Grade 2: "What Inspires You to Move During DPA?"
(From: OAME)
6 Day Mathematical Modeling Lesson Plan
Embedded Files
(From: OAME)
6 Day Mathematical Modeling Lesson Plan
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Content
Content
Big Idea:
Big Idea:
Mathematical Modelling
Expectations:
Expectations:
Algebra
C.4 apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations
Social Emotional Learning Skills (SEL) in Mathematics and the Mathematical Processes
A1. Throughout this lesson, 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.
To the best of their ability, students will learn to build relationships and communicate effectively as they apply the mathematical process of communicating (express and understand mathematical thinking, and engage in mathematical arguments using everyday language, language resources as necessary, appropriate mathematical terminology, a variety of representations, and mathematical conventions) and of selecting tools and strategies (select and use a variety of concrete, visual, and electronic learning tools and appropriate strategies to investigate mathematical ideas and to solve problems), so they can work collaboratively on math problems – expressing their thinking, listening to the thinking of others, and practising inclusivity – and in that way foster healthy relationships.
Learning Goals
Learning Goals
We want students to...
We want students to...
to understand the first component of the mathematical modeling process: to determine what information is needed to answer the question.
to understand the second component of the mathematical modeling process: to make assumptions about the criteria that inspire children to participate in a DPA routine.
to understand the third component of the mathematical modeling process: to develop a model for rating a DPA routine.
to understand the fourth component of the mathematical modeling process: to analyze and evaluate the model.
Success Criteria
Success Criteria
I can demonstrate that...
I can demonstrate that...
participate in discussions during all four components of the mathematical modeling process.
find the information necessary to determine the criteria in a DPA routine that inspires children to get moving.
make assumptions about the criteria that inspire children to participate in a DPA routine.
participate in the creation of a model to rate a DPA routine.
test the model for rating a DPA routine and modify it as needed.
Materials
Materials
Chart paper for teacher use
Grid paper or lined paper for students to use
Writing material for student use: chart paper or smaller paper, markers or pencils.
Accessibility of iPads for music
tools for calculating duration (chronometers, watches, clocks, etc.)
Rating Olympic Diving slide deck
Set up groups in advance. During the team work, the students will be able to discuss in order to formulate questions and formulate suppositions. They could use a virtual whiteboard to support their discussions, such as shared slides, Google Jamboard, Zoom Whiteboard, Padlet, to keep records of the engagement and collaboration of each team member.
teacher background
teacher background
Prior Learning:
Prior Learning:
Students should have experience working together in problem solving situations.
The students have already performed sequences of rhythmic and dynamic movements.
Pedagogy
Pedagogy
Understanding the situation
Understanding the situation
Day 1
Explain to students that the Ontario Ministry of Education asks teachers to get students moving every day. Teachers must also teach dance.
Dancing and moving make an ideal combination. Have you ever done a routine that gets people moving and dancing?
Our principal has asked our class to figure out some way of knowing what kinds of DPA lessons will inspire students to move and dance. All the classes in the school need to do their DPA, and we will be helping the other teachers figure out how to choose a good DPA routine for their classes.
Teacher Moves:
The goal for this lesson is for students to look at a DPA with a critical eye and determine if it is a routine that does what it should do: inspire kids to get up and move. They will need to agree on certain criteria to use to rate a routine. They will need to create a model, or rating sheet, to help them make this determination. They will need to work as a team to do this.
Do a Think/Pair/Share to start reflecting on what makes a DPA lesson or dance lesson inspiring for others.
Possible responses from students:
We have to think about …
What makes the DPA fun?
What makes it easy to do so students can follow along?
Does it need to have music?
Ask the class to come back together and share their ideas with the class. Write these down so that it can be displayed through this lesson.
Following the discussion, present three video sequences. Have the students perform the sequences together.
First exercise routine: Superheros Unite
Second exercise routine: Zumba Kids
Third exercise routine: Chair Stretch Routine
After performing each routine, ask students to record their observations about the routine. What did they find inspiring? What did they not like?
Here is an example of a possible template.
After completing all three routines, refer back to the list of criteria they made together earlier. Ask: Is there anything else we should include on this list? Have you thought of anything else that makes a DPA routine inspiring to others?
Teacher Moves:
While they are chatting with a partner, walk around and listen to see if they are thinking about what is really important in organizing a DPA lesson.
Possible discussion points to look for:
Music
Not too easy and not too hard
What length of time is considered
Fun characters are a part of the routine (if it is on video)
There is a chance to rest in between the big moves
After performing the first routine, ask students some questions to help them get started on their observations. Some possible questions include:
Did you like this routine? Why? What did you like, or dislike, about it?
Did it make you want to move?
