Systems Foldable

We will finish up our current unit on characteristics of functions this week!  Yea!  And then we dive right into a short, 4-day unit on systems of equations.  The only new information in this unit that my Algebra 2 students didn't do in their first year algebra course are the type of word problems.  Most of them have not had to do wind and river current problems, and these are required in our Algebra 2 curriculum.  I'm looking for ways to build depth/complexity into this unit since it is mostly review.  If you have ideas ... please share!

To review systems I created a "foldable" that fits in my students 3-ring binder.  I am debating about whether or not to leave my typed notes in the foldable ... and just have students work an example of each.  Students can snip the table on the dotted lines, cover up the information as their study guide.

Here is a link to the foldable if you want to check it out!  Print it double sided and it should line up.

If you have a favorite systems activity, please share in the comments!

Beth
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Student Reflection and Criteria for Success

In chapter Chapter 3, "Clarifying, Sharing, and Understanding Learning Intentions and Success Criteria: from Embedded Formative Assessment, Wiliam explores the value in and techniques for sharing learning intentions and success criteria with students.

Can students assess themselves against a set of criteria during the unit so that at the end of the unit, they have reflected on all of the criteria?  

What would this look like for me?  My goals for students would be task specific (solving equations) and process focused (being able to show steps clearly and accurately).

At the end of our unit on solving multi-step equations, students will need to be able to solve equations with grouping symbols and/or variables on both sides of the equal signs.

Learning Goal:  I can solve multi-step linear equations.

Steps to Success:

1. I can use the distributive property if the equation has grouping symbols.
2. I can simplify each expression on either side of the equal sign by combining like terms.
3. I can isolate the variable by adding the inverse to both sides of the equation.
4. I can isolate the variable by multiplying the inverse on both sides of the equation.
5. I can substitute my solution back into the original equation to check my work.

In order to experience success, students will need to know the terms that I highlighted in the success criteria.  They will also have already mastered one and two-step equations.

In developing this lesson, students will put together interactive foldable on solving equations.  An example of those notes are here.  Along with the "flip book," students will have a list of vocabulary words and the steps to success outlined above.  I'll put those items on a self-assessment sheet so that students can rate their own understanding before, during and after the unit.

During the lesson sequence, I will check for understanding on each step of success.  In addition, as we are solving equations, and students ask for help, I will ask them on which success step they are struggling.  In this way, students will be encouraged to become familiar with the five steps.

After routine practice, I plan to assign an error analysis task.  In that task, I will give students equations that have been worked out step by step but that also include at least one error.  Students will identify the errors and correct the work.  This example is not my work ... but I would create something like this!  "Using Error Analysis to Teach Equation Solving" by Kathy Hawes, published by NCTM in 2007 has good ideas for teaching solving equations.  A copy of this article is online here. 

How do you share your learning intentions and criteria of success with students?  

slope as rate of change

One of my go-to places for ideas for our units is the NSA website!  Yes, the National Security Agency sponsors math workshops where teachers write some awesome units!   Check out this website ... note the grade level links on the right side.


I took one of the units on developing the concept of slope as rate of change apart.  From the unit I pulled out 5 excellent examples for students to work on in class using "I do, We do, You do" model.  I can do one problem for students, then they can do one in their team.  And last there are 3 problems for them to work on independently.

Knowing that interpreting problem situations is challenging for my students, I found, borrowed, modified nine other problem situations found online to create a poster project that students will do in teams.  Each team will illustrate one problem, graphing it, and analyzing the x and y intercepts.  Each team will present their problem.  Then all students will complete all nine problems for homework.

Team Poster Project Rate of Change by Beth Ferguson

In our curriculum this work comes before actually teaching the various equations of lines and formulas.  So the work is more conceptual, more about giving meaning to slope before applying it to "naked" abstract linear functions.

During this unit I'll use Three_ways_for_finding_slope_foldable that I found on the Utah Education Network.  I'll introduce the foldable after we explore the problem situations above.

Solving Equations Foldable

Last week we struggled with solving equations.   I gave students a flow chart hoping that would help them with their work.  Then a colleague who is talented in creating interactive foldables took the flow chart to a whole new level!   She created this Solving Equation Foldable!

The solving equations foldable asks students about their equation step by step.  It shows them an example of what a next step might look like.

I'm looking now for a foldable on solving inequalities.  If you have one to share, I'd love to see it!

This 'n That Thursday (1)

Played a vocabulary game this week in "new teacher" orientation that I liked called Moving Words.  Choose enough vocabulary words so that you have one per 2 students.  Ask each pair to come up with a movement or signal  for their assigned word.  When all pairs are ready, stand in a circle.  The teacher leads by illustrating a word with a movement.  The class repeats her movement.  The next pair in the circle illustrates their word.  The class repeats it.  Then the class repeats the teacher's word and the first pair's word.  The 2nd pair illustrates their word.  The class repeats it.  Then the class repeats the teacher's word, the 1st pair's word, and the 2nd pair's word.  The process continues around the circle.   After the movement exercise, ask students to sit down and make notes on the vocabulary words.

Discovered a whole world of math bloggers online (this is just one list!) ... such great help not to mention very interesting people!

Attended a free online conference on foldables ... great fun!  I'm experimenting with interactive notebook foldables ... hope to post a pic soon!

Decided to have an estimation jar in my classroom ... maybe one per unit ... now to find a jar and something to fill it with!

Discovered I can print poster size enlargements (B/W) fairly cheaply at Office Depot!