This document provides information and resources for teaching fractions to 4th grade students. It discusses common core standards for fractions, learning targets, conceptual understanding students need, fraction word problems, using bar diagrams to solve problems, fraction representations including strips and number lines, defining fractions, strategies for comparing fractions, generating equivalent fractions, and multiplying fractions by whole numbers. Resources included are videos, websites, and book references to support fraction instruction.
HW. 2 Cooperative LearningReadings and Handouts· Johnson, D. W.NarcisaBrandenburg70
HW. 2 Cooperative Learning
Readings and Handouts:
· Johnson, D. W., Johnson, R. T., & Holubec, E. J. (1994). Cooperative learning in the classroom. Association for Supervision and Curriculum.
· Gillies, R. (2003). Structuring cooperative group work in classrooms. International Journal of Educational Research, 39(1),35-49.
· Mirrored Tiles Lesson Plan, Handout & Answers
Videos
· Incorporating Cooperative Learning Effectively (7:39 mins.) Social Studies Clips
https://www.youtube.com/watch?v=5PquzYeaex4
· Where Cooperative Learning Works: Increasing Classroom Interaction and Integrating Skills (ESL Lesson 43:46 mins.)
https://www.youtube.com/watch?v=iIiENACsEwo
Respond to Questions:
(1) Based on the Cooperative Learning Reading by Johnson, Johnson and Holubec (1994). Respond to the following:
(a) Why use cooperative learning? What is different between formal cooperative learning and informal?
(b) What are 5 essential elements of cooperative learning? Discuss what each means in your own words and why it is important.
(c) What do teachers need to know about monitoring and intervening when students are working in cooperative groups?
(2) Based on Gillies (2003) article on Structuring cooperative group work in classrooms, respond to the following:
(a) What are key research findings about cooperative learning? To what extent are these findings important for teachers, including yourself? Explain why.
(b) What theoretical perspective(s) inform cooperative learning research and practice?
(c) To what extent are findings in the reading similar to those reported in the short Video—Incorporating Cooperative Learning Effectively.
(3) Read the Mirrored Tiles Lesson Plan and provide specific examples to explain in what ways each of the five key elements of cooperative learning are evidenced (or not) in the lesson plan. If any of the five elements are not addressed, point those out and explain your observation; then suggest a way that it might be addressed in the lesson plan.
(4) Watch the Video Lesson—Where Cooperative Learning Works. Provide specific examples to explain in what ways each of the key five elements for cooperative learning are evidenced (or not) in the lesson. If any of the five elements are not addressed, point those out and explain your observation; then suggest a way that it might be addressed in the lesson. (As you observe the video, watch for teacher interactions with the groups (e.g., How does the teacher promote group interactions? Some teachers exchange communications with individual students (as if it was an individual task) rather than addressing the entire group when a member asks a question or when the teacher has a question or comment. This does not model cooperation in the group to the students.)
(5) What questions or concerns do you still have about using cooperative learning through the implementation of the 5 key elements that other classmates may respond to?
Rai2
Unit 2 Discussion Board Post: The Progressi ...
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Major Assignment 3 (Presentation)
Spring Semester 2020
English 272 T. Stuckert, Instructor
English 272: Introduction to Technical Communication
Major Assignment 3: Presentation
Information – Spring 2020
Important Note: Presentations similar to this one have been developed by students in previous semesters in this course as well as other Intro to Technical Communication courses. Remember that plagiarism on this assignment will not be tolerated. This includes copying text, slides, and/or graphics from another student’s work (from this semester or a previous semester) as well as incorrectly citing, paraphrasing or quoting information.
If you will be completing this as a collaborative assignment, it may be difficult to determine which group member is responsible for presentation content that contains plagiarized information. Because of this, all members of group will suffer the consequences of plagiarism. It is the responsibility of all group members to review the content of this assignment to insure that none of the work has been plagiarized.
Review the information on the University’s Honor Code and Academic Honesty Academic Integrity policies in the Syllabus for more information on this issue.
