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Group Math Unit Plans

Algebra 1-IE Approach to Teaching Quadratic Functions

• Explain big ideas or portions of the theory that have guided your construction of this unit.

In this theory, the teacher takes the central role of describing the concepts and is the transmitter of knowledge. Students lack prior knowledge of a quadratic equation. As this is a new concept, students need the guidance of a teacher in order to be able to process and generalize the new information.

• Explain the task that you will be asking students to learn and/or perform.

By the end of this unit, students will be able to:
•explain the meaning of a quadratic function
•understand the relationship between the graph of a function and its equation
•distinguish a quadratic function from other functions
solve quadratic equations using various methods: factoring, completing the square and quadratic formula
•identify the features (axis of symmetry, vertex , concavity, intercepts) of a graph
•graph manually and using technology
•identify, graph and solve different forms of quadratic equations

• Describe the role of the teacher in this unit. How will she//he promote learning?

The teacher will describe the general features of a quadratic function and model step by step approaches to solving equations both algebraically and graphically . The teacher will provide students with opportunities for guided practice. Quizzes will be given on a regular basis. The level of mastery will be assessed by asking questions and promoting further understanding through direct instruction. Students will be encouraged to ask questions and seek help when they don’t understand concepts.

• Describe at least 5 activities that students will complete during this unit. Descriptions can be brief (1 paragraph each).

Activity 1
Introduction
Students will be given 5 graphs and will have to identify the features of the graph (vertex, symmetry of the graph, x and y intercepts , concavity). These features will be revisited throughout the course of the unit as students are taught to solve quadratic equations in the three different ways. Students will be taught how to compare the graph of a quadratic function and the solutions to its related quadratic equation. The teacher will explain to students what is being found when solving quadratic equations. Students will be introduced to solving quadratic equations by factoring. There will be guided then independent practice.

Activity 2
Solving equations by completing the square
The teacher will begin the lesson by explaining that not all quadratic equations can be factored so we need another method . Students will be challenged with equations that do not have real solutions . By referring to the graphs, students will draw comparisons of quadratic equations that have no real solution and graphs that have no x-intercepts. They will be taught how to complete the square.

Activity 3
Solving equations using the quadratic formula
The teacher will introduce the concept of using the discriminate to determine the type and number of solutions . The quadratic formula will then be introduced. There will be guided then independent practice.

Activity 4
Graphing quadratic functions in vertex form
Beginning with the graph y=x2 the students will be asked to transform the function into vertex form. Students will look at the graph of y=x2 on the graphing calculator. They will compare that graph to the graph of an alternate vertex form with varying h and k values. Students will be asked to predict what the graphs will look like. They will be given drill and practice to match the vertex form of the equation with the graph. The teacher will then introduce the idea of transformations.

Activity 5
Written test
Students will be expected to complete a summative assessment including multiple choice and short answer questions based on material from this unit.

• Explain how your role and the activities you’ve chosen are consistent with the theory.

Although some of the activities could be somewhat constructivist, the role of the teacher is to transmit knowledge to the student. Students have limited opportunities to work collaboratively and rely heavily on the teacher’s expertise to learn the concepts.

• Explain how you’ll use technology and how the technology you use is consistent with the instructional activities and the theoretical approach.

Technology in the form of graphing calculators will be used. The calculators will be used for instructional purposes i.e. verifying and calculating solutions. They are not used for exploratory purposes. The view-screen will allow students to follow along with teacher-directed instruction.

Geometry-Constructivist Approach to understanding properties of quadrilaterals

• Explain big ideas or portions of the theory that have guided your construction of this unit.

Students are actively involved in hands on activities which facilitate the construction of content understanding. Students will be dialoguing with one another to help them construct their knowledge. In addition, the final assessment will be completed collaboratively.

• Explain the task that you will be asking students to learn and/or perform.

By the end of this unit students will be able to:
•classify quadrilaterals
•construct quadrilaterals manually and using technology
•understand the properties of diagonals
•find the area of quadrilaterals

• Describe the role of the teacher in this unit. How will she//he promote learning?

In this unit, the teacher acts as the facilitator. He or she promotes learning through investigation and collaboration.

• Describe at least 5 activities that students will complete during this unit. Descriptions can be brief (1 paragraph each).

Activity 1
Introduction
The teacher will display different quadrilaterals on screen using Geometer’s Sketchpad. Students will have access to this on their computers in order to find the measurements of each quadrilateral (measuring angles, side length, diagonals). The teacher will give students the definitions for types of quadrilaterals and the students will then classify them.

Activity 2
Students will construct a parallelogram and identify the properties related to the angles, diagonals and sides. Students will be challenged to find the formula for the area of their parallelogram.

Activity 3
Students will use Geometer’s Sketchpad software to construct a rhombus, square and rectangle. The students will work with a partner by then trading computers and checking each others work by measuring the quadrilaterals. They will then make sure that the quadrilaterals were accurately constructed and classified and give
feedback to their partner. Students will apply the appropriate formula to find the area of the quadrilaterals. In addition to the area of a parallelogram, students will be required to find the alternate formula for the area of a rhombus.

Activity 4
Students will use Geometer’s Sketchpad to construct kites, trapezoids and non-classified quadrilaterals. Once again students will work with a partner who will be challenged to measure and classify their quadrilaterals, when possible. Students will then find the formulas for the area of their trapezoids and kites.

Activity 5
Students will work with one or two partners and use available hands on materials (straws, toothpicks, paper) to design a mosaic table top using all types of quadrilaterals at least once and with a limited total area. They will have to calculate the cost of their table top using various materials.

• Explain how your role and the activities you’ve chosen are consistent with the theory.

In this activity, the teacher acts as a facilitator by mediating the dialogue between students. Assessment is on-going and performance based. Peer evaluation and consultation is used with students taking on the role as the more knowledgeable other. Students are able to apply their understanding in a real world situation by finding the cost of their table top.

• Explain how you’ll use technology and how the technology you use is consistent with the instructional activities and the theoretical approach.

Students use Geometer’s Sketchpad to discover the properties related to each of the classified quadrilaterals. They will also use this software to construct their own quadrilaterals.

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