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Learning Math: Number and Operations
Professional Development > Learning Math: Number and Operations > 4. Meanings and Models for Operations > 4.1 Part A: Meanings and Relationships of the Operations (40 minutes)
K-2, 3-5, 6-8
Meanings and Models for Operations Part A: Meanings and Relationships of the Operations (40 minutes)
In This Part: Addition
We will begin our look at the various meanings for each of the operations and the laws that govern the operations by examining addition.
Addition is the simplest of the four operations. The operation, however, may look quite different depending on whether a problem has an unknown result, starting point, or change. We can describe addition as a merger or joining of two or more things; we can also describe it as combining parts of a whole, with the whole or one of the parts unknown.
The following table gives an example of each kind of addition problem:
Problem Type
Starting Point Unknown
Result Unknown
Sam had some blocks. Billy gave Sam 7 more blocks. Sam now has 23 blocks. How many blocks did he have before?
? + 7 = 23
Sam had 16 blocks. Billy gave him some more blocks. Sam now has 23 blocks. How many blocks did Billy give him?
Sam had 16 blocks. Billy gave him 7 more blocks. How many blocks does Sam have now?
16 + 7 = ?
Parts of a Whole
Jennie has some green marbles and 9 yellow marbles. She has 24 marbles in all. How many green marbles does Jennie have?
Jennie has 15 green marbles and some yellow marbles. She has 24 marbles in all. How many yellow marbles does she have?
Jennie has 15 green marbles and 9 yellow marbles. How many marbles does Jennie have?
The merger or joining concept always requires some sort of combining action, whereas the parts-of-a-whole concept is static. See Note 2 below.
One of the most important facts about addition is that no two quantities can be added unless they are measured or reported in the same units. For example, you cannot add 2 tens and 3 ones, or 2 halves and 3 fourths, and expect to get 5 of anything. These quantities can only be combined if we can somehow find a common unit with which to measure or label them. See Note 3 below.
Problem A1
Label each of the addition problems with the correct situation label, and identify the units involved:
MR: Merger, result unknown
MS: Merger, starting point unknown
MC: Merger, change unknown
PW: Parts of a whole, whole unknown
PP: Parts of a whole, one of the parts unknown
a. Moisha has 7 cars. Three are red, and the rest are blue. How many blue cars does she have?
Write an equation and see if you can match it with any of the above descriptions.
b. Jake read 5 mystery books and 8 adventure books. How many books did he read?
c. Bret has $5, and Wendy has $4. How much will they have if they pool their money?
d. Natasha had 4 rabbits. One of her rabbits had babies, and now she has 7 rabbits. How many babies did the rabbit have?
e. Reed's parents gave him $5 for his birthday. He then had $12. How much money did he have before?
Part A: Meanings and Relationships of the Operations adapted from Chapin, Suzanne and Johnson, Arthur (1999). Math Matters: Understanding the Math You Teach (pp. 40-72). © 2000 by Math Solutions Publications.
In This Part: Subtraction
As in addition, no two quantities can be subtracted unless they are measured or reported in the same units. Thus, you cannot subtract 7 hundreds from 9 tens and expect to get 2 of anything. A quantity can only be subtracted from another quantity if we can first find a common unit between the two.
The operation of subtraction can be thought of as:
• a separator, when the result, starting point, or change is unknown (also known as "take-away")
• a comparison, when the result, starting point, or change is unknown
• a missing addend problem, where one of the parts is unknown – See Note 4 below.
This table gives an example of each kind of subtraction problem:
(Take-Away)
Billy gave 7 toy cars to Sam, so he now has 16 cars left. How many cars did he have before?
? – 7 = 16
Billy had 23 toy cars. He gave some to Sam. Billy has 16 cars left. How many cars did he give Sam?
23 – ? = 16
Billy had 23 toy cars. He gave 7 to Sam. How many cars does he have now?
23 – 7 = ?
Jennie has 15 more stickers than Sara. Sara has 9 stickers. How many stickers does Jennie have?
Jennie has 15 more stickers than Sara. Jennie has 24 stickers. How many stickers does Sara have?
Sara has 9 stickers. Jennie has 24 stickers. How many more stickers does Jennie have than Sara?
Missing Addend
Sara has some red chips and 4 black chips. She has 9 chips altogether. How many red chips does she have?
? + 4 = 9
Sara has 5 red chips and some black chips. She has 9 chips altogether. How many black chips does she have?
5 + ? = 9
The missing addend problems are written as addition problems, but the procedure to solve these problems requires the use of some subtraction strategy. The separating concept always requires some sort of separating action, whereas the comparison concept is static.
When negative numbers are introduced, we can more clearly understand the concept of subtraction as the addition of the inverse. Thus, we can write 13 – 6 as the equivalent of 13 + (-6 ), because -6 is the additive inverse of 6; i.e., 6 + (-6) = 0. Similarly, we can represent 13 – (-6) as 13 + 6, since 6 is the additive inverse of -6. So again, subtracting a number (13 – (-6)) is the same as adding its inverse (13 + 6).
Label each of the subtraction problems with the correct situation label, and identify the units involved:
SR: Separator, result unknown
SS: Separator, starting point unknown
SC: Separator, change unknown
CR: Comparison, result unknown
CS: Comparison, starting point unknown
CC: Comparison, change unknown
MS: Missing addend, starting point unknown
MC: Missing addend, change unknown
a. Moisha has 7 cars. She gave 3 away. How many cars does she have left?
b. Jake read 5 mystery books. He read 3 more adventure books than mysteries. How many adventure books did he read?
c. Bret has $5. Bret has $2 more than Wendy. How much money does Wendy have?
d. Natasha has 7 rabbits. She gave some rabbits to Joshua, and then she had 3. How many rabbits did she give away?
e. Reed's parents gave him some money for his birthday. He now has $12. He had $7 before his birthday. How much money did they give him?
f. Elyse had some candy bars. She ate 3, and she has 5 left. How many did she have to start?
In This Part: Multiplication
There are several ways in which we can think of multiplication:
Multiplication is often thought of as repeated addition of equal groups. While this definition works for some sets of numbers, it is not particularly intuitive or meaningful when we think of multiplying 3 by 1/2, for example, or 5 by -2. In such cases, it may be helpful to widen the idea of grouping to include evaluation of part of a group. This concept is related to partitioning (which, in turn, is related to division).
For example, three groups of five students can be read as 3 • 5, or 15 students, while half a group of 10 stars can be represented as 1/2 • 10, or 5 stars. These are examples of partitioning; each one of the three groups of five is part of the group of 15, and the group of 5 stars is part of the group of 10.
A second concept of multiplication is that of rate or price. For example, if a car travels four hours at 50 miles per hour, then it travels a total of 4 • 50, or 200 miles; if CDs cost eight dollars each, then three CDs will cost 3 • $8, or $24.•A third concept of multiplication is that of multiplicative comparison. For example, let's say that Sara has four CDs, Joanne has three times as many as Sara, and Sylvia has half as many as Sara. Thus, Joanne has 3 • 4, or 12 CDs, and Sylvia has 1/2 • 4, or 2 CDs.
Two additional situations require multiplication:
Finding the area of a rectangle using rectangular arrays. For example, an array with three rows by five each will have 3 • 5, or 15, square units in all. This model is often used to introduce multiplication.
Finding the number of possible combinations using a Cartesian product. For example, with two shirts and three pairs of pants, you could have 2 • 3, or 6, different shirt-pant combinations.
In the first three scenarios, one factor was clearly the multiplier (the number of groups), and the other factor was clearly the number being multiplied (the number of items or individuals in each group). These types of problems are called asymmetrical, because the factors are so different; exchanging the roles of the factors results in an entirely different scenario. For example, 3 CDs at $8 each is different from 8 CDs at $3 each, even though the "answer" is the same.
The two last scenarios present two examples of symmetrical problems, because it isn't important which of the two factors is the multiplier. The quantities are interchangeable.
The asymmetrical nature of some problems explains why the commutative law of multiplication is less intuitive than the commutative law of addition. The multiplication problem 3 • 4, interpreted as a grouping problem, means three groups of four items. This corresponds to the addition problem 4 + 4 + 4. In contrast, the multiplication problem 4 • 3, also interpreted as a grouping problem, means four groups of three items, which corresponds to the addition problem 3 + 3 + 3 + 3. It may not be obvious at first glance that 4 + 4 + 4 and 3 + 3 + 3 + 3 would give the same sum, or why. Manipulatives and other visual clues discussed later in this session can be helpful in showing the relationship between the two operations.
