Planning Guide

Creating Learner-Focused
Schools

* Madison-Oneida BOCES- This document may not be reproduced in any form without the expressed written consent of the District Superintendent or his designee.

CONTENT KNOWLEDGE

ESSENTIAL QUESTIONS

• Where do we see equality in life?
• Why is it important to recognize and preserve equality?
• Why is equality important in Mathematics?
• When can we use solving equations to solve real world problems? 

INITIATING ACTIVITY

The day prior to this activity ask the students, as a class, to choose a number between 1 and 10. Do not tell them why. Make a variety of representations of the number chosen on index cards. Also, set aside 3 or 4 blank cards. The next day, as students enter the room, hand each an index card but don't describe what will be done yet. Let students compare cards and have an informal discussion. Listen to student discussion and comments. Put enough equal signs on the board or around the room so that each student can put up their card. Have students put their cards on one side or the other of an equal sign. Do this until all cards are on the board. Ask those students with blank cards to make some more that are different but still convey the same message. They can then put their cards in the blanks left over. Conduct a class discussion about what is on the board. Solicit comments and ideas before interjecting comments. Be sure to reinforce the idea that different representations of the same thing are still equal. Extend this discussion to where equality occurs beyond Math class, to solidify the idea of equality and how things do not have to look the same to be equal. Next introduce the idea of what happens if you put something else on one side of the equal sign, but not the other. Leading into a discussion of the addition property of equality, and why it is important to recognize and preserve equality in Mathematics. You could also extend this discussion beyond the Mathematics classroom. You might collaborate with the Social Studies teacher on the issues of equal rights and people being treated as equals. You might also collaborate with the Science teacher on the topic of Balancing Chemical Equations. (Depending on the depth of the discussions this should take from 1 day - 1 1/2 days.)

Connection to State Learning Standards

Content Area: Mathematics

Level: Intermediate

Unit Theme:

Learning Experiences

Describe what will be done:

1. Students will do a These Are Equal, These Aren't Equal, Are These Equal worksheet, designed by the teacher, in pairs.(see attach. #1)
2. Class discussion will be held regarding answers given. Terminology of Equivalent Equations discussed.
3. The pairs will then develop their own These Are Equal, These Aren't Equal, Are These Equal worksheets, and answer key. They will model them after the teacher designed sheet used in the previous activity.
4. Student created sheets and answer keys will be collected and corrected by the teacher. Teacher will select questions from these sheets for a quiz. Student's initials will be placed next to each question.
5. Class discussion at the end. What did they learn? Was it helpful?

Learning Experiences

Describe what will be done.

1. Review what students remember about opposites, inverse operations, and integer subtraction.
2. Discuss the Addition Property of Equality again. (continued from initiating activity)
3. Demonstrate a few simple, basic equations on the board. Encourage students to predict each step.
4. Practice solving using textbook examples and worksheets. Encourage students to look for patterns or rules. Ask for verbal or written descriptions
5. Provide common, error examples from student work and have students analyze these and describe how to help the person correct the errors.
6. Create graphic organizer, flow chart, to describe a set of steps that can be used to solve addition and subtraction equations.
7. Students will be allowed to use their graphic organizer as a "cheat sheet" for a short quiz on solving equations.
8. Students will create at least 2 word problems of things of interest to them that can be solved using addition or subtraction equations. They will also provide an answer key. They will be informed that these will be sent to students in other schools, via e-mail. Teacher will provide guidelines for the word problem and answer key. (see attach #2)
9. Once the teacher approves a student's word problem and answer key, the student will type their problems into a word processing file to prepare for e-mail.
10. Once a student's word problem on the word processor is approved they may e-mail it to another student. The teacher will provide an e-mail address. If possible student should check daily for a response.
11. When a response is received student will use their answer key to correct it and provide feedback. Feedback must be approved by the teacher before being sent back.

Learning Experience

Describe what will be done.

