Differentiated Lesson Plan - Order of Operations

Algebra 1

Order of Operations

Content Standards:
1.0, 1.1 - Students identify and use the arithmetic properties of real numbers.
2.0 - Students understand and use the properties of taking the opposite and the reciprocal.
10.0 - Students add, subtract, and multiply monomials.

Review PEMDAS and present a few worked out problems to students. Students will read and analyze incorrect simplifications of expressions. They will demonstrate that although simplified incorrectly, there may be some correct steps in the process. They will discover the errors and explain the incorrect use of Order of Operations.

Strategically groups students.

Special Needs
Have students name and act out activities that work only when done in the correct order. such as putting on socks. shoes. and tying laces. Point out the parallel to the agreed-upon order of operations in mathematics.

Below Level Students
Remind students to write out all intermediate steps when simplifying and evaluating expressions. This will help them gain a better understanding and prevent errors.

Advanced Students
Challenge students to add grouping symbols in the correct places to make the following expression true (and others like it): 34x6"3 :2"2 x3"2- I = I70

EL Students
Suggest that students may find it helpful to think of the hue as carrying the exponent on its shoulder so that together they make up a power. Make sure students say “2 to the 4'“) and don't skip over those important little words!

Performance Assessment:

Informal: active listening. spot checks, play math games (if time). project
Formal: Assign problems in textbook strategically. Let students complete whichever 12 problems they wish. They can attempt more problems if they want, but need to get 12 correct for a perfect score.
Also: notes summary, quizzes, Unit test

Alternative Assessment: Have students choose numbers to substitute for x and y in
6xy"2 + 3(xy)"2 and evaluate the expression. Ask students to explain each step in their
calculations.

Assess: Checkpoint Quiz

Project Based Learning: Fahrenheit 451 Analysis

In this project, students create a presentation that covers the predictions Ray Bradbury made in his futuristic tale.

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  Lesson Objectives

  
  

  By the end of the project, students will be able to:

  1. Read and analyze important passages fromFahrenheit 451
  2. Present research and opinions with clarity
  3. Accurately cite information in MLA style
  4. Make appropriate text-to text connections

  
  

  Materials Required

  Copies of Fahrenheit 451Any other materials that are needed based on the choice of the student

• Lesson Procedures

  Project-based learning is purpose-driven. Thus, I ask my students to answer this question with their projects: “To what extent did Ray Bradbury’s vision of the future become a reality?”

  Ideally, if your students have some experience with project-based learning or are fairly independent, then the sky becomes the limit for them. However, most students will need more guidance than being told to complete a project that answers one question. So, here are some guidelines to get your students rolling.

  1. Start by giving students a few areas they can focus on. Choose technology, censorship, and our increasingly calloused society. Help them brainstorm some of the more obvious parallels (like flat-screen TVs, iPod ear buds, etc.).
  2. If you need to, give them a set of choices for which way they will present their findings. Most students opt for a poster or a Power Point, but urge them to think outside the box—they could put together a pamphlet, create a storyboard, or write a series of articles for their own self-published newspaper.
  3. Require students to have at least three outside sources to detail the answer to the driving question: one print source, one video source, and one internet source. (A good project will go beyond the minimum requirements.)
  4. To ensure students truly connect their findings with the novel itself, you may also wish to set a number of passages required to analyze. More advanced students should be able to figure this out on their own, but some students may need a little guidance. Practice quotation analysis with the students first.
  5. Students should present their findings to the class. During their presentations, each student should clearly answer the driving question and use evidence to support his or her claims. For example, a student may have investigated the evolution of technology since Bradbury wrote Fahrenheit 451. He may put together a slideshow that covered how ear buds came into being, delved into high-speed cars, and discussed the latest 3D televisions, all within the context of the book. Another student may present a series of articles about strange ways the government tries to control people, quoting the book along the way.

  
  

  Assessment

  There are multiple ways to assess this project, depending on what you emphasize with your students. Ultimately, the assessment should be of how well students answer the question, “To what extent did Bradbury’s vision of the future become reality?” If you set minimum requirements for the project, you should evaluate how well students went above and beyond these requirements. You can also emphasize any skill within the project—writing, speech, or research skills.
• Defense of Differentiated Assessment
• This project provides the student with choice, based on their learning preferences and intelligences. A student with any learning style or intelligence can be successful in this project. It is broad, but still is able to assess certain standards and content areas.

Cooperative Learning

Standard of Writing
CCSS.ELA-LITERACY.W.9-10.1
Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.

After reading Fahrenheit 451, students will create an essay debating the topic of censorship. The teacher can use a variety of grouping strategies as the students prepare to write their own essays. In order to group strategically for this essay, the teacher will have to have information on the students, both formal and informal assessments. Here are the options:

- Have a class discussion with the entire group about censorship. Have students research censorship throughout history and around the world. Randomly assign students to argue against or for censorship, creating heterogenous groups. Have each of those two groups organize their ideas and arguments. Music can be played softly in the background while they are researching. Have an organized class debate on censorship. This method addresses the following intelligences: kinesthetic, interpersonal, musical, linguistic and logical.

As students interact with each other and hear other viewpoints, they will be able to refine their own argument and the claims they need to support it. Some students will even have to argue for a viewpoint with which they don't agree. This will hone their own belief even more. The oral argument and hearing from others will invigorate students and make their writing even better.

