Day 2Professional Learning for Mathematics Leaders and CoachesNot just a 3-part series*

Four Corners activityGo to the corner for the View and Discuss between-session opportunity you took advantage of OR are most interested in.

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Four Corners activityShare some of your observations and/or thoughts with those from other boards in your corner.

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More sharingDid you try out any goal setting/question writing activities related to our last session? Share what happened with a partner.*

Responses to Sticky Note PileupIf you tried this activity, what was it connected to? (e.g. norms for collaborative group work)What was the value to you, your students or fellow colleagues?How else could you use it?*

Sticky Note Pileup Exemplar*

Responses to professional learning protocols sampleFor those of you who have been coached or been a coach, which of these protocols is one requiring more focus for you? Why? *

Responding to Day 1 QuestionsWere listening

Were listeningResponding to Day 1 Questions

Responding to Day 1 Questions* more time to work on consolidation/examples more big ideas/from where? order in PPQT handling consolidation in classrooms

Questions from Day 1If you have any other outstanding questions from Day 1, please post these on our parking lot.*

Revised Agenda*

What was our focus in Day 1?We looked at the ideas that:when planning a lesson, you design backwards: focus in on a goal and plan your lesson around that goal.

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the goal for a lesson is created based on curriculum expectations, but filtered through the lens of big ideas

What was our focus in Day 1?*

question(s) to consolidate the goal are essential and may inform other parts of the lesson

What was our focus in Day 1?*

responses to consolidating question(s) are useful assessment for learning information.

What was our focus in Day 1?*

The consolidation question(s) need to reflect the goal, whether the lesson is a concept-building lesson or a practice lesson.

What was our focus in Day 1?*

The consolidation question(s) is more than just do another one.

What was our focus in Day 1?*

Now lets change direction a bit

We have been focusing on the math.Now lets focus on the students.*

Thinking about differentiatingLets look at a problem we might plan to use to see how thinking about difficulties students might have could lead you to alter the problem or differentiate the task.*

Suppose this is the scenario..

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Suppose.. You want your students to solve this problem.Brandon and Alexis counted their money. Together, they had $7.50, but Brandon had $2.90 more than Alexis.

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Brandon and Alexis counted their money. Together, they had $7.50, but Brandon had $2.90 more than Alexis.a) How much did each have?b) How do you know there are no other answers?

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Lets talkLets make a top 5 list of anticipated difficulties.

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Look at one approach Have a look at the hand-out showing one approach to dealing with a possible difficulty. In pairs, suggest an alternate problem based on a possible difficulty.

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Lets talk How did your alternate problem address the difficulty?

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This approach might lead todifferentiating instruction, maybe offering one problem to some students and another to others.

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DI requiresa focus on big ideas (to have something big enough to differentiate)*

DI requiresprior assessment (to know the need and direction to differentiate)*

Anticipation Guide for Grade 8 Algebra*Agree or disagree. Explain.

Exit Card, Day 1*

DI requireschoice (to actually differentiate)*

What many of us do nowThe conventional approach to differentiating is to scaffold-- presenting problems in bits. Maybe this is not the only or the best way, to differentiate.*

Our focuswill be on two strategies: Parallel tasks Open questions*

Youve met themRemember Day 1s open question about creating a linear growing pattern beginning at -10 that grew slowly?*

Youve met themRemember Day 1s task where you matched questions to big ideas but different groups used different questions?*

Anticipated difficultyBy anticipating the difficulty some grade 7-9 teachers might have with grade 11 or 12 content, we differentiated the task.*

In parallel tasks..We look at the same instructional goal, with the anticipated student difficulty addressed.*

We couldLook at your listing of alternative Brandon/Alexis questions. You may have already created parallel tasks.*

All thats missingis how to handle the class when different students work on different tasks focused on the same goal. Well address that now.*

An example.*

You plan to ask: The slope of a line is -2/3. Tell us the coordinates of two points on the line.

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You could anticipate that some students may need more time with positive slopes before they are ready for problems involving negative slopes.

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Looking at the goal.negative slopes are not really required. Students could address the goal using either positive or negative slopes.

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So.we create parallel tasks, offering choices accessible to more students.

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Parallel tasksA line of slope 2/3 goes through (-4,-1). Name two more points on the line.A line of slope -2/3 goes through (-4,-1). Name two more points on the line.*

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

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

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Common questionsWhat are your points and how did you get them?Why did many of you choose points with x-coordinates of -1 and -7, but not -5?*

Parallel tasksare useful particularly for the main instructional activity in a 3-part lesson.*

The MATCH template*

Where you might use the previous taskThe previous parallel task could have been the Action! if slope had just been introduced.*

Where you might use thisThey could have been the Minds On if students already had significant experience with slope.*

Another example *

Original PlanYou had planned an activity where students would translate a series of algebraic expressions into words and vice-versa.*

Then you realized that some expressions may be much more difficult for students than others.*

SoYou want the more difficult ones addressed, but you need to build success.*

The parallel tasksWrite each of the three phrases as an algebraic expression.

