Unit 5 - Mentoring MindsUse the diagram to determine the ... Walk 3 Bus 14 Car 8 What percentage ......

MATH | LEVEL 6Teacher Edition Sample Page

mentoringminds.com

mentoringminds.com motivationmath™LEVEL 6 ILLEGAL TO COPY 39

Unit 1 Standards (Student pages 7–12)

California Common Core State Standards for Mathematical Content: 6.RP.A.1

Domain Ratios and Proportional RelationshipsCluster Understand ratio concepts and use ratio reasoning to solve problems. (Major Cluster)Standard 6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

Other Standards Addressed in this Unit4.NF.A.1

Common Core State Standards for Mathematical Practice Addressed in this UnitMP.1 Make sense of problems and persevere in solving them.MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others.MP.4 Model with mathematics.MP.5 Use appropriate tools strategically.MP.6 Attend to precision.MP.7 Look for and make use of structure.MP.8 Look for and express regularity in repeated reasoning.

Unpacking the Standards

Ratios and rates are introduced in grade 6. Students define ratios as the comparison of two quantities or measures. Students understand that ratios may be written in three ways ( a __

b , a to b, and a : b) , and

that ratios compare part to part or part to whole. Care should be taken in discussing ratios comparing part to part and written using fraction form to prevent confusion with the definition of a fraction. Students communicate that a ratio of 3 to 2 indicates there are three of each of the first quantity or measure for every two of the second quantity or measure. Students provide a description given a ratio or provide a ratio given a description. Students are expected to recognize ratios expressed in simplest form.

Unit 1

Standard 6.RP.A.1 Understand ratios and use ratio language


mentoringminds.com

40 ILLEGAL TO COPY motivationmath™LEVEL 6 mentoringmindsonline.com

Getting Started

Introduction Activity

The teacher provides a small bag of different numbers of items (5 paper clips, 4 eraser tops, 3 pennies, etc.) to each group of 2–3 students. Each bag should contain the same items. The teacher displays an incomplete statement about the items in the bag. (For every _____ pennies, there are _____ paper clips.) Students record the completed statement in math journals. (For every 3 pennies, there are 5 paper clips.) The teacher and class discuss the relationship between the number of pennies and paper clips in the bag, and the term “ratio” is introduced. Students write the ratio of pennies to paper clips in three forms (3 to 5, 3 : 5, 3 __ 5 ) in math journals. The process is repeated with other relationships such as eraser tops and total items.(DOK 2, Bloom’s Level: Comprehension/Understand)

Suggested Formative AssessmentThe teacher displays the following scenario and questions.

There are 11 boys and 12 girls in Mr. Tillman’s first-period class.

• What is the ratio of girls to boys in Mr. Tillman’s first-period class?

• What does the ratio 12 : 23 represent?

• Is the ratio of boys to total students in Mr. Tillman’s first-period class expressed as 11 to 23 or 23 to 11? Explain your answer.

Students write responses in math journals. The teacher reviews responses and uses the information to plan further instruction.(DOK 2, Bloom’s Level: Application/Apply)

Literature Connections

Beanstalk: The Measure of a Giant – Ann McCallum

Unit 1



mentoringminds.com


Vocabulary Focus

The following are essential vocabulary terms for this unit.

denominator numerator quantity tape diagram

equivalent ratios per ratio

Vocabulary ActivityFantastacrostic

The teacher covers a wall with butcher paper to create a graffiti wall space. Students are divided into small groups, and each group is assigned a vocabulary term. For the assigned term, each group creates an acrostic that demonstrates the meaning of the term using each letter in the term. Groups record the acrostic on the graffiti wall.

Example: Part for each Each/every one Related using ratios(DOK 1, Bloom’s Level: Synthesis/Create)

Suggested Formative Vocabulary AssessmentEach group presents the acrostic created during the Vocabulary Activity. Groups explain why each part of the acrostic was chosen and how it demonstrates the meaning of the term. The class discusses each group’s presentation. The teacher monitors student presentations, explanations, and discussions and plans further instruction or intervention as needed.(DOK 2, Bloom’s Level: Comprehension/Understand)

Suggested Instructional Activities

1. The teacher provides a set of pattern blocks to each pair of students. The teacher calls numbers of different shapes, and students display the appropriate blocks on their desks. For example, if the teacher calls three triangles and four hexagons, students would display the following.

