1) WWK: Radical, Perfect Square

2) Grade yesterday's assignment

3) Go over yesterday's Ticket Out the Door

• review rational/irrational
• review order of operations
• review properties of exponents
• review evaluating

4) Update ISN

• complete student work for properties of exponents
• complete page dedicated to negative exponents

1) Check yesterday's homework in groups

2) PT - Exponential Exponents

• Teams work together to find 4 different expressions describing a number from a given card
• Teams may find as many expressions as they like, but each property of exponents must be represented 
• At least one example of each property needs to be shown: Power to a Power, Mult. same bases, Dividing same bases, Negative Exponents
• Teams struggled greatly with the negative exponent property 

1) WWK: Power 

2) Make sure ISN are up to date, each page has correct parts

3) Direct Instruction via foldable notes - Properties of Exponents.  We started this on Friday, finished today

4) Student Practice: Summary Page of Properties and why they work.  Will go in ISN

5) Assignment: page 98, 25-35
Warning: this assignment contains some problems with negative exponents.  We have not talked about this very much in class and these will be tricky. Everyone should TRY.

1) Before the tardy bell: Students are given a small post-it note with a number written on it.  They are instructed to place it correctly on the Venn Diagram describing real numbers.  Their number should be placed in the most specific location based on its definition.

Before, as left by students:                                                                                                           After Class Discussion:

2) Grading homework in groups - went MUCH better today as kids had a second go around of classification of numbers.

3) PT: Alien Invasion

• Students worked in teams to identify patterns that describe rules of exponents and come up with a rule that works
• Rules formulated for 1) power to a power, 2) multiplication of same bases, 3) division of same bases, 4) negative exponents, 5) zero exponents and 6) products raised to a power.

4) ISN: Students received a foldable note to summarize rules of exponents. We only had time to identify each, but not put in notebooks.

NO homework!!! : )

1) Check last night's homework in teams

• I went over the tough ones that teams needed more explanation for
• Discussion in both classes turned into mini-lesson on what a square root means, and why we distinguish between real numbers and imaginary numbers.  Both classes were introduced to "i".

2) Interactive Student Notebooks (ISN) pages 18-19

• Direct Instruction with foldable note added for estimating square roots
• Student practice with classification of numbers and ordering them added
• See student example below.

3) Assignment: page 125, 28-46 evens

1) Fill in any new information based on PT: Nesting Dolls for the following learning target: When are exponents used and why are they important?  

• Student responses centered around using exponents to find a rule as opposed to using an exponent to simplify repeated multiplication.
  
• For both classes, I planted the idea of using exponents to describe something getting smaller (intro to decay)
  

2) Go over homework answers 1-19 in small groups followed by my explanation for lingering questions

3)  Three Act Task: Cubes

• Kids were completely mystified by the video and somewhat annoyed.  : )
• It's important to have models for kids to use when learning to draw isometric shapes
• We stopped after Act 2 and will complete this task tomorrow
• Video for Act 1 Here

1) Finish up ISN from Friday - pages 18 and 19, Rational/Irrational Numbers
2) Performance Task: Russian Dolls

• Many groups will use a height of 9 for the largest.  Check to see if groups have a value of 4 or 3 for the 3rd largest (part 1).  This generated a good class discussion.  Then, groups encouraged to go back to an initial height of n.
• Drawing dolls helps
• Groups will likely need more scaffolding on this one.  As a group made a step in the right direction, I had a team member show the class - this happened in about 4 steps for the performance task.
• Final Student Product:

3) Assignment: Skills practice, handout for simplifying exponents.  We did a few from each section together. Students finish others 1-19.

1. Watching kids suddenly make a connection on their own totally makes my day.

• "Can I use that A squared B squared thing to do this?"
• "Wait, isn't this the same thing as a translation?"
• "It seems like a reflection is changing the order of all the letters naming the triangle."

2.  My students are thinking of methods and connections that I've never considered.

• "Is a tournament the same thing as repeated multiplication?"
• "Can I just use a scale factor to solve this problem?"

3. I love listening to conversations that my students have that incorporate math vocabulary that we are learning in class.

4. I love when students get so excited to SOLVE a problem they start grabbing resources that I never expected such as patty paper, markers and calculators.

5. I love when students get so excited to COMMUNICATE with their team members that they grab resources such as patty paper, markers and calculators.

6. I love when student observations and connections they make lead to mini lessons on topics I didn't even intend on teaching such as the Pythagorean Theorem, orientation, proper notation, etc.

7. While my students are young and don't have the mathematical sophistication to always have the correct name for what they are doing, they are developing tools to get their point across.

• "unsquaring" a number
• "these (irrational) numbers go for the rest of your life"

8. For possibly the first time in my career, I feel like I'm helping kids learn to think and problem solve, not just "do the math."

9. I never know what to expect.  Honestly, I think this is a big hook for the kids, too.  There are surprises for the kids and for me.  Sometimes the surprises for the kids were totally intentional on my part, sometimes I'm caught up in it, too.

10.  When I had students clean out folders after the first test, they didn't want to recycle their learning target sheets. : )

2) In teams, students share what they came up for to complete yesterday's homework: finding an example in the real world of something that could model repeated multiplication.  Then, I asked for volunteers to share with the class ideas they learned from their teammates.  Some samples were: a tournament bracket (good one, since it demonstrates decay), a phone tree and the metric system.

3) Interactive Student Notebooks were updated with Gallon Guy (or alternate) colored, cut out and placed in back cover as well as two foldables for rational and irrational numbers.