Problem Solving Folio Component 2:
Problem Solutions from the Weekly Task Sheets The following problems from the Weekly Tasks sheets have been selected for the problem solution component of your Assessment Folio. You are to submit solutions for 6 problems. Note that with some problems there is a choice of two tasks – please just choose one, if you submit both, only one will be marked. You are to show your solutions to the problems, explaining and justifying your problemsolving process and mathematical thinking and reasoning. If you are not sure if your solution is correct, or you could not fully solve the problem, discuss this as part of your submission.
You don’t have to get all questions correct, or all problems fully solved to pass this component of the Folio. You do need to provide sufficient evidence of a reasonable level of mathematical knowledge and understanding, and the development of your use of appropriate problem-solving strategies and processes. Please see the marking rubric for full details of these criteria. You need to annotate all your work to provide this evidence. Correct answers alone will not guarantee a pass.
• Your interpretation of the problem (including any assumptions you may have made);
• Where you chose to start, and why;
• Which strategy you adopted to get started, and why (e.g., drew a diagram, acted it out, used manipulatives, etc);
• Your mathematical reasoning throughout the solution process (e.g., did your initial strategy work, or did you need to change direction? how did you know to what to do next? etc.);
• Any difficulties you encountered, and how you overcame these (e.g., collaboration with others, looked up similar problems online, etc.).
• You may also discuss how you explored the mathematics further, for further clarification and/or for further extension of your own mathematical knowledge and understanding. You will need to scan your work.
• Amber makes toys for the children in the Children’s Hospital at Christmas. She makes wagons (with four wheels) and trikes (with 3 wheels). She used 68 wheels for the toys for last Christmas. What number of wagons and trikes might she have made? Make sure you can verify you have all possibilities.
• An empty bus fills up this way: At the first stop 1 person gets on, at the second stop 3 more people get on, at the third stop 5 more people get on, and so on.
a) What pattern/s did you discover?
b) What is the total number of people on the bus as it leaves the 12th stop?
c) At which stop will the bus reach its capacity of 49 passengers?
a) Here is a 4 by 4 square. How many rectangles are there? Make sure you include ALL rectangles (check your dictionary and/or the week 5 content to ensure you have the correct definition of a rectangle). Include a mathematical argument explaining how you know you have found all rectangles.
b) Based on your reasoning from a) predict, clearly describing how you do this, how many rectangles would there be in a 3 by 3 square.
c) Test your prediction, clearly indicating which parts were correct and which parts were not. Include any refinements you need to make to your prediction.
d) How many rectangles would there be in a 5 by 5 square?