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The parallel tasksChoice 1:triple a number

subtract a number from 10

add a number to itself*Choice 2: add 1 to a number and then double it subtract a number from 10 and then divide by 4 triple a number, add 2 and then add 1 more

Common questionsWhat operation signs appeared in your algebraic expression? Why those?Were there other ways to write your expression? Explain.*

Common questionsDid it matter which letter you used for your variable? Why or why not? Which was easiest for you? Why?

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Common questions Could you have ended up with the same expression with slightly different words? Why might someone say its easier to use the algebraic expressions than the words?

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*One more example

The particular operation the student uses is irrelevant to the goal.*

So the choices might be:Use algebra tiles to model two polynomials that add to 6x2+8x.Use algebra tiles to model two polynomials that multiply to 6x2+8x.*

Some common questionsWhat algebra tiles show 6x2+8x? Is there any other way to model that polynomial?*

Some common questionsHow did you arrange your tiles?Is there any other way you could have arranged the tiles? *Virtual Tiles

Some common questions How did you figure out how to start?*

Your turn In your group, choose one of the suggested set of parallel tasks. Develop some common questions.*

Share Go to the one of the four corners for people who did your task. Share your questions with another group in your corner.*

Now Lets think about open questions.*

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Contrast Open:Describe a relation sort of like this one.

Not Open:What type of relation is this?

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The underlying idea To which big idea do you think this question might relate?

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Contrast Open: A graph passes through the points (2,4) and (3,8). Describe a relation the graph could represent.

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Not open: A line passes through the points (2,4) and (3,8). Write the equation of the line.

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What made it open? What made the first question open?

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Contrast Open: Write an equation and solve it.

Less Open: Solve 3x-2 = 8. Describe your strategy.

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Using open questions for assessment for learning An open question, as a minds-on activity, provides valuable information about how to proceed with your lesson.

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It might tell you that there are missing prerequisites that will get in the way.

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It might tell you that your students already know what you were planning to teach.

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It might tell you that your lesson is going in the right direction, but needs a few tweaks; recognizing what students have said could help.

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Comparing open questions and parallel tasks Open questions might be more vague than parallel tasks. Sometimes an open question can replace two parallel ones.

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For example For the parallel task where we used a positive slope vs a negative one, we could have said:*

For example A line goes through (-4,-1). Choose its slope. Once youve chosen it, name another point on the line. *

Open questions can work in all three parts of a three-part lesson. Parallel questions suit the Action! and perhaps Minds On, but not likely the Consolidate/Debrief where things are pulled together.

Where to use open questions*

For example, a Minds On open question related to Big Idea 5 might be: Create two linear growing patterns that you think are really similar.

Minds-on*

You could ask: What makes them similar? How are their pattern rules similar?

Minds-on*

For a lesson on linear equations:You know that x + y = 5. What else do you know about x and y? (Related to BI6)Some more examples*

For the action* Choose two different values for the missing amounts. Make them different kinds of numbers: 3x = 4 + xDraw a diagram or create a flow chart that would help someone understand how to solve your equation. (BI3)

How could this activity help the struggling student? How could it help the stronger student? What math is learned?

An Open Action!*

A linear growing pattern has 50 as the 25th term. Create a bunch of possible patterns. How does where your pattern starts relate to how fast it grows? (BI 6)More action examples*

Two lines intersect at (1,3).One is much steeper than the other. What could the pair of lines be? Give several possibilities. (BI6)More Action! examples*

Open questions are also very appropriate for consolidation. We saw many of these in our last session.

Consolidation questions*

Imagine that students have learned about the meaning of linear equations, e.g. what 4x 2 = 9 means.

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How are these equations alike and different? (BI 5)3x 2 = 6 + 9x3x 2 = 6 + 9x 6x -8

You might ask*

One parabola is very narrow and one parabola is very wide. What do you know or what dont you know about how their equations differ? (BI 4)

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You will be given a set of open questions. Work with a partner. In which part of a 3-part lesson would you consider using each question? Justify your choice using the Convince Me! section.

Matching Activity*

Share with another pair.

Matching Activity*

Which open questions did you find most difficult to place? Why? What similarities and/or differences did you observe between your choices and those of your colleagues?Matching Activity*

Often you can start from an existing lesson and open parts of it up.

