# 7.1B Instructional Lesson & Assessment (7.1)Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms.

The student is expected to: (B) convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator.

## 7.1B INSTRUCTIONAL LESSON & ASSESSMENT

For this TEKS students should be able torepresent and use rational numbers in a variety of equivalent forms. Given a rational number in one form the student should be able to convert it to an equivalent number in any of the other forms. The focus for this lesson is conversion between fractions and percents and decimals and percents. This lesson also reviews conversion between fractions and decimals.

BEFORE THE LESSON:

1.Make teacher transparencies.

2.Make copies of Student Activity sheets, Open-Ended and Mini-Assessment.

3.Materials for Instructional/Student Activity #3: Prior to this activity copy the Fraction Cards on yellow cardstock, Decimal Cards on blue Cardstock, and Percent Cards on pink cardstock and cut apart so that you will have one set of each per pair of students. Prepare one zipper gallon plastic bag with the cards and a 1-yard length of adding machine tape per pair of students. Make 1 copy of page 28 for each student. Extension Activity: Prior to the Extension copy the blank number cards page on cardstock and cut apart – each pair of students needs 3 blank number cards

MATH BACKGROUND

Understanding percent

Percent means “per hundred”. A percent is a ratio that compares a number to 100. For example, 63% means 63 parts out of 100 parts, or .

A number followed by a percent symbol (%) has a denominator of 100; therefore, it is easy to write

the percent as a fraction or a decimal.

Understanding how to convert between decimals and percents

To convert a decimal to a percent, multiply by 100. Place a percent sign after the product.

0.6 =0.6666666 …

To convert a percent to a decimal, divide the percent by 100 and omit the percent sign.

Understanding how to convert between fractions and percents

To convert a fraction to a percent, convert the fraction to a decimal by dividing the numerator by the denominator. Convert the decimal to a percent by multiplying by 100 and writing a percent sign after the product.

To convert a percent to a fraction, express the percent as a fraction with a denominator of 100 and omit the percent sign. If the percent is greater than 100%, it will be expressed as a mixed number.

##### Equivalent Fractions, Decimals and Percents

All grade 7 students should know the following equivalent fractions, decimals and percents by memory and should not need to take the time to go through a conversion process when using these equivalent values to solve problems.

Fraction / Decimal / Percent / Fraction / Decimal / Percent
= 0.5 = 50% / = 0.6 = 60%
= 1.0 = 100% / = 0.8 = 80%
= = 33% / = 1.0 = 100%
= = 66% / = 0.125 = 12.5%
= 1.0 = 100% / = 0.25 = 25%
= 0.25 = 25% / = 0.375 = 37.5%
= 0.5 = 50% / = 0.5 = 50%
= 0.75 = 75% / = 0.625 = 62.5%
= 1.0 = 100% / = 0.75 = 75%
= 0.2 = 20% / = 0.875 = 87.5%
= 0.4 = 40% / = 1.0 = 100%

,

### 7.1B INSTRUCTIONAL ACTIVITY #1

UNDERSTANDING PERCENT

Percent means “per hundred.”

If you have 100 marbles and 25 of them are black, 25% of the marbles are black.

If you use 100 out of 200 postage stamps, you used 50% of the stamps.

If the Science Club goal was to trim 50 trees at the NatureCenter in one day, and they trimmed 100 trees, they achieved 200% of their goal.

A percent is a ratio that compares a number to

100. For example, 63% means 63 parts out of

100 parts, or .

A number followed by a percent symbol (%) has

a denominator of 100; therefore it is easy to write

the percent as a fraction or a decimal.

A percent can be shown as a fraction or a decimal. 3%oror0.03

30%oror0.30

DECIMALS TO PERCENTS

To convert a decimal to a percent, multiply by

100. Place a percent sign after the product.

0.6 =0.6666666 …

Rewrite 0.675 as a percent.

______0.675 by _____. This moves the

______two places to the

______.

______ ______= ______

Write a ______sign after the product.

0.675 = 67.5___

The decimal 0.675 is equivalent to ______%.

Rewrite 2.25 as a percent.

______2.25 by _____. This moves the

______two places to the

______.

______ ______= ______

Write a ______sign after the product.

2.25 = 225___

The mixed decimal 2.25 is equivalent to _____%.

