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Differentiating Mathematics Instruction

Differentiating Mathematics Instruction. Session 4: Questioning to Evoke and Expose Thinking. Adapted from Dr. Marian Small’s presentation August, 2008. Goals for Session 4. Become familiar with and practise opening up questions and creating parallel tasks

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Differentiating Mathematics Instruction

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  1. Differentiating Mathematics Instruction Session 4: Questioning to Evoke and Expose Thinking Adapted from Dr. Marian Small’s presentation August, 2008

  2. Goals for Session 4 Become familiar with and practise opening up questions and creating parallel tasks Practise adapting lessons to be more inclusive Practise creating diagnostics

  3. Sharing Thoughts Stand Up/Hands Up/Pair Up With your partner share: • something you learned that would be useful. • something with which you disagree or about which you have doubts. • the role diagnostic assessment plays in differentiating learning and planning for instruction.

  4. Differentiating instruction… rather than consolidation

  5. Your answer is….? A Problem: A graph goes through the point (1,0). What could it be? • What makes this an accessible or inclusive question?

  6. Opening up Questions Opening up the question… You saved $6 on a pair of jeans during a sale. What might the percent off have been? How much might you have paid? A conventional question: You saved $6 on a pair of jeans during a 15% off sale. How much did you pay?

  7. Another Example You saved some money on a jeans sale. • Choose an amount you saved: $5.00, $7.50, or $8.20. • Choose a discount percent. • What would you pay?

  8. Another Example Opening up: Represent 88 as the sum of powers. A conventional question: What is 52 + 62 + 33?

  9. How can you open up these questions? Add: 3/8 + 2/5. A line goes through (2,6) and has a slope of -3. What is the equation? Graph y = 2(3x - 4)2 + 8. Add the first 40 terms of 3, 7, 11, 15, 19,…

  10. Using Parallel Tasks Provide 2-3 similar tasks designed to meet different students’ needs, but make sense to discuss together.

  11. Parallel Questions Reflection Questions: How do you know the number is more than 24? Is the number more than double 24? How did you figure out your number? • Task A: 1/3 of a number is 24. What is the number? • Task B: 2/3 of a number is 24. What is the number? • Task C: 40% of a number is 24. What is the number?

  12. Parallel Questions Reflection Questions: How do you know the charge would be more than $40? How did you figure out the fee? • Task A: One electrician charges an automatic fee of $35 and an hourly fee of $45. Another electrician charges no automatic fee but an hourly fee of $85. What would each company charge for a 40 minute service call? • Task B: An electrician charges no automatic fee but an hourly fee of $75. How muchwould she charge for a 40 minute service call?

  13. Parallel Questions • Task 1: Find two numbers where: - the sum of both numbers divided by 4 is 3. • two times the difference of the two numbers is -36. • Task 2: Solve: (2x + y) / 4 = 3 and 2(x – y) = -36 Reflection Questions: How did you use the first piece of information? The second piece? How did you know the numbers could not both be negative?

  14. Making it more inclusive

  15. Making it more inclusive

  16. Another example Bill has two part-time jobs. At the store he earns $9/h. At the recreation centre he earns $12/h. He would like to earn $240 to purchase a DVD player. What is the fewest number of hours he needs to work to save this amount of money?

  17. Another example A farmer wants to build an enclosure for pigs, chickens and ducks. He has 50m of available fencing to build three identical, adjacent enclosures. • Write an equation to represent the amount of fencing required. • Rearrange your equation to isolate one of the variables. • Graph the relationship. • Identify possible dimensions for the farmer’s enclosure.

  18. You try … Form grade groups. Work together with a TIPS or textbook lesson and make it more inclusive. Include one suggestion for differentiating assessment. Consider YOUR four students. Post your work for sharing with the group.

  19. Open up tasks Create parallel questions Interview Paper-and-pencil items Graffiti exercise Anticipation guide Making lessons more accessible

  20. Home Activity Journal prompt: • How did you differentiate your lesson? • What was the hardest thing for you to deal with? • How did you consider your four students? • How much did it help to do it with colleagues?

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