Starting from a source*

One strategy is to start with an answer and create a question. For example, a growing pattern has 20 as the 9th term. What could the pattern be?

Fail-safe strategies*

Another is to ask for similarities and differences. For example, how is factoring x2 +5x+6 like and different from factoring 3x2 - 2x 8.

Fail-safe strategies*

Another is to let the student choose values. For example, ask students to choose values for and and graph x + y = 8.

Fail-safe strategies*

From the other examples we have seen, you can see that these are not the only three strategies but they are helpful.

Other strategies*

Choose one of the following tasks. Make it more open

Your turn*

You have 14 $5-bills. How many toonies do you need to have $100? What combination of $2 coins and $5 bills have a total value of $100?

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Think about why you might use an open question in each part of the lesson. Would your reasons be the same? Discuss this in your group.

Consolidate*

*Co-Planning Work in board teams. Use the resource(s) that you brought today. Adjust one or more parts of a lesson by incorporating an open question and/or parallel task. Use the PPQT to record your work.

*Breakouts A/B participants C participants

To Do Between Sessions

Handout of PowerPoint and Revised View and Discuss on tables or at sign in tablePost Four Corners for View and Discuss (11 X 17)Create a Parking Lot**BLM 1 View and Discuss handoutBLM 1b Four Corners signage (View and Discuss titles)***Table copies needed?Return to groups discuss at table; share out a couple of comments**Table copies (from Day 1)Discuss at table; share out a couple of comments

Myrna will send script for slides 7 and 8***12:30 to 1:15 is Lunch only***Design down*****Teachers do this problem*Teachers do this problem*Note that the second question is rarely asked, but is important

*Record responses on chart paper, or create electronic paper

Lots of kids will not read carefully and say 2.90 and 4.60 so need to attend to decoding problems or checking that you meet all conditions.Lots of kids will have difficulty with the actual calculations with these complex numbers.Lots of kids will be very inefficient, e.g. start at 7.50, split it one step at a time.Lots of kids will get one answer and think that there are no other answers because there is always one answer.

*BLM2 Brandon and Alexis Money Problem (Possible difficulty and alternate problem)*

**Point out that we did that with the PPQT*Share some examples here, e.g. diagnostic, task; anticipation guide; etc.We modeled use of prior assessment using Day 1 exit card; your feedback and questions informed todays presentation (emphasis, focus, etc.)

We will only touch on this today but it is important when youre back in your classroom*Share some examples here, e.g. diagnostic, task; anticipation guide; etc.We modeled use of prior assessment using Day 1 exit card; your feedback and questions informed todays presentation (emphasis, focus, etc.)

We will only touch on this today but it is important when youre back in your classroom

We distributed a half sheet here for participants to write on*Share some examples here, e.g. diagnostic, task; anticipation guide; etc.We modeled use of prior assessment using Day 1 exit card; your feedback and questions informed todays presentation (emphasis, focus, etc.)

We will only touch on this today but it is important when youre back in your classroom*Will discuss later**************Teachers should solve one of these before the common questions are shared

Could have used positive coordinates if I see this as a problem

Graph paper on tables

*****Refer to program********Choice 1:N + (n +1) or 2n + 110 n3n

Choice 2:2(n+1) or 2n + 2(10-n)/43n + 2 + 1 or 3 (n+1) or

******Notice how different but ok*Place Algebra Tiles on tables*Link Virtual Tiles IWB file. Need Virtual tiles file**Distribute BLM 3 (Parallel Task Samples Youve Seen) and BLM 4 (Parallel Choices reformatted with common questions column blank)Could use Pentominoes here if you have themPost 4 corners signs while they are working*Post 4 Corners earlier: Signage needed here Each option name per corner*****Could be y = 4x 4 or y = 4(x-2)^2 + 4 or y = 2x^3 -8x^2 +6x +8 etc.***********We are trying to see if students have met the goal; coherent whole (BI); meet the curriculum expectations; may be considered modification if considering parallel tasks in consolidation*Other BI would be possible for examples; possible BI suggestedSelect examples from Minds-On, Action! And Consolidate/Debrief (2 from each) will appear in PPT; BLM 5 will include the other examples

*You dont just ask the open question and walk away you ask probing questions, just like we used common questions for parallel tasks*Ask them which big idea (its BI 5)*Answer at tables and share a few responses*Make sure they see that open activities benefit the weak and the strong.*****Want them to know the difference between equations with single solutions and identities**BLM 5 Open Questions_Matching Activity****BLM 6 Fail Safe Strategies********Recall BLM1*