Fifth Grade Tasks Weekly Enrichments Teacher Dreamers

Fifth Grade

Problem Solving Tasks – Weekly Enrichments

Teacher Materials

Summer Dreamers 2013

By the end of this lesson, students should be able to answer these key questions:

How do you generate equivalent rational numbers?

How do you compare rational numbers?

How does using benchmark fractions, decimals, and percents help you compare

rational numbers?

MATERIALS:

For each student:

Reasonably Speaking

Basically Speaking

Practically Perfect

Evaluate: Equivalent Forms of Rational Numbers

For each group of 3 students:

Base Ten blocks – 1 set of approximately 10 rods and 50 ones

Activity Master: Base Ten Mat

SOLVING MATH PROBLEMS

KEY QUESTIONS

WEEK 3

ENGAGE: The Engage portion of the lesson is designed to access prior knowledge about

equivalent rational number. This phase of the lesson is designed for groups of 3 students.

(10 minutes)

1. Distribute Reasonably Speaking to each student.

2. Prompt students to complete Reasonably Speaking.

3. Upon completion of Reasonably Speaking, prompt students to share and justify their

solutions with their group.

4. Based on their group discussions, students may make changes to their answers if

desired.

5. Actively monitor student work and ask facilitating questions when appropriate.

Facilitating Questions:

How could you determine if a fraction is less than ½? Answers may vary. Possible

answer: If the numerator is less than ½ of its denominator, then the fraction is less than ½.

How could you determine if a fraction is equal to ½? Answers may vary. Possible answer:

If the numerator is ½ of its denominator, then the fraction is equal to ½.

What is ½ as a percent? 50%

What is ½ as a decimal? 0.50

What is 1 as a percent? 100%

What is 1 as a decimal? 1 or 1.0

How could you determine if a fraction is greater than or less than 1? If the numerator

is greater than the denominator, it is an improper fraction and it is greater than 1. If the

numerator is less than the denominator, the fraction is less than 1.

How could you determine if a percent is greater than or less than 1? Answers may

vary. Possible answer: 100% is equivalent to 1; so if the percent is greater than 100%, then the

percent is greater than 1. If the percent is less than 100%, the percent is less than 1.

How could you determine if a fraction is greater than or less than 2? If the numerator

is more than twice the size of the denominator, it is greater than 2. If the numerator is less than

twice the size of the denominator, it is less than 2.

How could you determine if a percent is greater than or less than 2? Answers may

vary. Possible answer: 200% is equivalent to 2; so if the percent is greater than 200%, then the

percent is greater than 2. If the percent is less than 200%, the percent is less than 2.

EXPLORE: The Explore portion of the lesson provides the student with an opportunity to be

actively involved in investigating equivalent rational numbers. This phase of the lesson is

designed for groups of 3 students. (25 minutes)

1. Distribute a set of Base Ten blocks and a Base Ten Mat to each group of students and

distribute Basically Speaking to each student.

2. Prompt students to model each fraction with the Base Ten blocks on the Base Ten

Mat in order to generate a fraction model in hundredths.

3. Prompt students to complete Basically Speaking.



How could you model the fraction on the Base Ten Mat? Answers may vary. Possible

answer: Since my original fraction model shows fifths, I could divide my Base Ten Mat into 5 equal

sections. Then I could cover 2 of the sections with Base Ten blocks since 2 of the 5 sections of the

original fraction were shaded.

How do you know if your Base Ten model is correct? Answers may vary. Possible answer:

The two pictures cover the same area so I know that I have modeled the fraction correctly.

How could recognizing if the fraction is greater than or less than ½ help you

determine if your decimal and percent representations are reasonable? Answers may

vary. Possible answer: If my fraction is less than ½, then my decimal should be less than 0.5 and

my percent should be less than 50%. If my fraction is greater than ½, then my decimal should be

greater than 0.5 and my percent should be greater than 50%.

How could rewriting each fraction as hundredths help you write the decimal

representations of the fraction? Answers may vary. Possible answer: Decimals are just

fractions that have denominators that are 10, 100, 1000, etc. (powers of 10). So if I convert my

fraction to hundredths, I could write the decimal by using place value.