IMPORTANT NOTE: You are required to develop a PowerPoint presentation for MA3. DO NOT develop a presentation using Prezi or any other slideware (such as Google slides). You will receive zero (0) credit for a presentation that is in a format other than PowerPoint.
Introduction
The purpose of this assignment is to give you an opportunity to apply many of the concepts you have learned throughout the semester. The assignment will involve planning and developing a PowerPoint presentation. You will not deliver or present the PowerPoint to an audience. However, your presentation must be designed so it would be effective if it were presented in both of these situations:
· in-person presentation with the speaker and audience present
and
· digital presentation viewed by the audience on a digital device (without recorded audio narration)
It is very important to remember this when designing your presentation.
Designing the presentation so it will be successful in both situations will impact slide design and content. Remember, explanations of graphics and slide content that would be provided verbally with an in-person presentation must be provided in the slide content for a digital presentation that does not make use of recorded audio narration.
Presentation Goal and Topic
Your goal and topic for the presentation will be the same as your goal and topic for Major Assignment 1: Provide information for a general reader audience with an interest in the subject matter but little o.
Math Resources! Problems, tasks, strategies, and pedagogy. An hour of my 90-min session on math task design at Cal Poly Pomona for a group of teachers (mainly elementary school).
Distance Learning, Online Teaching [19+ Years]
• Possess substantial strengths in distance learning, adult education, teaching with technology, student and faculty relations, higher education, and curriculum development.
• Significant experience as an adjunct online faculty member, Core Faculty, Dissertation Chair, Committee Member, Curriculum Developer/Author, and Faculty Development Manager.
• Create a safe, respectful, and welcoming learning environment.
• Specialize in working with new students, first generation students, and academically under-prepared students.
• Developed an exceptional record of academic excellence, end-of-course evaluations, collaboration, communication, mentoring, coaching, and professionalism.
• Computer proficient with online classroom platforms that include WebCT, eCollege, Canvas, Sakai, Moodle, Educator, Desire2Learn, Blackboard, Brightspace and others.
Dissertation Chair and Mentor [Remote, 11+ years]
• Provide high quality instruction, direction and mentorship for assigned students throughout all phases of the dissertation process.
• Provide timely and supportive mentoring throughout the student’s process of developing, researching, writing, and revising the dissertation.
• Participate in the Defense process of a student’s Prospectus and final Dissertation.
• Facilitate the successful completion of all IRB protocols.
Faculty Development [Remote, 10+ years]
• Served as a Trainer and Mentor for New Faculty Members.
• Performed faculty peer reviews and assessed classes based upon best practices and adult learning theories.
• Inspired faculty to improve their facilitation practice by leading online faculty workshops.
Curriculum Development [Remote, 12+ years]
• Authored hundreds of courses as a SME for multiple schools, including undergraduate and graduate courses.
• Strong knowledge and application of adult cognitive learning theories and instructional design methodologies.
• Develop content and assessments that met learning objectives, including discussions and assignments.
Background Includes: Various Online Schools (08/05 – Present)
Online Instructor, Doctoral Committee Member, Dissertation Chair, Faculty Development, Curriculum Development.
Today’s Number Daily Math Routine Todays Number is 12.5(This TakishaPeck109
Today’s Number Daily Math Routine
Todays Number is 12.5%
(This is sometimes called “N(umber of the Day”)
Daily Math Routines are a set of 5-7 minutes math routines that are done daily. They are designed to develop number sense and other mathematical reasoning by connecting critical math concepts on a daily basis.
Next week you will be asked to share the Today’s Number Daily Math Routine with your small group. This assignment is designed to help you become an expert on the Daily Math Routine.
A. Learn about “Today’s Number”
1. Read about “Today’s Number” (Today’s number is 12.%) 5 from this handout from NCCTM. Respond to the questions below as you begin reading on page 5.
