Communication - Unit 1 in 4MAT 4 Algebra

This Unit Covers

The first two chapters in Algebra books tend to teach and review skills that build a solid foundation for future chapters. We believe the following skills should be taught in this unit.
Percents
Variables in Algebra
Exponents and Powers
Order of Operations
Equations and Inequalities (introductory)
Tables and Graphs
An Introduction To Functions
The Real Number Line
Addition of Real Numbers
Adding and Subtracting Matrices
Multiplication of Real Numbers
The Distributive Property
Division of Real Numbers
Statistics
Measures of Central Tendencies
Range
Stem and Leaf Plots
Frequency
Histogram
Box-and-Whisker Plot
Quartiles
Outliers
Sample
Survey
Population
Types of Sampling
Biased Sample
Biased Question

The Concept is Communication.
The Content is the meaning of the terminology and rules in Algebra.
There is a relationship between communication, terminology and rules and the relationship is meaning!

Learning Outcomes

Students will:
Recognize the importance of using good communication skills.
Recognize the importance of using precise terminology,
giving accurate directions and being a good listener.
Recognize the power of accurate language, and the confusion from not knowing proper terminology.
Learn the basic language of Algebra and begin to see how important good communication is to succeed in Algebra.
Practice the concepts.
Show that they can communicate more effectively using Algebra concepts.
Collaborate to fine-tune projects and share them.

Teacher Notes

This unit is authored by Michael Arlien and Colleen Hodenfield, authors of the 4MAT 4 Algebra Curriculum Series and 4MAT 4 Geometry Curriculum Series. This is the first unit of 10 conceptual Algebra 1 units.

Communication is the key to survival! Without the ability to communicate, we are not able to express our needs and interact with others. You cannot understand in a language you do not know. The same is true in mathematics. Without the ability to communicate, you will not be able to understand and perform the interactions.
In mathematics we communicate in many different ways: equations, graphs, exponents, symbols. Once you see it
and understand it, you will find the language of mathematics is beautiful!
In this unit you will look at many different ways to represent the world around you mathematically and learn to communicate those ideas with others.

This unit should take approximately 30 class periods (50 minutes each

Time Frame

Total time : 414 minutes

Concept :

Communication

Content :

The language of Algebra

Bridge :

Meaning

Essential Question :

In what ways can a person communicate more effectively using Algebra?

Outcomes :

Students will learn a vocabulary which will enable them to communicate using the language of Algebra.
Students will use their new vocabulary to solve algebraic problems.
Students will become mathematical communicators.

How well we communicate? Build a house. Have other students replicate without seeing it.

Reaction to communication activity.

Language used for communication. Slang word competition.

Sometimes the world is negative! Introduce terminology and rules essential to Algebra.

Worksheets, kinesthetic representation of number line, tic-tac-toe activity

Visual representation of key algebra content.

Critique and refine student project in peer groups.

Project scavenger hunt. Search for best in show.

Communication

1. Connect: Connecting to the Concept Experientially

Objective: Recognize the importance of using good communication skills.
Activity: Students use blocks to build the same design as their partner. This is done using only verbal directions.
Assessment: Students compare their design to their partners’ to see how well they were able to communicate.

Getting ready
This is the “Connect” octant of the unit, Step One. This activity connects learners directly to the concept in a personal way.

Activity directions
1. Teacher creates a set of blocks for each pair of students. Cuisenaire Rods work well because of their different colors and sizes. Each set should have two of each style of blocks/rods.*
2. Partner students up. Hand each pair of students a set of blocks/rods.
3. Number students in each pair as #1 or #2. Have them divide the blocks between themselves so that they each have an identical set.
4. Students are to put a divider between them and their partner using their textbook or folder. 
5. Teacher explains that student #1 of each pair will build any design using only his/her blocks. Student #2 may never look beyond the divider to see what is being built. 
6. Student #1 then gives directions to Student #2 on how to build an identical design. Student #2 cannot talk. Student #1 cannot look beyond the divider to see how Student #2 is doing.
7. Once both students are satisfied that they are done, have students remove the divider and see how well student #1
communicated and how well student #2 listened.

Notes
If blocks are unavailable for this activity, you could have student #1 draw a picture on a sheet paper. They would then give directions to their partner, student #2, on how to draw their
picture.
An alternative suggestion is to have students use walkie-talkies to give directions to a partner outside.

2. Attend: Attending to the Connection

4MAT 4 Algebra Student Activity Book page 3

Use this student page for this "Connect" activity.

Objective: Students should recognize the importance of using precise terminology, giving accurate directions and being a good listener.
Activity: Have students react to the block activity. Discuss what was successful, what needed improvement. What do you feel is more important: listening or giving directions? 
Assessment: Check for understanding through a class discussion.

Getting ready
This is the “Attend” octant of the unit, Step Two. This activity examines what just took place and begins to clarify the reason behind the learning.

Activity directions
Have students react to the block activity in their workbook using page 3.
Discuss what went well and what the students might have done differently if they repeated the activity.