How could rewriting each fraction as hundredths help you write the percent

representation of the fraction? Answers may vary. Possible answer: Percents are just

fractions that have denominators of 100. So if I convert my fraction to hundredths, I could write

the percent by using the numerator.

How could you change a fraction to hundredths without using the Base Ten blocks?

Answers may vary. Possible answer: Us a factor of change.

EXPLAIN: The Explain portion of this lesson provides students with an opportunity to

express their understanding of equivalent rational numbers. The teacher will use this

opportunity to clarify key vocabulary terms and connect student experiences in the Explore

phase with relevant procedures and concepts. (15 minutes)

1. Debrief Basically Speaking.

2. Use facilitating questions to lead the discussion.


How did you use the Base Ten models to rewrite the fractions with denominators of

100? Answers may vary. Possible answer: Once I modeled the fractions with the Base Ten blocks,

I counted the number of squares that were covered.

How did you rewrite the fractions with denominators of 100 without using Base Ten

blocks? Answers may vary. Possible answer: I found the factor of change that would convert the

fraction to hundredths. Then I used the factor of change to find the new numerator and

denominator.

What other denominators could you use to help you rewrite fractions as decimals?

Answers may vary. Possible answer: 10, 1000, 10000, etc. These are all place values for decimals.

How did you determine which denominator you should use when rewriting

fractions in order to change them to decimals? Answers may vary. Possible answer: I

checked to see if the denominator would divide evenly into 10. If not, I checked to see if it was a

factor of 100, then 1000, etc.

How could you use estimation to determine if your decimal and percent

representations were reasonable? Answers may vary. Possible answer: If my fraction is less

than ½, then my decimal should be less than 0.5 and my percent should be less than 50%. If my

fraction is greater than ½, then my decimal should be greater than 0.5 and my percent should be

greater than 50%.

How does generating equivalent rational numbers help you compare numbers?

Answers may vary. Possible answer: Converting all of the numbers to the same form makes it

easy to compare. Fractions with like denominators or decimals are easy to compare.

ELABORATE: The Elaborate portion of the lesson affords students the opportunity to extend

or solidify their knowledge of equivalent forms of rational numbers. This phase of the lesson

is designed for individual investigation. (15 minutes)

1. Distribute Practically Perfect to each student.

2. Prompt students to complete Practically Perfect.



How could you change each number to a percent? How might this help you answer

the question? Answers may vary. Possible answer: Rewrite the fraction with a denominator of

100 in order to change it to a percent. Use the place value of hundredths in the decimal to change

it to a percent.

How could you change each number to a fraction? How might this help you answer

the question? Answers may vary. Possible answer: Place the percent over 100 and simplify it in

order to write it as a fraction. Use place value to write the decimal as a fraction.

How could you change each number to a decimal? How might this help you answer

the question? Answers may vary. Possible answer: Change the fraction to tenths then use place

value to write it as a decimal. Change the percent to a decimal by using the place value of

hundredths.

How could you use benchmarks to compare the accuracy rates of the 3 girls? Answers

may vary. Possible answer: I know that ¾ of a dollar is 75₵, which can be written as 0.75. So, I

know that Kelly was more accurate than Elizabeth. Then I just need to compare Kelly and Cara.

EVALUATE: During the Evaluate portion of the lesson, the teacher will assess student

learning about the concepts and procedures that the class investigated and developed

during the lesson. (20 minutes)

1. Distribute Evaluate: Equivalent Forms of Rational Numbers to each student.

2. Prompt students to complete Evaluate: Equivalent Forms of Rational Numbers.

3. Upon completion of Evaluate: Equivalent Forms of Rational Numbers, the teacher

should discuss error analysis (shown below)to assess student understanding of the

concepts and procedures the class addressed in the lesson.

Answers and Error Analysis for Evaluate: Equivalent Forms of Rational Numbers

Question Number

Correct Answer

Conceptual Error Procedural Error

1 0.6

2 B A C D

3 C A B D

4 A B C D

STUDENT WORKSHEETS FOLLOW!!!!!


