unit: ccssm 5.nf - wordpress.com€¦ · unit 3 assessment kehoegreen 1 unit: goal: students will...

$: Unit: CCSSM 5.NF - WordPress.com€¦ · Unit 3 Assessment Kehoegreen 1 Unit: Goal: Students will master multiplying fractions by whole number and fractions, and dividing fractions$
Unit 3 Assessment Kehoegreen 1

Unit:

Goal:

Students will master multiplying fractions by whole number and fractions, and dividing fractions

by whole numbers and fractions.

Standards Alignment:

CCSS:

Lesson 1:

CCSSM 5.NF.4 Apply and extend previous understandings of multiplication to multiply a

fraction or whole number by a fraction.

a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts;

equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a

visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this

equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of

the appropriate unit fraction side lengths, and show that the area is the same as would be

found by multiplying the side lengths. Multiply fractional side lengths to find areas of

rectangles, and represent fraction products as rectangular areas.

Lesson 2:

CCSSM 5.NF.7 Apply and extend previous understandings of division to divide unit fractions

by whole numbers and whole numbers by unit fractions.

a. Interpret division of a unit fraction by a non-zero whole number, and compute such

quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction

model to show the quotient. Use the relationship between multiplication and division to

explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

b. Interpret division of a whole number by a unit fraction, and compute such quotients.

For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show

the quotient. Use the relationship between multiplication and division to explain that 4 ÷

(1/5) = 20 because 20 × (1/5) = 4.

CCSSM.6.NS. Apply and extend previous understandings of multiplication and division to

divide fractions by fractions.

1. Interpret and compute quotients of fractions, and solve word problems involving division

of fractions by fractions, e.g., by using visual fraction models and equations to represent the

problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction

model to show the quotient; use the relationship between multiplication and division to

explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.)

How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?

How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip

of land with length 3/4 mi and area 1/2 square mi?

Lesson 3:

CCSSM 5.NF.6 Solve real world problems involving multiplication of fractions and mixed

numbers, e.g., by using visual fraction models or equations to represent the problem.




c. Solve real world problems involving division of unit fractions by non-zero whole

numbers and division of whole numbers by unit fractions, e.g., by using visual fraction

models and equations to represent the problem. For example, how much chocolate will

each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup

servings are in 2 cups of raisins?

Technology Standards:

NETSS 1. Students demonstrates creative thinking, construct knowledge, and develop

innovative products and processes using technology.

c. Students use models and simulations to explore complex systems and issues.

NETSS.3.c: Students evaluate and select information sources and digital tools based on the

appropriateness to specific tasks.

NETST.2.a: Design or adapt relevant learning experiences that incorporate digital tools and

resources to promote student learning and creativity.

NETST.2.c: Customize and personalize learning activities to address students diverse learning

styles working strategies and abilities using digital tools and resources.

Unit Outcomes:

Students will solve multiplication and division of fractions by whole numbers and by fractions

on a post-assessment with 90% accuracy.

Specific Lesson Outcomes:

Lesson 1: The student will be able to solve multiplication fractions by whole numbers and by

fractions through the completion of pages 55 and 58 with 90% accuracy.

Lesson 2: The student will be able to solve division of fractions by whole numbers and by

other fractions through the completion of pages 61 and 64 with 90% accuracy.

Lesson 3a: The student will be able to apply knowledge of multiplying and dividing fractions

to problem solving with fractions through the completion of page 67 with 90% accuracy.

Lesson 3b: The student will be able to compare and contrast multiplying and dividing

fractions by producing a Venn diagram containing at least 4 similarities and differences.

Technology Outcomes:

1. Students will use technology to help them solve, mathematical problems and to assist them in

mastering the content.

Timeline:

Pre-Assessment: Topic Introduction – Page 11 in Appendix A – Tuesday October 16, 2012

Lesson 1:

Day 1: Multiplying fractions by whole numbers - Thursday October 18, 2012

Day 2: Multiplying fractions by fractions - Tuesday October 23, 2012

Lesson 2:

Day 1: Dividing Fractions by whole numbers - Thursday October 25, 2012

Day 2: Dividing fractions by fractions - Thursday November 1, 2012

Lesson 3:

Day 1: Problem Solving with Fractions – Thursday November 8, 2012


Post-Assessment: Topic Summary and Mixed Review (Problems 2 & 7) - Page 27 and 28

Appendix A -Tuesday November 13, 2012

Prior Knowledge:

The student just finished working with adding and subtracting fractions and has a strong mastery

of multiplication and division.

