Parallel Tasks Common Questions and Scaffolding while Keeping the Cognitive Demand High <75 min. in total for parallel tasks>

Student Travellers Work in pairs. Solve the following problem: Find a person you do not know and whom you have not worked with so far. Try to join someone from another division or in a different role from yours. 2

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? <10 min.> After 5 min. ask for volunteers to share their solutions on Doc. Camera if available. If not, then on chart paper. This problem is intended to be a mathematically useful problem, but also to begin the discussion of anticipating student difficulties and, as a result, considering a parallel more appropriate task for some students. The problem will be revisited to create a parallel task after discussion around potential student difficulties has happened. 3

Possible strategies- Estimation 24 % ≈ 25 % or ¼ 90 Whole school Which is approximately 360. Ask which it is < or >. Good reasoning question. Since 24% is 90. The total is slightly more than 4 times 90, hence > 360. Hence the whole school is < 360? > 360?

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 Alternate presentation is given on next slide (hidden). 5

Diagram 24% = 24/100 = 6/25 (1 colour group) 4 colour groups fit in a 5x5 square each colour group represents 90 students coloured sq’s: 4x90 = 360 students but 1 square is uncloured each square is 1/6 of 90 = 15 students So, total is 360(coloured) + 15(uncloured) = 375 students Alternate presentation

Friendly Numbers 24% = 90 students 12% = 45 students 4% = 15 students ÷2 ÷3 X 25 Students may choose to work down and then up using friendly numbers.

Double Number Line x25 ÷6 4% 15 90 24% 375 100% A similar representation is to use a ‘double number line’.

Ratio Tables ÷ 2 ÷ 3 x 25 90 24 % 45 12% 4% 15 100% 375 A similar strategy can be arranged in a ratio table. Sample given in proportional package in appendices. This graphic organizer is used to create equivalent ratios. Entries in a column are multiplied or divided by the same amount.

Elastic Meter Manipulative 100 24 x 90 = The elastic meter is another organizer for students to use. Students may find it useful when determining where to put the numbers in a ratio and then solve using a variety of strategies. Cross-multiply being one of then. The Elastic Meter video (GAINS website- {professional learning) shows how this strategy can be used. Show video if possible.

Anticipating problems What obstacles might students experience in solving this? Would those obstacles still exist if the percent were 50 instead of 24? 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? Allow participants to share ideas in small groups about the obstacles. 24% not as friendly as 25% Additonal number - two language: at least the part is given rather than the whole or they might relate to the numbers selected. 11

Parallel Tasks What they are Why we use them <2 min.> At this point, explain that parallel tasks are two or more tasks which are mathematically equivalent in terms of the concept required, but perhaps not in terms of skill details. It is intended that they be offered as a choice for students so that all students can succeed relatively independently. They are questions which allow for differentiation. They must be so similar that many of the same questions can be asked and answered by students no matter which task they did. They are designed to build student confidence and success. 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 are called upon to respond. Bring to their attention some steps for creating parallel tasks on pg. 23 in the package- useful for final activity on next slide. Big Ideas and Questioning K – 12: Proportional Reasoning p. 23

Example 1 <5 min. next 3 slides> This choice would suit students who are not ready for percents greater than 100, without making them feel they “don’t belong”. Teachers are free to make individual suggestions to students about which they might do, but shouldn’t make a habit of that– trust kids to make the right decisions; they usually do. The idea is NOT to do both. Ask participants to choose a question to do. Share at table. 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? Common questions you could ask

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?

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. <15 min.>Revisit our opening problem. Now that you have seen three examples create a parallel task(s) & common questions for the debrief/consolidation. Share with another group (group pair/share, Stay & Stray,…) 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. <15 min.> Participants to be arranged by division or grade band. Participants will work in small groups or with a partner. The parallel tasks on BLM 3C are provided to make the work easier. They only need to concentrate on creating the Common and Scaffolding questions. Eventually they would create their own tasks by beginning with a planned task and either simplifying details for struggling students or making the details more complex for advanced students to create the parallel task. Steps for creating parallel questions is in the Proportional Reasoning Package (p.23). Samples of Parallel Tasks, Common and Scaffolding questions are on pg. 24-25 of the Proportional Reasoning Package. 18

Gallery Walk Post your work. Group like tasks together Discuss how your work was similar and different. 10 min. 19