- Another grouping method would be small groups of 4-5 homogenous students. These groups can be created using the teacher's prior knowledge about the students' learning methods and intelligences or by student choice.
Group 1: Censorship of music. This group will research how music has been censored in the history of the US. They will need to find and listen to songs that have been censored in the past and discuss the validity of that censorship. This addresses the musical and interpersonal intelligences.
Group 2: Censorship of writing. Students will research what essays and books have been censored through the history of the US. They will individually read portions of these writings and together discuss the validity of the censorship. This addresses the logical and intrapersonal intelligences.
Group 3: Censorship of film. Students will research what films have been censored through the history of the US. They will look up these films and watch portions and will discuss the validity of the censorship. This addresses the visual and interpersonal intelligences.
Group 4: Censorship of dance. Students will research how dance has been censored through the history of the US. They will discuss the validity of the censorship in certain situations. This addresses the kinesthetic and interpersonal intelligences.

After these groupings, students will be able to write more passionately and clearly their arguments for or against censorship.

- Students may also be grouped into pairs. The pairs may be homogenous or heterogenous, depending on what the teacher wants to accomplish. The pairs will be randomly assigned a viewpoint on censorship. They will research together the censorship debate over time. After they become "experts" on their side of the debate, they will get with another pair to discuss the censorship of a presented essay, video, and song that the teacher will read to the entire class. This method addresses the following intelligences: musical, visual, interpersonal, intrapersonal, and logical.

- Lastly, students may work independently to research how the debate on censorship has changed over time. They will write an essay on presenting both sides and then arguing for the validity of ones side. This is best for intrapersonal intelligences.

These area all great ways to use cooperative learning to help students create an argumentative essay. The methods will motivate students an inform them in a way direct instruction cannot do. Their arguments will be honed and they will articulate them better in their writing.

180 degrees in a traingle

Subject: Geometry
Lesson: The three angles in a triangle add up to 180 degrees.

Five Ways to Present the Idea
1. Direct instruction: Using the whiteboard, discuss the proof suing different triangles to demonstrate. Use a large protractor and different triangle types.

2. Class activity: Cutting a triangle. Have each student cut a triangle out of a piece of paper. It should be larger that a 3x5 card. Students will then cut each vertex (corner) off of the triangle. When put together, the vertices will lien up to create a straight angle, or 180 degrees.

3. Group activity: Try to prove the theorem wrong. Is there any triangle that you can make so that the angles do not add up to 180 degrees, or do not create a straight angle when put together?

4. Youtube video: https://www.youtube.com/watch?v=umBdW7talCo

5. Group discussion/activity: If all the the angles in a triangle must add up to 180 degrees, what must the angles in a quadrilateral add up to? Angles in a pentagon? Hexagon? Is there a pattern relating the sides of a polygon to the sum of its angles?


The assessment for this lesson will include problems where student are given two angles in a triangle and must find the third. One problem will be for the student to CREATE a triable out of card stock paper, MEASURE the angles and VERIFY that they add up to 180 degrees. To challenge advanced students, they will be given a problem to try to create an equation that relates the number of sides of a polygon to the sum of its angles.

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The lesson and idea that the angles in a triangle add up to 180 degrees is fairly simple, but in math, we want the students to understand the WHY behind the theorems. The activities above will get them understand the WHY.

English Language learners will benefit from all the visual activities and the interaction with their peers. Special needs students will benefit from the grouping activities and form the tactile objects to demonstrate the theorem. Gifted and advanced students will be challenged by the final activity, generalizing the concept to a more broad category of Geometry.

Defending OMAM rubric

This assignment would be after reading the novel Of Mice and Men. Students will work alone or in pairs. The presentation must address the conflict of one of the three main characters: Lenny, George, or Curley's wife. The presentation may be 
- in a newspaper form 
- a debate 
- a jury/courtroom decision 
- a speech 
- an essay 
- another presentation approve by the teacher

The assignment allows for multiple methods of presenting the knowledge desired after the OMAM unit. Students have can write or speak. Students can use visual arts. Students can work alone or in pairs. The options are limitless and are diverse enough to cater to all levels and types of learning.

Kahoot! in the Classroom

I currently teach in a classroom with visually impaired high school students. When I taught sighted students, the class loved to use a game website called Kahoot! I can use it in my current classroom with some student that have some vision and the others use it with a sighted partner or aide.

Kahoot! is a great tool to use at the beginning or end of a lesson. It can gauge prior knowledge before a lesson is given. It can also be used as a great review tool at the end of a lesson or before an exam. The website is easy to use to create a multiple choice game. Students are able to use their own electronic devices (smart phones, tablets, laptops, etc.) so that everyone can participate. Students answer each question and can earn points for answering both quickly and correctly. The correct answer and the leaders of the game can be shown on the smart board or screen. The student choose a username, so they can be anonymous to everyone but the teacher and themselves.

While I don't recommend using it every day, Kahoot! is a great tool to keep students engaged and motivated. I caution against using it too much. I always like to follow the rule of "leave them wanting more..."

A Wide Range of Learners

I currently teach high school students who are visually impaired. Some of my students are blind and some have low vision. They use Braille or large print materials. My students also have a varying range of cognitive abilities. Some have gone on to four year colleges like UC-Berkeley while others are not on a diploma track and will attend a transition program for independent living skills after high school. Some of my students are in my class for instruction in high school level math, science, or spanish. Some are there for basic reading and math skills. Others are there for a study skills period to get help with other academic classes.

The wide range of eyesight and cognitive abilities forces me to get creative with my teaching. With the help of a paraprofessional, I often have to teach two totally separate lessons in the same one hour class period. Some things that I do:

- Teach an Algebra lesson to two students. Have them work together on some skills practice while I work on Braille instruction with another student.

- Create a standards-based game that my aide can play with 2-3 students, while I am teaching a lesson to other students.

- When the higher achieving students have some free time, I like to have them help the others with their work.

- I use many tactile objects and shapes so that my students can have access to visual materials used by their typically developing peers.

The diversity in the classroom is challenging, but also invigorating. Every day is different and new. While we have many set routines, the student learn to "go with the flow" and they never know what to expect, keeping them engaged with the lesson that may be coming their way.