What is more important: listening or giving directions?

What are important aspects of good communication?

Did you have that feeling of not knowing what to say to describe what you were trying to do?
 

3. Image: Creating a Mental Picture

4MAT 4 Algebra Student Activity Book pages 4-6

Use this student page for this "Image" activity.

Objective: Students recognize that language is powerful, and not knowing terminology leads to confusion.

Activity: Students interpret slang cards and create their own slang word/phrase card. Students discuss their interpretations with each other.

Assessment: Class discussion. Check for transfer of knowledge about good communication from previous activity. Students begin to realize that they need to understand the proper terminology to be successful in math as well.



Getting ready

This is the “Image” octant of the unit, Step Three. This step allows students to create a personal representation of the concept by drawing on their past experiences.

1. Have enough index cards for each person in the class.

2. Prepare the definitions so the students can view them on overhead, computer, etc.



Activity directions

1. Divide students into groups of 4. 

2. Tell students they have one minute to put a check mark next to each word or phrase that they are 100% sure of what it means.

3. After one minute, have each group discuss their results. As a class, discuss any words or phrases that students did not have checked.

4. Hand students a blank index card. On the blank card, the student should write his or her own slang word or phrase (this could be computer chat lingo, spoken slang, …)

5. Exchange cards with a nearby group.

6. The group takes their new set of 4 cards and tries to decipher them.

7. Class discussion. Have students share their interpretations of the cards. The teacher should display the answers to the slang cards. Finally, the teacher should lead the students to the realization that language is powerful, and not knowing terminology leads to confusion. The language of math is especially powerful…one symbol can represent a huge

concept.

8. Journal entry pages for this activity can be found on Student Activity Book pages 5 and 6.

9. Students could create a symbol that represents them and post it in the classroom.



Notes

See answers on Attachments page (Communication-3-Image-answers.pdf).

Student checklist can be found on activity book page 4.

4. Inform: Receiving Facts & Knowledge

4MAT 4 Algebra Student Activity Book page 7

Use this student page for this "Inform" activity.

Objective: Students learn the basic language of Algebra and begin to see how important good communication is to succeed in Algebra.

Activity: Introduce basic Algebra terms and how to communicate using math.

Assessment: Students complete notes, share thoughts and reactions through oral discussion, and journal their understandings.



Getting ready

This is the “Inform” octant of the unit, Step Four. This is when students learn the information, knowledge base, the content, using a variety of delivery systems.



Activity description

Mathematics is a very powerful language. We can say a lot using very few symbols or words. Here are just a few examples of how we can communicate mathematically:



1. Using a variable to represent a number. We used a box to represent an unknown in primary grades.

(   )+ 3 = 5.

Writing equations using a letter instead of symbols can help us communicate more effectively. In baseball, for example, it is sometimes clearer to use a B to represent the number of homeruns hit by Barry Bonds than it would be to use a symbol.



2. We can communicate expanded multiplication quicker and more efficiently using exponents. 



3.  Everyone must communicate using the same process when performing order of operations.



4. Data can often be communicated more effectively and efficiently using tables, graphs, and matrices.



5. Understanding rules is essential for good communication.  Rules for real numbers and what real numbers represent are vital for success in Algebra.



6. Sometimes the World is Negative! Activity

Have students draw a situation in the real world where negative numbers are involved using activity book page 7.

5. Practice: Developing Skills

4MAT 4 Algebra Student Activity Book pages 8-13

Use these student pages for these "Practice" activities.

Objective: Students practice the concepts.

Activity: Students complete assignments, explore applications, complete Tic-Tac-Toe Student Choice Activity, and play games for understanding real number properties and to practice the concepts.

Assessment: Check for mastery of concepts using worksheets, book problems, and a quiz or test.



Getting ready

This is the “Practice” octant of the unit, Step Five. These activities provide opportunities for the students to practice in multiple ways.



Activity description

Examples of activities that may be used here include but are not limited to:

1. Book assignments and worksheets.



2. A kinesthetic representation of the number line and real numbers.

Students stand in a straight line. The person in the middle is assigned the value of zero. Ask several students what number best represents their position in the line. Repeat the activity choosing a different position in the line to be zero. There are other activities you can develop with this activity such as adding positive and negative numbers. See Attachments page for directions for this activity as well as answers for the student Activity Book pages used in this octant (Communication-5-Practice.pdf).



3. Have students bring in examples of tables and graphs from magazines, newspapers, internet, etc. Student Activity Book page 8 has been provided for this activity.



4. Use games to develop understanding of properties of real numbers such as dice games for real number addition.



5. Tic-Tac-Toe Activity

This activity can be done individually or in small groups. Choose a row to complete. You can go horizontally, vertically or diagonally. The cut-apart cards can be found in the back of the Student Activity Book p. 139. See Attachments page of this unit to view a pdf of these cards. (Communication-5-TicTacToe.pdf)



Notes

Examples of practice activities can be found on Student Activity Book pages 8-13.