FRACTIONS TO PERCENTS

To convert a fraction to a percent, convert the

fraction to a decimal by dividing the numerator by

the denominator. Convert the decimal to a

percent by multiplying by 100 and writing a

percent sign after the product.

MAT H E MAT I CS

A bar over a decimal

Rewrite as a percent.

Divide the ______, 3, by the ______, 6.

_____ _____ = ______

Multiply by ______to convert the ______to

a ______.

______ 100 = ______

______= ______%

The fraction ______is equivalent to ______%.

Rewrite as a percent.

Divide the ______, 1, by the ______, 3.

_____ _____ = ______

.333333. . . is a repeating decimal. A bar over

a decimal number indicates a repeating decimal.

. is the decimal equivalent of .

Multiply _____ by ______to convert the ______to a ______.

______ 100 = ______

The fraction ______is equivalent to ______%.

### 7.1B STUDENT ACTIVITY #1

Part I: How do I convert to a decimal?

Divide the ______by the ______.

The quotient is ______.

Therefore, ______is the decimal equivalent to

.

Write a decimal equivalent for the fraction in each box.

For each fraction converted to a decimal, divide the ______by the ______.

The quotient is the ______of the fraction.

Part II: How do I convert 0.25 to a fraction?

Use ______as the denominator because it is the ______of the digit

farthest to the right of the ______point.

Use ______as the numerator because they are the ______to the ______of

the ______point.

Therefore, ______is the fraction equivalent to 0.25.

Write a fraction equivalent for the decimal in each box.

0.75 = 0.5 = 0.4 = 0.625 = 0.375 =

For each decimal converted to a fraction, use the ______of the digit

farthest to the right of the ______as the denominator. Then use the

______to the right of the ______as the ______.

PART III: How do I convert 0.75 to a percent?

Move the ______two places to the ______.

Put a ______sign after the number to replace the ______point.

Therefore, ______is the percent equivalent to 0.75.

Write a percent equivalent for the decimal in each box. Show your work on the back of this page.

0. = _____% 0.35 = _____% 0.25 = _____% 0.625 = ____% 0.8 = _____%

For each decimal converted to a percent, ______the decimal by ______. Place a

______sign after the product.

PART IV: How do I convert to a percent?

Convert the ______to a ______.

Divide the ______by the ______. The quotient is ______.

Therefore, ______is the decimal equivalent to

.

Then, convert the ______to a ______.

Move the ______two places to the ______.

Put a ______sign after the number. The decimal point can be omitted if it is to the right of all the digits.

Therefo

re, ______is the percent equivalent to 0.75, and therefore is the percent equivalent to the fraction ______.

Write a percent equivalent for the fraction in each box. Show your work on the back of this page.

For each fraction converted to a percent, ______the ______by the ______.

Convert the ______to a percent by multiplying by ______and writing a ______

sign after the product.

PART V: How do I convert 6.75 to a percent?

Move the ______two places to the ______.

Put a ______sign after the number.

Therefore, ______is the percent equivalent to 6.75.

Write a percent equivalent for the mixed decimal in each box.

For each decimal I convert to a percent, I move the ______two places to

the ______.

Then I put a ______sign after the number.

If the decimal point is to the ______of the digits I do not have to write it in the percent number. ______is the only one of these percents above that I must write the decimal point.

### 7.1B INSTRUCTIONAL ACTIVITY #2

PERCENTS TO DECIMALS

To convert a percent to a decimal, divide the

percent by 100 and omit the percent sign.

Rewrite 53.2% as a decimal.

Divide ______by ______. This moves the

______two places to the

______.

______ 100 = ______

The value ______% is equivalent to the

decimal ______.

PERCENTS TO FRACTIONS

To convert a percent to a fraction, express the

percent as a fraction with a denominator of 100.

Rewrite 48% as a fraction.

Use 48 as the ______and 100 as the ______.

Simplify the fraction.

The value ____% is equivalent to .

Rewrite 66% as a fraction.

Use 66 as the ______and 100 as the ______.

66 converts to 66..

Simplify the fraction.

The value ____% is equivalent to .

When converting a percent to a fraction, if the percent is greater than 100%, it will be expressed as a mixed fraction.

Rewrite 225% as a mixed fraction.

Use ______as the numerator and ______as the

denominator.

