##
* *Reflection: Data Analysis
Order of Operations - Section 4: Closure and Ticket to Go

I collected the tickets to go to see what the degree to which students can use the order of operations and what gaps in understanding they had. I corrected the tickets to go and grouped them in the following way:

**Novice:** These students struggled to use the correct order of operations. There were only a few students from each class in this category. A common problem was that students simply worked from left to right, without using the order of operations. For example, in number three this particular student subtracted 15 – 4 before multiplying by three. This student is also switching operations (multiplying instead of dividing). Unit 1.11 Student work N.jpg.

**Approaching Mastery:** These students were able to correctly use the order of operations but make a small error. This particular student incorrectly simplified four squared as 4 x 2, or 8. I will review the meaning of exponents in the next lesson. Unit 1.11 Student Work AM.jpeg.

**Proficient:** These students were able to correctly use the order of operations. They were able to complete the problems step by step and show their work. Unit 1.11 Student Work P.jpeg.

For this situation, I did not include an “advanced” category because the content did not require students to explain or analyze their work. Most students were able use the order of operations, but made a careless mistake while simplifying the expressions. For the few students who were novices, I will be pulling them to work with me on the review lesson before the test on order of operations.

*Data Analysis: New Reflection*

# Order of Operations

Lesson 11 of 16

## Objective: SWBAT: • Use OOO to simplify numerical expressions

## Big Idea: Students apply their knowledge of the order of operations to simplify numerical expressions for a second day.

*60 minutes*

#### Do Now

*10 min*

See my **Do Now** in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day. Here, students will use their number and logic skills to figure out the answers. I ask students to share their answers to problem 1. Then I write 4 x 3 + 116 / 7 on the board and ask, “Does this expression represent what you did?” I want students to realize that all of the numbers and operations are correct, but if you simplify it you get 14, instead of 4. I ask, “What do I need to do so that my expression matches what we did?” I want students to recognize that they need to add in parentheses so that their answer matches the expression. In connecting the steps with an expression, students are working on **MP2:** **Reason abstractly and quantitatively.**

Students may struggle with problem 2, since they must work backwards. I call up 1-2 students to show and explain their work. If I have time, I will write 2 ( ___ + 5 ) = 22 on the board and ask, “Does this represent what we need to figure out? Why or why not?” I want students to see that we double something and got 22. Since 2 x 11 = 22, then the expression inside the parentheses must result in 11, and 6 + 5 gets us 11.

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#### Analyzing Student Work

*15 min*

I tell students that they will Think Write Pair Share** **with the questions on the page. I read the prompt and have students work for 3-5 minutes independently. I walk around and monitor student progress and ensure that students are writing an explanation for each question.

Once most students have completed both questions we come back together. Students share with their partner for 1-2 minutes. Students are engaging in **MP3:** **Construct viable arguments and critique the reasoning of others. ** Then we open it to a class discussion. I ask for students to raise their hands to show who they believe is correct. If many students choose Julia as the correct answer, I declare that I think Jon is correct and then I explain my thinking. He correctly simplified the base and exponent. Then multiplication comes before division, so he multiplied 8 x 3 and got 24. Last, he needed to simplify 48 divided by 24. This is a common mistake that many students do.

My hope is that students hands shoot up and they want to argue with me! I call on a few students to share their thinking and specifically identify where Jon went wrong. I want students to articulate that in the order of operations you complete multiplication and division *from left to right. *That means, depending on the problem, we may multiply first or divide first.

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I have students work on the Order of Operations Review independently. **Posting A Key **helps me manage checking students work in a timely manner. I have scaffolded these problems so that each problem is more complicated than the previous problem. This way I can see where a student’s understanding breaks down as I walk around and monitor student work. For students who successfully complete the Review problems, they go on to work on the Riddle and the Challenge work.

For students who are struggling with the Review, there are a few ways I may intervene:

- Pull a small group to the back of the class to work on Review problems together. Once students are more comfortable, they return to their seats to work independently.
- I have them work with their partners together and I regularly check in with them.
- If there are enough students struggling, I’ll pass out whiteboards and markers. I have students show the step-by-step work on the first few practice problems.
- Give students a multiplication chart or calculator to help them access the problems.

For students who successfully complete the classwork, there are a few choices I give them:

- Serve as a tutor to a student I have identified who needs extra help
- Pair up with another student and take turns creating and evaluating numerical expressions using the order of operations
- Playing “Show me the Money!” from
**Show what you know Factors and Multiples + Introduction to Exponents**(students can use the 1-10 spinner for added difficulty).

Then I ask these questions:

- What would happen if we did not agree and we approached evaluating expressions in our own ways?
- What problems might arise?

I am looking for students to recognize that the order of operations is a set of rules that have been decided upon by mathematicians. Without these rules, different people would solve the same problems and get vastly different answers. I am interested to hear what problems students imagine would occur without agreement on the order of operations.

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#### Closure and Ticket to Go

*10 min*

For **Closure **I have students turn to problem 6 in the Review. What do we do first? I have students share out what to do and why. How do we know whether to add or subtract first? I want students to be able to articulate what to do and why.

With the last few minutes of class I give a **Ticket to Go** for students to independently complete. I pass out the **HW Order of Operations** at the end of class.

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- UNIT 1: Intro to 6th Grade Math & Number Characteristics
- UNIT 2: The College Project - Working with Decimals
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Fraction Operations
- UNIT 5: Proportional Reasoning: Ratios and Rates
- UNIT 6: Expressions, Equations, & Inequalities
- UNIT 7: Geometry
- UNIT 8: Geometry
- UNIT 9: Statistics
- UNIT 10: Review Unit

- LESSON 1: Welcome to 6th Grade Math
- LESSON 2: R-E-S-P-E-C-T
- LESSON 3: Tiles and Toothpicks
- LESSON 4: Mindset
- LESSON 5: Pretest
- LESSON 6: Brownies & Factors
- LESSON 7: Multiples, LCM, and GCF
- LESSON 8: GCF and LCM Word Problems
- LESSON 9: Show What You Know: Factors and Multiples + Introduction to Exponents
- LESSON 10: Why do we need an Order of Operations?
- LESSON 11: Order of Operations
- LESSON 12: True/False Equations: Working with the Order of Operations + Show what you know
- LESSON 13: Equivalent Numerical Expressions, Day 1 of 2
- LESSON 14: Equivalent Numerical Expressions, Day 2 of 2
- LESSON 15: Unit Review
- LESSON 16: Unit Test