2. Give a brief overview of the Today’s Number routine.
3. How does this number routine support students in growing in their mathematical thinking?
4. What are some ways the number of the day can be presented to students in each of these settings?
d. Early Elementary
d. Later Elementary
1. How might teachers structure the Today’s Number routine for older students?
1. What does the teacher do while older students are generating their representations?
1. What are some ways in which teachers can keep an ongoing record of student responses to the Number Routine? How might these records be used by students and teachers in the future?
1. Though the number used in Today’s Number will change across grade levels, consistent use of the routine across grade levels will continue to enhance student’s number sense. What is meant by number sense? Why is number sense important?
1. What are some common models that can be used across grade levels as students participate in Today’s Number? Provide examples of each.
1. Why is it important to allow students to share their representations with each other?
1. One of the hardest parts of this number routine for teachers is knowing what to look for in student work and how to highlight important mathematical concepts. What are some common big ideas to look for when examining student work?
B. Considering Grade Level Appropriateness
Go back to Page 3 from this handout from NCCTM.and spend some time thinking about the 3 examples given.
a. 1st Grade-
i. Share 3 others ways you might anticipate 1st graders would represent 15.
ii. Label each representation with the mathematical concept they represent.
b. 5th Grade
i. Share 3 other ways you might anticipate 5th graders would represent ¾?
ii. Label each representation with the mathematical concept they represent
c. 7th Grade
i. Share 3 other ways you might anticipate 5th graders would represent -8?
ii. Label each representation with the mathematical concept they represent
C. Watch a “Today’s Number” Daily Math Routine in an Intermediate classroom.
1. Before you begin, take 1 minute to show 135 in as many ways as you can. Record you thinking below.
2. Now watch this video and respond to the prompts below.
3. What prompt did the student use for the “Today’s Number Routi ...
1 Saint Leo University GBA 334 Applied Decision.docxaryan532920
1
Saint Leo University
GBA 334
Applied Decision Methods for Business
Course Description:
This course explores the use of applied quantitative techniques to aid in business-oriented decision
making. Emphasis is on problem identification and formulation with application of solution techniques and
the interpretation of results. Included are probability theory; decision making under certainty, risk and
uncertainty; utility theory; forecasting; inventory control; PERT/CPM; queuing theory; and linear
programming.
Prerequisite:
MAT 201
Textbook:
Saint Leo University. (2013), Quantitative analysis (custom). Boston, MA: Pearson Learning
Solution
s.
eBook with print upgrade option – ISBN: 978-1-269-86314-8
You will access the eBook via a link in the Course Home menu, where you can purchase the print
upgrade option.
Software
The use of statistical software is a required component in this course. It is expected that you already have
a basic understanding of computers and Microsoft Excel. In-depth training is provided during the course
on the appropriate use of the following packages:
TreePlan-Student-179 Excel Add In
Excel QM, version 4
POM QM, version 4
Analysis Tool Pack for Microsoft Excel must be activated
To access the information needed to install the software, click the Software Installation Information link
located under Resources in the course menu.
Learning Outcomes:
At the completion of the course you should be familiar with several decision methods of decision-making
in a business environment. You will find that almost every type of problem to which you will be exposed in
the business world has been explored and methods of solving them have been devised. You should be
able to apply these methods to the real-world situations in which you will one day find yourself. The skills
developed during this class include:
1. Explain the key attributes and differences between the normal, standard normal, and binomial
distribution of variables.
2. Identify and explain the underlying assumptions, key variables, theoretical basis, and solution
techniques for the following decision-making problems:
a. Decision Analysis
b. Probability Theory and Analysis
c. Regression Analysis
d. Forecasting Methods
e. Inventory Control Methods
f. Project Management (including PERT/CPM)
g. Network Models
h. Queuing Theory
i. Linear Programming Approaches and the Transportation and Assignment Special Cases
j. Statistical Process Control
2
3. Formulate and execute a solution to a variety of decision-making problems using computer
software.
4. Identify, explain, and interpret the key areas of computer output for the various decision-making
problems.
5. Apply one of the approaches covered in class to a real-world issue and present the findings.
6. VALUES OUTCOME: Demonstrate the core value of excellence by adequately preparing for
each class session, actively participating in cl ...
