the mathematical processes reflecting (demonstrate that as they solve problems, they are pausing, looking back, and monitoring their thinking to help clarify their understanding) and communicating (express and understand mathematical thinking, and engage in mathematical arguments using everyday language), so they can make connections between math and everyday contexts to help them make informed judgements and decisions.

Present the situation

Teacher: “We have tried several different DPA activities this year, and there are many others we could try too. How could we determine which DPA activities are the best for us?”

Students will start this process by looking at existing DPA activities and extracting criteria. (This could be done as a whole class, or in pairs or groups).

Virtual Learners: Use virtual breakout rooms and the recording tool.

Students may ask: “What do you mean: a good game/ activity?” (Teacher: “I don’t know. How could we define a good activity?” - Teachers shouldn’t answer this question, this addresses the idea of making assumptions)

Discuss favourite current activities to help them focus.”What is good about __________ as DPA activity?”

Students as a whole class will discuss one current DPA activity and begin to generate a short list of criteria from this discussion.

Opportunities for Differentiation

• More frequent check-ins to ensure students are focusing on creating the rating scale, not discussing DPA activities.

Opportunities for Assessment

• Listen to conversations. Students here are engaging in the process of identifying their assumptions about the problem.

• Listen to groups or prompt them to think of balance of criteria - i.e. not just things that are fun.

• Ask students what the purpose of DPA is. This may lead the class to look at the DPA document from the Ministry DPA4-6.pdf

• Identify variables that may change (inside or out, amount of time needed) and ones that should stay the same (needs to require exertion)

T: “Your next job with your group is to create a rating system that we could use. Use the criteria you have decided are important, and decide how an activity could be rated on each criteria.” (e.g. a 1- 5 scale, a 1-10 scale, a percent, or other numerical rating scale.

“Your rating scale should be able to give an activity a total score that reflects its value.”

“Remember, the purpose of your rating system is that it will help us decide whether we should continue using an activity or game.”

Give students some time in their small groups to decide on a rating scale to use.

Stop the class and add this prompt:

T: “We agree that activities should be safe (or any other criteria decided upon). You have also mentioned that it is important for an activity to be fun (or another criteria decided upon). Are some of these criteria more important than others when deciding which DPA activities we should keep or remove?”

T: “How could you adapt your rating system so that it allows you to give different values to more important criteria?” (e.g. assigning different numbers of possible points for more or less important criteria, or having some criteria be given multipliers so that they count more in the total score that an activity earns in the rating system)

T: “How could we decide if the game/activity is active enough? How could we decide if it meets enough criteria? How could we know if enough students are enjoying the activity?” (use any of the criteria your class has developed here)

“Do we need to collect some information? How could we collect information?”

Prompt students to decide how this will be collected.

E.g.:

• For the survey option: “What would your survey ask? How would you combine the answers from the different students who answer it?”

• For the observer option: “If you were watching an activity, what would you look for to make sure it is safe?” (or other criteria)

• For the option where another group uses your rating system: “Do you need to add any instructions to clarify this system for the other group who will use it?”

Teacher Moves:

The rating system that the groups create is the mathematical model that is the focus of the lesson.

*Note: A numerical rating system (as opposed to a scale with steps like “Somewhat”, “Very”) will allow students to develop a framework to determine which criteria is more important than other criteria.

The rating system needs to account for the fact that some criteria are more important than others.

Some rating systems could achieve this by simply giving more important criteria a larger total point score

E.g - level of exertion can get a possible total of 10 points, whereas amount of equipment may get a possible total of 3 points. This allows more important criteria to count for a greater amount of the total score.

A different scale might use multiplicative thinking and rate every criteria out of 5 (or 10), but more important ones may have their value multiplied to arrive at a total. E.g. Score for level of exertion, safety and inclusiveness might be multiplied by 3, and others (easy to understand, amount of equipment) be left with the original total out of 5 (or 10) points.

Students’ rating systems they are creating should be useful for evaluating any DPA activity.

Virtual Learners: Students use a shared document to produce their rating system. If students need to do some data collection (e.g., to observe a DPA activity to record it, they can watch videos on the OPHEA website or try them out with family members). One of the criteria could even be "ease of doing the DPA activity at home".

Once the groups have created their rating scale, they may ask how an activity is assigned their rating (if not, prompt them to think of this).

For example, how is it decided whether an activity is rated as a “4” or “5” for exertion? Some possible solutions to this are:

• Students who have done the activity are surveyed, and their scores combined.

• A given student in a group leading an activity observes and gives the rating

• A different group than the one who created the model gets to use it to rate a given activity.

Trying the rating system:

The class should then do a DPA activity, and use their rating systems (in the manner they have decided on) to evaluate it.

They will look at the results of the rating system and assess how well that rating of the DPA activity matches their perception of the quality of the activity.

Here is where the teacher discusses assumptions -- what they are, how they influence our work, why they need to be considered. Might some of the assumptions they made when creating their rating scale need to be reconsidered?

Student groups will decide if their model has worked well, and what they might change.

Students can present their findings to the class. They should include what they saw as successes and failures of their model and what they are planning to change.

• Students should revise their rating scales based on their first experience using it.

Then the class can try other DPA activities to test out their revised rating systems.

• The teacher can support students to create a composite rating scale for the whole class that can be used. (Choose some questions from different student groups, different descriptions of the rating scale etc.)

• Student groups can try out the model by looking at a new possible DPA activity and think about how it might meet the criteria in their rating system. If their rating system would predict it would be a good activity, then the students can teach that activity to the class.

• Student groups are responsible for choosing a new activity from a selection provided by the teacher (or a game of their own), teaching it to the class, writing it up for the class, including how it was rated based on the rating system. These could be kept in a binder. (see sample recording sheet here- you will add your own criteria and ratings to it)

Teacher note: If the class is not confident in their rating system, they could have their model assessed by a qualified physical education teacher to ensure safety and get his/her opinion on their rating system. The class may need to make some criteria non- negotiable. For example, safety and inclusiveness (whether every student can participate in the activity) are absolutely necessary.

• Once the class has created a system they are confident works well to find good DPA activities, they could offer it to other classes to use. Students could present the system to the students in other classes.

• An important feature of mathematical models is that they can be adapted and used in other contexts. Have a discussion with students about what other situations they could apply their model to. How could their model be adapted or modified to be useful in that new situation?