Analysis of Student:

As I am currently working only with students one on one, I choose one student to base this unit

around. Kasey (name changed) is an 8th

grade female, who was recommended to receive SRBI

support in math based on her STAR Math Winter and Spring 2012 benchmarks, as well as her

CMT scores (in 2011, 209 and in 2012, 215) . Her NWEA benchmark fell into the 24th

percentile

which is actually above the Tier III SRBI cut-off, but due to failing grades on quizzes and

assignments in math class and her CMT score is being kept in SRBI intervention until the end of

the quarter. Kasey’s strengths lie in that she is very hard-working and focused. A weakness is

that she tends to complete her assignments without always checking her work or thinking

through conceptually what she is doing. Kasey would benefit from a unit which shows her the

concepts behind the numbers and which has her verbalize or write the steps in the processes she

completes to have as a reference.


Lesson 1:

Goal:




CCSSM 5.NF.4 Apply and extend previous understandings of multiplication to multiply a

fraction or whole number by a fraction.

a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts;

equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a

visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this

equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of

the appropriate unit fraction side lengths, and show that the area is the same as would be

found by multiplying the side lengths. Multiply fractional side lengths to find areas of

rectangles, and represent fraction products as rectangular areas.




NETST.2.c: Customize and personalize learning activities to address students diverse learning

styles working strategies and abilities using digital tools and resources.

Lesson Objective:

The student will be able to solve multiplication fractions by whole numbers and by fractions

through the completion of pages 15-1C and 15-2C with 90% accuracy.

Materials:

Bedley, Tim. (2012). Cross-Simplify Fractions. Retrieved from

http://www.youtube.com/watch?v=0HfZcO3VPLg.

from http://nlvm.usu.edu/en/nav/frames_asid_194_g_3_t_1.html?from=search.html

Grade Math Help. Fraction Strips. Retrieved from http://www.gradeamathhelp.com/free-

fraction-strips.html (Adapted - Adding Elevenths Strip on Word, See Appendix A,

Page 10)

McGraw-Hill Wright Group. (2009). Pinpoint Math (Level G, Volume 3, Topic 15). Chicago,

Il.: McGraw-Hill. (Pages 12-17 in Appendix A).

National Library of Virtual Manipulatives. Fractions – Rectangle Multiplication. Retrieved

Lesson Initiation:

Student will review how to add and subtract fractions and predict if multiplying fractions will

use some of the same strategies or if it will be different.

Lesson Activities:

Day 1:

1. Students will complete 15-1A and 15-1B.

i. The teacher will model problem (Activity 1, 15-1A) using fraction strips.

ii. The student will then complete Practice 1 using fraction strips, with

teacher support.

http://www.youtube.com/watch?v=0HfZcO3VPLg

http://nlvm.usu.edu/en/nav/frames_asid_194_g_3_t_1.html?from=search.html

http://www.gradeamathhelp.com/free-fraction-strips.html

http://www.gradeamathhelp.com/free-fraction-strips.html


iii. The teacher will model problem (Activity 2, 15-1A) using the fraction

strips and explaining how the numerator, when added total the final

numerator over the original denominator.

iv. The student will then complete Practice 2 using fraction strips and

addition.

v. The student will complete On Your Own using the addition, without

teacher assistance.

vi. Student and teacher will verbally discuss the Write about It together, and

then write down their conclusion.

2. The same steps will be repeated on page 15-1B. When Activity 2 on 15-1B is reached,

the student will view the following video:

http://www.youtube.com/watch?v=0HfZcO3VPLg. The teacher will have the student

complete Practice 2, using the video as a reference and the provided steps.

3. On 15-1C, the students will independently solve problems 1, 3, 5 and 8, using the

technology as needed.