Similar to 4th grade multi.div word problems and fractions pd (20)
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TESDA TM1 REVIEWER FOR NATIONAL ASSESSMENT WRITTEN AND ORAL QUESTIONS WITH A...
4th grade multi.div word problems and fractions pd
1. 4th
Grade
Word Problems and
Fractions
Laura Chambless
RESA Consultant
www.protopage.com/lchambless
2. CCSS and Gaps
What are your gaps in curriculum?
1. Review CCSS for Fractions
2. Think about your resources
3. Think about your teaching
– Highlight anything your resources
covers well in YELLOW.
– Highlight any part of the standard you
would like more clarification on in
BLUE.
3. Learning Target
Extend understanding of fraction
equivalence and ordering.
4.NF.1, 4.NF.2
Build fractions from unit fractions by
applying and extending previous
understandings of operations on
whole numbers.
4.NF.3, 4.NF.4
4. Fractions
What conceptual understanding do students need?
1. Begin with simple contextual tasks.
2. Connect the meaning of fraction computation with
whole number computation.
3. Let estimation and informal methods play a big role in
the development of strategies.
4. Explore each of the operations using models.
Van De Walle Book: Number Sense and Fraction
Algorithms
5. Fraction Word Problem
40 students joined the soccer club.
5/8 of the students were boys.
How many girls joined the soccer
club?
Draw a picture and solve it.
1. 2 min. working problem on own
2. 5 min. sharing with group
3. Class discussion
Found at: http://www.mathplayground.com/wpdatabase/Fractions1_3.htm
6. Problem Solving with
Bar Diagrams
1. Understand: Identify what is known and what is
unknown. Draw the bar diagram to promote
comprehension and demonstrates
understanding. (Situation vs. Solution Equation)
2. Plan: Decide how you will solve the problem
(find the unknown). Analyze the bar diagram to
find a solution plan.
3. Solve: Execute the plan. Use the bar diagram to
solve.
4. Evaluate: Assess reasonableness using
estimation or substitution. Substitute the
solution for the unknown in the bar diagram.
7. Bar Diagrams
Watch Introduction Video
http://www.mhschool.com/math/com
mon/pd_video/mathconnects_bardi
agram_p1/index.html
http://www.mhschool.com/math/com
mon/pd_video/mathconnects_bardi
agram_p2/index.html
8. Practice Bar Diagrams
To: Rani earned $128 mowing lawns and $73
babysitting. How much money did Rani earn?
With: Jin had $67 in his pocket after he bought a
radio controlled car. He went to the store with
$142. How Much did Jin spend on the car?
By: There are 9 puffy stickers. There are 3 times
as many plain stickers as puffy stickers. How
many plain stickers are there?
You pick 2 more to do by yourself. Share with
partner
Draw Your Way to Problem Solving Success Handout, Robyn Silbey
10. Fractions
Stand and Share
Make a list of what you know and any
connections you have about the
fraction ¼.
11. Representations
(Part 2 video, 5:16)
Set Purpose of video: List why representations are
important in the classroom.
•Representations are mathematics content representing
mathematical ideas is a practice that students need to learn.
•Representations provide tools for working on mathematics
and contribute to the development of new mathematical
knowledge.
•Representations support communication about mathematics.
•Using multiple representations can help develop
understanding and support the diverse needs of students.
From: Dev-TE@M session 2
12. Examining Representations
(Part 3 & 4 Video 1:48/2:15)
Set Purpose of videos: listen to the set up of your task and
example.
1. Examining Representations of ¾ with
a partner (10 min)
2. Whole group discussion
3. Review math notes
From: Dev-TE@M session 2
13. Making Connections
(Part 6 video, 2:22)
Set Purpose of video: think about our discussion of ¾,
what connection types did we use?
Have you ever used connections for
the different math representations
in your classroom?
From: Dev-TE@M session 2
14. Benefit of Representations
(Part 4 video, 2:17)
Set Purpose of video: Did you benefit from our
discussions, and how will your students benefit from
class discussions?
