## Linear Equations and Inequalities

### Subject: Mathematics

### Grades: 9-12

**Standard:**

-Linear equations and inequalities

**Objective:**

-Students will apply the distributive property to real numbers to simplify an

expression to its smallest terms by combining like terms.

**Background**:

-This lesson takes place during the fall in the first quarter of the semester. The students have already demonstrated mastery of identifying and applying the associative and commutative properties of real numbers. The students have become accustomed to the routinesof the classroom and are familiar with the color-coded lessons and group work.

**Materials:**

-Projector

-SmartBoard

-Pre-made color-coded example problems

-Behavior Cards

-Pencils

-Paper

-Calculator

-Worksheet

-Algebra Tiles

-Markers

**Vocabulary Words:**Coefficient, term, like terms, constant

**Introduction:**

1. The teacher will project a premade example onto the SmartBoard with an orange background. The students have become accustomed to the routine and know that an orange background means they are reviewing past information.

2. The teacher will allow the students a few minutes to work the problems out on scratch paper. The teacher will then call on students to answer questions on how to get the answer. The teacher will reward students who are actively participating with behavior cards given out at random intervals.

3. The teacher will display a premade example onto the SmartBoard with a green background. The students have become accustomed to the routine and know that a green background means the teacher will be presenting new information. The students divide up into three groups that have been assigned.

4. The teacher will begin by showing the students an expression (3x + 2x–4). The teacher will identify the Coefficient, term, like term, and constant using different colored pens to highlight the differences. The students will copy the example onto a piece of paper.

5. The teacher will explain to the students that they can use the properties of real numbers to combine like terms in large expressions to simplify a problem and make it easier to solve. Using the premade examples on a green background the teacher will demonstratehow to combine like terms by using different colored pens to circle/highlight the similar terms and then simplify the expression.

6. After watching the teacher demonstrate several problems the students will begin working in groups to apply the knowledge they have of the associative and commutative property and the new knowledge of the distributive property to simplify expressions by combining like terms.

**Tier 1: Below Grade Level Learners**

(Special Materials: Algebra Tiles)

-Students in this tier will use manipulatives to be able to visualize the problems that they are solving. The students will be given algebra tiles

to set up the expression. Students will use the algebra tiles to combine the similar shape and colors to simplify the expression into smallest

terms. The students will work several problems out using the algebra tiles and then translate the answer onto their worksheet.

**Tier 2: Grade Level Learners**

(Special Materials: Markers)

-Students in this tier are able to solve mathematical problems without the use of manipulatives. However, they may or may not need

additional help to continue being able to visualize the expression. The students will use markers to circle or highlight similar terms. They will

solve several problems on their worksheet by circling or highlighting similar terms using a marker and then simplifying the expression.

**Tier 3: Above Grade Level Learners**

(No special materials needed)

-Students in this tier will utilize their knowledge of the properties of real numbers to simplify expressions. They will show demonstrate this knowledge by showing their work on paper. The students will combine the similar terms until they have simplified the expressions.

**Summary:**

-The goal of this lesson was for the students to apply the properties of real numbers to

teacher demonstrated several examples by utilizing the method that would be used during independent activity by the students who are working in Tier 2. After displaying and working through several examples the students divided into groups where they were able to explore the

new information through a variety of activities based on their specific learning needs. The students who needed more help with visualizing the activity were provided with algebra tiles as manipulatives so that they could see what they were doing. By using this method, the students

will be able to visualize and later be able to solve similar problems without the use of manipulatives.

-By splitting the groups up and allowing them to work using materials based on their individual needs, the teacher is meeting the specific needs of each of the students while still meeting the standards.

**Assessment:**

-The students will be assessed based on the completion of the worksheet. Within their groups the students have been provided with worksheets with several examples to solve based on their specific learning needs. The worksheets were developed with problems that were

appropriate for the students in the Tier to which they were applied. To explain, the problems in Tier 1 could be solved more simply using the algebra tiles. The problems in Tier 3 were more challenging and required the students to really demonstrate mastery of the content.