Day 2:

1. Students will complete pages 15-2A and 15-2B.

i. The teacher will model problem (Activity 1, 15-2A) using the fractions –

Rectangle multiplication manipulative found at

http://nlvm.usu.edu/en/nav/frames_asid_194_g_3_t_1.html?from=search.h

tml.

ii. The student will then complete Practice 1 using the rectangle

multiplication manipulative.

iii. The teacher will model problem (Activity 2, 15-2A) using the virtual

manipulative.

iv. The student will then complete Practice 2 using the manipulative.

v. The student will complete On Your Own using the technology, without

teacher assistance.

vi. Student and teacher will verbally discuss Write about It together, and then

the student will write down their conclusion.

2. The same steps will be repeated on page 15-2B. With Example 2 and Practice 2 the step

of changing mixed numbers to improper fractions will be explained.

3. On page 15-2C, the students will independently solve problems 1,2d, 4 and 6, using the


Lesson Closure:

The student will review and outline the steps taken to multiply fractions by whole numbers and

by other fractions.

Assessment:

- The student will complete pages 15-1C (problems 1, 3, 5 and 8) and 15-2C (problems

1,2d, 4 and 6) with 90% accuracy.

- List steps taken in solving multiplication of fractions

http://www.youtube.com/watch?v=0HfZcO3VPLg




Lesson 2:

Goal:






a. Interpret division of a unit fraction by a non-zero whole number, and compute such

quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction

model to show the quotient. Use the relationship between multiplication and division to

explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

b. Interpret division of a whole number by a unit fraction, and compute such quotients.

For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show

the quotient. Use the relationship between multiplication and division to explain that 4 ÷

(1/5) = 20 because 20 × (1/5) = 4.

CCSSM.6.NS. Apply and extend previous understandings of multiplication and division to

divide fractions by fractions.

1. Interpret and compute quotients of fractions, and solve word problems involving division

of fractions by fractions, e.g., by using visual fraction models and equations to represent the

problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction

model to show the quotient; use the relationship between multiplication and division to

explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.)

How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?

How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip

of land with length 3/4 mi and area 1/2 square mi?




NETST.2.a: Design or adapt relevant learning experiences that incorporate digital tools and

resources to promote student learning and creativity.

Lesson Objective:

1. The student will be able to solve division of fractions by whole numbers and by other

fractions through the completion of pages 15-3C and 15-4C with 90% accuracy.

Materials:

Khan Academy. Dividing Mixed Numbers. Retrieved from

http://www.khanacademy.org/math/arithmetic/fractions/v/dividing-mixed-numbers

McGraw-Hill Wright Group. (2009). Pinpoint Math (Level G, Volume 3, Topic 15). Chicago, Il.:

McGraw-Hill. (Pages 18-23 in Appendix A)

SMART Notebook File (“Kehoegreen Unit”).

Lesson Initiation:

The student will predict how multiplication and division of fractions will be similar and different

and if what she learned in regards to multiplication will carry over to division.

http://www.khanacademy.org/math/arithmetic/fractions/v/dividing-mixed-numbers


Lesson Activities:

Day 1:

1. Students will complete pages 15-3A and 15-3B.

i. The teacher will model problem (Activity 1, 15-3A) using slides 1-3.

ii. The student will then complete Practice 1 using question prompts and

number line on slide 4.

iii. The teacher will model problem (Activity 2, 15-3A) using slides 5-9. (Dr.

Tannahill, for your purpose, these slides have been broken down step by

step and the steps completed. However when teaching the lesson the steps

would be would be completed with the student).

iv. The student will then complete Practice 2 using the steps and number line

on slide 10.

v. The student will complete On Your Own using slide 11 with limited

teacher support.

vi. Student and teacher will verbally discuss Write about It together, and then

the student will write down their conclusions.

2. The same steps will be repeated on page 15-3B, watching the Khan Academy video from

1:09 to the end.

