Lindsay Claseman
April 23, 2006
PLC 915B: Dr. Mora
San Diego State University
Model Integrated Thematic Unit for English Language Learners
Lesson Plans
Subject: Algebra 1C
Grade: 8-9
Theme/Topic: Solving Linear Equations in One-Variable
ESL Level: 1-2
Content Standards:
5.0 Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
Lesson Rationale-Level 1-2:
Key components in understanding mathematics include not only comprehension of the mathematical procedures, but a solid conception of the required vocabulary as well. Students who are in the process of learning English as second languages have an extra step they need to take in gaining this latter concept and thus may have a more difficult time with understanding mathematics fully. This lesson is designed to introduce Level 1 and 2 learners to the process of solving equations. Students will be familiarized to the vocabulary using realia as well as by a graphic organizer. The concept will be introduced to the learners utilizing a situation that they may encounter in their present lives. The class will use the same word problem to build their mathematical understanding, moving from the scenario, to values, and finally to terms, thus gradually establishing a solid foundation. In this manner, expectantly students will learn not only the new mathematical knowledge but also a connection of how these mathematical concepts are important in their everyday lives.
Solving an equation if a very important concept for students to understand because the concept so often is implemented in everyday life. While many times in the form of mental math, for this mental math to be strong, they must have a solid understanding of the underlying mathematical concepts.
Lesson Objectives-Level 1-2:
Students will explain in short phrases how math is applicable in real life following the discussion of a real life word problem.
Students will classify various parts of the word problem and place these values with the appropriate locations/illustrations on the worksheet.
Students will distinguish what they know in the problem from what they need to discover.
Students will successfully complete a worksheet which takes the problem they just solved using arithmetic into an algebra equation.
Students will successfully identify variable as being the unknown as well as be able to distinguish the variable in other mathematical problems.
Students will be able to explain in short phrases how they figured the word problem out using arithmetic.
Students will successfully identify inverse operations including how they are used to solve an algebra equation.
Anticipatory Set:
The class is going to work towards being able to watch a movie in the near future. In order to watch the movie, students, after being given an allotted amount of money, will need to figure out how to spend that money under the given specifications. To introduce the topic, as a class we will discuss the word problem including what is expected of each student. We will also shortly discuss how mathematics fits into this scenario. Given that the students are in 8th or 9th grade, and assuming they have some experience with money, they will not need to use algebra, simply figure out a solution using arithmetic.
Instruction/Presentation-Level 1-2:
Following the class discussion about going to the movies, containing how mathematics fits into this idea, students will be working in groups to finish the problem (Independent Practice) With their groups, they will be working from a worksheet. The worksheet contains the word problem and pictures. As a class we will talk about the word problem and what it tells us. The students are to place the values from the word problem, which corresponds with the correct picture. For instance, if a soda costs $3, the students will put $3 next to the picture of a soda. Inevitably, they will be left with one picture, which they will not have a value for and will have to write a question mark. As a group, they must figure out what this value is. To accompany them they will have money to work with. Once the group has reached a consensus on the answer, they are to come to the front of the room where they can purchase a “bank voucher”, “food voucher” and “movie ticket”. They will know if they are correct if they have enough money to buy each item.
When the majority of the class has reached a solution, we will reconvene to discuss how we figured out the answer (Direct Instruction). Each group will have an opportunity to share what they did. Students will then receive another worksheet consisting of a series of equations. The beginning equation will have only pictures. These pictures will directly correspond to the problem just completed. As a class, we will walk through all the different equations on the sheet with each equation becoming vaguer. The end equation will have only letters and numbers. At this point, we will define variable. To tie back to the original problem, students will need to identify what the variable was in the beginning problem.
As a class, we will begin to talk about how this new equation ties into the movie problem. Most likely students will have subtracted when originally solving the problem. The new equation has us adding. This is an excellent point for discussion and a lead-in to inverse operations. Students will make a note on their worksheet that addition and subtraction are inverse operations as well as each step is to be done to BOTH sides. To help the students see this, we will talk about how we want to take the money from the total amount, but the only way to do this is by doing it to both sides.
Students will be left to once again work in their groups (Independent Practice). They will be writing a narrative that shortly explains how we solve problems like the movie problem. They will need to include information about variables, inverse operations, and being fair to both sides.
Guided Practice-Level 1-2:
As a class we will walk through another problem using both arithmetic and algebra so students can see how algebra is doing the same thing as they are used to with different words.
Independent Practice-Level 1-2:
The independent practice is described above. Students work in groups to solve a problem then later work together to write a narrative on how to solve these problems.
Closure/Evaluation-Level 1-2:
For students to have met the expectations of this lesson, their narrative will show accurate understanding or at least great effort in trying to convey their thoughts. The next day, students will hopefully be able to identify more easily the necessary vocabulary in these problems and brainstorm situations in life where they might need math such as that which has been learned. If the students have put a 3 on their homework and their work displays this rating, I will also consider the students successful.