What about it made you want to move, or made you not feel like moving? (It may have felt easy, or too complicated, just the right speed or too fast for them. They may have disliked the song.)
Ask them to share any other observations or questions that might be important to consider when determining their criteria. Were these videos good examples of those criteria?
Following the compilation of their observations after performing the exercise routines, invite students to come together in pairs and discuss their observations. Have students write down any observations or questions during the pair meeting.
You may want to pair two groups for further reflection before doing the whole class sharing. This can generate more questions.
Opportunities for Differentiation
Since you want everyone to develop the ability to ask questions, it is important at this point to observe whether both students are participating in the discussion with their partner. If one person comes up with more ideas, ask the other student "What do you think?" Can you think of anything else that is important to consider?"
To properly guide students, it is important to get them to think about the complexity of the routine they will have watched. If some teams seem to have difficulty concentrating on the teaching intention, you can question them by bringing them back to the exercise routines they did on Day 1.
When you watched the routines, what made you like them?
What made you feel like you’d like to do them again?
Is there anything that could have been different in the way the routines were presented that would have helped you perform the movements better?
Opportunities for Assessment
Save your observations for evaluation.
Keep track of the ideas and assumptions of each team. This Assessment notes recording sheet may be useful for you to use.
Analyze the situation
Analyze the situation
Say: "Let’s think about the routines we watched yesterday. We made a list of things that make a routine inspiring to others. We are going to create some kind of a tool that the principal and other teachers can use to rate how good a DPA activity or dance is to inspire students to move."
Invite students to go into groups of 4 to pick the top 3-4 or 5 criteria (depending on your class size and the groups) from the list already established on day 1, that they believe will help inspire students to move. Give them about 10 minutes to work on this.
Gather the class back together and have groups explain to the class why they think their criteria is important. These are their assumptions they are making about what makes the routine inspiring. As they present, make sure they include specific details. For example, instead of saying, “It can’t be too short.” Ask them what they mean by this. How long should it be?
As before, write these down for later reference.
Students' possible ideas / assumptions:
A good routine needs to vary movements to make the routine interesting.
It should not have too many movements because the students will have difficulty performing the routine. It should be easy to remember.
A good choice of music is helpful because it will help the students to memorize the movements.
A sequence of movements can be inspiring because it will help with memorization.
A routine should not be too short or too long. We need to figure out how long it should last.
A good routine has some slower movements or rest time in between the hard movements or at the end.
A good routine repeats a lot of the same movements.
After you write down the list of the students’ assumptions, ask questions to make them think further about their ideas. Choose a few of the common assumptions that a few groups may have shared. Also consider discussing some good assumptions that only one group may have considered.
For example, your students may make an assumption that inspiring routines have a variety of movements. Ask them:
How many movements should an interesting routine contain?
Should the routine have a lot of different movements or should it repeat some movements?
If they have not naturally identified timing, guide your students toward the assumption that the routine should not be too short or too long. Ask them:
What about the time? What is the “just right” amount of time for a routine? Are short routines okay? How long is too long?
Continue this questioning for the list of assumptions.
After the class has discussed their ideas and assumptions, the teams regroup again and decide which ideas change, which ideas should be added and what remains unchanged.
Opportunities for Differentiation
If some teams seem to have a harder time focusing on the essentials of the task, you can question them more specifically to get them to make certain changes.
For example, say, “I see that you have a lot of ideas for what makes a good DPA routine, but there doesn't seem to be a consensus on how to make a decision. Is it possible to combine two ideas together? ”
For example, say, "I see you have a lot of ideas for what is important but you don't write your ideas down. How can you remember all the ideas discussed?”
Teacher Moves
The goal for today is to create a list of criteria one could use to rate a DPA routine. Groups work toward creating their own list, then the whole class works to create a common list of possible rating criteria.
Before regrouping the teams, discuss the collaboration criteria.
Here are some suggestions and discussions in order to co-construct the collaboration criteria with the students.
Ask them to choose a spokesperson to represent them in communicating the team's ideas to the class.
You may want to discuss the role of a spokesperson beforehand.
What does a spokesperson do?
How will you choose the spokesperson?
How can you make sure everyone's ideas are noted?
How are you going to ensure that all members participate equally?
When the students are grouped together, walk around and observe how they work together.
When you see a situation where students are collaborating, highlight it so they know what is expected of them.
For example, say, "I see you taking turns adding an idea and you don't interrupt."
For example, say, "I can see you all writing down the ideas you have selected."
Ask the spokesperson of each team to explain their ideas. This may cause other students to want to modify or supplement the list of possible questions.
Note the team's ideas presented by the spokespersons. If some ideas are the same, put a checkmark next to it.
In the process of mathematical modeling, once the question has been chosen, students must now determine what information is needed in order to begin planning.