How do you determine if a set of fractions or decimals is in order from least to

greatest?

How do you determine if a set of fractions or decimals is in order from greatest to

least?

What procedure(s) may be used to order a set of fractions or decimals?

What procedure(s) may be used to compare two or more fractions or decimals?

MATERIALS:

Transparency: Problem‐Solving Board

For each student:

Activity Master: Problem‐Solving Board Bookmarks (optional)

Two to Solve

Fast‐N‐Furious

Evaluate: Compare and order Non‐Negative Rational Numbers


Activity Master: Mix and Match – cut apart

Scissors


KEY QUESTIONS

WEEK 4

TEACHER TOOLS

ENGAGE: The Engage portion of the lesson is designed to access students’ prior knowledge

of equivalent numbers. This phase of the lesson is designed for groups of 2 students. (10

minutes)

1. Distribute Activity Master: Mix and Match to each group of students.

2. Prompt students to create card sets by matching equivalent numbers together.



How could you use benchmark fractions to eliminate cards? Answers may vary.

Possible answer: Since I am trying to find the match for 2/5 and 2 is less than half of 5, I can

eliminate decimal cards that are greater than 0.5.

How could you rewrite a decimal as a fraction? Answers may vary. Possible answer: I

could use my knowledge of place value to write the decimal as a fraction then simplify the fraction

if needed.

How could you use place value to rewrite a decimal as a fraction? Answers may vary.

Possible answer: I could use the place value of the decimal to rewrite the decimal as a fraction

with a denominator of 10, 100, or 1,000 and simplify the fraction if needed.

How could you rewrite a fraction as a decimal? Answers may vary. Possible answer: I

could use my knowledge of equivalent fractions to rewrite the fraction with a denominator of 10,

100, or 1,000. Then use my knowledge of place value to write a decimal.

How could the rewriting of these fractions to have denominators of 10 (or 100 or

1,000) help to rewrite each fraction as a decimal? Answers may vary. Possible answer:

By rewriting the fraction to have a denominator of 10, 100, or 1,000, I can use place value to write

an equivalent decimal.


actively involved in using the See‐Plan‐Do‐Reflect Problem‐Solving Model by solving real‐

world problems. This phase of the lesson is designed for groups of 2 students. (25 minutes)

1. Display Transparency: Problem‐Solving Board and distribute Activity Master:

Problem‐Solving Bookmarks to each student.

2. Use Transparency: Problem‐Solving Board and the questions outlined on

Activity Master: Problem‐Solving Bookmarks to introduce the problem‐solving

model.

3. Distribute Two to Solve to each student.

4. Prompt students to complete Two to Solve with their partners.



Problem 1

What is the problem asking you to do? Order the fractions from least to greatest.

What will the answer look like? Answers may vary. Possible answer: A list of fractions will

have the smallest fraction first, the next smallest fraction, and end with the largest fraction.

What information in the problem provides insight into what needs to be put in

order? Answers may vary. Possible answer: The amount of writing each student completed

needs to be put in order.

How could you use the benchmark of ½ to begin sorting the fractions into order

from least to greatest? Answers may vary. Possible answer: I could use benchmark fractions

to determine which fractions are greater than ½ and less than ½.

What strategy could be used to solve this problem? Answers may vary. Possible answer:

I could rewrite each fraction using a common denominator and then compare the numerators.

Would a common denominator help? Why? Answers may vary. Possible answer: Yes, I

could find the common denominator between pairs of fractions and decide within each pair which

is larger while looking for the smallest fraction to start the list.

How could you determine the common denominator for these fractions? Answers

may vary. Possible answer: I could multiply the numerator and denominator of each fraction by

the same factor so that the new denominator of each fraction is the common multiple.

Once you have rewritten the fractions using a common denominator, how could

you determine which fraction is the greatest? The least? Answers may vary. Possible

answer: Since the fractions have the same denominator, I could compare the numerators to

determine which fraction is the greatest or the least.

Problem 2

What is the problem asking you to do? To order the numbers from greatest to least.