Unit 1



mentoringminds.com


On response boards, students record ratios as the teacher calls them, using all three formats for writing ratios.

• triangles to hexagons (3 : 4, 3 to 4, 3 __ 4 )

• hexagons to triangles (4 : 3, 4 to 3, 4 __ 3 )

• triangles to total shapes (3 : 7, 3 to 7, 3 __ 7 )

• hexagons to total shapes (4 : 7, 4 to 7, 4 __ 7 )

The teacher monitors and checks student work. Each pair selects one ratio and records a sentence on their board to describe the ratio. For example, the ratio 3 triangles to 4 hexagons is described as “for every three triangles, there are four hexagons.” The teacher and class discuss the statements, and the teacher clarifies misconceptions as needed. The process is repeated with different numbers and shapes, including ratios that can be simplified.(DOK 2, Bloom’s Level: Comprehension/Understand)

2. For each pair of students, the teacher provides an index card printed with two items located in the classroom. For example, a card might be printed with “student desks and windows.” The pair records statements on the back of the card comparing the items given. (There are _____ student desks for every _____ windows.) Pairs take turns sharing their statements with the class. The teacher provides feedback to pairs as needed.(DOK 2, Bloom’s Level: Comprehension/Understand)

3. The teacher gives an index card printed with either a ratio (1 : 5) or a description of a ratio (one rabbit for every five dogs) to each student. Each card should have a match as described. On the teacher’s signal, students move around the room to locate the card matching their own. When a match is found, pairs take turns sharing their ratios and statements. The teacher answers questions and provides clarification as needed.(DOK 2, Bloom’s Level: Comprehension/Understand)

Suggested Formative AssessmentEach student receives a blank index card. On one side of the card, students explain, in their own words, what a ratio is and how a ratio is written. On the opposite side of the card, students provide an example of a ratio by sketching a picture or recording a description of two items to be compared. Students write the ratio three ways and record at least two statements describing the ratio, as addressed in the unit. The teacher collects and reviews the cards and uses the information to plan additional instruction or intervention.(DOK 2, Bloom’s Level: Comprehension/Understand)

Unit 1



mentoringminds.com


Suggested Reflection/Closure Activity

The class is divided into teams of 3–4 students. When the teacher gives a signal, teams have 1 minute to write as many ratios as possible of objects in the classroom. When time is called, the teacher selects one group to read their list of ratios. If other groups have the same ratio, all groups must cross that ratio off their lists. When all duplicate ratios are crossed off, the group with the most unique ratios wins.(DOK 1, Bloom’s Level: Synthesis/Create)

Suggested Formative AssessmentIn math journals, students summarize what they have learned about writing ratios by responding to a 3-2-1 reflection prompt.

• 3 key words

• 2 new ideas

• 1 idea to think about

The teacher reviews student responses and plans further instruction or intervention as needed.(DOK 2, Bloom’s Level: Comprehension/Understand)

Interventions

1. Students play “Bucket Basketball.” Each student makes 10 attempts to toss a paper ball into a bucket. Students record ratios in various forms for the number of buckets to the number of misses or the number of buckets to the total number of attempts.(DOK 1, Bloom’s Level: Comprehension/Understand)

2. Before class, the teacher removes all blanks and doubles from sets of dominoes. The teacher provides several dominoes (facedown) to each student as well as an individual response board, marker, and eraser. Each student selects a domino to represent a part to part ratio. Based on the domino selected, the student sketches a model to represent the ratio. Then the student records two statements describing the ratio drawn. An example is shown.

Unit 1



mentoringminds.com


For every 5 stars, there are 6 hearts.The ratio of hearts to total objects is 6 to 11.