3. On page 15-3C, the students will independently solve problems 2, 3, 6 and 7, using the


Day 2:

1. Students will complete page 15-4A and 15-4B through the use of technology.

i. The teacher will model problem (Activity 1, 15-4A) using laminated pie

charts.

ii. The student will then complete Practice 1 using appropriate pie chart, with

teacher support.

iii. The teacher will use the model problem (Activity 2, 15-4A) to explain

how to find the reciprocal of the divisor and the change in operation that

occurs when going from division to multiplication.

iv. The student will then complete Practice 2 using by finding the reciprocal

of the divisor and then multiplying.

v. The student will complete On Your Own without teacher assistance.

vi. Students will verbally discuss Write about It together, and then write down

their conclusions.

2. The same steps will be repeated on 15-4B, focusing on canceling factors. If the student is

confused or needs reminders on how to do this, they can re-watch the video or look back

problems they have already completed.

3. On page 15-4C, the students will independently solve problems 1b, 2d, 3 and 8, using the


Lesson Closure:

The student will detail the steps you have to take to solve division of fraction problems.

Assessment:

- Completion of pages 15-3C (problems 2, 3, 6 and 7) and 15-4C (problems 1b, 2d, 3 and

8) with 90% accuracy.

- Listing steps in solving division of fractions


Lesson 3:

Goal:




CCSSM 5.NF.6 Solve real world problems involving multiplication of fractions and mixed

numbers, e.g., by using visual fraction models or equations to represent the problem.



c. Solve real world problems involving division of unit fractions by non-zero whole

numbers and division of whole numbers by unit fractions, e.g., by using visual fraction

models and equations to represent the problem. For example, how much chocolate will

each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup

servings are in 2 cups of raisins?

NETSS.3.c: Students evaluate and select information sources and digital tools based on the

appropriateness to specific tasks.

Lesson Objective:

1. The student will be able to apply knowledge of multiplying and dividing fractions to

problem solving with fractions through the completion of page 67 with 90%

accuracy.

2. The student will be able to compare and contrast multiplying and dividing fractions

by creating a Venn diagram containing at least 4 similarities and differences.

Materials:

McGraw-Hill Wright Group. (2009). Pinpoint Math (Level G, Volume 3, Topic 15). Chicago, Il.:

McGraw-Hill. (Pages 24-26 in Appendix A)

Lesson Initiation: The student will review multiplication of fractions and predict how division of

fractions might build on division or be similar.

Lesson Activities:

1. Students will complete page 15-5A and 15-5B figuring out whether the problem will

be solved using addition, subtraction, multiplication or division by looking for key words

such as “in all” (addition), or “how much more” (subtraction).

i. The teacher will model problem (Activity 1, 15-5A) using fraction strips.

ii. The student will then complete Practice 1 using fraction strips, with

teacher support.

iii. The teacher will model problem (Activity 2, 15-5A) using equivalent

fractions.

iv. The student will then complete Practice 2 with teacher support.

v. The student will complete On Your Own using equivalent fractions,

without teacher assistance.

vi. Students will verbally discuss Write about It together, and then write down

their conclusions.


2. The same steps will be repeated on page 15-5B, figuring out whether the problem will be

solved using addition, subtraction, multiplication or division by looking for key words

such as “times” (multiplication), “How many can..” (Division).

3. On page 15-5C, the students will independently solve problems 1, 4, 6, and 7, using

various technology as needed. They will have to decide whether they are using

multiplication or division and will decide which technologies will be appropriate to use

for each problem.

Lesson Closure:

The student will outline in writing the steps taken to solve division of fractions by whole

numbers and by other fractions. The student will then compare and contrast multiplication and

division through the use of a Venn diagram.

Assessment:

- Completion of page 15-5C (Problems 1, 4, 6, and 7) with 90% accuracy.

- Compare and contrast multiplying and dividing fractions by producing a Venn diagram

containing at least 4 similarities and differences


Appendix A: Materials

Lesson 1: Fraction Strips:

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11

1 11


Packet:

Topic Introduction


15-1A


15-1B


15-1C


15-2A


15-2B


15-2C


15-3A


15-3B


15-3C

15-4B


15-4A


15-4B


15-4C


15-5A


15-5B


15-5C


Topic

Summary


Mixed

Review

unit: ccssm 5.nf - wordpress.com€¦ · unit 3 assessment kehoegreen 1 unit: goal: students will...

Documents