What will the answer look like? Answers may vary. Possible answer: A list of fractions and

decimals with the greatest number first, the next smaller number, ending with the smallest

number.

What information in the problem provides insight into what needs to be put in

order? Answers may vary. Possible answer: The amount of rain water each student collected

needs to be put in order.

How could you use the benchmark of ½ to begin sorting the fractions into order

from least to greatest? Answers may vary. Possible answer: I could use benchmark fractions

and determine which fractions or decimals are greater than ½ and less than ½.


I could rewrite each fraction as a decimal then line up the decimals and use the tenths place to

compare the decimals.

By looking at the tenths place, how could you determine which decimal is the

greatest? The least? Answers may vary. Possible answer: The decimal with the largest value

in the tenths place is the greatest, and the decimal with the smallest value in the tenths place is

the least.

How could rewriting all of the decimals as thousandths help determine the order of

the decimals? Answers may vary. Possible answer: Since all the decimals would be written to

the thousandths place and contain the same number of digits after the decimal, I could use my

knowledge of whole numbers to place the decimals in order from greatest to least.

EXPLAIN: The Explain portion of the lesson provides students with an opportunity to express

their understanding of comparing and ordering non‐negative rational numbers. The teacher

will use this opportunity to clarify key vocabulary terms and connect student experiences in

the Explore phase with relevant procedures and concepts. (15 minutes)

1. Debrief Two to Solve.

2. Use the facilitating questions to lead the discussion.


Problem 1

What procedure did you use to solve the problem? Answers may vary. Possible answer: I

rewrote each fraction using a common denominator and then compared the numerators to

determine the placement of each fraction.

If you used a common denominator, how did you determine the common

denominator? Answers may vary. Possible answer: I listed the multiples of each denominator

until I found a multiple that the denominators have in common.

What is the common denominator you used? Answers may vary. Possible answer: 8, 16,

24, 32…

How did you rewrite the fractions using the common denominator? Answers may

vary. Possible answer: I multiplied the numerator and denominator of each fraction by the same

factor so that the new denominator of each fraction is the common multiple.

Once you rewrote the fractions using a common denominator, how did you

determine which fraction is the greatest? The least? Answers may vary. Possible

answer: I compared the numerators to determine which fraction is the greatest or the least.

What is the order of the amount of writing completed, from least to greatest, using

common denominators? Answers may vary. Possible answer: 2/8, 4/8, 5/8, 6/8

What is the order of the amount of writing completed from least to greatest? ¼, ½,

5/8, ¾

Is there another way to solve this problem? How? Answers may vary. Possible answer:

Yes, I could rewrite each fraction as a decimal and then compare each place value to determine

the order.

Problem 2

What procedure did you use to solve the problem? Answers may vary. Possible answer:

I rewrote each fraction as a decimal and then I lined up the decimals and used place value to

compare the decimals to determine the order.

How did you determine which decimal is the greatest? The least? Answers may vary.

Possible answer: The decimal with the largest value in the tenths place is the greatest, and the

decimal with the smallest value in the tenths place is the least.

How could rewriting all of the decimals as thousandths help determine the order of

the decimals? Answers may vary. Possible answer: Since all the decimals would be written to

the thousandths place and contain the same number of digits after the decimal, I could use my

knowledge of whole numbers to place the decimals in order from greatest to least.

What is the order of the amount of rain water collected from greatest to least using

decimals written to the thousandths place? 0.750, 0.625, 0.500, 0.250

What is the order of the amount of rain water collected from greatest to least? 0.75,

0.625, ½, ¼

Is there another way to solve this problem? How? Answers may vary. Possible answer:

Yes, I could rewrite each decimal as a fraction with a common denominator and then compare the

numerators to determine the order.

ELABORATE: The Elaborate portion of the lesson affords students the opportunity to extend

or solidify their knowledge of comparing and ordering non‐negative rational numbers. This

phase of the lesson is designed for individual investigation.

1. Distribute Fast‐N‐Furious to each student.

2. Prompt students to complete Fast‐N‐Furious.



What is the problem asking you to do? Determine which runner’s time is closest to 0.

