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Common to all 9 approaches

Nine task based strategies for dealing with diversity while offering experiences covering common content. Common to all 9 approaches. Building classroom community Task based, considering the trajectory of tasks (what comes next!) Explicit pedagogies

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Common to all 9 approaches

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  1. Nine task based strategies for dealing with diversity while offering experiences covering common content

  2. Common to all 9 approaches • Building classroom community • Task based, considering the trajectory of tasks (what comes next!) • Explicit pedagogies • Different ways of solving the tasks, and the different approaches are themselves educative • Representing solutions in different ways is both engaging and important mathematically

  3. What these approaches are not! • Asking questions that are so easy that everyone can do them • Setting up groups that allow some students to hide • Excessive repetition (of course, some is needed) • …

  4. Strategy 1 • Asking questions with multiple entry points and multiple exit points • Such questions will nearly always be open-ended

  5. Write a sentence with 5 words, with the mean of the number of letters in the words being 4. Do not use any words of 4 letters.

  6. Draw some rectangles with a perimeter of 20 cm. Work out the area of each of your rectangles.

  7. A set of 36 cubes is arranged to form a rectangular prism. What might the rectangular prism look like? What is the surface area of your prisms?

  8. Strategy 2 • Using enabling and extending prompts • These apply to any type of challenging task

  9. Suppose we posed this task: Seven people went fishing. The mean number of fish they caught was 5, the median was 4 and the mode was 3. How many fish might each of the people have caught? (Give at least 3 answers)

  10. Some enabling prompts • Seven people went fishing. The median number of fish caught was 4. How many fish might each of the people have caught? • Seven people went fishing. The mode number of fish they caught was 3. How many fish might each of the people have caught?

  11. What are enabling prompts? • Enabling prompts can involve slightly varying an aspect of the task demand, such as • the form of representation, • the size of the numbers, or • the number of steps, so that a student experiencing difficulty, if successful, can proceed with the original task. • This approach can be contrasted with the more common requirement that such students • listen to additional explanations; or • pursue goals substantially different from the rest of the class.

  12. Extending prompt • Seven people went fishing. The mean number of fish they caught was 5, the median was 4, the mode was 3, and the range is 6. How many fish might each of the people have caught? (Give all possible answers)

  13. What might be enabling and extending prompts for these tasks?

  14. A brick weighs the same as 3 kg plus half a brick. What does the brick weigh? Represent your answer in twodifferent ways, one of which involves drawings

  15. A brick weighs the same as 3 kg plus half a brick. What does the brick weigh? 3 kg

  16. A brick weighs the same as 3 kg plus half a brick. What does the brick weigh? 3 kg SA coaches day 5 September 12

  17. 3 kg SA coaches day 5 September 12

  18. I used 1 metre of string to tie up this box. The bow takes 300 mm. What might be the dimensions of the box?

  19. Race to 5x + 5y

  20. Strategy 3 • Realistic investigations that are multi faceted, take time and are meaningful for collaborative group work

  21. Which fits better: a round peg in a square hole or a square peg in a round hole?

  22. 1mm of rain on 1 sq m of roof is 1 L of water. Design a tank for this building that captures all of the rain that usually falls this month.

  23. Design a cola can that has the same volume as the current cans but requires less aluminium

  24. Calculate the volume of the cylinder that is made by bending an A4 sheet of paper vertically. Now calculate the volume if the sheet was horizontal.

  25. How many people can we fit into this room?

  26. A chameleon has a tongue that is half as long as its body ... • … how long would your tongue be if you were a chameleon?

  27. In what ways are the arch at St Louis and the Sydney Harbour Bridge similar to or different from a parabola, circle, ellipse, hyperbola, sine curve, catenary? The school is considering building an arch over the front gate. What curve would you recommend? Write the equation (using actual measurements) for your curve.