1. As you listen , list benefits for
students
2. Compare list with partner
From: Dev-TE@M session 3
15. Definition of Fractions
1. Make a list of what you would like
to have in a definition of a fraction
2. Partner up and compare lists
3. Group discussion
From: Dev-TE@M session 3
16. Definition of a Fraction
(Part 5 and 6 videos, 11:48/4:27)
Set Purpose of video: What are some key parts in
creating a definition of a fraction that you will use in
your room?
– Give handout of working definition
Article: Definitions and Defining in
Mathematics and Mathematics Teaching
by: Bass and Ball
From: Dev-TE@M session 3
17. Definition Of Fractions
• Identify the whole
• Make d equal parts
• Write 1/d to show one of the equal
parts
• If you have d of 1/d, then you have the
whole
• If you have n of 1/d, then you have n/d
• n and d are whole numbers
• d does not equal 0
Dev-TE@M • School of Education • University of Michigan • (734)
408-4461 • dev-team@umich.edu For review only - Please do not
circulate or cite without permission
20. Fractions
Fraction Activity
Paper Strips Fraction Kit:
1, ½, 1/4 , 1/8, 1/16
Add to Fraction Kit: 1/3, 1/6, 1/12
Add to Fraction Kit: 1/5, 1/10
Compare/Add/Subtract/with Strips
READ and DO:4.NF.3a, 4.NF.3b, 4.NF.3c
Play Greater Than, Less Than, Equal
• Prove with Fraction Strips
21. Ordering Fractions
Order Fractions
8/6, 2/5, 8/10, 1/12
How did you figure out what order
they went in?
22. Fractions
Prove with Fraction Strips
Number Line: (Benchmarks) 0, ½, 1
Compare (>/<): same numerator or same
denominator
Equivalent Fractions: Same Name Frame
23. Strategies for Comparing
Fractions
Key points
• The following practices are helpful when
analyzing students’ work on tasks:
• Anticipate the strategies and representations
students may use.
• Identify the strategies students did use. If the
student used a different strategy than
predicted, consider if is it a fitting choice.
• If the strategy is unfamiliar, explore whether or
not the strategy is mathematically valid.
• Identify questions to ask the student about
her/his strategy or new problems to pose that
would further reveal her/his understanding.
From: Dev-TE@M session 9
24. Strategies for Comparing
Fractions
Math Notes: Strategies for Comparing
Fractions
Which strategies do you
use in your classroom?
From: Dev-TE@M session 9
25. Fraction On A Number Line
Writing about Fractions:
Draw a number line.
Place 3/6 and 7/12 on the number line.
Compare the two fractions- why did put
them where you did?
26. Key Ideas About the Number
Line
What were some intentional talk
moves others used to explain their
number line?
(Part 5 video, 5:26)
Set purpose of video: Listen to the detail that is given in
explaining how to construct a number line.
From: Dev-TE@M session 4
27. Conventions Of A Number Line
Dev-TE@M • School of Education • University of Michigan • (734) 408-4461 •
dev-team@umich.edu For review only - Please do not circulate or cite without
permission From: Dev-TE@M session 4
28. Talking Through A Number Line
1. Understand the problem.
2. Think about which representation you
are going to use.
3. Describe your thinking process while
constructing the number line.
4. Sum up the solution that proved your
answer.
Model Example: 3/10 & 6/8
29. Fraction On A Number Line
Using a number line, compare 5/6 and
3/8 and tell which one is greater .
Have a partner listen to you as you
construct the fractions and find the
answer.
30. Student Errors
What value should be written
where the arrow is pointing?
What would kids write?
Session 4-6: Analyzing students’ errors when
labeling marked points on the number line- see
slides
From: Dev-TE@M session 4
31. Student Errors
Key points
When determining how to respond
to a student, it can be helpful to
consider:
• What question(s) could be asked to
learn more about the student’s
thinking?
• What key mathematical idea(s) might
be raised with the student?
32. Narrating a Representation
• Make clear the mathematical problem
or context.