Lesson Rationale-Level 3-4:
Key components in understanding mathematics include not only comprehension of the mathematical procedures, but a solid conception of the required vocabulary as well. Students who are in the process of learning English as second languages have an extra step they need to take in gaining this latter concept and thus may have a more difficult time with understanding mathematics fully. This lesson is designed to introduce Level 1 and 2 learners to the process of solving equations. Students will be familiarized to the vocabulary using realia as well as by a graphic organizer. The concept will be introduced to the learners utilizing a situation that they may encounter in their present lives. The class will use the same word problem to build their mathematical understanding, moving from the scenario, to values, and finally to terms, thus gradually establishing a solid foundation. In this manner, expectantly students will learn not only the new mathematical knowledge but also a connection of how these mathematical concepts are important in their everyday lives.
Solving an equation if a very important concept for students to understand because the concept so often is implemented in everyday life. While many times in the form of mental math, for this mental math to be strong, they must have a solid understanding of the underlying mathematical concepts.
Lesson Objectives-Level 3-4:
· Students will explain how math is applicable in real life following the discussion of a real life word problem.
· Students will classify various parts of the word problem and place these values with the appropriate locations.
· Students will distinguish what they know in the problem from what they need to discover.
· Students will successfully complete a worksheet which takes the problem they just solved using arithmetic into an algebra equation.
· Students will successfully identify variable as being the unknown as well as be able to distinguish the variable in other mathematical problems.
· Students will be able to explain how they figured the word problem out using arithmetic.
· Students will successfully identify inverse operations including how they are used to solve an algebra equation.
· Students will successfully solve equations using algebraic methods.
Anticipatory Set:
The class is going to work towards being able to watch a movie in the near future. In order to watch the movie, students, after being given an allotted amount of money, will need to figure out how to spend that money under the given specifications. To introduce the topic, as a class we will discuss the word problem including what is expected of each student. We will also shortly discuss how mathematics fits into this scenario. Given that the students are in 8th or 9th grade, and assuming they have some experience with money, they will not need to use algebra, simply figure out a solution using arithmetic.
Instruction/Presentation-Level 3-4:
Following the class discussion about going to the movies, containing how mathematics fits into this idea, students will be working in groups to finish the problem (Independent Practice) With their groups, they will be working from a worksheet. The worksheet contains the word problem spaces for them to identify various parts of the problem. In groups, the students are to identify various values in the word problem and fill in the corresponding blanks. For instance, if a soda costs $3, the students will put $3 in the allotted space for “food”. Inevitably, they will be left with one picture, which they will not have a value for and will have to write a question mark. As a group, they must figure out what this value is. To accompany them they will have money to work with. Once the group has reached a consensus on the answer, they are to come to the front of the room where they can purchase a “bank voucher”, “food voucher” and “movie ticket”. They will know if they are correct if they have enough money to buy each item.
When the majority of the class has reached a solution, we will reconvene to discuss how we figured out the answer (Direct Instruction). Each group will have an opportunity to share what they did. Students will then receive another worksheet consisting of a series of equations. The beginning equation will have only words. These pictures will directly correspond to the problem just completed. The class will work in groups up until a certain point where we will reconvene as a class. This is a point where the students have not seen the material and we will need to discuss the new material. At this point, we will define variable. To tie back to the original problem, students will need to identify what the variable was in the beginning problem.
As a class, we will begin to talk about how this new equation ties into the movie problem. The students will be guided to hopefully identify that the new equation is multiplying and adding, compared to their originally dividing and subtracting. This is an excellent point for discussion and a lead-in to inverse operations. Students will make a note on their worksheet that addition and subtraction, multiplication and division are inverse operations as well as each step is to be done to BOTH sides. To help the students see this, we will talk about how we want to take the money from the total amount, but the only way to do this is by doing it to both sides.
Students will be left to once again work in their groups (Independent Practice). They will each be writing a narrative that shortly explains how we solve problems like the movie problem. They will need to include information about variables, inverse operations, and being fair to both sides. They will also need to include another situation that may use the same math.
Guided Practice-Level 3-4:
As a class we will walk through more problems using algebra so students can see how algebra works with these types of problems. The problems will include multiple steps.
Independent Practice-Level 3-4:
The independent practice is described above. Students work in groups to solve a problem then later work together to write a narrative on how to solve these problems.
Closure/Evaluation-Level 3-4:
For students to have met the expectations of this lesson, their narrative will show accurate understanding or at least great effort in trying to convey their thoughts. The next day, students will hopefully be able to identify more easily the necessary vocabulary in these problems and brainstorm situations in life where they might need math such as that which has been learned. If the students have put a 3 on their narrative and their work displays this rating, I will also consider the students successful.