  28. Strategy 4: • Using a text book in different ways NB September 12 difference

  29. Some examples • Read the last question first. What do you need to learn to be able to do that question? Which of the earlier questions look like they might help? • Work in pairs. One of you does the odd questions. The other does the even ones. Then each of you can explain your working to the other. • In what ways are the questions different from each other?

  30. Strategy 5 • Asking questions that emphasise connections and are challenging (but at the right level for the curriculum)

  31. At the end of the season, the coach noticed that the mean and median of the number of goals kicked by the 20 players was 10. He also noticed that ¼ of the players kicked less than 5 goals, ¼ of the players kicked 5 or more but less than 10, ¼ of the players kicked 10 or more but less than 15, and ¼ of the players kicked 16 or more. How many goals might each of the players have kicked? CEOM 2012

  32. To give us something to discuss • On a train, the probability that a passenger has a backpack is 0.6, and the probability that a passenger as an MP3 player is 0.7. • How many passengers might be on the train? • How many passengers might have both a backpack and an MP3 player? • What is the range of possible answers for this? • Represent each of your solutions in two different ways.

  33. Some sample questions • Find two objects with the same mass but different volumes • Draw some closed shapes with 6 right angles • Draw a line 1 m long on this page • The perimeter of a rectangle is 20 cm. What might be the area? • Draw (on squared paper) as many different triangles as you can with an area of six square units • A number has been rounded off to 5.3. What might be the number?

  34. Strategy 6 • Creating task sequences where there is no expectation that all students can do the first one(s), but for which all can do the last one(s)

  35. A “constructing” task • In a tank there are 200 fish, 99% of which are guppies. • How many guppies do I need to take out to end up with 98% guppies?

  36. A consolidating task • At the football there are 50 000 spectators, 55% of whom are Collingwood supporters. • How many Collingwood supporters do I need to expel from the stadium to end up with 50% Collingwood supporters?

  37. A possible sequence of tasks..

  38. Write a sentence with 5 words, with the mean of the number of letters in the words being 4. Do not use any words of 4 letters.

  39. Seven people went fishing. The mean number of fish they caught was 5, the median was 4 and the mode was 3. How many fish might each of the people have caught? (Give at least 3 answers)

  40. At the end of the season, the coach noticed that the mean and median of the number of goals kicked by the 20 players was 10. He also noticed that ¼ of the players kicked less than 5 goals, ¼ of the players kicked 5 or more but less than 10, ¼ of the players kicked 10 or more but less than 15, and ¼ of the players kicked 16 or more. How many goals might each of the players have kicked?

  41. After the brick task A box weighs the same as 12 kg plus a quarter of a box. What does the box weigh? (do this in two different ways)

  42. Strategy 7 • Creating task sequences that proceed from simple (to engage students in the task) and which progressively become more difficult

  43. Getting to school John Hindmarsh 20 km How much does it cost John to get to work and back home again? Assume that it costs $2 per km for the full costs of the journey

  44. Getting to school John Hindmarsh 73 km How much does it cost John to get to work and back home again? Assume that it costs $1.37 per km for the full costs of the journey

  45. Getting to school 5 km Mark Hindmarsh John 20 km How much should Mark give John if he picks him up and takes him home? Assume that it costs $2 per km for the full costs

  46. Getting to school 17 km Mark Hindmarsh John 57 km How much should Mark give John if he picks him up and takes him home? Assume that it costs $1.37 per km for the full costs

  47. Getting to school z km Mark Hindmarsh John x km How much should Mark give John if he picks him up and takes him home? Assume that it costs $y per km for the full costs

  48. Getting to school 10 km 5 km Mark Hindmarsh John Susan 20 km How much should Mark and Susan give John if he picks them up and takes them home? Assume that it costs $2 per km for the full costs

  49. Getting to school 23 km 15 km Mark Hindmarsh John Susan 72 km How much should Mark and Susan each give John if he picks them up and takes them home? Assume that it costs $1.35 per km for the full costs

  50. Strategy 8: • Games that are a mix of skill and luck

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