One of the most important facts about the operations of multiplication and division is that the units of the quantities being multiplied or divided do not have to be the same for the operations to function properly. You can multiply 2 tens by 3 ones, and the result will be 6 tens. Likewise, you can divide 6 tens by 3 ones and get 2 tens. The unit for the answer is found in the same way that you found the numerical answer. For example, if you divided the numbers, then you must divide the units as well. Similarly, if you multiplied the numbers, then you must multiply the units as well. See Note 5, below.
Consider the following multiplication situations. For each one, identify the multiplication problem, the units involved, whether the problem is symmetrical or asymmetrical, and which multiplication concept it is demonstrating:
a. Dinner at the Ritz costs 4 times as much as dinner at the Savoy. My bill at the Savoy was $10. What would dinner cost me at the Ritz?
b. Bob & Jimmy's Ice Cream offers 6 different ice cream flavors and 5 different sundae toppings. How many different kinds of sundaes can be made using 1 flavor of ice cream and 1 topping per sundae?
c. My shower flows at 3 gallons per minute. How much water would a 6-minute shower use?
d. There are 9 content sessions in this course, and you have completed 1/3 of them. How many sessions have you completed?
e. My yard is 20 meters wide and 33 meters from front to back. What is its area?
In This Part: Division
All of the meanings of multiplication can be used for division, since if the product and one of the factors is known, division can be used to find the other factor. But for the asymmetrical example of equal groups, the process feels different depending on which factor is known — the multiplier or the number in each group.
As you will see, there are two very different concepts of division:
If the number in each group is known, and you are trying to find the number of groups, then the problem is referred to as a quotative division problem. Quotative division may also be called measurement, or repeated subtraction. You are, in effect, counting or measuring the number of times you can subtract the divisor from the dividend. Long division (remember long division?!) uses this concept.
If the number of groups is known, and you are trying to find the number in each group, then the problem is referred to as a partitive division problem. Partitive division may also be called equal groups, or sharing and distribution. You are, in effect, partitioning the dividend into the number of groups indicated by the divisor and then counting the number of items in each of the groups.
The following example demonstrates the distinction between the two types of division problems: See Note 6 below.
Partitive:
Quotative:
12 3 = 4
Partition into 3 groups.
Repeatedly subtract 3.
There are 4 in each group.
There are 4 groups of 3 in 12.
Twelve apples, 3 bags — how many in each?
Twelve apples, 3 in a bag — how many bags?
a. Draw a diagram that represents 15 3 as a partitive problem.
b. Draw another diagram that represents 15 3 as a quotative problem.
c. Write a problem for each diagram.
a. Which type of division, quotative or partitive, would be most efficient for computing 100 50? Why?
b. Which would you use for 100 2?
Video Segment
In this video segment, Susan and Jeanne explore the different notions of quotative and partitive division problems. They challenge their understanding with new insights. Watch this segment after you've completed Problems A4 and A5.
Think about which method is easier to do in a particular division problem.
You can find this segment on the session video approximately 4 minutes and 9 seconds after the Annenberg Media logo.
When division problems do not work out evenly, the context of the problem dictates the answer. Sometimes we may need to round the answer up or down to the next integer, and sometimes we may need the exact decimal value of the division.
a. Write a problem that uses the computation 43 4 and gives 10 as the correct answer.
b. Write a problem that uses the computation 43 4 and gives 11 as the correct answer.
c. Write a problem that uses the computation 43 4 and gives 10.75 as the correct answer.
Another important concept to remember, especially when working with rational numbers, is that division can be thought of in terms of multiplying by the inverse. This can be particularly useful when dividing by fractions. Thus, we could show that 12 2 = 12 • 1/2, where 1/2 is the multiplicative inverse of 2, and 12 (1/2) = 12 • 2, where 2 is the multiplicative inverse of 1/2. In these cases, you can see that the multiplicative inverse of every number except 0 is the reciprocal of that number, and that the product of a number and its reciprocal is 1.
a. The problem to solve is 3 + x = 7. This is a PP problem, since we are working with parts of a whole and the unknown is one of the parts. Here, the units are cars.
b. The problem to solve is 5 + 8 = x. This is a PW problem, since we are working with parts of a whole and the unknown is the sum of the parts. Here, the units are books.
c. The problem to solve is 5 + 4 = x. This is an MR problem, since we are merging two things (Bret and Wendy's money) and the unknown is the result. Here, the units are dollars.
d. The problem to solve is 4 + x = 7. This is an MC problem, since we are merging two things (rabbits) and the unknown is the change (the number of babies). Here, the units are rabbits.
e. The problem to solve is x + 5 = 12. This is an MS problem, since we are merging two things (Reed's money with his parents') and the unknown is the starting point (the amount of money Reed had before). Here, the units are dollars.
a. The problem to solve is 7 – 3 = x. This is an SR problem, since we are separating two things and the unknown is the result. Here, the units are cars.
b. The problem to solve is x – 3 = 5. This is a CS problem, since we are comparing two things and the unknown is the starting point. Here, the units are books.
c. The problem to solve is 5 – 2 = x. This is a CR problem, since we are comparing two things and the unknown is the result. Here, the units are dollars.
d. The problem to solve is 7 – x = 3. This is an SC problem, since we are separating two things and the unknown is the change. Here, the units are rabbits.
e. The problem to solve is 7 + x = 12. This is a missing addend problem (MC) since the change is unknown. Here, the units are dollars.
f. The problem to solve is x – 3 = 5. This is an SS problem, since we are separating two things and the unknown is the starting point. Here, the units are candy bars.
a. The problem to solve is 4 • $10 = x. The units are dollars. This is an asymmetrical problem, demonstrating a multiplicative comparison.
b. The problem to solve is 6 • 5 = x. The units are flavors, toppings, and sundaes. This is a symmetrical problem, demonstrating the use of a Cartesian product.
c. The problem to solve is 6 • 3 = x. The units are minutes, gallons per minute, and gallons. This is an asymmetrical problem, demonstrating a rate.
d. The problem to solve is 1/3 • 9 = x. The units are sessions. This is an asymmetrical problem, demonstrating partitioning.
e. The problem to solve is 20 • 33 = x. The units are meters, and the result is in square meters. This is a symmetrical problem, demonstrating the use of a rectangular array to find the area of a rectangle.
c. Answers will vary. Here are two examples:
For the partitive model, Graphic (a): Matt deals a total of 15 cards to 3 players (including himself). Each player gets the same number of cards. How many cards does each player get? (Here, you know the number of groups and need to find the number in each group.)
For the quotative model, Graphic (b): Nicole has 15 cans of soda. She gives 3 cans of soda to each of her friends. How many friends got the soda? (Here, you know the number in each group and need to find the number of groups.)
a. The quotative problem is easier to solve. It is equivalent to "How many 50s would you need to get 100?" Meanwhile, the partitive problem is "If 100 items are separated into 50 equal groups, how many are in each group?"
b. The partitive problem is easier. It is equivalent to "If 100 is separated into two equal groups, how many are in each group?" Meanwhile, the quotative problem is "How many twos would you need to get 100?"
Answers will vary. Here are some examples:
a. Arvind wants to buy some ice cream for his coworkers. Each ice cream cone costs $4, and Arvind has $43. How many cones can Arvind buy?
b. Michelle needs 43 batteries to keep her handheld organizer running during a long trip. Batteries come in packs of 4. How many packs of batteries will Michelle need to buy?
c. Lilian bought 4 cakes for a Tuesday night party. She paid $43 for the cakes. How much money did she pay for each cake?