What do you know? I know the time it took each runner to complete the 100‐meter dash.

What do you need to know? I need to know which runner’s time is closest to zero.


I could rewrite the times that are given in fractions as decimals then line up the decimals and use

place value to compare the decimals.

How could you estimate the answer? Answers may vary. Possible answer: I could use

benchmark fractions.

EVALUATE: During the Evaluate portion of the lesson, the teacher will assess student

learning about the concepts and procedures that the class investigated and developed

during the lesson. (20 minutes)

4. Distribute Evaluate: Compare and Order Non‐Negative Rational Numbers to each

student.

5. Prompt students to complete Evaluate: Compare and Order Non‐Negative Rational

Numbers.

6. Upon completion of Evaluate: Compare and Order Non‐Negative Rational Numbers,

the teacher should discuss error analysis (shown below)to assess student

understanding of the concepts and procedures the class addressed in the lesson.

Answers and Error Analysis for Evaluate: Compare and Order Non‐Negative Rational

Numbers

Question Number

Correct Answer


1 C A D B

2 D A B C

3 B A C D

4 C B D A


Name:

Two To Solve

Period: Date:

1 Joshua, Avi, Fidel, and Eduardo each completed part of their writing assignment over the

weekend. Joshua completed 3

4 of the writing, Avi completed

1

2

of the writing, Fidel

completed 5

8 of the writing, and Eduardo completed

1

4

of the writing. Place the amount of

writing each student completed in order from least to greatest.

Complete the problem-solving board below.

SEE: What is the question asking me to do?

What do I know?

What do I need to know?

PLAN: What strategy can I use to solve the problem? Why?

Estimate the answer.

DO: (Solve)

Answer:

REFLECT: Did I answer the question asked? Is my answer reasonable? Why or why not?


What do I know?



Estimate the answer.

DO: (Solve)

Answer:


2 The table below shows the number of ounces of rain water collected by each of Mrs. Hiozek’s students.

Rain Water

Student Ounces

Dillon

1/2Paul 0.75

Varsha 0.625

Gina 1/4

Place the number of ounces each student collected in order from greatest to least.


Name: Period: Date:

Fast-N-Furious

Four runners ran the 100-Meter Dash. Their completion times are recorded in the table below. Use the number line to determine which runner ran the fastest.

100-Meter Dash

Runner

Derek Ian John Roger

Time (minutes)

1

3 0.16

3

2 0.75

0 1 2



What do I know?



DO: (Solve)

Answer:


Name: ______________________________________ Date:_________________


How do you generate equivalent rational numbers?

How do you compare rational numbers?

MATERIALS:

Warm‐Up: Who is Correct?

Activity Master: Number Line – assembled and posted on the wall

For each student:

Fractions, Decimals, and Percents, Oh My!

Race Car Stat

Evaluate: Equivalent Rational Numbers


Activity Master: Fractions, Decimals, and Percents – cut apart, 1 set of cards per group


KEY QUESTIONS

WEEK 5

TEACHER TOOLS

ENGAGE: The Engage portion of the lesson is designed to access students’ prior knowledge of

percent models. This phase of the lesson is designed for groups of 2 students. (10 minutes)

1. Distribute “Who is Correct?” warm‐up.

2. Prompt students to individually complete the warm‐up “Who is Correct?”

3. Upon completion of the warm‐up, prompt students to share and justify their solutions

with a partner.



What is the question asking you to do?

Answers may vary. Possible answer: Determine who is correct by determining the percent of the flag

that is shaded.

What do you know?

Answers may vary. Possible answer: I know the answer given by each person, and I was given a

picture of the flag.

What do you need to know?

Answers may vary. Possible answer: I need to know the percent of the flag that is shaded in order to

determine who is correct.

What strategy could you use to determine who is correct?

Answers may vary. Possible answer: I could find the percent of the flag that is shaded then compare

my answer to the answer of each person to determine who is correct.

How many squares make up the flag?

32

How many squares are shaded?

12

How could you write a ratio that compares the number of shaded squares to the total

number of squares on the flag?

