# Decimal Notation VS. Fractions

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## Objective

SWBAT use decimal notation for fractions with denominators to compare the connections between fractions and decimals.

#### Big Idea

In this lesson students will use a variety of skills to determine the underlying connections between fractions and decimals.

## Warming Up!

20 minutes

Material: Hundreds.docx

To warm up I invite students to the carpet to review some vocabulary terms, and to discuss what we have been learning so far about fractions.  Because my students struggle with fractions it is important that I remind them of their prior knowledge. My students respond a lot better to new concepts if they connect it to prior experiences.

I ask students to share their own experiences, and ideas about fractions. Students name the parts of the fraction, and are able to discuss how and why fractions are used. Some students remember using models to explain the pieces verses the whole.  After the discussion I gain a better understanding about what my students know about fractions, and what they need to know about fractions in order to be successful in this lesson.

Teacher:

"Since you guys already know a lot about fractions, I know you are really going to enjoy learning how to convert a fraction to a decimal.  But, before we began I want to go over some new math terms that will assist you in your learning."  As I go over the new vocabulary, I ask them to write the definitions down in their math note book just in case they need to remember what they mean later on in the lesson.

Vocabulary Terms:

Fraction
fraction is a number between zero and 1 and is expressed as one number over another number, like this: 1/2

Decimals-A linear array of digits that represents a real number.

I intend  to show students the connection between fraction and decimal notation by writing the same number both ways.  I tell them that they will compare and contrast the difference and similarities between fractions and decimals.

Because this is the first time decimals are introduced, I want to make sure I incorporate a visual throughout the lesson.  I begin by drawing a large place value chart on the board.  I explain that a number can be represented as both a fraction and a decimal.

I start filling in the place value chart, by first placing a decimal in the center of the chart. I ask students to explain why I did this.  More than half of my students could not explain.  So, I take a moment to fill in the rest of the chart explaining the value of the numbers listed to the right and left hand side of the decimals. I explain that numbers written to the left of the decimal are whole numbers, while numbers written to the right of the decimal are parts of a whole number.  Some students make the connection between fractions with the denominator as being the number listed to the right of the decimal.  I enter 3 under the tenths place and 2 under the hundreds place.  Can anyone tell me if should write this number as a fraction or a decimal? You should write is as a decimal because it is written to the right of the decimal.  Several students wanted to write 32/100. I explain that if we were to write both 32/100 and .32 on a number line both would be placed closer to the .32.  I repeat this activity using different numbers, and invite student volunteers to help me use decimal notation for fractions with denominators. As students are working I constantly redirect their thinking to the intended purpose of this lesson by asking how and why the given decimal notation is related to the fraction. I use their responses to determine if I should move them deeper into the lesson.

Mathematical Practices:

]MP.4. Model with mathematics.

MP.7. Look for and make use of structure

MP. 8. Look for and express regularity in repeated reasoning.

## Interactive Learning!

10 minutes

Interactive learning

In this portion of the lesson, I invite students to the carpet to take part in a fun interactive lesson. I encourage students to take notes throughout the lesson.  note taking paper.pdf The purpose of this model is to deliver explicit instruction to provide students with a clearly explained task of how fractions are related to decimals. During the lesson I ask the following questions to guide students' thinking:

Does it help to create a diagram?

How would you prove that?

Does that make sense?

It is important that conceptual thinking is broken down into critical features/elements. Students note that the models help support their learning. Some students are able to explain, however, their explanations are a bit vague. I make a note to make sure I am showing them how to visually represent fractions.

15 minutes

# Material: Work Along With Me!

In this portion of the lesson I want to work with students a bit more on understanding that decimals are an extension of our whole number base ten system. To do this I ask students to move back into their assigned seats. I choose to stand at the board, so that students can work along with me independently.  First, I draw a large chart on the board to model how to write fractions and decimals in expanded form.  I give each student their own chart to work along with me.  I write 7  82/100.  I explain that 7 is a whole number, and it value is 7 ones. (They should remember this from previous school years.  If they don't, do a quick mini-lesson on place value with whole numbers). I remind students that numbers written to the right of the decimal are parts of a whole so the number 8 is 8 tenths, and 2 is 2 hundredths.  I ask, "Can anyone tell me how to write the given fraction in expanded fraction form?"  7 + 8/10 + 2/100  Great! Since, 7 is in the ones place, it remains 7. The number 8 is in the tenths place, so I write 8/10 to make sure it has its correct value. The number 2 is in the hundredths place, so I write 2/100 to make sure that 2 have its correct value.

Now, I direct their attention to expanded decimal form.  I tell them it is basically the same method we used to understand writing fractions in expanded for, but we use decimals and add zeros to make sure the given numbers are aligned with the correct value.  I say, who can help me write the same number, but arrange it in expanded decimal form.  Several students raise their hand, so we all give it a go.  I ask, "How do I write the 7?  How can I write the number 8 in decimals to represent its correct value?  How can I write the number 2 in decimals to represent its correct value?  So we write 7 + 0.80 + 0.02. We double check our answer by counting the correct spaces on a place value chart.  Students seem to catch on quickly to this concept.  However, I repeat this activity using a different fraction just to make sure students fully understand the connection between fraction and decimal notation.

## Independent Thinking!

20 minutes

Materials: place value chart.docx Work along with me

In this portion of the lesson students will work on their own to demonstrate how and why fractions and decimals are related. I ask them to be sure to show and explain the connection between fraction and decimal notation by writing the same number in both ways. I remind them that we did this earlier in the lesson.  I tell them that they may draw visual representations like the ones seen in the interactive video if they need to.

Some students tend to think that I was asking them to demonstrate a new skill.  So, I explain that they will still be working on the same type of problems completing from our group setting.  However, I want them to choose two of the numbers to explain the correlations. As students are working, I circle the room to remind students of the intended purpose of this lesson.

Probing Questions:

How you can express the fraction to show its correct number value?

Can you explain how the numbers to the right and left of the decimal differ and how they are the same?

Can you represent the given number in both expanded decimal and fraction form? Explain your reasoning.

Some students tend to bit confused at times, but the questions seem to refocus their attention.  I use their responses to determine if additional time should be spent on this concept.