0 About the Learning Math Courses
1 What Is a Number System?
1 Part A: A Simpler Number System (70 minutes)
2 Part B: Comparing Number Systems (15 minutes)
3 Part C: Building the Number Line (35 minutes)
4 Homework
2 Number Sets, Infinity, and Zero
1 Part A: Number Sets (35 minutes)
2 Part B: The Size of Infinity (35 minutes)
3 Part C: Examining Zero (50 minutes)
3 Place Value
1 Part A: Base Two Numbers (45 minutes)
2 Part B: Exponents and Logarithms (35 minutes)
3 Part C: Place-Value Representation in Base Ten and Base Four (40 minutes)
4 Meanings and Models for Operations
1 Part A: Meanings and Relationships of the Operations (40 minutes)
2 Part B: Area Models for Multiplication and Division (45 minutes)
3 Part C: Colored-Chip Models (35 minutes)
5 Divisibility Tests and Factors
1 Part A: Alpha Math (35 minutes)
2 Part B: Divisibility Test (50 minutes)
3 Part C: Factors (35 minutes)
6 Number Theory
1 Part A: Models for Multiples and Factors (75 minutes)
2 Part B: Looking for Prime Numbers (45 minutes)
7 Fractions and Decimals
1 Part A: Fractions to Decimals (65 minutes)
2 Part B: Decimals to Fractions (30 minutes)
3 Part C: Ordering Fractions (25 minutes)
8 Rational Numbers and Proportional Reasoning
1 Part A: Interpreting Fractions, Units, and Unitizing (45 minutes)
2 Part B: Fractions With Cuisenaire Rods (45 minutes)
3 Part C: Absolute and Relative Reasoning (30 minutes)
4 Session 8: Homework
9 Fractions, Percents, and Ratios
1 Part A: Models for the Multiplication and Division of Fractions (45 minutes)
2 Part B: Decimals and Percents (45 minutes)
3 Part C: Fibonacci Numbers (30 minutes)
10 Classroom Case Studies, K-2
1 Part A: Observing a Case Study (25 minutes)
2 Part B: Reasoning About Number and Operations (40 minutes)
3 Part C: Problems That Illustrate Reasoning About Number and Operations (55 minutes)
11 Classroom Case Studies, 3-5
2 Part B: Reasoning About Number and Operations (40 minutes) – Exploring Standards
3 Part B (continued): Reasoning About Number and Operations – Examining Students' Reasoning
5 Homework – Grades 6-8
4.1 Part A: Meanings and Relationships of the Operations (40 minutes)
4.2 Part B: Area Models for Multiplication and Division (45 minutes)
4.3 Part C: Colored-Chip Models (35 minutes)
4.4 Homework
How to Use 0 About the Learning Math Courses
Session 1 What Is a Number System?
Understand the nature of the real number system, the elements and operations that make up the system, and some of the rules that govern the operations. Examine a finite number system that follows some (but not all) of the same rules, and then compare this system to the real number system. Use a number line to classify the numbers we use, and examine how the numbers and operations relate to one another.
Session 2 Number Sets, Infinity, and Zero
Continue examining the number line and the relationships among sets of numbers that make up the real number system. Explore which operations and properties hold true for each of the sets. Consider the magnitude of these infinite sets and discover that infinity comes in more than one size. Examine place value and the significance of zero in a place value system.
Session 3 Place Value
Look at place value systems based on numbers other than 10. Examine the base two numbers and learn uses for base two numbers in computers. Explore exponents and relate them to logarithms. Examine the use of scientific notation to represent numbers with very large or very small magnitude. Interpret whole numbers, common fractions, and decimals in base four.
Session 4 Meanings and Models for Operations
Examine the operations of addition, subtraction, multiplication, and division and their relationships to whole numbers. Work with area models for multiplication and division. Explore the use of two-color chips to model operations with positive and negative numbers.
Session 5 Divisibility Tests and Factors
Explore number theory topics. Analyze Alpha math problems and discuss how they help with the conceptual understanding of operations. Examine various divisibility tests to see how and why they work. Begin examining factors and multiples.
Session 6 Number Theory
Examine visual methods for finding least common multiples and greatest common factors, including Venn diagram models and area models. Explore prime numbers. Learn to locate prime numbers on a number grid and to determine whether very large numbers are prime.
Session 7 Fractions and Decimals
Extend your understanding of fractions and decimals. Examine terminating and non-terminating decimals. Explore ways to predict the number of decimal places in a terminating decimal and the period of a non-terminating decimal. Examine which fractions terminate and which repeat as decimals, and why all rational numbers must fall into one of these categories. Explore methods to convert decimals to fractions and vice versa. Use benchmarks and intuitive methods to order fractions.
Session 8 Rational Numbers and Proportional Reasoning
Begin examining rational numbers. Explore a model for computations with fractions. Analyze proportional reasoning and the difference between absolute and relative thinking. Explore ways to represent proportional relationships and the resulting operations with ratios. Examine how ratios can represent either part-part or part-whole comparisons, depending on how you define the unit, and explore how this affects their behavior in computations.
Session 9 Fractions, Percents, and Ratios
Continue exploring rational numbers, working with an area model for multiplication and division with fractions, and examining operations with decimals. Explore percents and the relationships among representations using fractions, decimals, and percents. Examine benchmarks for understanding percents, especially percents less than 10 and greater than 100. Consider ways to use an elastic model, an area model, and other models to discuss percents. Explore some ratios that occur in nature.
Session 10 Classroom Case Studies, K-2
Watch this program in the 10th session for K-2 teachers. Explore how the concepts developed in this course can be applied through case studies of K-2 teachers (former course participants) who have adapted their new knowledge to their classrooms.
Session 11 Classroom Case Studies, 3-5
Watch this program in the 10th session for grade 3-5 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 3-5 teachers (former course participants) who have adapted their new knowledge to their classrooms.


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Local Ceramics, Imported Wines and a Pierneef Landscape Shine in Strauss & Co's November Online Sale
A lodestar at auction in 2021, JH Pierneef once again proved his appeal to collectors when his 1945 oil composition, Landscape with Cliffs with Cypress Trees, sold for R328 300, topping the individual rankings in Strauss & Co's November online-only auction. The three-part auction, jointly organised by Strauss & Co's decorative arts, wine and fine art departments, featured 13 sessions and netted a total of R7.1 million.
"Strauss & Co successfully concluded its first ever online-only auction in November 2013, and over the ensuing eight years this automated format has contributed to streamlining our digital infrastructure and, at the same time, enabled us to reach new audiences globally," says Susie Goodman, an executive director with Strauss & Co. "Our November 2021 sale attracted nearly 500 bidders of whom 69 were new to us, which is very encouraging. The staggered conclusion of the 931-lot sale enabled us to better service our clients, as well as offer our collaborating partners adequate exposure."
All five lots by Pierneef in November Online sold above their pre-sale estimates, confirming the momentum established with Strauss & Co's sell-out auction devoted exclusively to this much-loved landscape painter in July. The auction also saw robust interest in contemporary artists. Painter Lionel Smit posted the next highest results after Pierneef, with two portraits from 2012 and 2013 selling for R175 875 each.
Other notable sales in November Online included William Kentridge's ink and conté on dictionary paper, 2nd Hand Reading, offered with an accompanying book, which sold for R117 250. Sam Nhlengethwa's Street Scene with Red Taxi, an oil and collage on canvas from 2001, sold for R93 800. The work appeared in a session guest curated by Nhlengethwa, who follows Kutlwano Mokgojwa, a curator at the Wits Art Museum, as invited contributor to Strauss & Co's online sale programme.
In addition to the large consignment of fine art, November Online included collectable furniture and silverware, rare Italian and Spanish wines as well as ceramics by Andile Dyalvane. An important figure in contemporary ceramics, Dyalvane's Elwalweni, IIndonga Series, a vessel made with white stoneware and charcoal clay in 2019, fetched R117 250. The lot formed part of a concise session jointly organised by Strauss & Co, Sanlam Private Wealth Bakusasa Trust and Dyalvane, with proceeds from the sale benefitting the artist's former school in Qobo Qobo in the Eastern Cape.
South African ceramics has a storied history, as was highlighted in a consignment of important makers presented by Strauss & Co's decorative arts department in November Online. A mottled blue-glazed bowl by Ceramic Studio, the art pottery established at Olifantsfontein in 1926 and a precursor to Linn Ware, drew justifiable interest and sold for R14 070. A Linn Ware mottled celadon-and-russet-glazed vase sold for R3 752.
A 20th-century Mexican silver two-handled tray that sold for R35 175 was the highlight of the decorative arts department's fine consignment of silverware. Among the English makers, a Victorian silver two-handled tray by Atkins Brothers of Sheffield achieved R12 898, while a George III silver coffee pot by Peter and Ann Bateman of London sold for R14 070. Connoisseurs also delighted in a silver rhinoceros beetle set to a petrified wooden base, which sold above estimate for R3 283.
Notable furniture pieces in November Online included an LPC plastic reclining chair designed by Kartell, Italy, sold for R15 243, and a bone inlaid kist, probably of Indian origin, sold for R10 553.
Strauss & Co's wine department ended a robust year of trade with a curated selection of rare Italian and Spanish wines. Wines by producers from Piedmont in northwest Italy were among the top performers, with a six-bottle lot of Gaja's Barbaresco (2009) fetching R29 313. Also from Piedmont, three bottles of Giuseppe Rinaldi's Barolo Brunate-Le Coste (2001) sold for R19 933. Interest in the revered Tuscan wine producer Tenuta San Guido saw three bottles of The Sassicaia (2012) sell for R18 760.
The top performing Spanish wines were all non-vintage blends from Vega Sicilia, a producer whose founder, Don Eloy Lecanda y Chaves, trained in the Bordeaux wine region of France. All offered in three-bottle lots, the Ribera del Duero Unico Reserva Especial sold for R22 278, the Ribera del Duero Unico Reserva Especial for R25 795, and the Unico 2010 Release for R25 795.