6. Extend: Extending Learning to the Outside World

4MAT 4 Algebra Student Activity Book page 18

Use this student page for this "Extend" activity.

Objective: Students show they can communicate more effectively using Algebra concepts.

Activity: Students create a visual representation of a given concept.

Assessment: Rubric for project.



Getting ready

This is the “Extend” octant of the unit, Step Six. This activity provides opportunities for learners to design their own open-ended exploration of the concept.

Partners will be assigned an Algebra concept developed in this unit.* Partners will create a visual representation of their choice that demonstrates their knowledge of their assigned concept.

*Allow students to work alone if they choose.



1. If needed, teacher will edit list to match concepts taught. You may want to include what section the concept came from to help students locate the concept.



2. Copy the list and cut the list into strips. Notice that we are developing 42 concepts in this unit. Every effort should be made to make sure that all 42 concepts are covered. If you are not planning to edit the list, you do not need to copy the list. Have students draw numbers and refer to the Student Activity Book page 18 to see what concept(s) they got.

If you have only one Algebra class, you may need to assign more than one concept to each group. If you have multiple Algebra classes, each group would draw one concept. The next class would continue drawing until all concepts were gone. If you run out of concepts then repeat some of the concepts.

Tip: Copy and cut extra concept strips ahead of time.



3. Cut tag board into desirable size. (18” x 24” works well.) Teacher may choose to have a supply of markers, colored

pencils, construction paper, yarn, glue, scissors...



Activity description

1. Partner students up. If a student wishes to work alone they may.



2. Students then select a concept strip and write down the facts about their concepts. See Attachments page for a list of concept choices. (Communication-6-Extend.pdf)



3. Groups exchange their concepts with another group. Each group peer edits the facts to make sure they are accurate.



4. After peer reviewing, students begin transferring their information to the poster board. Give students the opportunity to use a computer to generate images and/or use a word processor to type their facts.



Notes

Give students time out of class to finish the project. One suggestion would be to allow them time over a weekend to

add creative touches to their project. See next page in this manual for the list of project concepts.

7. Refine: Refining the Extension

4MAT 4 Algebra Student Activity Book page 19

Use this student page for this "Refine" activity.

Objective: Students collaborate to “fine-tune” projects.

Activity: Students critique and refine projects.

Assessment: Student participation.



Getting ready

This is the “Refine” octant of the unit, Step Seven. This activity helps turn mistakes into learning opportunities.



Activity description

Have students partner up and score each other’s project based on the rubric that was developed together. It may be helpful to randomly select partners and do this several times. Students benefit from seeing other projects as well as providing valuable feedback for their partner. This should be done prior to transferring their information to the poster board.

An example of the project rubric can be found on Student Activity Book page 19.

8. Perform: Creative Manifestation of Material Learned

4MAT 4 Algebra Student Activity Book page 20

Use this student page for this "Perform" activity.

Objective: Students share their project.
Activity: Projects are posted in the classroom. Students participate in a scavenger hunt. Leave the projects posted for future reference.
Assessment: Teacher assesses projects using a pre-agreed upon rubric.

Getting ready
This is the “Perform” octant of the unit, Step Eight. This activity gives the learner the support they need to teach and share with others.
Create a list of questions based on the projects/posters that were turned in. Questions should assess students’ knowledge about the concepts. There should also be questions that ask them to find creative ideas that were used to convey the concept. See ideas listed below.
After completing your project, write about one thing that made you say ah-hah!

• Find the poster that used yarn.
• What was the concept for the poster that used a rainbow to show the rule?
• What food was used to show counter-example?
• Think of a concept that you don’t understand. Find the poster related to it. What is the concept? What about their poster helps you better understand that?

Activity description
Students do a gallery walk looking for the items on their list.
They will use Student Activity Book page 20 to journal reflections for this activity.

Files attached with this lesson are :

1. Communication-5-Practice-Tic-Tac-Toe.pdf
2. Communication-5-Practice-Answers.pdf
3. Communication-3-Image-Answers.pdf

1. Level of Engagement, Fascination :

.....

2. Seeing the Big Picture :

.....

3. Success with Acquiring Knowledge :

.....

4. Success with Acquiring Skills :

.....

5. Performance, Creative Use of Material Learned :

Project Performance Rubric

4MAT 4 Algebra Student Activity Book page 19

Use this student page for the Project Performance Assessment.

Use this rubric to peer critique projects as well as for final teacher evaluation. Student Activity Book page 19.



It is time to communicate what you have learned!



(10 points)  – 1. All necessary info is there

(10 points)  – 2. Info is correct

(5 points)  - 3. Creativity/Professionalism

Total      (25 points possible)



Concept: ___________________________   

Did I do my best work on this project? Why?



Your job will be to create a poster for your concept. Be as informative as possible but also as creative as possible. Poster board, markers, colored pencils, glue sticks, construction paper will be supplied for you. You supply the rest! They will be displayed in the room for everyone to see and use when they need help remembering your concept!

Author : Melinda Zanetich