The teacher checks student responses and corrects any misunderstandings. The process is repeated with other dominoes.(DOK 2, Bloom’s Level: Comprehension/Understand)

3. The teacher gives a bag of items (similar to the bags described in the Introduction Activity) to each student. Students are provided a list of ratios about different relationships represented in the bag. In writing, students explain the meaning of each ratio listed. The teacher selects students to share responses.(DOK 2, Bloom’s Level: Comprehension/Understand)

Suggested Formative AssessmentThe teacher places marbles or cubes of various colors in a sack. Each student takes a handful of the items, records numbers and colors of each, and returns the items to the sack. In math journals, students write three different ratios represented by the objects. For each ratio, students write a sentence that explains the meaning of the ratio (e.g., For every 3 red marbles, there are 5 yellow marbles.). Based on student responses, the teacher determines the need for further interventions.(DOK 2, Bloom’s Level: Comprehension/Understand)

Extending Student Thinking

Students research the golden ratio, focusing on the history of the ratio and its use as a golden rectangle in advertising. Students create a multimedia or poster presentation showing their research.(DOK 3, Bloom’s Level: Synthesis/Create)

Unit 1



mentoringminds.com


Answer Key and Codings

Page Question AnswerDOK Level

Bloom’s Original/Revised

7

1

a. 13; Explanations will vary. 2 Comprehension/Understand

b. 10 : 13 1 Comprehension/Understand

c. 23 to 13 1 Comprehension/Understand

d. 10 __ 23

1 Comprehension/Understand

e. Answers will vary but might include that the ratio in part b compares part to part while the ratio in part d compares part to whole. Both ratios compare the numbers of students in Mr. Johnson’s class.

2 Analysis/Analyze

2

a. 4, 5 1 Analysis/Analyze

b. 5, 6 1 Analysis/Analyze

c. 2 to 1 (or equivalent) 1 Analysis/Analyze

d. 2 : 3 (or equivalent) 1 Analysis/Analyze

e. Explanations will vary, but students should recognize that 20 is the total number of coins in LaTonya’s purse and 9 is either the number of pennies in her purse or the number of nickels and quarters in her purse. Models will vary.

2 Analysis/Analyze

8

1 A 1 Comprehension/Understand

2 C 2 Comprehension/Understand

3 B, D, and F 1 Comprehension/Understand

4 A 1 Application/Apply

5 C 3 Analysis/Analyze

6

A–FalseB–FalseC–TrueD–False


9

1 B, C, and F 1 Comprehension/Understand

2 A 3 Analysis/Analyze

3 B 2 Comprehension/Understand

4 D 2 Comprehension/Understand

5 A, C, D, and E 2 Comprehension/Understand

10

1 B 2 Comprehension/Understand

2 D 2 Comprehension/Understand

3 B and F 1 Comprehension/Understand

4 A 1 Application/Apply

5 3, 2; 4, 1; 4 : 3; 2 to 5 1 Comprehension/Understand

Unit 1



mentoringminds.com


Answer Key and Codings

Page Question AnswerDOK Level

Bloom’s Original/Revised

11

1 2 _ 5 ; 3 _

5 ; 18 quarts of red paint and 27 quarts of blue paint 2 Analysis/Analyze

2 Answers will vary. 3 Synthesis/Create

Journal Student responses will vary. 2 Comprehension/Understand

12Motivation

Station

3 to 2; 3, 21 : 3; 1, 34 to 3; 4, 32 : 2; 2, 2


Unit 1


MATH | LEVEL 6Student Edition Sample Page

mentoringminds.com

Name __________________________________________

Standard 6.RP.A.3c


1. Shade the model to represent 1 __ 4 .

What percentage of the model did you shade? Explain your answer.

2. Coach West placed 28 of his athletes on suspension due to failing grades. There are a total of 200 athletes in the athletic department. Use the model to determine the percentage of athletes Coach West placed on suspension.

What percentage of the athletes did Coach West suspend? Explain your answer.