Social engagement with the wider art community is central to Strauss & Co's daily operations. Every year Strauss & Co assists the Friends of the Tatham Art Gallery with a charity auction to raise funds for the purchase of new art works for this public museum in Pietermaritzburg. This year's online format did not disadvantage the cause: all 21 lots on offer sold. Ayanda Mthethwa-Siwila's Ngiyiqanda, a terracotta clay vessel from 2012, was the star performer, selling for R19 933. Other notable sales included paintings by Hussein Salim and Siyabonga Sikosana.
Strauss & Co frequently assists corporate partners to equitably and transparently dispose important works from their collections. November Online included a consignment of high-quality botanical, bird and wildlife artworks from the FirstRand (including FNB and RMB) corporate art collection. Various watercolours depicting birds by Gail Denise Darroll and Liz McMahon were among the notable pieces sold. FirstRand will reinvest the earnings in contemporary South African art.
Strauss & Co will conclude its 2021 sales activities with a benefit auction in service of the Norval Foundation, a centre for art and cultural expression located in Steenberg, Cape Town. The in-person auction will be held on Thursday, 9 December 2021 at Norval Foundation, with proceeds benefitting its mission of research, education and the exhibition of 20th- and 21st-century visual art from South Africa and beyond.
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Counting calories can help you identify weak links in your diet. Learn how and when to calorie count without going crazy.
Few topics generate more debate then whether counting calories is an effective strategy for long-term fat loss.
The anti-calorie counting camp says that obsessing on calories alone can cause people to ignore the nutritional composition of their diet, and continue to eat unhealthy even if they are eating fewer calories. Theyll also point out that counting calories accurately and consistently can be a tedious and time-consuming activity, and may actually de-motivate people to eat healthier.
The pro-calorie counting side, advocates will point out that without having a good idea of how many calories you are consuming each day, it can be difficult to lose fat and avoid hitting fat loss plateaus later on. And because most people underestimate how many calories they are actually eating, counting calories can help provide a reality check.
So what should you do? Count calories or not count calories?
Both groups make valid points.
If all you look at is the total number of calories you eat each day, you can find yourself falling into the trap of eating empty calories.
For example, lets say your target is 1500 calories a day. Your look at your total calorie count at the end of the day and feel pretty good about yourself. You ate 1500 calories. The problem is the calories were made up of soda, pizza and potato chips. You end up feeling hungry at the end of the day, youre grouchy, your energy levels are low and you still look flabby and unfit.
Contrast this against another person who at the same amount of calories, but their diet that day was made up primarily of fresh fruits and vegetables, lean protein like chicken breast, complex carbohydrates like oatmeal and some healthy fats from nuts or avocados. Same amount of calories, but in terms of volume, the person who ate the nutritionally-dense foods actually ate more and better, and still hit their calorie target.
Empty calorie foods tend to be higher in calories, but lower in nutrients and volume. So you have to eat less (and feel hungry) when your diet is based on them in order to hit your calorie goal.
This is one of the main reasons that so many people fail at fat loss.
They think that eating less will cause them to lose fat. So they continue to eat their favorite junk food, but just skip a meal or eat less frequently. But nutritionally-dense foods are more filling, provide critical nutrients that can promote fat burning and general health and well-being, and typically allow you to eat more of them at the same calories levels.
So clearly, just looking at calorie counts alone isnt enough. You have to look at the types of food you are eating, as well.
So why count calories at all?
The best reason to keep track of your daily calories is to get a better handle on what you are actually eating. Research has shown that many people underestimate their daily calorie consumption by as much as 25%. For a 1500 calorie diet, this can mean an extra 375 calories a day. Over the course of a week, this adds up to 2625 calories which is almost a pound of fat (1 lb of fat contains 3000 calories.) And the more processed and fast food people eat, the easier it is to consume more calories than your body needs.
Keeping track of your food and calories each day can help you get a true picture of what you are eating, how much of it, and whether its nutritionally balanced.
Notice I said keeping track of your food and calories, not merely counting your calories. There is a big difference. Unless you track the nutrient profile of the foods you eat in addition to the calories, you can easily fall into the calorie counting trap I discussed earlier.
Remember, this is about what you eat, not just how many calories you eat.
But Isnt Counting You Calories and Food Hard?
In the past, keeping a detailed food journal with nutrient and calorie information was difficult thing to do. To be really accurate, you need to weigh your foods, keep a calorie-counting book handy and be pretty skilled with a calculator.
However, keeping track of your daily food intake has actually become fairly easy over the past couple of years thanks to the Internet. There are dozens of free websites online that do most of the hard work for you, including SparkPeople, FitDay, DietTV, Calorie King and The Daily Plate. These sites look up the food from USDA nutrition or user created food databases, let you enter the quantity and pretty much do the rest for you with a click of a button.
Most sites also provide you with tools to calculate not just your target calories based on your goals, but also your target macronutrients (protein, carbohydrates and fats), as well as track sodium, dietary cholesterol, fiber and vitamin and mineral intake. This can give you a very accurate view of what you are eating, the nutritional profile of your meals and yes how many calories you are consuming.
All of these sites also offer exercise logs, which not only track your progress in the gym, but also help you keep track of calorie expenditure via exercise and daily activity.
One critical piece to successfully tracking your daily food and calorie consumption is accurately measuring portions. You can eyeball it, but like calories, most people underestimate their portions. Supersized meals and giant portions at resturants have skewed peoples perceptions of what a serving is. So its not unusual for these misperceptions to find their way into a persons own kitchen, as well.
The most accurate way to determine portions is to weigh it.
There are inexpensive electronic kitchen scales that make this easy. All nutritional labels accompanying food (and nearly all online calorie and food tracking websites) provide serving data by weight (grams.) They will also often provide serving size by volume (tbs, cup, tsp, etc.) Volume is less accurate than weighing the food, but in a pinch its better than not measuring at all, or going by sight.
Buy an electronic scale and keep it on the kitchen counter with an empty glass bowl on it. This makes it easy to just throw your food in the bowl on the scale and measure it. If its dry food like oats, cereal or vegetables, you can simply rinse the bowl after each use. If you are weighing meat, poultry, fish, diary or eggs youll obviously need to wash it properly between uses.
Also, keep a set of measuring cups handy as well as a two cup Pyrex measuring cup. These are very accurate when measuring liquids and dont require the scale.
Once you start seeing what you are actually eating, it becomes simple to identify where your extra calories are coming from. But you have to do the measuring and tracking in the first place to discover this.
Is Calorie Counting The Only Way to Lose Fat?
You dont have to calorie count to lose fat.
Highly fit people generally have developed a pretty good sense of the energy and nutritional content of their food and have become skilled (mostly from habit) to accurately determine portions. That said, most fit people have kept food logs at one point or another to help put these habits in place.
Certain diet plans, like Jenny Craig or NutriSystem basically do the calorie-counting for you. These diets typically rely on pre-packaged, pre-portioned meals with a set amount of calories and nutrients. As long as you eat the meals they provide you, and in the daily quantity the prescribe, youll more or less hit your calorie targets without having to log every bite you take.
And then theres Weight Watchers. Weight Watchers is basically a calorie counting diet that has been simplified by the addition of a point system to help you easily estimate calories.
Each day you have a certain amount of points to allocate and higher calorie foods cost you more points. There are other nuances to the program, but at its core, Weight Watchers is calorie counting. They just simplify calorie counting and make it less tedious for people.
While many people have had success with Weight Watchers, the diet still requires proper portion estimates to work and it is possible for you to blow all of your points on junk food. Still, it may be a good place to start if the idea of recording all of your food makes your head spin.
Do I Need to Count Calories and Food Forever?
Some people find that long-term tracking of their food is the best way to ensure that they dont slip back into their old habits. However, this requires a fair amount of commitment and discipline, which many people simply dont have. Online tools have made this easier, but it still takes time.
The most effective strategy Ive found is to cycle food and calorie counting.
Try weighing and recording all of your meals for two weeks minimum to establish a baseline. This will usually be long enough to identify those weak links in your diet and will allow you to start getting a true idea of servings and portions. Based on this information, make some adjustments to your servings and measure your fat-loss progress. Give yourself an additional two weeks of calorie and food counting, which will enable you to develop some new habits around portion size.
Eventually, youll find that you can estimate servings pretty accurately by sight alone.
Once you feel like you have a pretty good handle on portion sizes and how much (and the types of food) you need to be eating to hit your diet and calorie targets, you can back off on the tracking for a while. If you feel like you are hitting a wall later with your fat loss or fitness goals, or if your portions start to become larger again, go back to tracking your food for a week or two to reset your serving sense.