Rewrite the ______fraction as a ______

number.

Divide ______by ______.

225 100 = ____ R25

Place the remainder over ______.

Simplify the fractional part of the mixed fraction.

The value ______% is equivalent to ____ .

### 7.1B STUDENT ACTIVITY #2

Part I: How do I convert 3.275 to a mixed fraction?

I use ______as the ______part of the ______because it is to

the ______to the left of the ______point..

I use ______as the denominator because it is the ______of the digit

farthest to the right of the ______point.

I use ______as the numerator because they are the ______to the ______of the ______point.

Therefore, _____ is the mixed fraction equivalent to 3.275.

Write a mixed fraction equivalent for the decimal in each box.

21.5 = 33.2 = 8.75 = 1.25 = 87.4 =

For each decimal number I convert to a mixed number, I use the ______of

the digit farthest to the right of the ______as the denominator. I then use

the ______to the right of the ______as the ______.

Finally, I use any ______to the left of the decimal point as the ______-number part

of the ______fraction.

PART II: How do I convert 4.5% to a decimal?

Move the ______two places to the ______.

Place a leading ______before the number. Drop the ______sign after the number.

Therefore, ______is the decimal equivalent to 4.5%.

Write a decimal equivalent for the percent in each box.

For each percent converted to a decimal, move the ______two places to

the ______.

Then drop the ______sign after the number.

PART III: How do I convert 75% to a fraction?

Express the ______as a ______with a denominator of ______.

Therefore, ______is the fraction equivalent to 75%.

Write a fraction equivalent for the percent in each box.

20%= _____ 10%= _____ 45%= _____ 30%= _____ 25%=_____

For each percent converted to a fraction, express the percent as a fractionwith a denominator of _____. Then simplify the fraction if needed.

PART IV: How do I convert 145% to a fraction?

Express the ______as a ______with a denominator of ______.

The percent is greater than ______%, so it may be expressed as a ______fraction.

Therefore, ______is the fraction equivalent to 145% and ______is the

______fraction equivalent of 145%.

Write a fraction or mixed fraction equivalent for the percent in each box.

150% = 555% = 272% = 37.1% = 87.4% =

For each percent converted to a fraction, express the ______as a

______with a denominator of ______.

If the percent is greater than ______%, express the fraction equivalent as a ______

______.

PART V: Simeon answered 21 out of 25 questions correctly on his quiz. What percent of the quiz questions did he answer correctly?

The fraction of questions Simeon answered correctly is .

Convert this fraction to a decimal by dividing ______by ______.

The fraction is equivalent to the decimal ______.

Convert the decimal to a percent by moving the decimal point ______places to the ______.

The decimal ______is equivalent to ______%.

Simeon answered ______% of the quiz questions correctly.

PART VI: At a school football game 45% of the people watching the game were middle school

students. What fraction of the people watching the game were middle school students?

Convert ______to a decimal. Move the decimal point ______places to the ______.

______% = ______

Rewrite the decimal 0.45 as a fraction.

Simplify the fraction.

Of the people watching the game, were middle school students.

### 7.1B INSTRUCTIONAL ACTIVITY #3

MATERIALS: Prior to this activity copy the Fraction Cards on yellow cardstock, Decimal Cards on blue Cardstock, and Percent Cards on pink cardstock so that you will have one set of each per pair of students. Prepare one zipper gallon plastic bag with the cards and a 1-yard length of adding machine tape per pair of students.

Make 1 copy of page 28 per student, but do not give students this page until they ask for it during the activity.

Extension Activity: Copy the blank number cards on green cardstock and cut apart. Give each pair of students 3 blank green number cards.

Place the transparency for Student Activity #3 on the overhead.

Use the adding machine tape as a blank number line. Pairs of students work together to secure the blank number line on a desktop.

Each pair of students make a benchmark line in the middle of the tape and at the left and right ends of the tape.

Then the students place the 0, and 1 cards on the number line. Discuss the placement of those cards as a class.

Students place the Fraction, Decimal and Percent Cards on their number line.

When a pair of students has placed all their cards on the number line provide them with a copy of page 28 to enable them to self-assess their work.

The whole class discusses placement of all the cards on the number line. List observations of the placement of the cards.

Ask the following question before student pairs place their benchmark cards on the number line:

How do you determine where to place your benchmark numbers on the number line?