3. Mrs. Martinez assigned pages of reading for homework. Jace had time to read 3 pages before he left school. This was 15% of the total assignment. Use the diagram to determine the number of pages Mrs. Martinez assigned for homework.

0% 15% 100%

0 3

How many pages does Jace need to read at home?

4. Marcela is shopping for a new winter coat. She finds a coat that is regularly priced at $60 on sale for 30% off. Use the model to determine how much money Marcela saves by purchasing the coat on sale.

0% 100%

$0 $60

How much does Marcela save on the coat?

How much does Marcela pay for the coat?

Unit 5 Introduction

decimal number fraction percent rate

double number line diagram model percentage ratio

equivalent ratios per quantity tape diagram

Words for the Wise


mentoringminds.com

Name __________________________________________

Standard 6.RP.A.3c


1. This year, Mrs. Fisher has 8 students who are new to the school. The number of new students represents 5% of all her students.

0% 100%

0 8

How many students are in Mrs. Fisher’s classes this year?

A 40 students C 144 students

B 80 students D 160 students

2. The shaded model represents the percentage of students at Judson Middle School who bring their lunches to school.

There are 650 students who attend Judson Middle School. How many students bring their lunches?

A 32 students C 442 students

B 208 students D 618 students

3. Natalie saved $20 when she purchased a new phone. The phone originally cost $125. What percentage of savings did Natalie receive on the purchase of a new phone?

A 25% C 16%

B 20% D 6.25%

4. Kareem correctly answered 85% of the questions on his math test. He missed 6 questions. How many questions were on the math test?

A 20 questions C 40 questions

B 30 questions D 70 questions

5. Berkley surveyed students in his fourth-period class to determine how they travel to school each morning.

School TransportationType Number of Students

Walk 3

Bus 14

Car 8

What percentage of the students Berkley surveyed ride the bus to school?

A 56% C 14%

B 32% D 12%

6. Leticia wants to go on a band trip to New York during spring break. The band will pay 25% of the cost for each student.

Total Cost $25 $50 $100

Paid by Band $25 $50

For each student, the total cost of the trip is $1125. How much of the cost will the band pay?

A $45 C $275

B $256.25 D $281.25

Unit 5 Partner Practice


mentoringminds.com

Name __________________________________________

Standard 6.RP.A.3c


1. Jefferey has a collection of marbles. He gives his best friend 36 marbles from the collection for his birthday. This represents 30% of Jefferey’s total collection.

0% 100%

0

How many marbles did Jefferey have in his collection?

A 60 marbles C 240 marbles

B 120 marbles D 360 marbles

2. During a school assembly, 15 out of 60 students wore orange shirts to show school spirit. What percentage of the students did not wear orange shirts?

A 8% C 25%

B 15% D 75%

3. Nadia scored 96% on her math test.

Total Questions 50 100

Correct Questions 96

There were a total of 75 questions on the test. How many questions did Nadia answer correctly?

A 74 questions C 70 questions

B 72 questions D 3 questions

4. The shaded model represents the percentage of the total stock of pencils sold at the student bookstore.

The store began with 625 pencils. How many pencils are left at the bookstore?

A 64 pencils

B 225 pencils

C 400 pencils

D 561 pencils

5. The different types of vegetables sold at the farmers market are shown in the table.

Farmers MarketVegetable Number Sold

Carrots 23

Peppers 8

Celery 24

Onions 5

What percentage of the vegetables sold is celery?

A 24%

B 33%

C 40%

D 60%

Unit 5 Independent Practice


mentoringminds.com

Name __________________________________________

Standard 6.RP.A.3c


5. Brady recorded the number and color of cars in the parking lot. He found that 45% of the cars in the lot were white. There were 81 white cars in the parking lot. Use the table to determine the total number of cars in the parking lot.

Explain how you determined your answer.

____________________________________________

____________________________________________

____________________________________________

1. To receive a score of A on an 80-question test, 90% of the questions must be answered correctly. What is the maximum number of questions that can be missed to still receive an A?

