I. Curricular Framework

Concept:

Equality

Essential Question:

What role does balance play in achieving equality?

Bridge:

Balance

Content:

Algebraic Equations

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To introduce the concept of equality.

Activity: Teacher presents an experiment. Students work in four teams. Each team is given a beaker of an unnamed liquid (lemonade). Two of the teams are to add the exact same amount of red and blue food coloring to the beaker. The other two teams are to add the exact same amount of green and yellow food coloring to their beakers. Each beaker must be an exact duplicate of the matching team's beaker. Jars are compared to see if results look exactly the same.

Assessment: Studentsí ability to follow directions and their curiosity at the task.

2. Attend: Attending to the Connection

Objective: To analyze the results of experiments.

Activity: 1. Using overhead projector, teacher creates chart from student input analyzing numbers of color drops which were added to each beaker. 2. Liquid is divided equally among group members for tasting. Teacher leads students' analysis as follows: Were color drops equal? Is the color identical? If not, what might have affected the results other than the number of drops? Does all liquid taste the same? Did the color change the taste? Why should there be at least 2 samples that are identical in all respects?

Assessment: Student contributions to discussion and analysis of the experience.

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: To introduce the concept of equality as balancing two sides to maintain equality in non-mathematical life instances.

Activity: Students relax while teacher conducts a guided imagery of weight lifting in competition, focusing on feelings of being in balance and out of balance. In small groups, students discuss the commonalties between a weight lifter, pharmacist, assayer, and the lemonade experiment. Each group produces a visual portraying their understanding of the concept of in balance and out of balance.

Assessment: Teacher observation of contributions to small group discussion and group visuals.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To teach about equality in mathematical equations.

Activity: 1. Using overhead transparency of balance scale and red and blue manipulatives, teacher demonstrates fundamental rule of working with equations: Whatever is done to one side of the equation must be done equally to the other side to maintain the balance. One-step addition and subtraction problems are demonstrated. Teacher reviews inverse property and zero property of addition. Students solve sample problems for immediate guided practice. (See Step Six.) 2. Teacher lectures on inverse property of multiplication, reciprocals, and reviews the property of one. Again using the overhead and manipulatives, teacher demonstrates 2 methods for solving sample equations focusing on the advantages/disadvantages of using reciprocals over inverse operations. Students experiment with sample equations to choose which method is most comfortable. (See Step Six.) 3. Teacher shows four ways to solve two-step equations. Students practice problems using the methods used for addition/subtraction and multiplication/division. Working in cooperative groups, they practice sample equations helping each other. (See Step Six.)

Assessment: Teacher checking for understanding and students' work on sample problems.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: To practice solving equations using addition and subtraction. To practice solving equations using multiplication and division. To practice solving multi-step equations using reverse order of operation.

Activity: 1. For homework using textbook problems, students solve simple equations using addition and subtraction. 2. For homework using textbook problems, students practice one-step equations using multiplication or division. 3. Students work additional multi-step equations for guided practice.

Assessment: Self-checking of problems in cooperative groups; teacher review of homework.

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Objective: To apply what has been learned about equality to word problems.

Activity: Working in cooperative groups, teacher reads a sentence aloud, such as, “There are seven more boys than girls in class today with a total entrollment of twenty-seven. How many boys are there?” Each student in the group composes an equation derived from the words. Group compares equations and agrees on correct form to be shared with rest of class. Groups receive points for correct answers. Groups are given six additional sentences to solve cooperatively.

Assessment: Ability to work together. Quality of completed sentence equations.

7. Refine: Refining the Extension

Objective: To use real-life data to write word problems using equations.

Activity: Cooperative groups use an almanac and their own calculators. Their task is to select a factual topic from the almanac, collect necessary data, and write a word problem which sets up an equation. They must solve their own equation.

Assessment: Cooperative efforts of students; understanding of task, and ability to apply what has been learned.

8. Perform: Creative Manifestation of Material Learned

Objective: To share what has been learned with others.

Activity: Students share word problems with other groups. Group solution cards are compared as each group tries to solve the other equations.

Assessment: Quality of completed problems and equations.

Assessment, Phase Five,Performance, Creative Use of Material Learned: