Taking the Pizza Out of Fractions discusses the importance of fractions and strategies for teaching them effectively to students. It emphasizes starting with equal sharing problems to draw on students' natural understanding of fair partitioning. Using different models like regions, lengths, and sets can help clarify fractional concepts. Problem solving strategies like bar modeling provide visual representations to solve word problems. Hands-on learning allows students to construct their own understanding rather than just memorizing procedures.
These slides are from a webinar on why reading mathematics is challenging for many students and what teachers can do. We will examine how mathematics symbols, vocabulary, and content presentation can create roadblocks to students’ mathematics understanding. Learn how to address students’ difficulties by approaching mathematics as a language and to use specific strategies to improve mathematics learning.
These slides are from a webinar on why reading mathematics is challenging for many students and what teachers can do. We will examine how mathematics symbols, vocabulary, and content presentation can create roadblocks to students’ mathematics understanding. Learn how to address students’ difficulties by approaching mathematics as a language and to use specific strategies to improve mathematics learning.
Teaching Mathematics to English Language Learners admills
This session will present strategies to help teachers teach mathematics to English language learners including hands-on differentiation activities for teachers to do in the session.
Hand out from Defining Roles and the Necessary Skills for the 21st Century Paraeducator Given by Mindy Speichler and Cecilia Laughlin at NRCP conference April 1-3, 2016
Teaching Mathematics to English Language Learners admills
This session will present strategies to help teachers teach mathematics to English language learners including hands-on differentiation activities for teachers to do in the session.
Hand out from Defining Roles and the Necessary Skills for the 21st Century Paraeducator Given by Mindy Speichler and Cecilia Laughlin at NRCP conference April 1-3, 2016
Hand out from Defining Roles and the Necessary Skills for the 21st Century Paraeducator Given by Mindy Speichler and Cecilia Laughlin at NRCP conference April 1-3, 2016
Hand out from Defining Roles and the Necessary Skills for the 21st Century Paraeducator Given by Mindy Speichler and Cecilia Laughlin at NRCP conference April 1-3, 2016
308. Don't FAL out;Techno IN!
This session will share several formative assessment lessons, activities and strategies that we have used within our classes as well as technology resources we have found very useful. Handouts are available online. You will feel like a kid leaving a candy shop!
Presenter(s): Jo Harris, Olivia Valk, Cody Powell
Location: Biltmore
Hands On Fractions- Using Manipulatives in Math InstructionJamie Carberry, MEd
This presentation was delivered district-wide in Cobb County, GA. It focused on informing staff about a new program that was purchased from the math department, and included ways teachers can use fraction manipulatives to increase student achievement in mathematics instruction
Creating Mathematical Opportunities in the Early Years
Presenter, Dr Tracey Muir, for Connect with Maths Early Years Learning in Mathematics community
As teachers, we are constantly looking for ways in which we can provide students with mathematical opportunities to engage in purposeful and authentic learning experiences. On a daily basis we need to select teaching content and approaches that will stimulate our children through creating contexts that are meaningful and appropriate. This requires a level of knowledge that extends beyond content, to pedagogy and learning styles. As early childhood educators, we can also benefit from an understanding of how the foundational ideas in mathematics form the basis for key mathematical concepts that are developed throughout a child’s school.
In this webinar, Tracey will be discussing the incorporation of mathematical opportunities into our early childhood practices and considering the influence of different forms of teacher knowledge on enacting these opportunities.
The workshop will provide middle level mathematics teachers with ideas for engaging students in the understanding of math concepts and the creative aspects of mathematics topics in the 6-8 curriculum. The workshop will be hands-on and based upon a constructivist approach to learning and teaching. Handouts will be provided.
Presenter(s): Shirley Disseler
KUD Lesson Planning TemplateGrade LevelPre-Kindergarten and ki.docxsmile790243
KUD Lesson Planning Template
Grade Level
Pre-Kindergarten and kindergarten (3-4) because I believe this is the most appropriate age for students to begin to learn numbers in different ways
Instructional Model
I will use the direct instruction model is applied in this case because it allows explicit and straightforward teaching techniques and allows high levels of student involvement (Huitt, 2003). I also chose this method because the class will be grouped in small and large groupings, which will allow room for explaining and provides the students opportunities to practice.
Standards
CCSS.MATH.CONTENT.K.CC.B.4
Know the connection between numbers and quantities; link counting to cardinality (Common Core State Standards Initiative, n.d.)
Objectives
Students will understand
· Students will understand that number can be shown in multiple methods such as numerals, dots, and tallies
Students will know
· Students will know the sequence of numerals from 1-10
· Students will know how the relationships among numbers and the number system
·
Students will be able to
· Students will be able to sum loud successively from 1-10
· Students will be able to match digits to objects from 1-10
· Students will be able to recognize numerals 1-10 in isolation
· Students will be able to use one-to-one correlation when counting
· Students will be able to write digits from 1-10, draw dots, tallies to signify the number of items counted
·
Assessment Plan
Formative:
I will write the numbers 1-10 on a four-index card and assign the students in four groups and each group will have a teacher. In this assessment, the teacher will remind the students to write their names on their paper. This will be followed by the teachers instructions on the grab and count game. I will show the students how to play the game, which involves the taking counters, placing them in a line them and counting them by utilizing one-to-one correlation . The students will have the opportunity to; first grab the counters and count and then count the set again for accuracy. They students will also say the number they counted last and write the number in the first square either a tally, a dot or a numeral. The game involves four squares and the students will have the opportunity to show how group of items can be represented in three diverse ways.