As the groups discuss, walk around, listen, and see if they ask you questions for more information. Are they focusing on the right information to move them into the planning phase? (Third component - Create a model of the situation).
When discussing student assumptions with the group, remember that there might not be one right answer. For example, there is no exact “just right” amount of time that a routine should last. Your students may have decided that ten minutes is too long, and two minutes is too short. Or they may have decided that two minutes is just right and five minutes is too long. If the group has trouble coming to a consensus deciding “about” how long a routine should take, use a timer to test this assumption. Have them watch the previous videos again and watch the time. Talk about why a routine that is too long would not appeal to kids who have trouble memorizing or performing all the moves.
Discuss how a routine that is too short won’t get their heart pumping, especially when the reason for the lesson is to move, to expend energy, and to make our heart beat.
create a mathematical model
create a mathematical model
Days Three, Four:
Students will now create a model to help rate how good a DPA activity is at inspiring students to move. They will work with the same group as before.
Ask groups to think about how important each of their top 3 (or 4 or 5) criteria are. Are they all equally important? Are some criteria more important than others?
Say: Have you ever watched the Olympics? The Olympics are a sports competition where athletes from different countries compete against each other. In some sports they can win a gold medal by winning a game, like soccer or hockey. In other sports there are rates the judges use to decide who gets the gold, silver or bronze medal. To make it fair for all the athletes they have a set of rating criteria. They compare each athlete on the same criteria.
Show the students the Rating Olympic Diving slide deck. End with the discussion slide: How do you think rates keep track of each athlete’s score? Discuss how they will know they have the best score.
Say: How can we use these same ideas to rate the DPA routines? In the Olympics, only one person can win the gold medal for each sport. But we might have several DPA routines that we think are inspiring.
Refer back to the criteria list the class made previously.
Have groups take their own set of criteria and decide how important each criterion is by assigning a maximum number of points they can give to each of those elements in a routine.
Teacher Moves:
Today’s goal is to have each group choose at least 3 but not more than 5 criteria they want to add to their scoring sheet. Each group will choose the criteria they think should take priority. You can differentiate for the class by telling them how many criteria to work with, or you can ask them to decide for themselves. Each group may have a different number of top priorities. This conversation is part of them figuring out their model.
In addition to choosing the criteria, students will need to create a rating criteria sheet. You will discuss different ways a rate might keep track of their scores but do not decide for the students how this should look. Creating the model with their group is an important part of the learning in this section of the lesson.
Rates keep track of scores in the Olympics using a computer program that computes the final score for them. Students may suggest this. How can they create it on their own?
Students should determine how many points each criteria is worth. They might decide to make each criteria worth the same number of possible points, or they might decide one is more important than the other and should be worth more points. Point out that the diving rate has to make sure the points add up to no more than 100. But in some other Olympic sports, like gymnastics, the top score is 10. It is important here to not give students a range for scores, but to prompt them to choose some smaller numbers. Say: “What do you think? Would it be helpful to choose a maximum number of points for each DPA routine we are going to rate?”
Opportunity for Differentiation
Resources shared in this section focus on the Olympic sports of diving. However, you may find it useful to tailor this to your own community. If your students are involved in animal rating at a fair, for example, it might make more sense for you to use this as an example. If you are teaching this during an Olympic year you may find some current athletes to highlight.
Opportunity for assessment
Keep records of changes made by students for evaluation.
Opportunity for Differentiation
An Excel spreadsheet could be used to create the score sheet, but grade 2 students are unlikely to be familiar with this application. Pairing up with a student in an older class to collaborate may be useful to some or all of your class.
Analyze and Assess the model
Analyze and Assess the model
Day 5
Have students all do a few dances / DPA activities and each use their model to rate how "inspiring" they were. At the end of each, the students should get together with their group and rate each routine. After each group has had a chance to rate two routines using their own rating criteria sheet, have them trade with another group. They will now use another groups rating sheet to rate two routines. Have the two groups get together and compare their ratings. Did they have the same criteria on their sheet? Was the rating sheet easy to understand and use?
Gather students in their groups once more. Say: Now that you have used your own criteria sheet as well as someone else's, you might want to make some changes.
Discuss what they might want to do to make their models better. Give them time to make these revisions.
After everyone has watched and rated another routine with their revised rating sheet, display copies of the final rating criteria sheet that each group has made and bring the students together for a gallery walk to examine the similarities and the differences.
Then gather for a math congress to discuss this:
Possible answers for similarities:
All teams have variety in their movements as one of their criteria.
All teams have a routine of more than 5 minutes.
All the teams thought fun music is important.
All teams liked having repeated movements.
Possible answers for the differences:
Some teams thought music was the most important, but other teams thought length of time was the most important.
Some teams gave one point for each criteria, and other teams rated each criteria differently.