Answers may vary. Possible answer: 3 to 8, 3:8, 3 out of 8, 3/8

What do you know about percents? Answers may vary. Possible answer: I know that percents

are how many out of a 100.

How could you use the ratio of the shaded squares to the total number of squares to

help you determine what percent of the flag is shaded? Answers may vary. Possible answer:

I know the ratio of shaded squares to total squares is 3/8; therefore, I could use a factor of change to

rewrite the ratio as a fraction with a denominator that is a power of 10, such as 1000.

What factor of change could you use to change 3/8 to thousandths?

Multiply by 125

What is 3/8 written as thousandths?

375/100

How could you rewrite 375/1000 as a percent?

Answers may vary. Possible answer: Multiply the numerator and the denominator by 1/10 in order to

generate an equivalent fraction with a denominator of 100, 37.5/100. Then I could use the numerator

as my percent, since percent means out of 100.


actively involved in investigating equivalent rational numbers. This phase of the lesson is

designed for groups of 2 students. (25 minutes)

1. Distribute 1 set of Activity Master: Fractions, Decimals, and Percents to each group of

students and Fractions, Decimals, and Percents, Oh My! to each student. (NOTE: Have

Activity Master cards pre‐cut for student use.)

2. Prompt students to complete Fractions, Decimals, and Percents, Oh My!



What information is found on the cards?

Answers may vary. Possible answer: The cards contain rational numbers written in different forms.

Rewriting Fractions as Decimals

How could rewriting each fraction as hundredths help you write the decimal

representation of the fraction?

Answers may vary. Possible answer: Decimals are just fractions that have denominators that are 10,

100, 1000, etc. (powers of 10). So if I rewrite the fraction as hundredths, I could write the decimal by

using place value.

What factor of change could you use to rewrite this fraction as hundredths?

Answers may vary.

Rewriting Fractions as Percents

How could rewriting each fraction as hundredths help you write the percent

representation of the fraction?

Answers may vary. Possible answer: Percents are just fractions that have denominators of 100. So if I

rewrite the fraction as hundredths, I could write the percent by using the numerator.


Answers may vary.

Rewriting Decimals as Percents

How could rewriting each decimal as a fraction help you write the decimal as a percent?

Answers may vary. Possible answer: Place value is based on powers of 10: 10, 100, 1000, etc. So if I

rewrite the decimal as a fraction, I could apply a factor of change to the fractions to rewrite the

fractions as hundredths then I could write the percent by using the numerator.


Answers may vary.

x 125

. 62.5%

Rewriting Decimals as Fractions

How could place value help you write each decimal as a fraction in simplest form?

Answers may vary. Possible answer: Place value is based on powers of 10: 10, 100, 1000, etc. So I

could rewrite the decimal as a fraction with a denominator of tenths, hundredths, or thousandths then

simplify.

Rewriting Percents as Fractions

What procedures could be used to write a percent as a fraction in simplest form?


rewrite the fraction as hundredths, then I could simplify.

Rewriting Percents as Decimals

How could rewriting a percent as a fraction help you write a percent as a decimal?


rewrite the percent as a fraction, I could write the decimal by using place value.

Ordering from Least to Greatest

Which representation is the easiest to use to help you determine which rational number

represents the largest amount? Why?

Answers may vary. Possible answer: To compare the rational numbers, I could use the fractions

written as hundredths, the percent, or the decimal form to compare easily.


represents the smallest amount? Why?



Comparing 83.5%

How could you determine which of the numbers are equivalent to 83.5%?

Answers may vary. Possible answer: I could rewrite 83.5% as a fraction and as a decimal and compare

my values with the values of the answer choices.

What process could you use to rewrite 83.5% as a fraction with a denominator of 100?

Answers may vary. Possible answer: Percents are just fractions that have denominators of 100. So I

could rewrite 83.5% as a fraction where 83.5 is the numerator and 100 is the denominator.

What process could you use to rewrite 83.5% as a fraction with a denominator of 1000?

Answers may vary. Possible answer: I could rewrite 83.5% as a fraction where 83.5 is the numerator

and 100 is the denominator then use a factor of change to rewrite the fraction as thousandths.