Personally, I tend to do meal and calorie audits about four times a year for one month. This seems to be enough to reset any misperceptions I might have developed around portion size while not actively tracking every gram of food I eat. It also lets me spot certain nutritional gaps I might have developed, for example increased sodium intake or decreased dietary fiber.
When Does it Make Sense to Count Calories?
Keeping a diet log and tracking calories is also one the first tactics your should try when you hit a fat-loss plateau, since it can expose some of the weak areas in your diet where you may be overeating.
If you are just beginning to clean up your diet and trying to eat more healthy, keeping track of your food and calories can help you become a more educated eater and make better choices regarding which foods you choose and what a serving actually means.
Also, if you are a competitive athlete or serious body builder, diet logs can play a critical role in making sure you are providing yourself with the right levels of energy and nutrients, without gaining too much body fat in the process.
Finally, keeping track of your food, either by through a diet journal or by a more simplified method like Weight Watcher points will quickly show you that there are certain foods like vegetables that you can eat large volumes of without significantly impacting your total energy consumption for the day. And since these low-calorie foods are often some of the best for you, it will encourage you to eat more of them.
I started counting calories again after I hit a plateau, which was a good thing, because I found I was not eating nearly enough calories!
It is so true. This article is written very well. I also use bitelog.com, another site for tracking my food.
Valeri, youre right counting your calories can definitely be work, but as you point out, it does have its advantages.
I think the biggest advantage is that it lets you get a sense for what you are really eating, how much and where some of your "weak points" are. Portions in the U.S. keep expanding at rate that is about equal to our increasing waist-lines, so many people have an extremely skewed view of what an actual serving is. Counting and measuring your food even if just for a few weeks can help give you a reality check when it comes to servings.
Congrats on your fat loss and I hope youll stop by again.
Thanks for your sharing.. Losing weight is simply a matter of expending more calories than you take in, through exercise and your daily activities. To win the battle, it helps to know how many calories you are consuming in a day.
Although you made some intelligent and balanced comments, I believe that all that is necessary is becoming aware of what you really eat. Then, reduce your portions (of meat) by about 20%. To eye it is not very difficult. To ward off still feeling hunger, increase the portions of vegetables and fruit.
Of course, reading labels and educating yourself along the way about calories is critical. Bless you if you can maintain a habit like weighing food or keep logs (even in cycles). I compare that to parolees wearing monitoring ankle braces! I believe that the most effective way for long-term weight loss is do undertake small, slow changes that you will be able to maintain in your lifestyle. I speak with authority, entering my third year of a 40 lb weight loss (which actually took two years I was patient and had the long-term in mind. Most people are too darn impatient and want to be rescued).
Completely agree with the pro-counting lobby. I lost 14kgs in 5 months and have kept it off in the past 3 months through calorie counting. But whenever I mention it to others they suggest that calorie counting is a touch obsessive.
I have come to the conclusion that in order to serously lose weight and then keep it off you do have to be obsessive. I have developed my own principles behind losing weight – no charge, free, and not trying to sell you anything, they are on my website http://diet.mondrop.com – please take a look and let me know your views.
The main principle after calorie counting I had was not to eat breakfast before 9.30am. This meant I could easily get through to a late lunch and then a nice dinner. Even had plenty of opportunities for little freebies, such as wine or beer or a small pudding occasionally.
One thing I would really like to touch upon is that weightloss program fast can be achieved by the right diet and exercise. An individuals size not simply affects appearance, but also the overall quality of life. Self-esteem, despression symptoms, health risks, plus physical skills are influenced in excess weight. It is possible to make everything right whilst still having a gain. In such a circumstance, a problem may be the perpetrator. While a lot food and not enough work out are usually responsible, common medical conditions and trusted prescriptions could greatly help to increase size. Thx for your post in this article gywl512.
Shouldnt your metabolism be taken into account when calorie counting. If you have a higher metabolism doesnt it mean you need to take in more calories as your body burns through them faster?


We work with early stage companies to help develop their plan, the team, fine tune investor presentations and launch. We typically invest, then take a seat on the Board of Directors or have Advisory Board representation. Perhaps more hands on than other investors, we only invest in projects we are passionate about. Our most common question is "whats the fastest path to cash flow positive? Typical clients range from $0 to $50 million revenue.


Milo Ventimiglia Explains How He's Different From Jack Pearson - Do Men Like Jack Pearson Exist?
This Is Us's leading man reflects on his character's role outside of the show.
Let us start by saying Milo Ventimiglia is not Jack Pearson from This Is Us.
Yes, he plays the beloved Pearson patriarch on one of NBC's most acclaimed dramas, and, yes, there are striking similarities between the two. (Milo believes his "earnestness to look out for other people" is like Jack's, as is his "desire to not make his problems anyone else's.") But Milo knows the boundaries between who he is, and who Jack is as a fictional character. Of course, it doesn't always work that way when it comes to the show's fans. And that's where Milo says he must practice a little patience.
"I can't take Jack's face off. I wear it every day. Even though, I, Milo, was here before Jack, I can't take off the association," Milo says. "So when people out on the streets see me, first they see Jack and then I have to patiently let them know that, no, hey, I'm Milo."
Of course, this doesn't mean he isn't thinking about Jack all the time — in fact, in many ways, he very much lives in the character's world on a regular basis. After being sent an episode script, usually 10 or so days before they start to film, Milo will instantly print his lines out and begin carrying the pages with him in his pocket. At the grocery store, he'll randomly pull them out to re-read them again. While grabbing lunch, he'll take them out once more to let them "soak in" a bit more. And yet, Milo says he can snap out of it all and return to reality when he needs to — that is, for the most part.
"Taking him off is not difficult anymore. There are moments that have impacted me, where I may get a little quiet just as a human being. A lot of that happened this year with the Vietnam storyline," Milo explains.
Having a Vietnam veteran as a father made portraying Jack's time in the war throughout season 3 that much more meaningful. Moreover, Milo reveals that some of his close friends, who are veterans of Iraq and Afghanistan, shared their own experiences in combat, which helped him gain perspective. Still, even though these conversations made him see Jack's path more clearly, there was looming uneasiness for him playing a soldier from such a controversial, devastating event.
"I think being a guest in a place where the history that we were telling actually happened, the history in the story, actually happened in reality ... I know I had a little bit of weariness of wearing an American uniform while over in Vietnam," Milo recalls. "I think we were all very aware of it ..."
It's not something that Milo would call a struggle necessarily, though. Just something he was very conscious of when he put on his costume. If we're talking his greatest hurdle in season 3, Milo would say, instead, that it was having to rewind the tape on Jack's life.
"I've gotten so used to playing Jack with his 11-year-olds or Jack with his teenagers. I knew those two men very well," Milo begins. "Going back to who he was ... before any of that attachment, or family, or anything, and knowing my choices I was making for the character were going to have to lead us to that man. That was the challenge of the year."
But any and every obstacle Milo faces as an actor is made much easier thanks to the This Is Us crew and cast members he gets to interact with the most — particularly, the kid and teen versions of The Big Three, and Rebecca (played by Mandy Moore). He may not be around Chrissy Metz, Justin Hartley, and Sterling K. Brown very much, but that doesn't mean he has any less fun. When it comes to his and Mandy's relationship, he says it just keeps getting better.
"I think Mandy has probably heard everything that I've said a billion times, so therefore she just kind of knows what's coming. We spend so much time together that all of a sudden all my stories have been used up," Milo says. "When you do spend more time with somebody ... those relationships get deeper. And there's more meaning to them and more significance to them, and I think that reflects in the work when Mandy and I are on set. I know she's looking out for me, and I'm looking out for her."
Outside of the set, Milo is typically doing press junkets across the world with the full cast. While he's out traveling, he gets to meet a lot of the show's most dedicated fans. Ask him what his "craziest" fan interaction was, and he won't tell you about a time someone screamed "It's JACCCK!" or begged him to take a selfie. The most wild story for him derived from a fan doing the simplest thing while he was getting off a plane in New York City.
"[I'm] walking with Chrissy, and a woman quietly walks up to me, and she just says, 'Excuse me. You're Milo?' And I said, 'Yeah.' And she goes, 'And you play Jack?' And I said, 'Yes, I do.' And she says, 'I just wanted to thank you.' And she puts her hand out to shake my hand. She said, 'I just want to thank you, because my husband and I adopted a little boy, and we've been having a hard time with him. And watching your show, we learned a lot of patience. Especially my husband, [he] learned a lot about relating to his son, that is his son, but not by blood. And I just wanted to thank you.' And then she pulls up her phone and shows me a photo of her husband and her adoptive son, and then she just said, 'thank you' and just walked away."
