Friday Two Cents: A Problem Solving Model


In it there are four levels to achieve your goal to solve a problem.  The great thing is that you can use this problem-solving model not just for mathematical problems but also other problems in you may face in your life.  Here is my break down of the model…

A couple of weeks ago I wrote several posts about resolutions and making plans to help you beat the winter blues.  I have always thought that planning out things helps to solve the problems that I face on a daily basis, yet I have wanted something tangible that I can see in black and white to help me explain it to others.  I did find such a piece when I took a mathematics additional qualification course a couple of years ago.  It was in the Ontario curriculum, Grades 1–8: Mathematics (revised) document of all places. It is on page 13, figure 1: Problem Solving Model.  

Understand the Problem (the exploratory stage)

This stage should be self-evident.  I cannot tell you how many times I would have students come up to me and say, “I don’t get it.”  Then I would ask, “Did you read the question?”  Most of them would say ‘Ahhh no.’  ‘READ THE QUESTION’ I would say and then look in the question for the pieces you need to answer it.  Others I would rephrase the question to emphasize the important information they may need.  Basically what is the question asking of you: what is the problem?  The best advise I say to people is talk to someone about the problem so you can see it for different angles, especially after you read it several times.  

Make A Plan

Is there another situation that you may have seen a similar problem?  I tell students don’t try and reinvent the wheel.  Or in other words don’t start from scratch look at another situations where you solved a similar problem and try and rework it for this situation.  In essence, “Make a Plan”, think of a strategy you used before and use that plan.  Tweak the plan to fit your needs.  

Carry Out the Plan

Put you plan into motion.  Draw, write, use objects to help you visualize the plan and then implement it. Use different tools to make you plan work, monitor it and make adjustments when needed.  If you planned for something and you don’t need it, don’t use it. Why waste time and energy when you do not need it. 

Look Back at the Solution

Check you results, go back to the question to make sure that it actually answers it.  Does it make sense?  You have to go through the process again from the beginning to refine you answer or correct any mistakes you may have seen.  Could you get the same result another way, perhaps and easier way? This way you can use that revised plan in the future.  

I created this visual to help myself and others try and visualize how to solve a problem.  Maybe it will inspire other teachers and students to think more about how any problem can be solved so long as you have the tools and desire to make the effort in trying.  Remember what Napoleon Hill once said …

‘Effort only fully releases its reward after a person refuses to quit.’ Napoleon Hill

A Problem Solving Model

Ontario Ministry of Education. (2005). The Ontario curriculum, Grades 1–8: Mathematics (revised). Toronto: Queen’s Printer for Ontario. http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

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Art Inspiration: Art and Math in One Lesson


ArtInspirationPaulGLogo

During my practicum I had the opportunity to do the art lessons with the students. They are the younger primary but I wanted to do something that was different and challenging with them. Yet I also taught different lessons though out my stay there. One of the areas was Math. Yes many people do not like to teach or even learn math, but there are ways that you can introduce math concepts that are both fun and educational.

My mentor teacher and I were about to begin the next math unit with the students. It was the unit on 2 and 3 dimensional shapes. We wanted the students to be familiar with the different shapes we were going to use in the unit. Therefore I created a lesson plan for them around this idea. It was also fortunate that I had to use a type of lesson called a Choice Centres for one of my other classes. The Choice Centre strategy allows for a variety of activities providing different modalities and different levels of responses that help students investigate the topic further. Some adaptations can include drama, writing, reading, technology, viewing and experimenting. We were to use this model on a literacy lesson but our professor said we could use it on any subject matter, so long as we stayed true to the model. The model calls for a student to choose a centre and then stay there to explore the subject material. I adapted the lesson so that the students would be rotated to allow all the students an opportunity in each centre. The centres I created are as follows …   Centres (Materials And Instructional Notes)

  1. Blocks 3D shapes / construction toys
    1. Use building blocks and pattern blocks to create structures
    2. Use Kapla Blocks to model real structures
  2. Shape exploration 2D shapes – triangles, rectangles, squares, circles
    1. Use coloured 2D plastic shapes to explore patterns
    2. Different sized triangles, rectangles, squares and circles
  3. Work Sheets with 3D shapes (assessment for learning)
    1. Make the 3D shape into something real (ex. sphere – baseball)
  4. Geoboards – with elastics create different shapes
    1. Students will explore what shapes they can create using the boards and elastics. They can create, rectangles, squares and different shaped triangles.

