Parallel TasksCommon Questions

and Scaffolding while

Keeping the Cognitive Demand

High

• Work in pairs.

• Solve the following problem:

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?

Student Travellers

Possible strategies- Estimation

24 % ≈ 25 % or ¼

90 90 90 90

Whole school

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

Friendly Numbers

• 24% = 90 students

• 12% = 45 students

• 4% = 15 students

• 100% = 375 students

÷2

÷3

X 25

Double Number Line

4%

15 90

24% 100%

375

÷6

÷6

x25

x25

Ratio Tables

90

24 %

÷ 2

÷ 2

÷ 3

÷ 3

x 25

x 25

45

12% 100%

375

4%

15

Elastic Meter Manipulative

100

24

x

90 =

• What obstacles might students experience in solving this?

• Would those obstacles still exist if the percent were 50 instead of 24?

Anticipating problems

Parallel Tasks• What they are

• Why we use them

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 are called upon to respond.

Big Ideas and Questioning K – 12: Proportional Reasoning p. 23

Example 1

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?

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?

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.

Student Travellers

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.

Gallery Walk

• Post your work.

• Group like tasks together

• Discuss how your work was similar and different.