A 5 questions

B 8 questions

C 9 questions

D 10 questions

2. The chart shows the number of fish in an aquarium.

Aquarium PopulationType Number

Gold�sh 14

Tetras 18

Rainbow �sh 5

Angel �sh 3

What percentage of the fish are tetras?

A 18%

B 32%

C 40%

D 45%

3. A moving van travels 560 miles to reach a new house. The drivers stop for rest after traveling 75% of the total distance.

0% 100%

0 56 112 168 224 280 336 392 448 504 560

How many miles have the drivers traveled when they stop?

A 25 mi C 420 mi

B 140 mi D 485 mi

4. Shelby purchases a watch on sale. The original price of the watch was $145, and Shelby pays $101.50.

$0 $145

0% 100%

Use the tape diagram to determine the percentage discount Shelby receives on the watch.

A 30% C 70%

B 43.5% D 80%

Unit 5 Assessment

White cars 9 45

Total cars 100


mentoringminds.com

Name __________________________________________

Standard 6.RP.A.3c


Unit 5 Critical Thinking

1. In Mrs. Dudley’s sixth-grade class, each student was challenged to read 75 books by the end of the school year. Lamar read 60 books by winter break. He read an additional 30 books by the end of the school year. Sketch a model to find the percentage of the challenge Lamar met by the end of the school year.

What percentage of Mrs. Dudley’s challenge did Lamar meet?

2. At a yard sale, Celia purchased an electric guitar for 85% of its original value. Celia paid $75.65 for the guitar. Use a model and words or numbers to explain how to determine the original value of the guitar.

What was the original value of the guitar?

Application

Apply

Application

Apply

Jonah shops for school clothes with his dad. They walk into a store where the shoes are 50% off the lowest price marked. Jonah finds a pair of shoes that were previously 50% off the original price. With the sale, are the shoes free? Justify your answer using words, numbers, and/or a model.

______________________________________________________________________________________

______________________________________________________________________________________

______________________________________________________________________________________

Journal Analysis

Analyze


mentoringminds.com

Name __________________________________________

Standard 6.RP.A.3c


Unit 5 Motivation Station

On a Roll

Play “On a Roll” with a partner. Each pair needs a number cube and a game board. Each player needs a pencil and a sheet of paper. In turn, players roll the number cube and solve the corresponding problem. Each player shows work on his/her paper and explains how the answer was determined. If correct, the player is awarded the number of points in the banner next to the problem. If incorrect, the other player can claim the points by working the problem correctly. If a player rolls the number of a problem that has already been solved, play passes to the other player. The winner is the player with more points after all problems have been solved.

Crystal won 84% of the skating competitions she entered last year. If Crystal entered 250 competitions, how many did she win?

On one day in February, 3 out of 20 spider monkeys at the zoo were ill. What percentage of the monkeys were ill?

Luke works in the produce department at the local grocery store. On Friday, 35 people bought a

pumpkin. If this number is 28% of the total number of customers, how many customers were in the store on Friday?

A total of 115 students voted for class favorite. Denny received 60% of the vote. How many students voted for Denny for class favorite?

During the school year, Tiffany received 12 perfect scores on her math papers. If these scores

represent 30% of all the scores Tiffany received in her math class over the year, how many scores did Tiffany receive during the school year?

The girls’ basketball team lost 7 out of 25 games this season. What percentage of games did the team win this season?

10 10

20 20

30 30

Answer __________ Answer __________

Answer __________ Answer __________

Answer __________ Answer __________

1. Practice finding discounts while shopping. Find different items that are marked with a percent discount. Determine how much the discount will be as well as the final cost of the item.

2. Look through newspapers and magazines to find examples of percents. Find examples in which the percent and the whole or the percent and the part are given. Then, find the missing value. Bring one or more examples to share with the class.

Connections

Unit 5 - Mentoring MindsUse the diagram to determine the ... Walk 3 Bus 14 Car 8 What percentage ......

Documents

Transcript of Unit 5 - Mentoring MindsUse the diagram to determine the ... Walk 3 Bus 14 Car 8 What percentage ......