1. Student discussion of the index cards in the initiating activity leads them to a generalization of the idea of equality within and beyond the mathematics classroom.
2. Students will compare the left and right sides of equations to discover how to maintain and preserve equality.
3. Construction of the graphic organizer leads them to a general set of rules for solving equations.
4. Evaluating fellow student's work, analyzing and correcting problems, and providing feedback.

Planning Guide
Unit: Equality For All

Rubric:

Key Questions:

What are the key elements, traits, or dimensions that will be evaluated?

Are the identified elements of equal importance or will they be weighed differently?

 NOTE: Rubric or other performance assessment instruments may be used.

Have You Considered These Yet?

Learn to Learn Skills:

Students will learn to provide positive, constructive feedback to peers. Students will interact with students from around the country or world and see how they approach the topics we are learning. They can then compare similarities and differences. Students will learn to produce products for their peers. Students will learn how small the world can become with the use of technology.

Assessment Modifications:

Student's who have difficulty reading or writing for various reasons should be paired with students who can help them understand and express their ideas. Word processors can be used throughout the unit if needed by students with writing difficulties. Hearing impaired students can have lessons transcribed to a word processor or use an interpreter. Another student to whom they can give instructions can assist students with manual dexterity problems. Suggestions for students who may have already mastered this material: they can be used as student helpers or they can be given assignments to connect the topic to other classes in more depth (i.e. the Science and Social Studies connections mentioned in the initiating activity.)

Unit Schedule/Time Plan:

Total time approximately 2 weeks. This may be modified as the unit becomes more familiar. It could probably be done in 1 1/2 weeks.

Initiating Activity - 1 day

Concept of Equality - These Are Equal, These Aren't Equal, Are These Equal worksheets and Quiz - 2 to 3 days.

Solving Addition/Subtraction Equations - Flowchart, Quiz, Practice - 5 days

Culminating Activity - Create word problems, send and e-mail - 4 to 6 days.

Written Overview:

This is a learning unit designed to help students learn the formal steps of how to solve algebraic addition and subtraction equations. It begins with the concept of equal, a fundamental concept to understanding how to solve all algebraic equations. Students will produce several small products throughout the unit, and have a couple of quizzes as well, all leading to a culminating performance.

Prior to this unit students should have been exposed to the following concepts and procedures: integer operations, opposites, additive inverse, use of a word processor and sending and receiving e-mail.

One of the activities the students are involved in is the use of and creation of a Concept Attainment or Compare/Contrast Activity called These Are, These Aren't, Are These. The idea behind this activity is for students to compare examples that demonstrate a concept with examples that do not demonstrate that concept. Then they try to draw conclusions about the concept which will help them determine if other examples do or do not demonstrate the concept.

In this Learning Unit students will look at a column of information that consists of examples, or models of things that are equal. They then analyze these things and in writing describe why they are equal. The second column consists of things that are not equal, and students must describe why they are not equal. The third column consists of examples of both, things that are equal and things that are not. Students must look at each problem and determine whether each is equal or not, and provide a written explanation of each based on the conclusions reached from the first two columns. This hopefully helps them to solidify the idea of equal. The follow up activity is for them to create their own These Are Equal, These Aren't Equal, Are These Equal forms.

The culminating performance will be based on the students ability to use the information presented and discovered in the unit to develop word problems, create associated answer keys, and evaluate another's work on the problems. They will use the technology of word processing and Internet e-mail to share their work with other students around the state, country or world.

This unit could easily be extended or modified to a unit on Multiplying and Dividing Equations also.

This unit could be planned to coincide with lessons in Science on Balancing Equations, or in Social Studies on Equal Rights.

The most difficult part of execution of this unit was finding schools to participate. I sent about 10-15 messages before I got a response from someone. Students continually ask about the status of it.

I had to make some minor modifications to the Learning Unit based on the limited availability of technology in our school. We currently have only two Internet computers in our building, and they are in use almost continually. I combined all of the student work into one word processing file and sent it out to a teacher at another school. Then the file was sent back as a whole also, and divided up appropriately for evaluation and feedback. The same procedure was used for the feedback. This becomes a little cumbersome, but where there is a will there is a way.