##
* *Reflection: Gradual Release
Back to The Line - Section 1: Do Now

If you have been reviewing this Unit you may have noticed that I have mentioned several big changes to my pacing calendar this year. First, my time increased per lesson, from 60 minutes to 90 minutes. Secondly, I have chosen to begin the year with a review of operations with fractions and decimals including word problem solving strategies. These changes have affected this particular lesson in a major way: it is taught later in the year and includes additional resources attached to this reflection.

My first unit this year is titled “Positive Rational Numbers”. I spend the first 19 days of school reviewing basic operations with fractions and decimals and also included a word problems and solving strategies. My second Unit, titled “Integers and Rational Numbers” included the introduction to negative integers FIRST followed by a dive into negative fractions and decimals.

My choice to spend more time on review of operations with positive rational numbers has had a positive impact on my students’ growth. It meant that when we got to this point in the curriculum, students had already spent time reviewing conversions between fractions and decimals AND had had ample time to work with negative integers, familiarizing themselves with their placement on the number line. The materials for this initial lesson on conversions can be found here. For a better idea of the pacing in objectives this year, a copy of my scope and sequence for the 2014-2015 school year can be found here.

Within this reflection I am including the Do Now we used this year. It included decimal/fraction conversions which we used as a check for understanding before completing the notes and classwork for the day. Students completed 3 minutes of independent work. Then, they were given the answers and checked their own papers. They were given post it notes and asked to write their names on them. Then, they were asked to place themselves in one of three groups by putting their post it under the group descriptions written on the board:

1) “I got most of these problems correct and feel like I can help someone else”

2) “I got about half of these problems correct. I need more practice”

3) “I didn’t get many correct. I need more practice”

Students who elected the first group were asked to bring me their papers. After reviewing their work, I sent back students who needed to show more work. Those who showed an adequate amount of work were given directions to split themselves up into two different groups to help the rest of their teammates finish the worksheet. They were asked to provide additional examples on the back of the paper for students who elected the 2^{nd} group, noting their names on the board.

This is a great activity that uses student peer tutors. It increases the amount of help we can give in class and provides more practice to master concepts for those teaching the material to their peers.

*Gradual Release: Reviewing Conversions*

# Back to The Line

Lesson 4 of 19

## Objective: SWBAT combine positive and negative fractions with like denominators by graphing on a number line.

*50 minutes*

#### Do Now

*10 min*

Students will complete a worksheet that will assess their knowledge of the locations of positive fractions on the number line (Webb’s DOK1). Students will input their answers into clickers and we will review together.

Because the SMART Response program can instantly generate this data, we will be able to target any misunderstandings in this topic. For example, students often get confused when they are asked to divide a section of the number line between two integers into given fractional pieces. For example, if students must identify and draw fifths between 0 and 1, they may draw five different tick marks in the given space, creating six fractional pieces instead of 5. Some students may not yet understand the concept of a fraction and thus have trouble knowing where to start when identifying positions. Completing this activity ensures that students are ready for negative and positive fractions on the number line, or it ensures that I will be ready to help students who are struggling with the basic identification and understanding of fraction positions on the number line. I will be focusing on asking students to review the meaning of a denominator and the numerator (i.e. the denominator represents the number of pieces between each consecutive pair of integers on the number line while the numerator indicates the number of pieces in question). Thus, 3/5 is three pieces out of five, or 3 pieces to the right on a number line between two integers.

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#### Intro to Lesson + Task

*30 min*

There are ** 4 different parts of the task**. We will review the first problem in each part and then students will work with neighbors in groups of 4 to complete the rest of the problems for that section.

