##
* *Reflection: Developing a Conceptual Understanding
Algebra: Equal or Not Equal - Section 3: Closure

In order to gain a conceptual understanding of the order of operations, the counters worked really well to help the students find the values of the expressions. It helped the visual and kinethetic learners feel comfortable with grasping a new skill. By using the sentence, "Please Excuse My Dear Aunt Sally", the students could work the problem step by step with the counters. For example, (4 x 2) + 6. The students used the counters to find 4 x 2 = 8. Then the students adding 6 more counters. The students added all of the counters to find their value of 14. I sensed a level of confidence in the students just because they had the counters available for their use.

*Using Counters*

*Developing a Conceptual Understanding: Using Counters*

# Algebra: Equal or Not Equal

Lesson 1 of 3

## Objective: SWBAT determine if an equation is true or false.

*50 minutes*

#### Whole Class Discussion

*15 min*

*Rationale: With this being the end of the school year and our state test complete, our curriculum moves more into preparing the students for next level. Our district has outlined lessons that will help prepare our 4th grade students for 5th grade.*

In today's lesson, the students learn how to determine if an equation is equal or not equal by solving the two expressions using the order of operations.

I have the Equal or Not Equal.pptx displayed on the Smartboard. I begin by reviewing the definition for an equation. I remind the students that an equation states that two expressions are equal. I tell the students that this can be true or not true. I let the students know that the equations can have any of the four operations: addition, subtraction, multiplication, and division. Because the equations can have more than one operation, we must use the order of operations to solve the equations.

I share with the students that when I was in elementary school, I learned the sentence "Please Excuse My Dear Aunt Sally" to help me learn the order of operations. P stands for parentheses. This means that in the order of operations, any thing with parentheses must be worked first. Next, "E stands for exponents." I let the students know that we will not work exponents in 4th grade, but this will help prepare them for 5th grade. I write 5 with an exponent of 2 on the white board. I explain to the students that this means 5 x 5 = 25. Next, "M means multiplication, and D is division." I want to make it clear to the students that we look for multiplication and division at the same time, going from left to right in the expression. Which ever one we find first in the equation, we work that operation first. Last, "A is addition and S is subtraction." Just as with multiplication and division, when solving an equation, you look for addition and subtraction at the same time, looking from left to right. Whichever operation comes first is the operation that you work.

To model using the order of operation, I solve a problem for the students to help guide them to an understanding of the skill.

Problem:

(5 x 2) + 3 = 10 + 3

First work the parentheses of 5 x 2 = 10. Then, add 10 + 3 = 13. The first expression equals 13. Next, we must work the second expression to determine if the equation is equal or not equal. I explain to the students that the second equation only has one operation, so we can go ahead and add 10 + 3 = 13. This equation is true because both sides are equal.

To model this in the power point, I use counters to show the students that this tool can help them determine if both expressions are equal or not equal.

Let’s try another one!

15 + 3 – 2 = (4 x 3) – 5

We have addition and subtraction, so solve from left to right. The addition comes first.

15 + 3 = 18

18 – 2 = 16

Next, we work the second expression of (4 x 3) - 5. Solve the parentheses first.

4 x 3 = 12

12 – 5 = 7

The first expression equals 16, and the second expression equals 7.

I ask, "Is this equation true?" The students all know that this equation is not equal because they do not equal the same number.

To give the students practice before they get in groups, I ask the students to try this problem at their desks using the counters.

(2 x 4) + 6 = 7 x 3 - 2

As the students work at their desk, I walk around and help guide the students through the order of operations.

Are these expressions equal or not equal? The students knew that this equation was not equal because one side equaled 14 and the other side equal 19.

#### Resources

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#### Skill Building/Exploration

*20 min*

I give the students practice on this skill by letting them work together. I find that collaborative learning is vital to the success of students. Students learn from each other by justifying their answers and critiquing the reasoning of others (**MP3**).

For this activity, I put the students in pairs. I give each group a Equal or Not Equal Activity Sheet.pptx. The students must work together to find the value of the expressions to determine if the two expressions are equal or not equal. They must communicate precisely to others within their groups **(MP6)**. They must use clear definitions and terminology as they precisely discuss this problem **(MP1). **

The students are guided to the conceptual understanding through questioning by their classmates, as well as by me. The students communicate with each other and must agree upon the answer to the problem. Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students **(MP3)**. From the Video - Equal or Not Equal , you can hear the students discuss the problem and agree upon the answer to the problem. As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill **(MP6).** As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.

As they work, I monitor and assess their progression of understanding through questioning.

1. Which part of the expression will you work first? Why?

2. Are the expressions equal? How do you know?

3. Is this equation true or false?

As I walked around the classroom, I heard the students communicate with each other about the assignment. From the video, you can hear the classroom chatter and constant discussion among the students. Before Common Core, I thought that a quiet class working out of the book was the ideal class. Now, I am amazed at some of the conversation going on in the classroom between the students. As I walked past one group, I heard a student say, "I get it now." I was proud of this student because he is one of my lower students. He worked really hard during this lesson, and I can tell that he was determined to master this skill.

There were a few students who struggled with the order of operations. This is okay because this is the first day that the students have learned about this concept. I question students as I walk around to guide them through this concept. With that being said, I still like to pull students for small group to reinforce the skill the next day. Any students identified for intervention will work with me first thing the next day to make sure they have an understanding of how to use the order of operations to work equations with multiple operations.

Early Finishers: Write your own equations. Use the counters to see if they are equal or not equal.

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#### Closure

*15 min*

To close the lesson, I call on different pairs of students to share their answers. The students must explain why they worked the problem in the order that they did. This gives those students who still do not understand another opportunity to learn it. I like to use my document camera to show the students' work during this time. Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson. Students need to see good work samples (Student Work - Equal or Not Equal), as well as work that may have incorrect information. More than one student may have had the same misconception. During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class.

Misconceptions:

A few students needed more practice with using the order of operations. They wanted to work from left to right solving their problems. I used questioning and our phase, "Please Excuse My Dear Aunt Sally" to help the students understand that if they is more than one operation, then the order must be considered.

#### Resources

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- UNIT 1: Fractions
- UNIT 2: Skills Review
- UNIT 3: Algebra
- UNIT 4: Geometry
- UNIT 5: Patterns & Expressions
- UNIT 6: Problem-Solving Strategies
- UNIT 7: Decimals
- UNIT 8: Measurement and Data
- UNIT 9: Multiplication and Division Meanings
- UNIT 10: Place Value
- UNIT 11: Adding and Subtracting Whole Numbers
- UNIT 12: Multiplying and Dividing