What factor of change could be used to convert 83.5/100 to thousandths?

10

What process could you use to rewrite 83.5% as a decimal?

Answers may vary. Possible answer: I could rewrite 83.5% as a fraction with a denominator of 1000

then write the decimal by using place value. 0.835

EXPLAIN: The explain portion of the lesson provides students with an opportunity to express

their understanding of equivalent rational numbers. The teacher will use this opportunity to

clarify vocabulary terms and connect student experiences in the Explore phase with relevant

procedures and concepts. (20 minutes)

1. Display assembled Activity Master: Number Line on the wall in front of the room.

2. Prompt 1 group of students with Card Set 1 to post their cards in the appropriate place on

Activity Master: Number Line. Students will need to approximate the placement.

3. Prompt 1 group of students with Card Set 2 and 1 group with Card Set 3 to add their cards

to the number line.

Note: There are repeated rational numbers throughout the 3 different sets of cards;

however, the repeated rational numbers are in different forms.

4. Use the facilitating questions to lead a whole‐group discussion as students add their cards

to the number line.

Number Line Key

0.625

12.5% 20/32

1/8 1/5 20.4% ¼ 32.6% 5/8

0 0.5

Facilitating Questions





Which representation would be the hardest to use to determine which rational number


Answers may vary. Possible answer: To compare the rational numbers, I would not use the fractions

in the simplest form because these fractions are not easily compared without a common denominator.

How could you use the placement of the cards on the number line to determine which

rational number represents the largest amount?

Answers may vary. Possible answer: The number that represents the largest amount would be the

number that is farthest to the right on the number line.




written as hundredths, the percent, or the decimal form to easily compare.

Which representation would be the hardest to use to determine which rational number


Answers may vary. Possible answer: To compare the rational numbers, I would not use the fractions in

simplest form because they do not have a common denominator.

How could you use the placement of the cards on the number line to determine which

rational number represents the smallest amount?

Answers may vary. Possible answer: The number that represents the smallest amount would be the

number that is farthest to the left on the number line.

Which representation is the easiest to use to help you determine where a rational

number lies on the number line? Why?

Answers may vary. Possible answer: Since the number line is in decimal form, it is easier to determine

the placement of the decimal representations.

5. Debrief questions 3 on Fractions, Decimals, and Percents, Oh My!

6. Use the facilitating questions to lead the discussion.


How did you determine which of the numbers are not equivalent to 83.5%?

Answers may vary. Possible answer: I rewrote 83.5% as a fraction and as a decimal and compared my

values with the values of the answer choices.

Did you eliminate any of the answer choices? Why?

Answers may vary. Possible answer: Yes, since 83.5% is less than 100% and 100% is equivalent to 1, I

was able to eliminate 8.35 because it is greater than 1.

What process did you use to rewrite 83.5% as a fraction with a denominator of 100?

Answers may vary. Possible answer: Percents are just fractions that have denominators of 100. So I

rewrote 83.5% as a fraction where 83.5 is the numerator and 100 is the denominator.

What process did you use to rewrite 83.5% as a fraction with a denominator of 1000?

Answers may vary. Possible answer: I rewrote 83.5% as a fraction where 83.5 is the numerator and

100 is the denominator then used a factor of change of 10 to rewrite as thousandths. (835/1000)

What process did you use to rewrite 83.5% as a decimal?

Answers may vary. Possible answer: I rewrote 83.5% as a fraction with a denominator of 1000 then

wrote the decimal by using place value.

Which number is not equivalent to 83.5%? Why?

8.35

ELABORATE: The Elaborate portion of the lesson affords students the opportunity to extend or

solidify their knowledge of equivalent rational numbers. This phase of the lesson is designed for

individual investigation. (10 minutes)

1. Distribute Race Car Stat to each student.

2. Prompt students to complete Race Car Stat. (Answer A)



What is the question asking you to do?

Answers may vary. Possible answer: Determine between which 2 fractions 3/8 lies on a number line.

What do you know?