This exercise will allow me to evaluate the student’s attention during the assembly and their knowledge of the class. By assessing their question sheet and listening to their explanations of how they write the counted items.
Summative:
Students will work independently and with the assistance of the teacher to write their names on top of their paper grab and count objects in this activity. The teacher observes and provides feedback when required.
This will allow the teacher to assess the child’s motor abilities and skills, how they write numerals, how they hold their pencils and assists them where necessary.
Procedure
1. Review previously learned m ...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
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
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!
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
1. Taking the Pizza Out of Fractions
BECKY UNKER, M.ED.
EDUCATION SPECIALIST, SPECIAL EDUCATION
UTAH OFFICE OF EDUCATION
BECKY.UNKER@SCHOOLS.UTAH.GOV
2. Why Are Fractions So Important?
• Proficiency with fractions is an important foundation for learning more advanced
mathematics.
• Fractions are a student’s first introduction to abstraction in mathematics and, as such,
provide the best introduction to algebra in the elementary and middle school years.
• Time and emphasis are necessary for students to develop the links among fractions,
decimals, and percent's and solve problems involving their use.
Francis (Skip) Fennell, NCTM President 2006-2008
NCTM News Bulletin, December 2007
3. The Big Ideas in Fractions…
• Fractional parts are equal shares or equal-sized portions of a whole or unit. A unit can
be an object or a collection of things. More abstractly, the unit is counted as 1. On the
number line, the distance from 0 to 1 is the unit.
• Fractional parts have special names that tell how many parts of that size are needed to
make the whole. For example, thirds require three parts to make a whole.
• The more fractional parts used to make a whole, the smaller the parts. For example,
eighths are smaller than fifths.
4. Big Ideas continued
• The denominator of a fraction indicates by what number the whole has been divided in
order to produce the type of part under consideration. Thus, the denominator is a
divisor. In practical terms, the denominator names the kind of fractional part that is
under consideration. The numerator of a fraction counts or tells how many of the
fractional parts (of the type indicated by the denominator) are under consideration.
Therefore, the numerator is a multiplier—it indicates a multiple of the given fractional
part.
• Two equivalent fractions are two ways of describing the same amount by using
different-sized fractional parts. For example, in the fraction 6/8, if the eights are taken
in twos, then each pair of eights is a fourth. The six-eights then can be seen to be three-
fourths.
6. • The white parts shows
what part of this
brownie Joe ate. How
much of the brownie
was eaten?
7. Two Students Responses:
FIRST GRADER:
• A first grader studied the
picture for a moment and
then said the missing piece
was “half of a half”.
THIRD GRADER:
• A third grader said it was an
impossible amount, because
the pieces were not all the
same size and it therefore
could not be “1 out of 3”.
8. • The first grader’s response suggests that children have some
conceptually sound understanding of fractions, even before instruction.
• The third grader’s response suggest that children can learn to ignore this
understanding in favor of models introduced in school that portray
fractions in narrow ways.
• If models do not draw on children's formative experiences of sharing and
partitioning, then they are likely to prevent teachers from cultivating the
natural insights about quantities that young children have.
9. Sharing and the Concept of Fractional Parts
• The first goal in the development of fractions should be to help children construct the
idea of fractional parts of the whole—the parts that result when the whole or unit has
been partitioned into equal-sized portions or fair shares.
• Children seem to understand the idea of separating a quantity into two or more parts
to be shared fairly among friends.
• They eventually make connections between the idea of fair shares and fractional parts.
• Sharing tasks are, therefore, good places to begin the development of fractions.
11. Equal Sharing
• Four children want to share 10 brownies so that
everyone gets exactly the same amount. How much
brownie can each child have?
Your Task:
• Create and Represent a solution to the
problem
• Share and discuss your solutions with your
table group
• Be ready to share with the group
12. Equal Sharing
• 16 kids need to share 12 pounds of clay. If they share
the clay equally, how much clay would each kid get?
Your Task:
• Create and Represent a solution to the
problem
• Share and discuss your solutions with your
table group
• Be ready to share with the group
13. Sharing Tasks and Fraction Language
• During the discussions of student’s solutions (and discussions are essential!) is a good time
to introduce the vocabulary of fractional parts.
• This can be quite casual and, at least for younger children, should not involve any fraction
symbolism.
• When a brownie or other region has been broken into equal shares, simply say, “We call
these fourths. The whole is cut into four parts. All parts are the same size—fourths”.