• Describe how a particular
representation is useful for this
problem.
• Construct the representation and use it
to solve the task while describing and
giving meaning to each step.
• Summarize what the representation
has helped to do.
From: Dev-TE@M session 5
33. Number Lines
(Part 2 video, 1:21)
Set purpose of video: listen to directions and practice
narrating on the number line.
Partner Work
Compare ¾ and 4/3
From: Dev-TE@M session 5
34. Number Lines
(Part 3 video, A 3:32/C 1:29/ E :28)
Set purpose for video: Where are the problems when
narrating the number line?
(Part 5 video, 4:24)
Set purpose for video: review narration
(Part 6 video, 1:53)
Set purpose for video: What fractions do you use for
examples
From: Dev-TE@M session 5
36. Add/Subtract Fractions with
Unlike Denominators
Developing Equivalent Fractions
• Slicing Squares
Van de Walle book: pg. 304-305
3 x = 3 x
4 =
4
3 x 3 x =
= 4
4
37. Developing Equivalent
Fractions
Missing-Number Equivalencies
Van de Walle book: pg. 304-305
5 2 6
= =
3 6 3
38. Methods for Generating and
Explaining Equivalent Fractions
Math Notes: Methods for Generating and
Explaining Equivalent Fractions
Pair Share
1. Partner 1: Reads - Reasoning about
equivalent fractions using an area model
2. Partner 2: Reads - Reasoning about
equivalent fractions using a number line
3. One minute report
4. Report on how your model was different
than your partners.
From: Dev-TE@M session 9
39. Fractions
Multiply a fraction by a whole number
READ and DO: 4.NF.4a, 4.NF.4b
• Work as a group
• Use Fraction strips to show answers
4 x 1/3
¼ x 12
• What connection can you make to
multiplication? What other
representations can you use? Can you
use a number line?
40. Multiple a Fraction by a Whole
Number
4 x 1/3 (4 groups of 1/3) = 4/3 = 1 1/3
I want 4 ribbons each at 1/3 of a yard. How much
ribbon will I need to purchase?
1/3 2/3 3/3 4/3
¼ x 12 (1/4 of 12) = 3
I have 12 cookies and want each of my friends
to have ¼ of them. How many cookies will
each friend get?
41. MOPLS
http://mi.learnport.org
Search: MOPLS Math
(navigate by using top tabs)
Look at Concepts Tab
– Introduction
– Math Behind the Math
– Misconceptions
– Tasks & Strategies
43. Learning Target
Extend understanding of fraction
equivalence and ordering.
4.NF.1, 4.NF.2
Build fractions from unit fractions by
applying and extending previous
understandings of operations on
whole numbers.
4.NF.3, 4.NF.4
45. Thanks for a great day
Please contact me if you have any questions or
would like more information.
Editor's Notes
Activity 15.8Slicing SquaresGive students a worksheet with four squares in a row, each approximately 3 cm on a side. Have them shade in the same fraction in each square using vertical dividing line. You can use the context of a garden or farm. For example, slice each square in fourths and shade three-fourths as in Figure 15.20. Next, tell students to slice each square into equal-sized horizontal slices. Each square must be partitioned differently, using from one to eight slices. For each sliced square, they record an equations showing the equivalent fractions. Have them examine their equations and drawings to look for any patterns. You can repeat this with four more squares and different fractions.What product tells how many parts are shaded?What product tells how many parts in the whole?Notice that the same factor is used for both part and whole
Give students an equation expressing an equivalence between two fraction but with one of the numbers missing and ask them to draw a picture to solve. Here are four different examples:5/3 = _/62/3 = 6/_8/12 = _/39/12 = 3/_The missing number can be either a numerator or a denominator. Furthermore, the missing number can either be larger or smaller that the corresponding part of the equivalent fraction. (All four possibilities are represented in the examples.) The examples shown involve simple whole-number multiples between equivalent fractions. Next, consider pairs such as 6/8 = _/12 or 9/12 = 6/_. In these equivalences, one denominator or numerator is not a whole number multiple of the other.
