1. Parallel Tasks Common Questions and Scaffolding while Keeping the Cognitive Demand High

2. Student Travellers • Work in pairs. • Solve the following problem:

3. Student Travellers 90 students in a school have visited at least two other provinces. If this represents 24% of the students in the school, how many students are in the school?

4. 90 90 90 90 Whole school Possible strategies- Estimation 24 % ≈ 25 % or ¼ Which is approximately 360. Hence the whole school is < 360? > 360?

5. Diagram 24% = 24/100 = 6/25 In a shape with 25 squares 6 represents 24% How big is the whole? 4 groups of 6 fit into the shape and 1 square is empty BUT 24% = 90, and in the shape there are four 90s. So 4 x 90 = 360 (shaded) 1/6 of colour cluster is unshaded 1/6 of 90 = 15 (unshaded) Total = 360 + 15 = 375 5

6. ÷2 ÷3 X 25 Friendly Numbers • 24% = 90 students • 12% = 45 students • 4% = 15 students • 100% = 375 students

7. x25 ÷6 15 90 4% 24% ÷6 x25 Double Number Line 375 100%

8. x 25 ÷ 2 ÷ 3 45 15 375 12% 4% 100% ÷ 3 ÷ 2 x 25 Ratio Tables

9. 100 24 x 90 = Elastic Meter Manipulative

10. Anticipating problems • 90 students in a school have visited at least two other provinces. • If this represents 24% of the students in the school, how many students are in the school? What obstacles might students experience in solving this? Would those obstacles still exist if the percent were 50 instead of 24?

11. Parallel Tasks What they are Why we use them

12. Parallel Tasks/Common Questions • Select the initial task. • Anticipate student difficulties with the task (or anticipate what makes the task too simple for some students). • Create the parallel task, ensuring that the big idea is not compromised, and that enough context remains similar so that common consolidation questions can be asked. • Create at least three or four common questions that are pertinent to both tasks. You might use processes and Big Ideas to help here. These should provide insight into the solution and not just extend the original tasks. • Ensure that students from both groups arecalled upon to respond. Big Ideas and Questioning K – 12: Proportional Reasoning p. 23

13. Example 1

14. Example 1 Common questions: • Is the second number greater or less than the first one? How did you decide? • Is there more than one answer? How do you know? How far apart are they? • What strategy did you use? • How else could you compare the two numbers?

15. Example 1 Scaffolding questions: • How else can you think of 80%? 150%? • How do you know that the second number can’t be 50? • What picture could you draw to help you? • What’s the least the second number could be? How do you know?

16. Student Travellers Recall the problem: 90 students in a school have gone to at least two other provinces. If this represents 24% of the students in the school, how many students are in the school? • Create a parallel task that addresses the anticipated student difficulties. • Create common questions for the task questions. • Share with a neighbouring group.

17. Creating common questions Choose either JI or IS sets of parallel tasks with which to work. In a small group or with a partner, create at least 3 or 4 common questions and a few scaffolding questions.

18. Gallery Walk Post your work. Group like tasks together Discuss how your work was similar and different.