Benchmark Math - Paper Example

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912 words
Carnegie Mellon University
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Algebra is essential in moving students from understanding simple arithmetic and their operations to focus on the use of symbols to represent numbers and express mathematical relationships. Algebra is an essential in several branches of mathematics, which apply to real life examples. It is thus important that students understand the topic as early as possible so that they internalize it for application later on. It is, however, a little complicated to design strategies and plans to ensure students, particularly average learners get to comprehend the concepts of algebra to apply them in other branches of mathematics, or even in real life. Below are practical strategies that can be used to enable students to understand algebra and its applications among students.

Part One: Strategies

Marias goals are to understand basic algebraic operations. More importantly is to use the operations together with symbols to express mathematical relationships. The student will also be able to manipulate the expressions to come up with meanings and solutions to problems. The first strategy should be to use solved problems to engage students in analyzing algebraic reasoning and strategy. Solving algebra problems requires students to think more abstractly. However, algebraic thinking requires students to process multiple pieces of complex information. That, however, is not the best strategy for students who cannot comprehend complex information. For such students, using solved examples offers the best preview of the problem without the need to calculate each part separately. Such a strategy minimizes the burden of abstract reasoning, making it easy to understand the problems more quickly. Analyzing and discussing such solved examples among students can also see them develop a deeper understanding of the logical processes needed to solve them.

Secondly, students should be taught how to use the structure of algebraic representations. That enables them to understand the numbers, type, the position of quantities and even the operation. For example, 2x + 4 = 8, 2(x + 2) = 8, and 4x = 8. In all those three equations, there is a two multiplied by quantity, and an addition of then the answer is given as 8 in all the operations. Paying attention to structure helps students to establish connections among problems, solution strategies and representations that may appear different even though they are the same in the real sense. Illustrating this using a graphical assistive technology will be more useful to help the students understand the issue. The strategy will be effective, in solving more complex algebra problems.

Creating a visual representation of the algebra systems will help students understand the problem, establish relations ad even derive solution strategies. For instance, illustrations and putting examples in visual illustrations will be one mnemonic to all students. They should also be made to connect the numbers they abstractly use into a real life problem. Lastly, students should be encouraged to choose different strategies in solving algebraic problems. If allowed to choose from multiple strategies, and allowed to discuss and analyze on their own, they will get to understand how they interpret and represent algebra problems, how to develop solutions among other things.

Part Two: Unit Plan


Teacher Candidate:

Grade Level:



Instructional Plan Title 9


Teaching Algebra to Grade 9 Students

I. Planning

Lesson summary and focus: The central focus will be for the students to represents algebra problems in different structures, and be able to develop solutions using various strategies.

Classroom and student factors: In terms of understanding algebra concepts, the students is two grades below where she is. That means the student should be treated as a special case.

National / State Learning Standards: Understanding different algebraic structures and how to represent them.

Use mathematical operations on those structures.

Utilize different strategies to come up with solutions.

Specific learning target(s) / objectives:

Understand algebra more deeply. Teaching notes:


Agenda: Formative assessment:

Academic Language: English Key vocabulary:

Algebra, mathematical expressions, operations, representations. Function:

The language will help students know what they are doing, and understanding the parts that consist algebra problems. Form:

Moving from one vocabulary to show how it develops the other. That will enable comprehensive understanding..Instructional Materials, Equipment and Technology: White board, tablets, charts, and continuing materials of different structures.

Grouping: Making students in a group of two to three students to discuss and analyze problems.

II. Instruction

A. Opening

Prior knowledge connection: This lesson uses the basic arithmetic knowledge learned in previous lessons.

Anticipatory set: It will enable them put real life problems into a mathematical form, enabling them to develop solutions.

B. Learning and Teaching Activities (Teaching and Guided Practice):

I Do Students Do Differentiation

Use solved examples.

Allow discussions and self-analysis among students.

Create visual charts. Discussions and analysis.

Interpret charts and other practical materials.

Encourage tolerance and listening among students. Encourage differing opinions and choose of different strategies when solving same problems.


Summative Assessment: Giving students problems structured differently solved.

Giving students real life problems and asking them to express them mathematically. Differentiation:

Using different strategies to solve problems. Identifying other structures which the same question can be expressed.


When discussions and analysis will start to flow, students will be okay to go. Also, identifying real life situations whose solutions can be developed using algebra will highlight that they have achieved the objectives.

Homework: Best homework is to give students one real life questions, ask them to formulate it algebraically, then put it in different structures before utilizing more than one strategy to develop an answer. That should be accompanied with another problem which they should identify on their own and solve it in multiple steps as the first one.

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