Algebra 1: Unit 2

Here's your visual tour of my Unit 2.

Unit Overview

This is what the "What I need to remember on my retest" looks like.

Since my district uses common assessments my students are not allowed to take their exams out of the classroom. We use a reflections page similar to this one shown for each unit to write reminders and study notes that students take home with them. 

An updated version of THIS page from last year.

The blank boxes on the right side were for partner practice problems like the ones shown here.

Inside the "How to Calculate and Approximate a Decimal" foldable.

Not-so-fantastic Exponents foldable.

Students worked through the following two pages with teams.

Once they were comfortable with their own rules and generalizations, we wrote the names of the rules on the front of the two folded pages.

And we wrapped up with radicals.

YOUR COPIES:

Unit 2 Overview

Calculating a Decimal foldable

Laws of Exponents investigation

the Simplifying Radicals Maze idea is from here

Algebra 1: Unit 1

Yes this was from back in August--September. I'm just now getting to it. Kind of... Alright, full disclosure, I don't love some of the things in my Algebra 1 interactive notebook this year. I feel like I could have done better and they're sub-par from time to time. But I guess that's the reality of teaching. I'm glad I'm looking at myself and my profession critically. That's a positive way to approach it, right? :)  I have gone back and forth so many times about sharing these pages or not. I don't love them. They're not life-changing. Oh well. Sometimes that's the best we've got, right? I decided to go ahead and share these because I like when other teachers share their not-so-brilliant moments. It makes me feel more okay about mine, ya know?

Without further ado...

We started Unit 1 refreshing some accelerated 7th grade ideas of sampling, biased data, and representing data. We did a Lucky Charms investigation. Yours is HERE if you want a copy.

We discussed the ideas of more precision with larger samples, random vs. biased, relative frequency, precision in plotting, and estimating predictions. We then recorded all of our heights and shoe sizes, separated by boys and girls.

The "Our Data" page flips open so that when you turn to other pages of the notebook the data is still visible. This came in handy when we created dot plots, box plots, and histograms on the next pages. It's also getting ready to come in handy again when we use this same data to talk about correlation, scatter plots, lines of best fit, and residuals in Unit 5.

Here's our plots on the next page. See... super handy that students could see the data and also these pages at the same time. Saved lots of time and headaches not flipping back and forth and losing our place over and over.

We then did a Standard Deviation Investigation.

Yours is HERE if you want a copy.

We summarized in our notebook and complete the practice pages that are taped in. I don't remember exactly where I got the practice page, possibly Teachers Pay Teachers. Or maybe a blog link through Twitter. I'm so sorry to whoever deserves credit for the practice activity. It's about five different cars and fuel efficiency. If it's your activity please leave a comment or email me, I'd love to give you credit!

We also did a couple days on Two-Way Tables but I didn't do notebook pages on them. Can you tell I love them? Ha! **oozes sarcasm**
If you want either Investigation or Homework, they are linked.

Lastly we wrapped up by summarizing vocabulary. I don't usually devote much page space to vocabulary since students build a glossary at the end of their notebooks, but this unit was just too vocab-rich to avoid it. Students referenced this more often than I thought and it has proven useful.

Well, there you have it. My Algebra 1 Unit 1 that I don't completely love.

This is definitely a unit that I'd LOVE to see how you approach these topics; I need some new ideas!

Solving in One Variable

First and foremost... this lesson is not orginally mine!!
Remember when I told you how much I loved this blog? When I was first starting INBs last year, I clung to a few blogs for ideas and tips. Sarah's was definitely one of them! HERE is Sarah's original post of this lesson.

I started with the scales just like she recommended. Your copy is here if you want it.

Students worked for a few minutes individually and then discussed ideas with a partner. Of course #3 and #6 really caused some problems... they don't have a solution! I encouraged students that if they got stuck on any particular problem to skip it and come back. Inevidably #3 and #6 were left til the end!

We discussed all six as a class and wrote the solution types. Our notes looked something like this when we were done.

We talked about one solution, no solution, and infinitely many solutions at this point. This was the first time most of my students had heard these ideas so we talked them through quite a bit. And yes...we wrote them algebraically. At first they moaned and groaned, espeically at the all real numbers, but by the end of the year, after coming back to these ideas repeatedly, they really felt acomplished. They would brag about being able to write things like "real mathematicians." I love math nerds!!! :)

Then we made a foldable, including one of each type of solution set.
**From here on the pictures are tiny. GRRRR. If you click they will enlarge. 

We talked about how the algebraic process of solving relates to the scale. For example, in the equation where the only solution is x=3, when we subtracted 2x from each side the resulting 2x=6 could be seen on the scale where two boxes line up to the 6 box. This really helped students grasp what was happening as they solve equations.