Answers may vary. Possible answer: I know 4 different possible sets of fractions that 3/8 may fall

between.

What do you need to know?

Answers may vary. Possible answer: I need to know a common denominator so that I can make

comparisons.

What procedure could you use to determine which pair of fractions 3/8 may fall

between?

Answers may vary. Possible answer: I could find a common denominator, simplify, or use a factor of

change to rewrite each fraction using the common denominator then compare numerators.

EVALUATE: During the Evaluate portion of the lesson, the teacher will assess student learning

about the concepts and procedures that the class investigated and developed during the lesson.

(20 minutes)

7. Distribute Evaluate: Equivalent Rational Numbers to each student.

8. Prompt students to complete Evaluate: Equivalent Rational Numbers.

9. Upon completion of Evaluate: Equivalent Rational Numbers, the teacher should discuss

error analysis (shown below)to assess student understanding of the concepts and

procedures the class addressed in the lesson.

Answers and Error Analysis for Evaluate: Equivalent Rational Numbers

Question Number

Correct Answer


1 B A C D

2 B A C D

3 A B C D

4 A B C D


Warm‐Up: Who is Correct?

Kobie shaded 3/8 of the flag black, as shown below.

Cassie stated that 12% of the flag was shaded, and Kobie said that 37.5% of the flag was

shaded. Who is correct? Explain your answer.

Activity Master: Number Line

1

0.5

Activity Master: Number Line

0

Activity Master: Fractions, Decimals, and Percents

Cut each card out along lines. 1 set per group of students – 3 cards per set.

20.4%

Set 1 Card 1

Set 1 Card 2

Set 1 Card 3

0.625

Set 2 Card 1

Set 2 Card 2

Set 2 Card 3

Activity Master: Fractions, Decimals, and Percents

Set 3 Card 1

Set 3 Card 2

Set 1 Card 3

Name: ______________________________________ Date:_________________

Fractions, Decimals, and Percents, Oh My!

Complete the table below.

CARD Fraction (in simplest form)

Decimal Percent

Card 1

Card 2

Card 3

1. List the cards in order from least to greatest.

2. Which representation is the easiest to use to help you determine the order from least to greatest?

Why?

3. It is estimated that Jimmy Johnson completed 83.5% of the laps in the 2004 Talladego Race. Which

number is NOT equivalent to 83.5%?

A.

B. .

C. 0.835

D. 8.35

Name: _______________________________________Date: ________________

Race Car Stat

Tony Stewart was either the winner or the runner‐up in 3 out of the last 8 races in the series.

The fraction 3/8 is found between which pair of fractions on a number line?

A. and

B. and

C. and

D. and

Justify your answer choice and state why the other answer choices are incorrect.

Name: ______________________________________Date:________________

Evaluate: Equivalent Rational Numbers

1. The fraction is found between which pair of fractions on the number line?

A. and

B. and

C. and

D. and

2. A specialty paint shop had 4 different race cars to complete. The shop completed , , , and of the

work on each car. Which list shows the percent of the work completed on each car in order from

greatest to least?

A. 50%, 62.5%, 75%, 20%

B. 75%, 62.5%, 50%, 20%

C. 0.75%, 0.625%, 0.5%, 0.2%

D. 20%, 50%, 62.5%, 75%

3. Tyler estimated that 48.2% of the crystals in his sugar project developed correctly. Which number is NOT

equivalent to 48.2%?

A. 4.82

B. 0.482

C.

D. .

4. The table shows the driver and the portion of allowable gas each driver used in the race.

Gas Usage

Driver Portion of Allowable Gas

Used

Busch

Johnson

Burton 48.3%

Earnhardt

Harvick 48.2%

Which of the following lists the racers in order from least to greatest portion of allowable gas used?

A. Busch, Earnhardt, Harvick, Burton, Johnson

B. Busch, Earnhardt, Burton, Harvick, Johnson

C. Johnson, Burton, Harvick, Busch, Earnhardt

D. Johnson, Burton, Harvick, Earnhardt, Busch

Fifth Grade Tasks Weekly Enrichments Teacher Dreamers

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