##
* *Reflection: Connection to Prior Knowledge
Fractions Make a Come Back - Section 1: Do Now

This school year I decided to reverse my 1^{st} and 2^{nd} units. Rather than starting out the year with Integer operations, I began the year with rational number operations, focusing on positive numbers only. I made this decision after recognizing students’ struggles year after year in terms of their mastery of operations with fractions and decimals. The struggle to pace your class appropriately without feeling pressure from state testing is something I’m sure many teachers feel across the country. The change to common core most likely adds to this pressure, despite the fact that one of the shifts expects us to take our time building these important blocks. However, I am sure many teachers can also agree that the building blocks did not become “strong” from one year to the next simply because our states have adopted CCSS. This means we are continuing to see gaps in students’ conceptual understanding and fluency in skills. Despite the fact that I fell behind my network in terms of pacing at the beginning of the year, I have seen now that it has paid off to review these topics before moving into algebraic concepts.

On the first day of school I gave students a diagnostic to complete for homework. This allowed me to spend more time on routines, expectations, and big goals during class. More on these routines is included in the reflection attached to the “Intro to Teacher and Game” section of this lesson [link].

You'll notice within this unit that my review of fractions spanned over three days. In this first lesson I review concepts visually during the do now, fraction/decimal addition and subtraction algorithms in the notes section, and then dive right into word problems for the task. All of this happened in under an hour last year because our math periods were shorter. This year, my periods last 90 minutes each. Thus, the biggest difference to my pacing calendar has been the amount of time I spent reviewing concepts and skills at the beginning (19 days). I was able to take my time to review and build confidence around these topics with my students before starting new topics with integers and negative rational numbers. Essentially, I spent the entire 1^{st} unit reviewing 6th grade topics dealing with fractions and decimals, and boy has it paid off! Their confidence and mastery is so much higher at this time of year than I have observed in past years. Because they are able to perform operations with fractions and decimals more fluidly, they are able to focus on developing algebraic concepts around integers and other rational numbers on the number line.

Some of the the new materials I created are included in this reflection. It has not been easy to balance my anxiety feelings about moving slowly into 7^{th} grade standards (in comparison to past years) with my understanding that students NEED more time to review important topics. But I am entirely convinced now that this is the right way to begin.

*Connection to Prior Knowledge: The Need for More Extensive Review*

# Fractions Make a Come Back

Lesson 1 of 19

## Objective: SWBAT add and subtract fractions and decimals by working in pairs (no borrowing in subtraction).

## Big Idea: Students complete unit tests ans work in pairs to review fractions addition and subtraction.

*51 minutes*

#### Do Now

*6 min*

Students enter silently according to the Daily Entrance Routine. They are given 10 minutes to complete their **Unit test** from the previous day if they were not already finished.

For students who have completed the test, they are asked to follow the directions for the “Do Now” indicated on the SMART board and then take out a book to read quietly.

The directions read:

1. Take out a blank sheet of paper.

2. Write a full heading. (name, date, class)

3. Copy the AIM: **KWBAT add and subtract fractions and decimals **

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The first group activity that we will complete today is to begin copying the notes from the SMART board, leaving blanks where appropriate (see Day 20 - Notes). The notes read as follows:

**Fractions**

- When we add and subtract fractions, we have to make sure that they have the same ____________. After we get an answer, we should always ___________.
- If the fractions have the same denominator, we add the numerator only and leave the denominator the same.
- If the fractions have different denominators, we have to:
- Find the LCM or LCD
- Convert each fraction so that it has the same denominator
- Solve and simplify

**Decimals**: When we add and subtract decimals, we have to ______________.

The blanks are to be completed together after students have been given an opportunity to copy the information.

**Teacher's Note**: One of my aims is to expose students to as many different note-taking experiences as possible. Sometimes I will have their Cornell Notes already set up and printed. Other times I think it is valuable to have the experience of setting up their own notes.

I also plan to complete a series of fluency skills to warm up and review for the task. The examples include:

**Equivalent Fraction**s –

- ¾ = ?/12
- ?/8 = 6/24

**Word Problem** –

- The price per share of stock on A-Plus company was $54 6/8. It rose by $3 5/8. What is its price per share now?

**Adding and Subtracting Decimals** –

- 81 + 31.75
- 52.7 – 0.07219

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#### Task - Partner Work

*20 min*

Students are asked to work in pairs for ten minutes of class to complete Day 20 - Task - Fractions and Decimal. As they work I urge my students to continually consider “what is this problem asking me to do?” I find this to be especially important when my students experience frustration. When students misunderstand a problem, I provide them with the following questions to guide them to persevere and figure out the problem (**MP1**):

- What are we trying to find?
- Can I use numbers to represents different parts of this problem?
- What model can I draw to help me visualize this problem?

After about ten minutes, I will ask students to enter their answers into the Senteo clicker (PRS) so that I can gather data about their performance on these problems.

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#### Closing

*10 min*

Today, I will close the window for entering answers into clickers 10 – 15 minutes before the end of class. I usually give my students a 5-minute warning about the closing of the window. After I give this warning, I monitor the rolling results for each question, identifying the three questions we should discuss as a class. Then, I will have students who finish early write their answers to the chosen questions on the board. We'll review their work on the board as a class.

Cycling back to the notes, I select more students to explain HOW they solved a particular problem. These students are selected based on their performance during the "task" section of class. During that time, I am flagging students I will want to cycle back to during the closing to either check for understanding or to explain how they solved. Some students have cleared ways to communicate these steps than myself. For example, one problem we are likely to review is #9 since it involves a word problem and changing denominators to make them "alike". Review of this answer would go something like this:

**Teacher:** (After one student reads the problem) Can I get another student volunteer to review the solution? what did you do first?

**Student: **I lined up the numbers to subtract them.

**Teacher: **How did you know you needed to subtract? and how did you line them up? horizontally? vertically?

**Student:** I lined them up vertically, and I knew to subtract because it says "she spilled"...

**Teacher:** Good! Now talk to me about your subtraction steps. Are the denominators in the original problem alike or not alike?... how do you get them to be alike?... what must you find?... what is that called?

**Student:** (goal answer before moving on to the next question) the LCD which was 8...

At this point if the student says 16 instead of 8 it would be a great opportunity to ask if anyone used a smaller LCD and why it might be better to use a smaller LCD... its also a good idea to run through both solutions, using 16 and 8, to show students that the answer is still the same, provided simplifying is included and also completed correctly. Where I take the conversation at this point really depends on the discussion and misunderstandings observed during the task. Whatever helps most students is what I push students to share.

Here is tonight's Homework - Fractions and Decimal.

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##### Similar Lessons

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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