1. Plenary 4

2. I spin a spinner. I am twice as likely to get red as blue. I am half as likely to get blue as green. What could the probability of green be? A Colourful Spinner

3. Open questions What they are and what they are not

4. Examples For a lesson that relates to rates, we might ask: Create a sentence that uses the words double, triple, 3 and 8.

5. Examples For a lesson that focuses on properties of multiples, we might ask: How are the numbers 40 and 35 alike? How are they different? OR You can arrange a batch of almost 400 counters into equal groups. How many groups might it be?

6. Examples ____ is 40% of ____. An item costs more than $60. Imagine you have saved $35. What might the percent discount have been? What might each of these lessons be about?

7. Examples One number is 2.5 times as much as another. What might they be? Eight muffins cost about $3. Choose a different number of the same kind of muffins and tell how much they cost.

8. Examples You write a fraction as a decimal and it looks like 0.000 0. What else do you know about the number? is equivalent to another fraction where the numerator and denominator are about 50 apart. What could ☐ be? Where do you think the relations y = 3x + and y = 3x +Δ are most alike?

9. Examples Describe some situations that this graph might depict.

10. Examples The length of a long, thin rectangle is doubled. The width stays the same. What happens to other measures of the rectangle?

11. Examples π is a number that describes a set of related ratios. What other numbers describe a set of related ratios?

12. Scaffolding questions What if the student doesn’t even know how to start? e.g. One number is 2.5 times as much as another. What might they be? You might ask:

13. Scaffolding questions Which number is bigger? How do you know? If the first number were less than 10, what do you know about the second number? Does either number have to be a decimal?

14. Scaffolding questions What if you had asked: An item costs more than $60. Imagine you have saved $35. What might the percent discount have been? If the student doesn’t know how to start, you might ask:

15. Scaffolding questions Suppose you had saved 50%. What do you know about the original price? Suppose you had saved 25%. What do you know about the original price? What would be an easy price for you to figure out the percent discount for?

16. Scaffolding questions Suppose you had asked for situations this graph could describe and the student did not know how to begin. You could ask:

17. Scaffolding questions Suppose you use two variables. If one increases, what should the other do? How do you know? If one doubles, what should the other do? How do you know? Would it help to put numbers on the axes? How?

18. The 3-part lesson Open questions can be used in each part of the 3-part lesson. They may sound different in the different parts (as we discussed earlier).

19. Part 1 Open questions for Part 1 should build on what students already know. For example, for a lesson related to scale ratios: If you drew a picture of a human, what fraction of the height would you make the head? How would you figure it out?

20. Part 1 The population of a country increases by 0.2%. Is that a big increase or not? A proportion is solved by substituting x = 22. What might the proportion have been?

21. Part 2 Open questions for Part 2 of the lesson should be more substantial. For example, Choose to double either one, two or three dimensions of a rectangular prism. What happens to other measurements of the prism?

22. Part 2 For example, a scale diagram of Canada just fills the width of each page. What might the scale ratio be? a)a 22 cm x 29 cm page b)a 29 cm x 44 cm page c)a 48 cm x 100 cm page

23. Part 2 For example, for a lesson focusing on proportions related to similar triangles: The corresponding hypotenuse lengths of two similar right triangles are exactly 1 cm apart in length. What could all the side lengths be?

24. Part 3 These open questions should serve to consolidate the lesson. They should focus on the goal of the lesson.

25. Part 3 For example, Why is every second multiple of 6 also a multiple of 4? A shade of paint uses 4 parts blue to every 2.5 parts yellow. How can you figure out how much blue and yellow paint you need to make a litre?

26. Part 3 For example, The ratio for a scale diagram that fits on a piece of paper is 1: 100 000. What might it be a diagram of?

27. Assessment of Learning It is feasible to use certain open questions in assessment of learning situations. Students need to know the rubric or criteria to be used to make this fair. The value is in finding a lot out about the student’s thinking.

28. Assessment of Learning For example: I might say: The ratio 2:1 compares the number of hands to the number of noses for a person. List as many things as you can that the ratio 4:1 describes.

29. Assessment of Learning Or I might say: Choose a number to skip count to 200 by. Tell how you can predict which numbers you won’t say when you actually do the count.

30. Assessment of Learning Or I might say: Choose a price between $1 and $2 for 8 cookies. Then tell the price for another brand of 6 cookies so that each cookie costs just a little more.

31. Fail-safe strategies There are many ways to create open questions, but there are a set of techniques that work in many situations. Let’s have a look.

32. Your turn Consider closed questions you’ve used in the past, whether self-created or from another resource. Use questions for all three parts of the three-part lesson.

33. Your turn Create a number of open questions for each part of the lesson, indicating the lesson goals, and using different ones of the suggested strategies. List some scaffolding questions for several questions. We will post these and do a gallery walk.

34. Let’s consolidate Complete these sentences: 1) What makes an open question valuable is __________. 2) I would avoid open questions when _______. 3) I should aim to make about ______ % of my questions open. Turn in your answers.