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Illustrative Math Grade 7 Unit 3 Reformatted Teacher Presentations and Student Materials

11/24/2018

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Here are the reformatted materials for Unit 3: teacher presentations, student task statements, and practice.  Again, I have reformatted the student task statements as "student_summaries", with the summary moved to the top, as a resource for parents and students.  When I needed the tables or graphs, I made "student_worksheets."  I reformatted the teacher presentations to gather stray sentences that cross pages or make charts or tables and instructions are on the same page.  This time I have also included materials from Grade 6 Unit 1 that covered the area of parallelograms and triangles, since my students did not come from a classroom that used the IM materials in grade 6. 

Depending on when you view this, the materials may not be complete, but I will be adding to them as I move through the unit.

Unit 3 Teacher Presentation PDFs
Unit 3 Homework and Classwork Docs
Unit 3 Student Summary Docs

Unit 3 Student Summary and Classwork PDFs
Unit 3 Homework PDFs
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Little Steps, Big Ideas

11/4/2018

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It is easy for students to get fixated on the "how" of mathematics.  As much as we try to emphasize thinking and discussion and as often as we praise clear explanations and celebrate insights, there is still a lot of pressure from parents and siblings and tutors and society at large to focus on getting the answer.  And let's be honest, for many students (especially the middle schoolers I see each day), any schoolwork is time taken away from the truly important stuff.  So just tell them what they need to do so they can be done and move on.

In trying to get them to value both the process of exploring and the connections that come from it, I realized that they might not actually see the difference between rote procedures and conceptual understanding the way I do.  After all, from a student's point of view, if she knows how to do a problem, then she understands it.  So this year I put a poster up in my room that says Little Steps / Big Ideas.  When we started using fraction operations at the beginning of the year, and we re-examined the equivalence of multiplying by 1/3 and dividing by 3, or why we can multiply just the numerator in a problem like 3 · 4/5, we were able to talk about the Big Ideas behind the Little Steps and the difference between the two.

Area formulas are a perfect opportunity to highlight the difference between the memorized rules and the geometric principles behind them.  Once students appreciate the difference, then they can see the value of assessment items that look for evidence of understanding the Big Ideas.  Someone once told me the students know what teachers value by what they test and grade.  Is that Big Idea going to be on the test?  If you give tests, it should be.

I like to remind them of the long history of development in mathematics; that the procedures we have today weren't always obvious to even full-time mathematicians, and took a long time to evolve.  Anytime your students' explorations culminate in a procedure or a "shortcut"  that makes calculations quicker and easier, you can bring into relief the algorithm that makes the mathematics handy, and the big ideas that justify it and connect it to  the rest of the field of mathematics. 
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Illustrative Mathematics Unit 2 Reformatted Lessons and HW

11/4/2018

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The doc and pdf files from Open Resources often need reformatting.  I am posting what I have done here for anyone to use.  I also found that lesson 4-6 went too fast for my students, so I rearranged some of the activities, and cut lesson 5 into two parts.  My students have not been through the 6th grade program.  They struggled with:
- how to write the general equation for a table and what it meant
- understanding the units attached to the constant of proportionality
- seeing the direction of the relationship in a table... the independent and dependent variables

So in the lessons and the practice, I made some changes. 

Lesson 4: 
- I asked more explicitly about the units of the constant of proportionality
- I included a multiplication sign in the equation so that they would understand  m = 3 · h as "the number of miles is equal to three times the number of hours" instead of "1 mile equals 3 hours."
- I stressed the direction of the relation, using phrasing like "relating hours to miles" instead of "relating hours and miles."

Lesson 5:
- I broke this into two parts and reordered some of the problems.  In part 1, I added more basic problems and scaffolded the problems to ask for two tables instead of one, emphasizing the two different ways to look at the same relation: relating miles to hours and hours to miles.  We started with tables instead of equations.
- In part 1, I also used whole number/unit fraction constants of proportionality.
- In part 2, we moved into more challenging constants of proportionality, still beginning with tables.  In the final activity, I asked the students to reason about equations.
- Also, as a warm up I made a note to ask the students to fill in tables using equations to again give them experience with the multiplication in the equation.  They often want to interpret the equation as a ration. 
- I also took a day before part 2 and after part 2 for a lab on tongue twisters as an application of proportional relationships.

Lesson 6:
- This year the students were not really using the equations to solve for the unknown quantities... they were really using tables.  The math is the same, but they weren't introduced to the usefulness of equations.  I rewrote the lesson to emphasize the use of equations, and I will need to rewrite the practice sheet next year.

Here are links to the teacher presentation PDFs (I use Openboard... let me know if you would like the Openboard files) and classwork and practice sheet docs and PDFs.  I have reformatted the student sheets two ways.  I usually just have students work off the screen from my teacher presentations. If there are tables or graphs for them to use, I make a student worksheet.   I have also reformatted the students sheets so that parents can see what we are doing in class.  I moved the summary section to the top, and tightened up the formatting to make them shorter page-wise.  I call those Student Summaries.


Unit 2 Teacher Presentation PDFs
Unit 2 Homework and Classwork Docs
Unit 2 Student Summary Docs
Unit 2 Homework PDFs

Unit 2 Student Summary and Classwork PDFs

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