Plenary 3 Summer Institute 2009

Differentiating instruction We will focus in this and our next few sessions on ways to differentiate instruction (not just differentiate practice). 2

DI requires a focus on big ideas (to have something big enough to differentiate) 3 prior assessment (to know the need to and direction to differentiate) choice (to actually differentiate)

What we do now The conventional approach to differentiating is to scaffold – presenting problems in bits. Maybe this is not the only or the best way, to differentiate. 4

We could.. think about what difficulties students have and actually plan to address these difficulties. 5

Our focus… will be on two strategies: -Open questions - Parallel tasks 6

We’ve used these before… Remember the 1 st plenary’s open question about creating a pattern with a particular 30 th term? 7

Remember the 1 st plenary’s parallel task where you matched questions to big ideas but different groups used different questions? 8 We’ve used these before…

Anticipated problem By knowing that some grade 7-9 teachers might be uncomfortable with grade 11 or 12 content, we differentiated the task by creating that parallel task. 9

In parallel tasks… We were looking at the same instructional goal, with the “problem” (obstacle) removed. 10

Recall… the money problem about Brandon and Alexis… We discussed difficulties students might have. 11 Brandon and Alexis counted their money. Between them, they had $7.50, but Brandon had $2.90 more than Alexis.

The problem… a) How much did each have? b) How do you know there are no other answers? 12

We could… provide alternate versions of the problem to make the problem more accessible without sacrificing “too much”. What might they be? 13

A different example… You pose this: The slope of a line is -2/3. Tell us the coordinates of two points on the line. 14

You could anticipate… some students start with a point, go 2 to the right and 3 down OR 15 some students start with a point, go 3 to the left and 2 down OR students write y =-2/3 x + 8 and substitute two different values for x but have trouble with the arithmetic OR…

You could anticipate… that negative slopes cause trouble and recognize that some students need more time before they are ready for them 16

Parallel tasks A line of slope 2/3 goes through (-4,-1). What is the equation? 17

18 Do you know which way your line slants? How do you know? Common questions

19 Could (-4, 3) be on your line? How do you know? Could (-3, 0) be on your line? How do you know? Common questions

20 What do you need to know to write the equation? How can you get that information? Common questions

21 What is your equation? How can you be sure you’re right? Common questions

Typical question 22 Lisa : $1.15 in quarters and nickels Amy : $0.80 with half the quarters and twice the nickels How many of each coin does Lisa have?

Parallel tasks 23 Option 1: Use equations to model the problem and then solve it. Option 2: Solve the problem using only number thinking.

Common questions 24 Did you need to know how much each coin was worth or just the relationship between them? How did you know that Amy had an even number of nickels?

Common questions 25 Could you be sure that Amy had an even number of quarters? How do you know that each girl had fewer than 5 quarters?

Common questions 26 How did you solve the problem? How do you know your solution is correct?

One more example 27 Use algebra tiles to model two polynomials that add to 6x 2 +8x+2. Use algebra tiles to model two polynomials that multiply to 6x 2 +8x+2.

Common questions 28 What algebra tiles show 6x 2 +8x+2? Is there any other way to model that polynomial?

29 How did you arrange your tiles? How did you figure out how to start? Is there any other way you could have arranged the tiles? Common questions

Your turn 30 In your group, choose one of the suggested sets of parallel tasks. Develop some common consolidating questions.

Share 31 Go to the one of the four corners with people who did your task. Share your questions with a few people in your corner.

Consolidate 32 Create a “flow chart” to show the steps you would take to create parallel tasks. Draw on chart paper.

Consolidate 33 Discuss at your table. Which of the steps would be hardest to do alone?

Consolidate 34 Post your flowchart. Participate in a gallery walk.