LiteracyCarocel Important Notes For The Teacher

  • Circulate around the room and observe and listen to what the students are calling the shapes. Are they using the proper terms? What are they calling the 3D shapes? How are they using the material? Is their something you saw that you did not expect?
  • Have a timer (I use an iPad timer displayed on the screen) to allow the students to explore the different stations.
  • Have a class list to write down anecdotal notes of the students for assessment and documentation. (Assessment As during the learning)
Many people may think that this is not Art just a math lesson.  But I say when you create something don’t you use shapes.  When you paint a picutre of a flower doesn’t it start with a circle?  Or when you create Mondrian Art isn’t it divided into geomentric shapes?  Math and Art are a part of each other.  It is a match like ice cream and chocolate fudge.  They are great apart but fantasic together.

Below are some images of the lesson. Who said that art and free expression are not part of learning math?

Art Inspiration: Shaving Cream Easter Eggs


 

ArtInspirationPaulGLogo

During my practicum I had the opportunity to do the art lessons with the students. They are the younger primary but I wanted to do something that was different and challenging with them. I wanted to do an art activity that had to do with a different medium, something other than paints, crayons or drawing. This was a simple art activity that would be utilized during Easter and incorporate spring colours or pastel colours. So I decided to incorporate a sensory aspect to the art activity. Therefore I decided on using a shaving cream activity I used many years ago.

Because it was my first few days back from the university strike I did not create a lesson plan but I did it off the top of my head. I not the Learning goals or success criteria but I did write down the steps and create a rubric for marking after.

 

Resources/Materials:

Craft Supplies – a tray or I used construction paper sheets, shaving cream, white construction paper or art paper, acrylic paints, a squeegee, I used a straw or you can use a paintbrush or Popsicle stick

(Warning this activity is messy, use a sheet to cover the table.)

Action: Step-by-Step

  1. Draw egg shapes on the white construction paper and have the students cut them out. Make sure they print their names on the back of the egg.
  2. Squirt enough shaving cream on the tray or sheet to be able to cover the surface.
  3. Have the students spread it around to make the surface relatively even, it won’t be smooth. (Essential questions ‘How does it feel on you hands? What does it smell like?’)
  4. Once you have your shaving cream evenly spread on the tray or sheet, squirt some acrylic paint vertically onto it. (Ask the students which colours they want to use. Limit to two – three colours.)
  5. Then using a straw or paintbrush or what every you used, zigzag gently though the paint to give it a marbled effect. Do not over mix the colours you just want the colours to start mixing not completely turn into another colour. You want a marble look of the colours.
  6. Place the egg shapes on the shaving cream/paint mix.
  7. Have the students press their paper into the shaving cream/paint and let it sit for a few seconds.
  8. Remove the paper by lifting it straight up. Let the paint/shaving cream sit on the paper for a couple of minutes before squeegeeing it off the paper.
  9. Gently and smoothly squeegee the shaving cream off the paper. It will remove the shaving cream, but not the paint.
  10. Once dried you have a wonderful decoration for Easter and you can use this technique on any other art project.

 

I hope you enjoy the examples below.

Art Inspiration: Pastel Hearts


 

ArtInspirationPaulGLogo

  For my 250th post I would like to share one of my lesson plans I did during my practicum.  They are the younger primary but I wanted to do something that was different and challenging with them. I got a suggestion to use different drawing mediums such as pastels. It was near Valentines Day and so I decided to incorporate a lesson with warm and cool colours. Below are the learning goal, what I want them to learn and the steps to be taken for the lesson.

 

Learning Goal (student perspective): I want to learn to use warm and cool colours to create a drawing with pastels. I want to use the warm and cool colours to make the areas I colour look different.

(Student perspective) I am successful when I can …

“use only warm colours in one area and cool colours in the other.”

“draw different wavy horizontal and vertical lines to make sections that I can colour.”

‘trace the heart shape to have different areas for warm and cool colours.”

Resources/Materials:

Craft Supplies – pastels, construction paper, desk covers, pencils, three heart-shaped tracers

iPad – with the PowerPoint of the lesson

Minds On: How will I engage the learner?

Use the puppet George to ask them about warm and cool colours. Have George show images of warm and cool colours in the iPad. Have George show his drawing and ask the students to see the warm and cool colours.