 How have you taught this idea? Got any great foldables or activities to share??



Solving Systems of Equations

One of my favorite pages from this year was our Solving Systems of Equations page. In my opinion, this page was truly interactive. Students were sorting, classifying, and studying with these notes. YAY!!

This page took a few days to complete. First, we discussed solving systems graphically. After some exploration and activities, we completed THESE notes (new file link that the bottom). They were still connected as one piece of colored paper. Students then put those notes away in their handy-dandy pocket. We came back the next day and completed notes over solving by substitution and solving by elimination (new file link that the bottom). Students then put those in their pocket as well.

After making sure students were comfortable with solving systems, we started talking about one/none/infinitely-many solutions. Students were already thinking about these ideas because each colored set (graphically, substitution, elimination) had one system with each type of solution set. Here's where the fun part happened!

On page 103 of their notebook we took basic boring notes about what a system of equations is, the notation for a system, and what a solution point means. On page 104 we created a flipable pocket. The pocket is one full sheet and one half sheet of blank paper. Fold the full sheet in half width wise (hamburger style if you know what I mean) and then put the matching sized half sheet inside the larger, now folded paper. I know... it sounds confusing... it's really simple! Tape up the sides and fold the whole thing in half. You have four pocket areas. We only used three for our purposes. Do these pictures help at all??

 

 Anyway...

Students cut their colored papers apart and sorted into three piles: one solution, no solutions, and infinitely-many solutions. They looked for themes and commonalities within these new groups. We then had a class discussion about their observations and added general notes to the fronts of each pocket. We visually represented how one/none/infinitely-many looks on a graph and the type of solution when solved algebraically.

 ifinitely??? yeah... I dunno either...

The sorting and processing part really made things click for students. I also saw them studying with these notes later. They were able to take out all notes of the same color to study how to solve with a given method, or take our all notes within a pocket to study solution types.
Overall...success!

How have you done systems of equations in the past? Any great ideas to share??

New links that should *hopefully* work!

Real Number System & Approximating Radicals

Here is one of the first lessons of the year in our curriculum - the Real Number System! During the 2012-2013 school year, my district opted to teach three years of curriculum in one year (AHHH!!!!) to the Pre-AP Algebra 1 students. Since we were implementing Common Core and wanted to make sure to fill in all the gap items before high school, we taught CCSS 7th Grade, CCSS 8th Grade, and CCSS Algebra 1. With that in mind, most of my lessons covered multiple standards and levels. This is one such lesson...

Students were already somewhat familiar with the idea of rational and irrational numbers. While it had been a year and the concepts were definitely fuzzy, they had a little familiarity with the terms.

This was the first year for most of my students using an interactive notebook and they were concerned about writing too big/spacing/logistics. So cute! I put up the following diagram before we got started and eased some of their worries. They felt more confident knowing the layout of the entire page as we filled in portions.

In the top rectangular section we completed the Real Number System information. We created nesting rectangles to show which groups were subsets of other groups. I really liked the way the layout created a number line! The students seemed to understand this layout very well.

Under that section we discussed how to approximate numbers without using a calculator. Some students panicked, but eventually became confident. Don't get me wrong, this was NOT and overnight transformation! Ha! But with enough encouragement and "put the calculator down!" moments, we all made it through.

That night students completed a few problems in classifying and approximating numbers.

We came back the next day, checked our answers with our cooperative teams, and then did a little Stand Up, Hand Up, Pair Up Kagan activity. Students all divided the right side of their notebook into quadrants and drew a card with a radical. They worked individually for a few moments to approximate their radical, then they began pairing up. I also had a card and was a member of the activity. I've found that students partner up much more quickly and wander less if there's the impending doom of having to partner with the teacher, especially during the first week of school! Ha! I'm okay with that, whatever it takes.

Once students had found they partner, they each worked to approximate the other's radical. Then they compared their decimals using <,>, or =, added their decimals, and multiplied their decimals. This gave students four different practice opportunities very quickly, as well as the added benefit of meeting their classmates and learning that our classroom is a place of active learning. Success!

What ideas do you have for this topic that I could implement next year? Any tips to make these pages better? I'd love to hear from you!!

Interactive Notebooks

Whoa! Has it really been a year?! I'm so sorry!! Trying to implement a completely new curriculum kept me very busy this year...as did buying a home, moving, and getting a dog. ha! 

Anyway... I'm back! :) 

I used Interactive Notebooks this year in my Algebra 1 class and 

LOVED

them! I cannot wait to share some ideas with you.

Stay Tuned!

I'll be back in less than year this time, promise.