Ask these questions at various times as student pairs place cards on their number lines:

What strategies can you use to locate the position of your number on the number line?

What is the greatest number on your number line? How do you know?

What is the least number on your number line? How do you know?

What benchmark is the most helpful in placing your numbers on the number line? Explain.

Did you need to rearrange previously placed numbers to appropriately place other numbers on the number line? Why or why not?

What do you notice about the placement of your numbers in relation to the benchmark numbers?

Listen for the following as your roam the room and students describe how they place their cards on their number line:

Do the students use accurate vocabulary to describe the relationships between two rational numbers? For example, two-fifths is less than four-eights?

Do the students verbalize patterns such as the number always being before, between or after a particular number?

What strategies do the students describe as they decide where the place a particular number?

Do the students compare the numbers in a variety of equivalent forms?

Do the students use benchmark language to place fractions, decimals and percents on the number line?

Look for the following as you roam the room and students place their cards on their number line:

Do the students attempt to place the number at a specific place on the number line (e.g., 2 inches from the left, exactly in the middle, etc.)?

Do the students position the number on the number line without assistance?

Do the students check for reasonableness of number placement on the number line?

Answers to these questions can be used to support decisions related to further whole class instruction or group and individual student instruction during tutorial settings.

### 7.1B STUDENT ACTIVITY #3

You will work in partner pairs for this activity.

Your teacher will give you a zipper baggie with a

1-yard length of adding machine tape and cards.

Work with your partner to secure the adding machine tape to a desktop to make a blank number line.

Make a benchmark line in the middle of the tape and at the left and right ends of the tape.

Separate your cards into fraction, decimal and percent stacks.

Place the 0, and the 1 cards on the number line.

Discuss the placement of those cards as a class.

You and your partner must place the remaining

cards on your number line. Describe how you

decide to place each card on the number line as

you place the number.

Place a new 1-yard length of adding machine tape and all your number cards back into your zipper bag for the next class. Discard your blank number line.

EXTENSION

Your teacher will give each pair of students three

blank cards. Write a fraction that is NOT on the

number line on one card, a decimal that is NOT on thenumber line on the second, and a percent that is NOT on the number line on the third card.

Trade cards with another pair of students.

Place the new cards on your number line.

Orally explain how you decided where to place the

new cards on your number line.

Show the other pair of students where you placed

them to explain why they agree or disagree

with your placement of the cards.

BENCHMARK AND FRACTION CARDS

Copy this page on yellow cardstock, cut apart cards and place in a zipper quart baggie. This page makes 5 sets of benchmark and fraction cards. DECIMAL CARDS

Copy this page on blue cardstock, cut apart cards and place in a zipper quart baggie. This page makes 5 sets of benchmark and decimal cards. PERCENT CARDS

Copy this page on pink cardstock, cut apart cards and place in a zipper quart baggie. This page makes 5 sets of benchmark and percent cards. BLANK NUMBER CARDS

Copy this page on green cardstock, cut apart cards. Each pair of students will need 3 of these cards for the Extension. This page makes 110 blank number cards. You will need one page per class of 30 students. ##### Equivalent Fractions, Decimals and Percents

All grade 7 students should know the following equivalent fractions, decimals and percents by memory and should not need to take the time to go through a conversion process when using these equivalent values to solve problems.

Fraction / Decimal / Percent / Fraction / Decimal / Percent
= 0.5 = 50% / = 0.6 = 60%
= 1.0 = 100% / = 0.8 = 80%
= = 33% / = 1.0 = 100%
= = 66% / = 0.125 = 12.5%
= 1.0 = 100% / = 0.25 = 25%
= 0.25 = 25% / = 0.375 = 37.5%
= 0.5 = 50% / = 0.5 = 50%
= 0.75 = 75% / = 0.625 = 62.5%
= 1.0 = 100% / = 0.75 = 75%
= 0.2 = 20% / = 0.875 = 87.5%
= 0.4 = 40% / = 1.0 = 100%

,

### 7.1B OPEN ENDED #1

Part of each diagram is shaded.

In each diagram write the part shaded as a fraction, percent and decimal.

NAME______DATE______SCORE ___/5

7.1B Mini-Assessment

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TEKSING TOWARD TAKS 20056 Weeks 2 - Lesson 1 Page