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Back in the Classroom

Welcome Back!

Well, it has been a while.

I have forced myself to take a month and enjoy teaching again. Reduce the demands and distraction and enjoy being with my kiddos. I took the time for change and created some things in my classroom to fit this year’s student. I have thoroughly enjoyed September!

Last year, I took a year to consult for a private firm. What an amazing opportunity to work in so many great schools. I learned so much about elementary classes and different disciplines, but mostly, I was wanting my classroom back so that I could implement all the great things I was seeing around me! The opportunity to learn about education from outside my classroom was eye opening.

The three most important things I learned:

  • Positivity is more important than content – After seeing hundreds of classrooms, the teachers that enjoyed their students saw more growth than those that had awesome understanding of the content. (Attitude)

Simply, kids must feel safe to learn!

  • Kids need meaning – While I have always been a proponent of allowing kids the opportunity to learn in an application based classroom, this has been reinforced with a vengeance. Students must have a desire to learn. This is more and more true in today’s world. (Retention)
  • Let them move at their own pace – Students will accomplish more than we imagine if we set them free to learn. Get rid of the idea that you must walk them through the curriculum page by page…there is simply not enough time for that! (Time)

This year is off to a great start. I cannot wait to share more details with you!

 

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Algebra 1 Livebinders

Algebra 1 Livebinders

Livebinders are a great way to organize your content!

I hate finding a great lesson and then looking for it the next year and I can’t find it anywhere. So when I found Livebinders a few years ago, I found the best solution for me. (While there are many tools, I have found that choosing one and sticking with it is the key!)

As you know, when I began organizing my lessons around the Common Core I used the Dana Center’s resources. My next step was to create an Algebra 1 livebinder for each unit and find the best lessons, practice sheets, and assessment examples for each unit and start sorting.

These livebinder folders for Algebra 1 have been out there for some time, but I believe that they have been harder to find with some of my updates. So, due to popular demand, here they are for you.

Do you use Livebinders? If so, would you be willing to share? If not, would you appreciate a tutorial? Let me know below.

Pinterest is also a hot topic. If there is interest, I was considering setting up Pinterest Boards for the Units that we could post (FREE) content to.

I would love to hear from you!

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Week 28 – Polynomial Operations

Polynomial Operations

Unit 11 – Week 28

Day 136 – Operations with Polynomials (add, subtract, distribute)

Day 137- Operations on Polynomials (multiply more difficult problems)

Day 138 – Special Products

Day 139 – Putting it all together

  • Review WS – Kuta software (Great Questions for a “Race at the Board” or other game.)
  • Story Problems and Applications (Regents)

Day 140 – Assessments /h3>

 

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Week 29 – Closure

Closure

Unit 11 – Week 29

  • Identify sets that are closed under operations and those that are not. (A.APR.1)
  • (N.RN.3)

Day 141 – Understanding closure with Rational Numbers

Day 142 – Understanding closure with Polynomials

  • Shmoop has a short practice sheet along with some suggestions for teaching this concept.

Day 143 & 144 – Using the “Finger Rule” to multiply 9s 

  • Using the following article from Mathematics Teacher 2002 to gain an understanding of number theory. There are great assignment ideas at the end of the article. I plan to use different ones depending on the ability of my students.

Day 145 – Assessments /strong>

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How to Use Gapminder to Teach Statistics (S.ID) in Algebra 1

Real-data Graphing with Gapminder (Updated)

If you have not seen GapMinder yet, it is a must from every math and history teacher! Stop and watch this now.

I was introduced to this amazing graphing software about a year ago at a conference, and I was so excited to play with it and use it in my classroom. But the how was a bit vague… Unfortunately,  the craziness of getting back to my classroom after three days out distracted me from the goal of figuring it out.

Well, the Common Core placing statistics back into Algebra 1 pushed me forward. I am so grateful. I want my students to understand numbers in the context of the larger world around them. And this is the perfect tool!

I created an Introduction to Gapminder activity and a line of best fit activity. You can find more statistics lesson plans in Unit 4. Be sure to take a look!

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What is GapMinder?

If you have never heard of it before, feel free to take a look at the video below. Please know that the great part about the software is the depth of the data. You can change the x and y axis to reflect data on world health, environment, family size or GDP among others. You can change the countries to be shown by selecting them from the right or select them all. It really allows a teacher to meet the needs of their students.

The Lesson Plan

I created a task for my students to complete while taking their first look at GapMinder. This will take place in my Modeling Linear Data Unit. It was an introduction to the program helping them to understand the notation and symbolism. It also incorporated the mathematics of independent and dependent variables, creating a table from a graph, and understanding how to read a graph. For my students, class time must be structured to be valuable as I am still in training mode and this was the perfect way to achieve discovery and structure in one step.

Thinking Ahead…

I am really excited to see what my students do with this software. While I was playing with this software I changed the y-axis to number of children and left the x-axis as GDP. It was amazing to see in numbers the history I thought I understood. I have so many Bosnian students that escaped the war in their country. To focus on Bosnia and see the turmoil the war caused on their country was extremely powerful. I can see the history teacher using this to track the main players in WWII. You can identify the major dates or even show them the graph and have them research the reasons for the discrepancy in the graph. All very powerful.

Common Core Standards

I am working on creating lessons using this software to help students understand box and whisker (S.ID.1) , correlation coefficient (S.ID.8), central tendencies(S.ID.2), and line of best fit (S.ID.6). I can see the outliers (S.ID.3) being very powerful as well with this software. I am very excited about the possibilities.

How will you use GapMinder?