Action: Step-by-Step

  1. Draw three horizontal wavy lines going from one end of the paper to the other.      
  2. Draw three vertical wavy lines going from one end of the paper to the other.
  3. Trace a heart using one of the heart stencils.
  4. Decide if you are going to colour the inside of the heart using warm or cool colours. Colour the outside of the heart with the opposite.
  5. Colour between the lines using warm or cool coloured pastels.
  6. After you colour the entire page trace over the lines using a dark colour (black)

 

Below is the PDF Presentation I used with the students.

WandCValentine

I hope you enjoy the examples below.

 

Art Inspiration: Mondrian Art Lesson


 ArtInspirationPaulGLogo

During my practicum I had the opportunity to do the art lessons with the students. They are the younger primary but I wanted to do something that was different and challenging with them. I got a suggestion to do a Mondrian inspired art lesson so I came up with one. I decided to incorporate a lesson on primary colours and connect it to the geometric shapes lesson we are doing in math. Below are the learning goal, what I want them to learn and the steps to be taken for the lesson.

 Learning Goal: We are learning about the primary colours and introduce how the colours are seen as warm or cool colours and how do they make us feel. As well the use of geometric shapes and what do they represent in the image.

 (Student perspective) I am successful when I can …

“see what are the primary colours and which ones are called warm and cool colours.” “create geometric shapes using the ruler like squares and rectangles.”

 Resources/Materials:

Craft Supplies – paper, paints, brushes, cups with water, pencils, rulers, black markers/pencil crayons

iPad – to show examples of Mondrian art

 Essential Questions:

Why are they warm and cool colours? What makes them so? What examples can you think of as warm and cool colours? What do think about the artists work? How does this colour (ask for all the colours) make you feel?

 Minds On: How will I engage the learner?

Use the iPad to show different images of warm and cool colours and ask them how do they make them feel. (Cool – blue; warm – red) also geometric shaped art and ask them what do they think about them.

 Action: Step-by-Step

 Step 1 – Use a ruler and a pencil to divide your paper into shapes. (Only use vertical and horizontal lines… no diagonal lines)

Step 2 – Use a black marker to trace over the lines to make them thinker.

Step 3 – Use primary colours and black paint to fill the shapes. Paint only three (3) of the shapes for each colour.  3 red, 3 blue, 3 yellow and 3 black

 

I hope you enjoy the examples below.

Friday Two Cents: Their Heart’s Are In The Right Place


twoCentsOldNew

This week was an exciting one because I was able to do my first two lesson plans with the students. I was so excited to begin that I could feel my heart racing while I did them.  At one point I noticed I needed to calm down when I was printing on the board. When I get excited or nervous my handwriting is, to put it mildly, terrible. But if I am calm and focused on the task I have pretty good penmanship, so I have been told. My mentor teacher noticed my enthusiasm and said that it was good to see and for me to keep it up. But back to the lesson plans.

Tubes - A Cooperative Game to help with motion, teamwork skills and strategy

Tubes – A Cooperative Game to help with motion, teamwork skills and strategy

The first was a physical education lesson centred on cooperative games to foster teamwork and strategy. The activity starts in one corner of the gym and the students needs to get a Ping-Pong ball into the bind at the centre of the gym. However, you have to do this by rolling it through pipes or tubes that are about 30 cm or 1 foot long and cut in half. The team only gets 5-6 of these tubes and that is only about 1.5 m. They still have 3-4 m to go so the first person must go to the end and continue the tube system and the next person and so on. The team must work together to achieve their goal of getting the ball into the bin. I have to tell you they were excited to do the activity and their enthusiasm was amazing to see.

The next plan was a read-a-loud to the children in the class. I selected “How Full is Your
Bucket” to read to the class. It is about a boy who is told that everyone has an invisible bucket above his or her head. When their bucket is empty they feel terrible. But when it is full they feel great. Every time you feel badly because of what some says or does to you, you lose a drop from your bucket. But if someone does something nice to you, a drop will fall into your bucket. The trick also is if you do something nice for someone else you not only drop into his or her bucket, but you also drop one into yours.

I read the book to the class but I added the sound effect of water drops dripping with my mouth. This little effect added so much to their interest in the book. They enjoyed the story and I also had a reflection question for their religion lesson. “What can you do to fill someone else’s bucket?” They came up with some great ideas such as, sharing with others, caring, helping, giving compliments but I really enjoyed one sentence a student wrote. “We can pray for others to help them feel better.” That is what’s so amazing about children; they have their hearts in the right place.

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