The 3-Part Problem Solving Lesson -An overview to get you started

1. The 3-Part Problem Solving Lesson -An overview to get you started Adapted from Ministry and Curriculum Services Documents By Emily Wagner

2. Teacher Role:

3. Student Role:

4. Strategies For Creating Problem Solving Questions: • Strategy A: Working Backward • Identify a topic. Example: counting • Think of a closed question and write down the answer. Example: How many chairs are in the room? (4) • Make up a question that includes or addresses the answer. Example: I counted something in our room. There were exactly 4. What might I have counted? • Strategy B: Adapting a Standard Question • Identify a topic. Example: Measuring using nonstandard units • Think of a standard question. Example: How many popsicles sticks long is your desk? • Adapt it to make a good question. Example: Can you find an object that is three popsicle sticks long?

5. Strategies For Creating Problem Solving Questions Strategy C: Ask for similarities or differences Example: How are squares and rectangles alike? How are they different? Strategy D: Leave certain information out of the problem Example: The answer is 12, what is the question? Strategy E: Provide several numbers and math words; the student must create a sentence using all the numbers and words Example: Create a sentence that uses these words and numbers: 3, more, 5, and

6. Sample Problem Solving Questions: Primary Good Questions for Math Teaching By: Peter Sullivan & Pat Lilburn Math Solutions Publications Number Sense and Numeration: Number Operations Using base 10 materials how many ways can you show the number 25? I have written a secret number between 50 and 70. It is an even number. What might it be? Write down everything you can about the number12. Make a two-colour train with snap cubes, using two of one colour, two of the other, continuing for as long as you like. How many cubes are in your train? Count by 2’s until you land on 20. What other numbers can you count by and still land on 20? What numbers can you make that are below 100 and have a 6 in the tens place? I am thinking of a number between 10 and 100 with a single 9 in it. What might my number be? What numbers can you make using 6, 5, and 8? Yesterday I put some counters into groups with the same number in each group. I can’t remember the groups, but I can remember that there were 12 counters. What might the groups have been? When the children in a class each got a partner, there was one child leftover. How many children might there be in the class?

7. Money How many different ways can you make 20 cents? In my pocket I have 75 cents. What coins might I have? I bought something and got 5 cents change. How much did it cost and how much money did I give to pay for it? I spent exactly $1.00 at our class store. What might I have bought? I have 2 coins in one hand and 1 in the other hand. The coins in each hand are worth the same amount. What could the coins be? Fractions You see a sign in a shop window that reads ½ off sale. What does this mean to you? Half of the people in a family are males. What might a drawing of the family look like? Draw a shape. Show how to cut the shape into two halves. Measurement: Weight What can you find that is lighter than a pencil? Find something that you can lift that is heavier than this bucket of water. A book is on one side of a pan balance and two objects are on the other side so the pans are level. What might the 2 objects be? What can you find that is bigger than a potato but lighter than it?

8. Volume and Capacity Find a container into which you can fit 6 cubes so that they do not move around too much. Ella used 12 blocks to build a building. What might her building look like? Sandy filled a container using 3 cups of water. What container might she have filled? At the grocery store, I bought a container shaped like a rectangular prism but the label came off. What might have been in the container? Area What are 3 things this page would completely cover? What are some things your hand will cover so that they cannot be seen? What are some things you cannot cover completely with your hand? Max made a flat shape using five square tiles with their sides touching. What might Max’s shape look like? Time What is something we could do that takes exactly 1 minute? (Read Aloud connection for this problem is “A second is a hiccup.” What are some things you do in the morning and some things you do in the afternoon? What things could you do that take about 1 hour? Show a time on an analog clock face with movable hands. Tell what you might be doing at that time on a school day?

9. Length and Perimeter Can you find something that is the same length as your height? Give children a stick or piece of string. Ask- Can you find some things longer than/shorter than/same length as your string? How many objects can you find that are longer than 3 hand spans but shorter than four hand spans? Location and Position Allow children to walk around the room until you say stop. Then ask- Who has the door behind them? Who is near the door? And so on… On the playground/gym make your own obstacle course by going over 3 things, through one thing, under one thing, and between two things. Geometry: 2D Shapes What is it that makes these shapes triangle? (Draw three different triangles with question) I drew a shape with 4 shapes. Draw what my shape might look like? I made a picture using only circles and squares. What might my picture have looked like? Make a design with pattern blocks. What did you make? Draw a design or shape made up of three shapes. The design should have symmetry. 3D Shapes Say- In my hand I have an object that is able to roll. What might it be? How are these shapes alike? How are they different? (draw 2 shapes with question)

10. Data Management and Probability: Chance If 2 coins are tossed, what could happen? Two children were playing a dice game. One child tossed 2 dice together and when they landed one was a 6 and one was a 4. What other number combinations might the child have tossed? A family has 3 children. We know that at least 1 of the children is a girl. Draw what the family might look like? Data On a graph about pets owned by children in our class, I counted more dogs than cats. What might the graph look like? In a survey of this class exactly half of the children said “yes” and half said “no.” What might the survey be about? You did a survey to find out who was happy and who was sad. What pictures could you use to represent these feelings? How could you make a representation of the children in our class who can swim and the children who cannot? What might this be a graph of? Patterning and Algebra: Create a repeating pattern using 3 colours and two shapes. Create a pattern with 2 attributes that repeats. Create a skip counting pattern starting at 14 that someone else can continue.

11. -Good webcasts to check out Go to: Curriculum.org Click on: “Webcasts for Educators” left hand side Click on: “Archives” Find: 1. Differentiating Math Instruction –Maryan Small 2. High Yield Strategies for Improving Mathematics Instructions and Student Learning