Please share below how you think this software can be used in the classroom. I would love to hear from you!
**This blog post was featured on Free Technology for Schools.
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Pi symbol clip artDon’t you love when you find something that makes your job easier?

Not only that, it does exactly what you have been looking for to solve a problem in your classroom. I have stumbled upon a couple of those lately and thought I would share them here.

Shortcuts to those symbols we always need and use would be a great place to start. I found this on accident while searching for π day ideas. I always found it a time waster to stop typing and “insert symbol” and what if I was not in word, but, let’s say Blogger, instead. There had to be a better way to do this!

Well my online searching paid off. The alt key has the answer. Here are a few examples. Click here for a more complete list.

Hold down the alt key and hit… (Use your number pad, the numbers across the top will not work.)

  • 227 for π
  • 243 for ≤
  • 0215 for ×
  • 0247 for ÷

Equations for Google Docs is a great resource for adding mathematical equations to a document. This site is easy to read and shows you step by step how to add equations to any Google Doc.

How to Write Mathematical Equations, Physics Derivation, Chemistry Formula in Word 2007 This is an extremely detailed account of how to use word 2007 to insert equations. The screen shots are great for anyone beginning this for the first time.

LaTeX shortcuts in equations within Google docs helps those that do not want to stop typing to insert an equation. It allows you to type things such as sqrt and it will automatically change it to the correct notation. What a time saver! If you are interested in a more detailed description of LaTeX, you may appreciate this site.

Math Characters – This is a list of common math symbols that you can copy and paste anywhere. So easy! Love it!

In Microsoft Word the ctr shortcuts can be quite useful. It includes many of the Greek symbols that can be hard to find. I really like this link because it is quick and easy and I don’t have to read through a bunch of jargon to find exactly what I am looking for. This one is printed and on my wall for reference for all those times I am pressed for time.

Formulas for open office is a great resource if you use Open Office. It has many options depending on what you are most comfortable with. I really like that they show you how to use their presentation software as well.

web equation from Vision Objects is an amazing tool. This must be listed as my favorite and easiest to use. If you can copy and paste, you can use this amazing feature. Be sure to bookmark it, because the hardest thing about this is remembering the web address. You simply hand write the equation you need with your mouse and it converts it to the equation you want, ready to copy and paste.

host math is another easy to use site, a lot like web equation without the writing. Just click the symbols you need and it will convert it to LaTeX, Tex, AMSmath or ASCIIMath notation.

This one from SciWeaver is great as well. But on top of this text to latex tool, they have an assortment of productivity tools that most of us would find helpful. Be sure to take a look around.

Teacher Activity: Mathematical Expressions in Microsoft Word. This is a homework assignment that is given to pre-teachers. I appreciate the step by step directions that are very clear. I also love that they show you how to create your own shortcuts for those symbols you use the most.

Please comment below if you have any additional tips.

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Week 32 – Systems and Quadratic Formula Lesson Plans

Systems and Quadratic Formula Lesson Plans

Unit 12 – Week 32

Common Core Says…

Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social, and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data.

As we create our quadratic formula lesson plans we need to be sure to give our students context. Understanding a student’s needs to be able to connect the discriminant to the end product can be very powerful for many students.

  • Use the quadratic formula to solve quadratic equations
  • Be able to identify which process is best to solve a quadratic equation
  • Solve a system of equations containing one quadratic and one linear function

Day 156 – Deriving the Quadratic Formula

Day 157 – Quadratic Application Practice

Day 158 & 159 – Systems of Linear Quadratic Equations

Day 160 – Assessments /h3>

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Week 31 – Completing the Square Lesson Plan

Completing the Square Lesson Plan

Unit 12 – Week 31

  • Complete the square
  • Use completing the square to find maximum and minimum values (A-SSE.3b)
  • Derive the quadratic formula using the form (x-p)^2 = q

Day 151 – Visual Understanding

Day 152 – Maximum and Minimum Values

Day 153 – Derive the quadratic formula using the form (x-p)^2 = q

Day 154 – Put it all together (Fluency!)

Day 155 – Assessments /h3>

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Week 30 – Factoring

Factoring

Unit 12 – Week 30

  • Factor quadratic equations
  • Solve quadratic equations by factoring

Day 146 -

Day 147 -

Day 148 -

Day 149 -

Day 150 – Assessments /h3>

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Unit 12 Solve Quadratic Functions

Owachomo_bridge Quadratic Equations

Solve Quadratic Equations

Unit 12

Week #30 Factoring

  • Factor quadratic equations (A.SSE.3a)
  • Solve quadratic equations by factoring (A.SSE.3a)

Week #31 Completing the square

  • Complete the square (A.SSE.3b)
  • Use completing the square to find maximum and minumum values (F.IF.8)
  • Derive the quadratic formula using the form (x-p)^2 = q (A.REI.4)

Week #32 Quadratic formula and systems

  • Use the quadratic formula to solve quadratic equations (A.REI.4)
  • Be able to identify which process is best to solve a quadratic equation (A.REI.4)
  • Solve a system of equations containing one quadratic and one linear function (A.REI.7)

Lesson Ideas

All of these resources and more can be found in the livebinder below.

Common Core Standards

A.SSE.3.a Factor a quadratic expression to reveal the zeros of the function it defines.

A.SSE.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*

A.REI.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x + p)^2 = q that has the same solutions. Derive the quadratic formula from this form.

A.REI.4.b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x and the circle x2 + y2 = 3.

A.REI.11Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* (Emphasize linear, absolute value, and exponential functions)Video Explaination

F.IF.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

N.RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

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