What made the moment so special for Milo was the fact that, as he says, she didn't "need anything from me" in that moment: She just wanted to share her experience, which "fills me up the most" as an actor.
Indeed, it's impossible to ignore the connection viewers feel to Milo's character. The obsession with looking for "men like Jack" is very real, and has even sparked anger among some guys who think Jack has set "unrealistic standards." In fact, one of the most searched questions on Google around his character is "Do men like Jack Pearson from the show This Is Us exist?"
Milo's short answer is, well, yes. There are men who have gone through war, struggle with alcoholism, and love their families unconditionally. But on a deeper level, Milo believes the mania surrounding his character could signal that there's a larger void in our culture.
What's important is not only Milo's optimism, but his recognition that Jack isn't the perfect dad or husband, either. He's flawed, just like everyone else. On the inside, and, as Milo jokes, on the outside, too.
"I have this hair cut that works in the '80s but man, oh man ... when I jump back to Milo in 2019, oh man," Milo quips. Now the mustache, on the other hand, that's about as close to perfection as it can get. "It's funny, 'cause now I feel like I've seen in real life a lot more mustaches. And I'm half-wondering, 'Did Jack do that?'"
Honestly, probably. But Milo may have had a part to play, too.


At Tailored Dental Ceramics, we are dedicated to quality, service and helping patients regain their smiles and self-confidence. Our commitment to world class training with renowned dentists such as Dr. Peter Damson, Dr. Frank Spears . Lee Cup,Aki Yoshida ,Otto Prandtner,and LVI combined with our longstanding membership in American Academy of Cosmetic Dentistry ( AACD )and our self-imposed standard of excellence have been the secrets to our success for nearly 3 decades. We are not a "tooth factory." We carefully craft each specialty piece to the exact specifications ordered by you, the dentist, to benefit your patient with pristine form and functionality. We offer up-to-date technology, meticulous attention-to-detail and superior artistry, which means your patients get better function, fit, and comfort, while you benefit from less chair-time per patient, so you can schedule more patients and enjoy a healthier bottom line.


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text:
Patrick T. Doherty, Esq.
Ian V. Gallo, Esq.
Andrew Alston, Esq.
Nathaniel X. Rivera, Esq.
Enrique Rosario, Esq.
Vincent J. Gallo, Esq.
Patricia Failor
DUI Charges
Skilled Legal Representation For the People of Philadelphia & Beyond SCHEDULE A CONSULTATION
Andrew Alston has a talent for quality advocacy—both oral and written. Though he has been a trial lawyer for most of his career, he has shifted his focus to persuasive legal writing. His use of plain English, easy formats, and quality visuals provide a breath of fresh air for the reader. And, in turn, his style improves the client's posture. For this work, he consults with other attorneys—primarily solos and small firms—to improve and to provide engaging written advocacy.
By providing the necessary backup when issues are complex, different insight is needed, or deadlines are tight, Andrew's legal writing services enable attorney clients to focus on the other aspects of their practice, business, and lives. Hourly and flat-fee options are available to help you budget for the drafting of demands, pleadings, motions, briefs, and memoranda. Andrew's unique creativity with the persuasive use of visuals tied into focused legal writing has met with much success.
Prior to this, he focused his practice primarily on personal injury litigation, criminal defense, and family law. He is an experienced trial attorney with significant courtroom experience and a track record of trial successes. Andrew has a reputation for compassionate, effective, and honorable advocacy. He enjoys advocating for the underdog, and he carries that into his practice.
Andrew is an Honors graduate of Gwynedd Mercy University with his Bachelor of Science in Biology with a minor in Chemistry. After taking his Emergency Medical Technician training at Jefferson University Hospital, he was licensed and served in that role.
"In every case I work on, I call upon my courtroom experience and my compassion for others."
Andrew is a graduate of Temple University, Beasley School of Law. At Temple Law School, Andrew graduated with Dean's Honor List recognition and numerous Trial Advocacy and trial performance awards. During law school, Andrew had the privilege to serve in an intern and extern clerkship in the Eastern District of Pennsylvania for Federal District Court Chief Judge Juan Sanchez as well as Federal Magistrate Judge Timothy Rice. From Temple Law and separately from the Pennsylvania Bar Association, Andrew received awards for his public interest law service.
After law school, Andrew practiced law at one of the largest criminal defense organizations in Philadelphia where he represented hundreds of clients as lead counsel through all stages of hearings and trials—both bench and jury.
To continue to refine his courtroom skills, Andrew completed an LL.M. in Trial Advocacy at Temple University, Beasley School of Law. During the LL.M. Program, Andrew received the Faculty Award for Outstanding Achievement in Courtroom Presentation and Performance.
Andrew volunteers his time to speak at continuing legal education and training programs, including PBI and NITA. Outside of the law and the courtroom, Andrew enjoys hiking, biking, spending time outdoors, and traveling with his family.
LL.M. - Temple University Beasley School of Law, 2018
J.D. - Temple University Beasley School of Law, 2013
B.S. - Gwynedd Mercy University, 2008
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Opower was founded in 2007 and secured an additional $50 million in funding last November. In 2010, the company doubled in size and by then had abated nearly 500 million lbs of CO2. And President Obama during a visit to their offices called the company "a model of what we want to be seeing all across the country." You couldn't fully appreciate these accomplishments by looking at Opower.com a week ago. Like most companies who experience accelerated success, some aspects of the business play catch-up. Viget partnered with the energy-efficiency start-up to completely re-imagine Opower.com and elevate the site to a position reflective of the company's continuing accomplishments and growth.
This wasn't just a redesign, however. A polished, compelling presentation is one way to solicit credibility, but the responsibility of Opower.com extends beyond putting on a pretty face. One of the site's key goals is to answer the frequent question: What is Opower? It's not as easy an explanation as you might think, particularly because Opower isn't a product or service for which you as the average consumer can sign up. Through considerate user experience design, content strategy and visual presentation, we've helped answer this question in a way that tells an approachable story as opposed to simply presenting content.
Through the course of our relaunch effort, Opower hired dozens of employees and even refreshed their brand. This ongoing maturation of the company presented some challenges, but more opportunities. Not only were we setting the style, tone and positioning of the site, but we were also influencing the brand at large. Opower pushed us to test certain visual directions and concepts through the lens of adopting those elements beyond the site. These exercise(s) were challenging, but most certainly worthwhile and fun.
Four swift months later the refreshed face of energy efficiency is online and happy (and sometimes winking). And it should be. The new site is a much better reflection of the culture and continued success of Opower, and a positive story-telling device to express who the company is and the industry they are leading.


The highlight of CIT's coin portfolio at World Money Fair 2019 is a breathtaking three ounce silver issue for the Isle of Man (often referred to simply as Mann). While depictions on modern coins often lack a significant connection to the country of issue, Manannán – 1st King of Mann – is a treasure of folklore and cultural identity.
The outstanding numismatic tribute to Manannán measures 55 mm in diameter, features an antique finish and nominal value of 5 £. Only 999 pieces will be struck of this Isle of Man issue. As a self-governing Crown dependency, Queen Elizabeth II is the head of state holding the title "Lord of Mann".


Formative assessment is a pedagogic practice that has been the subject of much research and debate, as to how it can be used most effectively to deliver enhanced student learning in the higher education setting. Often described as a complex concept it embraces activities that range from facilitating students understanding of assessment standards, to providing formative feedback on their work; from very informal opportunities of engaging in conversations, to the very formal process of submitting drafts of work. This study aims to show how cultural historical activity theory can be used as a qualitative analysis framework to explore the complexities of formative assessment as it is used in higher education. The original data for the research was collected in 2008 by semi structured interviews and analysed using a hermeneutic phenomenological approach. For this present paper three selected transcripts were re-examined, using a case study approach that sought to understand and compare the perceptions of five academic staff, from three distinct subject areas taught within a UK university. It is proposed that using activity theory can provide insight into the complexity of such experiences, about what teachers do and why, and the influence of the community in which they are situated. Individually the cases from each subject area were analysed using activity theory exploring how the mediating artefacts of formative assessment were used; the often implicit rules that governed their use and the roles of teachers and students within the local subject community. The analysis also considered the influence each aspect of the unit of activity had on the other in understanding formative assessment practice. Subsequently the three subject cases were compared and contrasted. The findings illuminate a variety of practices, including how students and staff engage together in formative assessment activities and for some, how dialogue is used as one of the key tools to do this. In conclusion, activity theory is considered a useful methodological framework both from a research perspective, as in this paper, and one that can be used as a tool for the reflective practitioner to promote change in pedagogic practices.


