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* *Reflection: Modeling
Number Operations - Section 1: Do Now

Rational number operations are pivotal concepts in the upper elementary grades. Often, students with significant gaps in skills with fractions and decimals lack the important building blocks to attack the negatives. It is equally important to expose students to models that help them understand these concepts. This year, about half of my 7^{th} grade cohort continued to miss problems that involved positive and negative rational numbers. Whether they were working with order of operations or with word problems, half of my students continued to get these problems incorrect, according to weekly and quarterly assessment data.

Thus, when it came time to put ether a test prep unit, I knew I was going to have to bring this lesson back. I decided to start it this year with a review of integers on the number line and a discussion of what it meant to “add”, “combine”, or subtract numbers on the number line. It is important to note here that I am sure I was not able to fill all the gaps within this one lesson, or within any of the other lessons we used this year specifically targeted at rational number operations. Helping ALL students to fill these gaps takes longer than one lesson, and sometimes, longer than a school year. The number line models and other problem solving strategies are the way to get there. As educators, we have to continue to push ourselves away from the procedural tricks we “teach” our students to use. They do not work and they hold our students back in higher levels of math. It is MUCH easier to teach it this way and much harder to teach through models and strategies, but it pays off in really immense and wonderful ways. This is why I focused the Do Now this year on a “model” to show these rational number operations.

*Modeling: Modeling With Number Lines*

# Number Operations

Lesson 1 of 8

## Objective: SWBAT meet a mastery percentage goal to review number operations and prepare for the NY State test

#### Do Now

*10 min*

Student enter silently according to the Daily Entrance Routine. Do Nows are NOT handed out until after everyone has taken a seat and heard some announcements from me.

I explain to students that for the next two weeks we will be reviewing important topics likely to show up on the state exam. I share the percentage matrix, given by the state, which shows how much of the test will cover a given topic. I only show students the “major clusters” of this resource as it includes most of the work we will be reviewing during this period.

I explain that the base of everything we’ve done this year is number operations with positives and negatives. This is the first topic we will review. For the next two days, students will enter and receive a Do Now with number operations questions. Word problems may also be included. I explain that the first 5 minutes are given to students completing as much as they can on their own. Then, I will share the answers and allow students to ask questions if they don’t understand how to get the correct answer. I make sure to have one student review the process for solving, as well as sharing his/her mistake. All Do Nows will be turned into me so that I may check them and hand them back before the end of the day.

As part of their homework, students must write a paragraph for each problem they answered incorrectly. I provide paragraph stems which I have students copy onto their Do Nows before handing them to me.

*“My incorrect answer for # ____ was ______. I made this mistake because _____(2 sentences; claim + evidence)_____. The correct answer is _____ because ____(2 sentences; claim + evidence)____”.*

I make sure to speak to the writing teacher at our school to ensure I am using the same words (claim, evidence) used in their class.

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#### Class Notes: Review

*10 min*

Students receive a sheet of class notes titled “Rewind” each day for the next two days. Students are to take notes using these sheets and will be allowed to use them in the open note quiz on Friday. Over the following two days we will review the following essential topics:

*The number line extends in both directions including positive numbers to the right of zero and negative numbers to the left**Integers are whole numbers and their negatives**Rational numbers include any number that can be written as a fraction (pos/neg, dec, frac)**Rational numbers follow the same operation rules as integers**Integer operation rules**identifying the operation in word problems by using visualization strategies (i.e. drawing the number line)*

I won’t be able to cover every one of these topics in extensive detail, that’s not really the point during review. These are however, the most common misunderstandings students continue to have, and so I quickly review some major definitions saving most of this time for students to practice together, up at the board, and for me to be walking around answering questions students may have.

Any student who asks about rules or details in procedures must write down the feedback I give so that they have this information during the quiz this Friday. My goal is to allow students to review the topics with as many of their classmates as possible in as many ways as possible. Reviewing can be a boring endeavor and the last thing I want is to lose student motivation in these next two weeks before the state test.

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#### Class Work

*20 min*

After we’ve reviewed and practiced together, Classwork is distributed. Students must work independently and silently for 15 minutes. Those who finish early or are making good progress in their classwork will be asked to put correct work and answers up on the board. Some students may be targeted to help struggling peers with the class work. Identifying great pairs means I will need students who are able to explain topics without giving answers paired with students who are willing to listen and complete work.

Below I am including a couple of video examples of the ** visual strategies** I and my student leaders use to help struggling students review. It’s a good idea to highlight problems based on complexity to help student leaders identify the problems they should focus on helping their peers complete. It is probable that the students they are helping will not be able to get through all of the problems, thus

*my students leaders need to know how and which concepts/problems to prioritize.*

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#### Closing

*10 min*

Each day students will be handed a half sheet of paper with two problems, written on the board. One ought to be related to **basic number operations** or **fluency** while the other should be a **word problem situation**. It is best to tailor these problems skills/concepts the teacher notices students struggle to complete AND spent time practicing each day. This gives students a final opportunity for feedback. The exit tickets are graded and returned with said feedback, usually pointing out essential ideas and where these notes can be found. Again, these exit tickets are resource which students will have the option to use during the quiz. For example, in these lessons many students struggled with subtraction of rational numbers and word problems involving said rational numbers with multiple steps. Here are the problems I gave my students each day:

**Day 1: Integers**

- –26 – (–15)

- Morning temperature: -5 degrees

Evening temperature: 9 degrees

By how much did the temperature change?

**Day 2: Rational Numbers**

- -3/5 + (-1/4) ÷ 5

- Jeremy has $214.94 in the bank. He buys 3 chairs costing $14.80 each. Then, he deposits half of his paycheck and spends the rest. He is paid $250.18 per paycheck. How much money does he have in the bank now?

Once students turn in their exit tickets, they may pick up their homework and work on it until the end of class.

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##### Similar Lessons

###### Adding and Subtracting Integers on a Number Line

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- UNIT 1: Integers
- UNIT 2: Operations with Rational Numbers
- UNIT 3: Expressions and Equations - The Basics
- UNIT 4: Multi-step Equations, Inequalities, and Factoring
- UNIT 5: Ratios and Proportional Relationships
- UNIT 6: Percent Applications
- UNIT 7: Statistics and Probability
- UNIT 8: Test Prep
- UNIT 9: Geometry

- LESSON 1: Number Operations
- LESSON 2: Algebra: Expressions and Multi-Step Equations
- LESSON 3: Quiz + Test Corrections
- LESSON 4: Unit Rates, k?
- LESSON 5: Algebra: Additional Strategies for Simplifying Expressions
- LESSON 6: Quiz + Composite Figures with Circles and Trapezoids
- LESSON 7: Benchmark Analysis
- LESSON 8: Final Review