**Students will need to simply label each of the tick marks shown on their number lines. I will model #1 for students, indicating that negative fractions are graphed to the left on the number line. The points labeled in red indicate the positive numbers and in blue are negative numbers. This is**

*Part 1 addresses the identification level of understanding.***and should be helpful when conceptualizing operations with positive and negative fractions.**

*consistent with our chip models*

By correctly identifying the positions of positive and negative fractions students are using **MP8** to understand the organization of rational numbers along the number line. By identifying different types of fractions (i.e. halves, thirds, fourthds, etc), students will begin to understand the idea that there are an infinite amount of point between two consecutive integers. While students are only expected to identify the un-labeled position on each number line, I may ask students who struggled with the Do Now to label the whole numbers as well.

**Part 2** of the task will ask students to combine positive fractions and decimals and show their work on the number line. This is a great opportunity to practice counting by sixths for #1 and by 0.5s for #2. Question 7 presents a great opportunity for students to connect fraction conversions to decimals as this questions asks students to add decimals and the number line given is split into fifths. *Look out for students who may not have full mastery of these conversions; they may require a reminder of the process for converting. *

**Part 3** of the task will introduce negative fractions. All fractions will have the same denominator. Students will combine a positive and a negative fraction, alternating the type of fraction at the beginning of the expression. It will be important for me to target a group of struggling students to work with them to complete this section and to draw it correctly. We will be displaying answers on the board for the rest of the class to see. ** Look out for students who are only completing the algorithm without using the number line. Hold on to this expectation!** Understanding the number line can help with more challenging, abstract problems involving variables on the number line (

**7NS1c**).

Part 4 of the task will have students combining two negative fractions. All arrows will point to the left. This visual will help students begin to understand that fractions and decimals follow the same rules as integers when combining two negatives. ** Look out for confusion with double signs as exhibited by #12.** Students are able to use different strategies: simplify double signs to make 1 sign (same signs, add, different signs subtract) OR remember that (+) says "right" and (-) says "reverse" when there are multiple signs next to each other.

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#### Closing

*10 min*

All answers will be displayed and drawn on the SMARTboard, white board, and chalkboard during the Task. Students will have 5 minutes to discuss answers with neighbors if they are finished or to work independently to copy down the work and ask clarifying questions.

There are a couple of problems I want to make sure I review with a small group of students. Thus, after 5 minutes of review with neighbors, ** I will be pulling a small group of 6 - 8 students** outside of my room or to a corner of the room to review the answers to problems #7, #8, and #12. These are the problems I noticed most kids struggling to depict on the number line.

**The following questions will be on an index card to help guide my student helpers through the review, they are the same questions I use with my small group:**

*The students who remain in the larger group will be led by a student helpers (or a pair) through the same review.*- Which problem was the most difficult (ask no more than 5 students for that opinion)
- how many of you agree that this was the toughest?
- Why was this problem difficult?
- Now that you've seen the answers, can some describe how to solve this problem?

(in my group this might require more scaffolding questions): - where should we start? what is the first number in the problem?
- in what direction should we move? how do we determine in what direction we move?
- how to we decide the direction when there are double signs (+ (-) )?
- how many spaces should we move in that direction? which number tells us this?
- where can we locate the answer on the number line?
- (if there is time) does anyone have any other questions?

At the end of this section homework will be distributed and students will pack up for their next 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: Fractions Make a Come Back
- LESSON 2: Rolling with Fractions
- LESSON 3: Musical Math
- LESSON 4: Back to The Line
- LESSON 5: Number Line Subtraction
- LESSON 6: Quiz + Unlike Denominators
- LESSON 7: Word Problem Applications A
- LESSON 8: Word Problem Applications B
- LESSON 9: Back to Basics: More Skill Drills
- LESSON 10: Word Problem Applications C
- LESSON 11: Multiplying Signed Fractions
- LESSON 12: Using the Properties of Multiplication
- LESSON 13: Express Yourself
- LESSON 14: Divide and Conquer
- LESSON 15: Pizzeria Profits!
- LESSON 16: Expressions and Word Problems
- LESSON 17: Sign Up Day
- LESSON 18: Practice on Khan Academy
- LESSON 19: Unit 2 Test