• Children need to be aware of two aspects or components of fractional parts: (1) the number
of parts and (2) the equality of the parts(in size, not necessarily in shape).
• Emphasize that the number of parts that make up a whole determines the name of the
fractional parts or shares.
• They will be familiar with halves but should quickly learn to describe thirds, fourths, fifths,
and so on.
14. Reflecting
• Equal Sharing problems allow your students to learn fractions using what they already
understand as a foundation.
• If students are just beginning to learn fractions, solving Equal Sharing problems makes
it possible for them to draw on what they know about partitioning and sharing to
create and reflect on fractional quantities.
• If students are further along in their understanding of fractions, solving and discussing
Equal Sharing problems helps them use what they know about division and benchmark
fractions to reason about increasingly sophisticated relationships between fractions
and whole numbers.
15. Models for Fractions
• There is substantial evidence to suggest that the use of models in fraction tasks is
important (Cramer & Henry, 2002).
• Unfortunately, many teachers in the upper grades, where manipulative materials are
not as common, fail to use models for fraction development.
• Models can help students clarify ideas that are often confused in a purely symbolic
mode.
• Sometimes it is useful to do the same activity with two quite different models; from the
viewpoint of the students, the activity is quite different.
• We will discuss three types of models: area or region models, length models, and set
models.
16. Region or Area Models:
• The Equal Sharing Task involved something that could be cut into smaller parts.
• The fractions are based on parts of an area or region.
• This is a good place to begin and almost essential when doing sharing tasks.
18. The Problem:
• Zack had 2/3 of the lawn left to cut.
• After lunch, he cut ¾ of the lawn he had left.
• How much of the whole did Zack cut after lunch.
Your Task:
• Fold the paper provided to solve
the problem.
• Be ready to share your answer
and your experience.
19. Length or Measurement Models:
• With measurement models, lengths are compared instead of areas.
• Either lines are drawn and subdivided, or physical materials are compared on the basis
of length.
• Manipulative versions provide more opportunity for trial and error and for exploration.
• The number line is a significantly more sophisticated measurement model. From a
child’s vantage point, there is a real difference between putting a number on a number
line and comparing one length to another. Each number on a line denotes the distance
of the labeled point from zero.
21. Activity:
Please find the activity
sheet, and a partner.
Take a deck of playing
cards for each
“partnership”.
22. Set Models:
• In set models the whole is to be understood to be a set of objects, and subsets of the
whole make up fractional parts. For example, three objects are one-fourth of a set of
twelve objects. The set of 12, in this example, represents the whole or 1.
• It is the idea of referring to a collection of counters as a single entity that makes set
models difficult for elementary school students.
• The set model helps establish important connections with many real-world uses of
fractions and with ratio concepts.
• Counters in two colors on opposite sides are frequently used. They can easily be flipped
to change their color to model various fractional parts of a whole set.
25. Bar Modeling Strategies
• Model drawing is a powerful problem-solving tool that opens
new pathways to learning mathematics for students at every
skill level.
• Model drawing is just what the name implies: drawing simple
visual models to represent problems.
26. Let’s Try One Together:
• “ There were 80 air conditioners at a local warehouse.
If 3/5 of the air conditioners were sold during one day
when the heat was overwhelming, how many air
conditioners were left for sale after that day?”
28. S
16
S
16
S
16
L
16
L
16
5 Units = 80
80 ÷ 5 = 16
1 Unit = 16
16 x 2 = 32 There were 32 air conditioners left for sale at
the local warehouse after the hot day.
29. Your Turn:
• Grace has 28 marbles. Of the total marbles, 3/7 are
red and the rest are blue. How many blue marbles
does Grace have?
Your Task:
• Use Bar Modeling to solve the word
problem.
• Be ready to share with the group.
30. Student Commentary:
• “Last year I had a teacher who was telling me what to do. He told me all
these different things to do with fractions. It took me a long, long time to
learn his ways. This year my teacher allows me to try to do everything
myself. She helps me, but she doesn’t show me exactly what to do. I am
working hard this year figuring out how to solve problems, but I kinda
like it.”
--Selma, seventh grader
Excerpt taken from: Extending Children’s Mathematics Fraction and Decimals by: Susan B. Empson, Linda Levi
31. Something To Ponder:
“I know that many kids get to middle school without knowing procedures for fraction
computation. If we show them what to do, they can get the right answer. But this doesn’t
mean that they learned it. My goal isn’t to get them to be able to get the right answer for
twenty problems. My goal is for them to learn mathematics.”
-Kathy Oker
sixth to eighth-grade teacher
Wingra School; Madison, Wisconsin
( excerpt taken from: Extending Children’s Mathematics Fraction and Decimals; Empson & Levi; 2011 pg. 188)
32. Resources:
• Elementary and Middles School Mathematics Teaching Developmentally by: John A. Van
De Walle
• Extending Children’s Mathematics Fraction and Decimals by: Susan B. Empson, Linda
Levi
• Bar Modeling A Problem Solving Tool –From Research to Practice, An Effective
Singapore Math Strategy by Yeap Ban Har, PhD