Here are some key methods for generating and explaining equivalent fractions:
- Using a visual model like a number line, fraction strips, or area model to show that fractions representing the same quantity or portion are equivalent.
- Using the definition of a fraction to explain that equivalent fractions have the same value since they represent the same parts out of the whole.
- Generating equivalent fractions algebraically by multiplying/dividing the numerator and denominator by the same quantity.
- Explaining that equivalent fractions can be used interchangeably since they name the same fractional amount.
- Having students generate equivalent fractions and explain/prove their equivalence using visual models and the definition of a fraction.
The goal is building understanding that equivalent fractions
Have you ever dreamed of teaching a pre-calculus level course where the algebraic manipulation is de-emphasized and the emphasis is shifted to conceptual understanding and practical skills that directly apply to transfer classes? Learn how your wishes can come true by making simple changes around curriculum, pedagogy, and technology.
Have you ever dreamed of teaching a pre-calculus level course where the algebraic manipulation is de-emphasized and the emphasis is shifted to conceptual understanding and practical skills that directly apply to transfer classes? Learn how your wishes can come true by making simple changes around curriculum, pedagogy, and technology.
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 ...
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).
Socially Shared Metacognition in CSCL PlanningMariel Miller
Socially Shared Metacognition: Convergence & Divergence in CSCL Planning
Allyson Hadwin, Mariel Miller, Elizabeth Webster, Philip Winne
Paper presented at the EARLI 2011, Exeter, UK
Change is happening in Pre-College Mathematics! Pressure is mounting to get students into certification and degree bearing tracks. The GED now demands more conceptual math understanding as well as more algebraic content. How Can Faculty Address These Shifts? After a brief overview of institutional responses, Carren Walker of Collaborative for Ambitious Mathematics presents online resources to support teachers who seek to change both content and pedagogy in their courses, with a focus on active learning and formative assessment and specific examples of tasks and approaches. Watch the Blackboard Collaborate Recording of "Transforming the Classroom through the Standards for Mathematical Practice."
Language in the Math Classroom; A Workshop for Mathematics and Special Educators focuses on ways in which middle- grades math and special education teachers can support students with the language demands of the middle grades math classroom. This presentation is part of a broader workshop for educators. More information at http://middlegradesmath.org
PAGE
- 8 -
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.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
2024.06.01 Introducing a competency framework for languag learning materials ...
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
Math Notes: Strategies for Comparing
Fractions
Which strategies do you
use in your classroom?
From: Dev-TE@M session 9
24. 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?
25. 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
26. 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
27. 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
28. 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.
29. 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
30. 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?
31. 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
32. Number Lines
(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
34. 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
35. Developing Equivalent
Fractions
Missing-Number Equivalencies
Van de Walle book: pg. 304-305
5 2 6
= =
3 6 3
36. 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
37. 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?
38. 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?
39. 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
41. 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
43. 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.