Founded in 1929, Pellettieri, Rabstein & Altman is one of the largest law firms in New Jersey. The legal field is very competitive and PR&A needed a Web site design company to communicate the firm's professionalism, dedication and track record while also helping them rank in the top of search engine results. Stonehouse Media Incorporated worked with PR&A and built this content managed web site to not only look great and represent them well, but also take them to the top of the search engines through a search engine optimization strategy and gain exposure of their talent and expertise through a creative Web site design.


Current Opportunities | Virginia / North Carolina Alliance for Minority Participation, U.Va.
The Alliance maintains a listing of summer and academic year research, internship, and scholarships available to students and partner institutions. Please contact Mr. Maurice Walker (emw5m@virginia.edu or 434-982-0310) with questions or additions. A list of opportunities from previous years is also available.
Overview: The Constellation Undergraduate Summer Program (CUSP) is an REU program that provides undergraduate research opportunities to work in High Energy Density Physics (HEDP). The Constellation Fellows are paired with host mentors that are some of the world's pioneers and leaders in HEDP that comprise a nationwide network including UC San Diego (lead institution), UC Davis, UC Berkeley, UCLA, UC Santa Cruz, UC Irvine, the University of Chicago, and Florida A&M University. Research projects are related to the experimental, theoretical and computational study of material properties and energy transport of matter under extreme conditions of temperature and pressure. This research provides a unique blend of Fusion Energy Sciences, Computational & Experimental Plasma Physics, Nuclear Physics, Planetary Science and Astrophysics and employs some of the nation's fastest supercomputers and cutting-edge facilities related to understanding matter under extreme conditions.
REU Participant Benefits: $4,000 stipend ($500/week); travel support to host institution and an allowance for 8 weeks of housing; assistance securing housing at the host institution; tutorials on high performance computing, numerical modeling, scientific visualization, and high performance computing; travel reimbursement and comprehensive training to move participants toward intellectual and research independence.
• Must be US citizen or permanent resident.
• Completed junior year with major in physical science or engineering (or equivalent) with a 3.0 GPA.
• Some exceptional sophomores will be considered.
• Background in astrophysics, plasma physics, or energy science is not required.
• Computer programming experience (Matlab, Python, C, Fortran, C++, etc) recommended but not essential.
Overview: Undergraduate Robotics Research in Human-Swarm Interaction project will provide training, mentorship and support to undergraduate students so that they can become independent researchers in the area of robotics. Throughout the project, the faculty and graduate student mentors will encourage creative thinking and frequent interactions to enhance the students' problem-solving skills. Visit https://robotics.wvu.edu/ for more information about WVU Robotics research and educational activities.
REU Participant Benefits: Stipend of $5,000, lodging, meal expenses, travel reimbursement and comprehensive training to move participants toward intellectual and research independence. Participants will be expected to conduct research full-time, minimum of 4 hours per week for 10 weeks.
• Citizens, nationals, or permanent residents of the U.S. or its territories.
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Overview: Harris-Stowe State University (HSSU), located in midtown St. Louis, and National Science Foundation - HBCU- UP present a conversation about workable methods that could increase the number of African-Americans in STEM. A free Community STEM event will be held on thursday, April 4th. Guest speakers include Dr. Aprille Ericsson, Rocket Scientist, Technologist & STEM Educator and Christopher Emdin, Professor of Science Education & Author and Minorities in Energy Ambassador for the Department of Energy.
Overview: The Student Research Participation (SRP) program encourages undergraduate students to pursue science, technology, engineering, and mathematics (STEM) careers by providing research internships. A student will spend the first week of his/her Argonne experience with an Argonne staff member devising a research strategy and attending mandatory safety classes. For the next few weeks, the supervisor will provide considerable program assistance and guidance to implement the research plan. Subsequently, the student will be required to give a poster presentation at the end of their appointment.
In addition to their research activities, participants attend a series of weekly seminars and tours dealing with current topics in science and engineering and career development. During the appointment period, participants receive a stipend of $500 per week and on site housing. Dormitory type lodging is available on site at no direct cost to the student.
Pathways to Science.org: Search 1,500 STEM programs and funding opportunities nationwide. Check out our webinars and professional development materials. Students can find summer research listings on this site.
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If students need help finding programs that fit their interests, please email me at ldetrick@ibparticipation.org and I would be happy to search our database of programs and send you recommendations.
The Molecular and Cellular Biology (MCB) graduate program at Virginia Tech offers students the opportunity for PhD studies in four broad categories: Cellular Signaling and Cancer, Inflammation and Immunity, Microbology, and Neurobiology. MCB provides career development opportunities, leadership skills, teaching opportunities, and grant writing workshops to complement rigorous scientific training, providing each student the opportunity for career placement and success. For more information and how to apply: www.mcb.vt.edu.
Computer science is a growing field that has incredible career opportunities. Our guide focuses on helping minority students on why they should consider getting into the field, exploring different computer science programs and colleges, and what to look for in a computer science degree. Explore areas of computer science, career options, coding guides (including Java, C#, Python, etc.), scholarships, and more.
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MUNI is a NanoEarth signature initiative. With only 11% of underrepresented people working in science and engineering jobs, MUNI strives to provide an opportunity for inspiring those groups to pursue nanoscience degrees and careers. MUNI provides access to and training opportunities on state-of-the-art nanoscience-relevant instrumentation, as well as nano-synthesis and processing laboratories, for underrepresented professionals and students. For students, MUNI serves all academic levels, from K-12, to community college students, to students in four-year programs and even graduate school.
Centrally located in the mid-Atlantic region, MUNI is able to accommodate nationwide. An easily manageable day's drive (seven hours or less) to Blacksburg, Virginia includes cities such as Atlanta and Columbia to the south, Indianapolis, Cincinnati, and Columbus to the northwest, Cleveland and Pittsburgh to the north, and Washington, D.C., Baltimore, and Philadelphia to the northeast. An additional two hours of travel, includes northern Florida and New York. MUNI covers travel costs and usage fees to all its facilities. MUNI participants will also get a chance to interface with a variety of professors and gain valuable insight into the field of nanoscience and nanotechnology, especially as it relates to Earth and environmental science.
Students, faculty and advisors can now search for opportunities in real-time using this database tool. There are two separate search tools - one for undergraduate and one for graduate students. Check it out!
Complete a single application and make your data accessible to more than 100 companies simultaneously! Eligibility Requirements: at least 18 years of age; attending a Virginia university, college, or community college; Virginia residents attending accredited out-of-state colleges may also apply; should be taking at least six credit hours per semester and making demonstrated progress towards a STEM degree; completed at least 30 hours of post-secondary education credits; rising sophomore to graduated senior; STEM major; U.S. citizen or permanent resident; 2.7 GPA. Download flyer here.
This material is based upon work supported by the National Science Foundation under Grant Number 1202181. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.


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Tag Archives: actresses
[CFP] Infinite Variety: The Older Actress On Stage 1660–Present
Dame Judi Dench as Titania (2014). Photo by Nobby Clark.
Infinite Variety: The Older Actress on Stage 1660–present
A two-day symposium on 18–19 October 2019, taking place at Christ Church, University of Oxford, UK.
Symposium Directors are Dr Sophie Duncan and Professor Mary Luckhurst
The event is jointly convened by the School of Arts, University of Bristol and Christ Church, University of Oxford, with support from The Oxford Research Centre for the Humanities (TORCH).
Confirmed keynote speakers include Professor Gilli Bush-Bailey (Central School of Speech and Drama), Professor Jacky Bratton (Royal Holloway) and Dr Fiona Gregory (Monash University).
We welcome proposals for 20-minute papers from scholars and practitioners in theatre and related disciplines. Suggestions for topics include, but are not limited to:
older actresses on and off stage: as performers, managers, stage-managers, playwrights, producers, directors, and teachers, 1660–present.
older actresses – their approaches to acting and their creative and career strategies
older actresses and the one woman show
older actresses – stage v. film and television
older actresses on ageism and the politics of transgression
writing by older actresses, e.g. memoirs
genealogies of female performance and concepts of female 'succession'
retirement and its alternatives
'canonical' roles for older women; repertoire and ageing
older actresses and non-traditional casting
the depiction of older actresses and/or fictional older actresses in criticism, journalism, literature, the visual arts, and film
ageism, ageing, and the body in casting, rehearsal, performance, and reception
older actresses with additional marginalised identities, including LBT older actresses, BAME actresses, and actresses with disabilities (including age-related disabilities); the intersection of age with other kinds of marginalisation
the older actress in theatre historiography and as theatre historian
retrospectives, gala performances, honours lists and becoming a 'national treasure'.
Proposals, which should be 300 words long and accompanied by a brief biography, should be sent to the symposium's directors, Dr Sophie Duncan (sophie.duncan@chch.ox.ac.uk) and Professor Mary Luckhurst (mary.luckhurst@bristol.ac.uk) by May 31 2019.