Only one team thought it was important to have fun characters doing the dance.
Ask questions about the fourth component of the mathematical modeling process.
Say: Now you have to go back to the previous components to refine the model based on the new information.
What elements of your rating criteria sets a great example for other teams? (Which works very well and which should you keep?). Why?
Is there something you would like to change in your rating criteria now that you have analyzed and noted the similarities and differences between the different rating sheets?
Allow time for teams to come together again and assess the change they will make to their rating sheet based on the new information.
Teacher Moves
At this point, it will be necessary to provide enough space for teams to test their rating criteria sheets. Together the class can view more DPA videos or participate in familiar DPA routines the class already knows.
Ask the two groups who exchanged rating sheets to meet and give each other feedback. Improving communication is the SEL goal for this lesson set. Direct groups to give each other specific feedback.
Did their rating sheet make sense?
What was the same about the two rating sheets?
What was different?
Are there any improvements you would recommend?
(Since these two teams were able to apply the model of the other team, they’re also able to give them feedback.)
Do you want to make any changes to your own rating sheet?
The teacher should guide their students while they reassess their routine.
Ask questions regarding the fourth component of the mathematical modeling process:
(At this point, you have to manage socio-emotional skills during these changes.)
Here, the teacher can act as an instigator by presenting a voluntary change forcing a re-evaluation of the model:
For example:
The principal would like to share these rating sheets with other teachers so they can learn how to rate DPA routines and choose routines their students will like. You will need to show the principal and other teachers how to use your rating sheet. Will this change your rating sheet at all? For example will the rating be the same if it’s shared with a grade 1 teacher or with a grade 6 teacher?
Regardless of the changes made or the discussion around which elements they decide to remain unchanged, take the time to question the teams to clearly identify the reasons that push them to make changes in their rating sheet, or how they justify keeping them the way they are.
Here are some possible examples of changes students might decide to make in their rating sheet.
Some teams may decide to use fewer/more criteria.
Some teams may decide to choose different criteria.
Some teams may decide to change the way they score the routines. Maybe they wanted to give each section a score out of ten and now they realize a score out of 5 is enough.
Consolidation of learning
Consolidation of learning
Day six:
Have each group present their final criteria sheet to the class. After each team has presented, the group must decide how to choose one to share with the principal.
After this, discuss the process of Mathematical Modelling with the class. Ask them:
Can you think of other times when someone might find a model like a rating system helpful? When else might we need to create a rating system to analyse something? (possible answers: rating an assembly or other class activity, rating a restaurant, rating some recess equipment, rating the choice of caterer for hot meals at school)
Why did some groups have different criteria?
How do our assumptions about what is important affect our models? (Possible answers: Some children think music is most important and others think short routines are the best. Some people like to dance for DPA, other people like to do other exercises. They rate each assumption differently therefore the scores are different for each model).
Do you think another class that did this activity would come up with exactly the same rating sheet? Why or why not?
How did you use communication skills when making your models with your group? Why is communicating important in math class?
Think of other times when you’ve had to communicate with each other in math class. How was this time the same, or different?
Opportunity for Assessment
Students could make a video of themselves explaining their rating sheet to others. They could do this as a team, or individually, depending on your assessment goals.
Teacher Moves:
It is important to let the students decide how they will go about choosing the final criteria sheet to share with the principal. Will they vote on one that has already been created? Will they decide to combine several ideas that have been presented to create a new sheet.
After this has been decided, have the class test out their final decision by watching and rating one more DPA video or completing one more DPA routine. Finish up by having them share their criteria sheet with the principal or other teachers.
Afterwards, lead a short discussion with your class to help them reflect on the process of mathematical modelling and how models can be helpful.
Extension
Extension
Using the criteria they have agreed on, have students now create their own DPA dance sequence. Have them present these to the class. Have another adult come in to “rate” the routines based on the criteria.
You could also have students make a collective routine. Each team would have a predetermined time to organize then the routines would be assembled as a collective sequence of movements (thus differentiating depending on the students needs).
If possible, plan to review a mathematical modeling task several times during the year, which will allow students to make connections between different subject areas, different problems sharing similar underlying structures, different tools and different strategies.
Completing this «Further Consolidation/Next Steps» will also address the following curriculum expectations:
Health and Physical Education:
B: Active Living:
B1. participate actively and regularly in a wide variety of physical activities, and demonstrate an understanding of how physical activity can be incorporated into their daily lives;
C: Movement Competence:
C2. apply movement strategies appropriately, demonstrating an understanding of the components of a variety of physical activities, in order to enhance their ability to participate successfully in those activities.
D: Healthy Living:
D2. demonstrate the ability to apply health knowledge and social-emotional learning skills to make reasoned decisions and take appropriate actions relating to their personal health and well-being.
Technology
Technology
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