This entry was posted in ACADEMIA, christ church, lgbt, oxford, Shakespeare, TELEVISION and tagged actresses, age studies, cfp, conference, infinite variety, older actresses, shakespeare, symposium, THEATRE, theatre history, theatre studies on 16 May, 2019 by clamorousvoice.
Mrs Patrick Campbell and George Cornwallis-West
Mrs Pat as Paula Tanqueray.
At the moment, I'm researching Mrs. Patrick Campbell (born Beatrice Tanner; familiarly called Stella). Mrs. Campbell is most famous for her "Pinerotic" roles in the 1890s, such as The Second Mrs Tanqueray and The Notorious Mrs Ebbsmith; for her Hedda Gabler; and as the original Eliza Doolittle in George Bernard Shaw's Pygmalion.
I, however, am interested in her Shakespearean roles. In the late 1880s and until about 1893, she had several successes in roles like Rosalind; then, at the other end of the decade, she played the trio of tragic roles that most interest me. These were, in order, Juliet (1895), Ophelia (1897) and Lady Macbeth (1898).
With the Bodleian Library doing various interminable and obscure things in the way of moving book depositories, I wasn't able to get my hands on Mrs. Pat's autobiography for weeks, and ended up reading everything but; finally, I caved, and bought it myself, on Ebay.
I originally conceived my doctoral project as a study of Shakespearean actresses' autobiographies (and later, as a study of writings by actresses on the women of the Late Plays), and even though my textual focus has shifted (both in and out), I feel as if, until now, my research has been hobbled by not having My Life and Some Letters in front of me.
I may say that Mrs Pat's name-dropping makes Madge Kendal and Constance Benson look positively restrained. I enjoy old theatrical memoirs very much for their own sake (and am looking forward to reading Irene Vanbrugh's, on Simon's recommendation), but this one balances incredibly useful, challenging/problematic insights (v. wholesome and good for thesis) with delicious and irresistible snobbery. Bless her, it seems she had no friends without titles. She makes me want to be called Frances something, COUNTESS of MADEUPPLACE. And then write gushy, borderline-homoerotic letters to actresses. An impulse which society cruelly demands I subdue.
Campbell is much more open about her life than Langtry (although omitting the affair with Johnston Forbes-Robertson) and – unlike Ellen Terry – absolutely fascinating in her detailed discussion of her children. I've just got to the bit where her son, Beo, dies in the First World War. For the first time reading one of these memoirs, I found myself welling up.
I'm also interested in Campbell's apparently disastrous second marriage, which goes from huge affection (her son, particularly, seems to have held him in high esteem) to breakdown in a very few pages. Reading about the suicide of Elizabeth Robins's first husband, who put on a suit of armour, then jumped into the Charles River; and about the complicated life of William Hunter Kendal has interested me in theatrical husbands.
George Cornwallis-West.
Mrs Patrick Campbell's second husband was George Cornwallis-West. Major Cornwallis-West (who had been rumoured to be Edward VII's lovechild) first married the stunning Lady Randolph Churchill, mother of Winston and twenty years his senior; he remarried to Stella Campbell just five days after their divorce. The marriage broke down in 1921; Cornwallis-West also seems to have been plagued by financial troubles for most of his life. In 1940, the year of Stella's death, he remarried for a third time, to a Mrs. Georgette Hirsch. In 1951, while suffering from Parkinson's Disease, he took his own life.
Never a dull moment, with this lot, but what sad & eventful stories.
This entry was posted in THEATRE and tagged ACADEMIA, actresses, autobiography, books, ellen terry, george cornwallis-west, ibsen, madge kendal, mrs patrick campbell, nineteenth century theatre, THEATRE, william hunter kendal on 4 June, 2011 by clamorousvoice.
Britgrad 2011 and a summer of conferences…
On Sunday, I returned to Oxford from the Britgrad 2011 conference, where I was part of the Victorian Theatre Practices panel with the fragrant Jem Bloomfield.
KENDAL 4 LIFE. Or similar.
Jem was talking about mid- and late-Victorian productions of The Duchess of Malfi, while my paper was entitled '"Marriage of Orlando and Rosalind": Madge Kendal and Victorian Shakespeare". The conference organisers charitably having given us a panel in which to get REALLY EXCITED to the bemusement – and, thankfully, amusement – of our colleagues, we waved our arms and talked actresses to our hearts' content.
A large proportion of the delegates at our panel had strong interests in performance; sometimes both as scholars and practitioners. I'd hoped one of the main points of my paper – that our current theatrical historiography is problematic in its accommodations for women, as evinced by Madge Kendal, acclaimed and central Victorian actress, falling through the gaps of history – might be disproved by someone bouncing up to say they, too, are a ridiculous enthusiast/horrified onlooker at the fireworks of her life. But no. While this does tell me I'm probably on the right track (conference full of excitable Shakespeare postgrads = not a flicker of recognition, but much interest), it's such a shame!
Overall, a productive three days. Having swotted up on posts from (all I really need to know, I learn from) Thesis Whisperer, I made myself ask questions at most panels. I usually struggle to think of them (and am slightly allergic to Q&As as it is), but found that if I went in determined to ask, it made me a more proactive listener and I ended up with genuine queries. So hurrah for that. My only Britgrad regret is that there was a girl in my panel who asked a really fascinating question about Victorian theatrical fan literatures. I'd hoped we'd get more of a chance to talk afterwards (Victorian fan literatures are honestly one of the most exciting, and weirdest, things on God's earth), but sadly I didn't see her again.
My conference schedule for the rest of the summer is ridiculously busy. Should you have an inexplicable yen to see a short girl in glasses talk about Victorian actresses, you can catch me at any of the following:
10 June 2011: Oxford English Graduate Conference, University of Oxford: "The Famed and the Forgotten".
7-9 July 2011: Universities of Birmingham and Lancaster, The Storey, Lancaster: "Politics, performance and popular culture in nineteenth century Britain".
18-19 July 2011: Victorian Popular Fiction Association Conference, University of London: "Sex, Courtship and Marriage in Victorian Popular Culture".
If you're attending any of these events, please let me know! It'd be great to make some new conference-friends beforehand…
This entry was posted in ACADEMIA, oxford, STRATFORD-UPON-AVON, Uncategorized and tagged ACADEMIA, actresses, conferences, friends, madge kendal, nineteenth century theatre, oxford, presenting, STRATFORD-UPON-AVON, THEATRE on 2 June, 2011 by clamorousvoice.


It's been awhile since a crowd cheered an indie band's… lighting.
But here we were in L'Olympia, where Grizzly Bear was going to showcase some of the best elements of the catch-all category we call indie, while repudiating some of the negative implications of the category.
In some ways, Grizzly Bear is a central representative of the indie ethos: oblique song and album titles, bed-sit presence, complicated songcraft, offbeat instrumentation (hello, omnichord). Hey, they live in Brooklyn. But when you write things as lovely as Foreground, and when you deliver creative stagecraft to differentiate yourself from the herd, you have elevated your band to a level that "indie" or "alt" don't cover.
It was after a rapturous welcome in yet another packed, luridly memorable Montreal theatre, after Speak In Rounds, an oddly bumping song that unfolds melodic colour, something Grizzly Bear would do all night. Ed Droste's plangent vocals were hanging in the air as a dozen or so amber lightboxes shaped like IV bags slowly, magically floated to the ceiling like illuminated jellyfish during Sleeping Ute, leaving their electrical cables dangling like tails. It was a remarkable deployment of onstage décor, drawing awed, delighted applause. They weren't about to lose that momentum.
Cheerleader opened with thundering drums and a big distorto riff, followed by the akimbo Yet Again. Daniel Rossen's Little Brother was a stomper with a ballad heart. We'd already heard five distinctly different but related song structures, mainly on the healthy side of fussy. These were songs that never settled into anything stock; neither were they weird for weirdo sake, and the band was moving into the haunting centre of the set. The almost hymnal Shift made further use of that remarkable lighting. Gun-Shy was vintage alt, something that might have sat in a Cure or Pumpkins setlist. The chugging A Simple Answer kept that mood, before delivering one of the stellar moments of this festival.
With minimal twinkling, hushed instrumentation, Droste sang Foreground as the jellyfish floated. It was a spectral, moving four minutes that capped this and expressed the maturity in this music and performance. Because Grizzly Bear isn't in any way a hit-making band, just a band that delivers brainy, musically complex moments.
Small criticism: Grizzly Bear wasn't massively late, but the 20 or so minutes might have cost someone who wanted to make another gig on the final night of Pop Montreal 2012. But as it turned out, nothing was going to follow this anyway.


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