Direct Instruction, Part 1

Direct Instruction, Part 1

Several months ago, in the NCTM regional conference in Boston, I attended a session on Direct Instruction. It immediately dawned on me that our high school series, Integrated Algebra 1, Geometry, and Algebra 2 and Trigonome! try uses elements of direct instruction.

We purchased a book, Designing Effective Mathematics Instruction: A Direct Instruction Approach, 4th Edition, so that I could better acquaint myself with direct instruction.

So what is direct instruction? According to the National Institute for Direct Instruction, direct instruction is

…a model for teaching that emphasizes well-developed and carefully planned lessons designed around small learning increments and clearly defined and prescribed teaching tasks.

Of course, no program is perfect and you'll need to use your experience and common sense. For example, if you take this definition to its logical conclusion, you may stifle student creativity. If you've recently learned something new and complex, you know what I'm talking about—as you first struggled to understand the new topic or skill (whether it's a home improvement project, an arts and crafts project, or a work project), you appreciated the gentle learning curve (small learning increments). But as you gained confidence and mastery, you had to take "leaps and bounds"; otherwise, the project would have never been finished.

Applying this to the classroom, students need a gentle learning curve when approaching new and intimidating topics. But, eventually, once students start to master the topic, it's OK to provide a more challenging environment.

Tip #1: Topic Order Is Important

In retrospect, it seems obvious that the order in which you present topics and skills matters. Yet, when creating a lesson, we are always tempted to mindlessly mix topics together. Direct instruction recommends to:

• Teach pre-skills first
• Teach easy skills before more difficult ones
• Don't teach complex strategies and/or concepts that are likely to be confused one after the other.

Some examples are in order: When teaching how to graph linear functions, make sure students know how to plot points on a coordinates axes. That's teaching pre-skills first. When teaching the rules of exponents, it may be a good idea to explain the rules with concrete numerical examples before using variables. The average student may struggle with variables.

The third bullet above caught my attention. At first glance, it may appear that teaching similar complex topics one after the other is a good idea. After all, students can use compare-and-contrast to better understand the two concepts, right? Unfortunately, that view assumes that the student is talented or at least motivated to want to keep the concepts straight. That's not always the case (as I'm sure you well know). It's better to keep similar complex topics separate. For example, at the lower grades, students may confuse congruence and similarity. But what do you think? Leave your comments below.

By the way, a strategy is a set of skills. For example, how to factor a quadratic is a strategy that uses the skills factoring a perfect square, etc. Pre-skills are skills that students need to master before learning the current topic. An easy example is: students need to first know how to plot points on a coordinate axes before attempting to graph linear functions.

Well ,that's it for this time. Over the course of the next few months, I'll be blogging my journey as I (more formally) explore direct instruction.

how to graph linear functions

How to calculate square roots without a calculator (square root calculator)

Square Root Calculator

Many mathematical operations have an inverse, or opposite, operation. Subtraction is the opposite of addition, division is the inverse of multiplication, and so on. Squaring, which we learned about in a previous lesson (exponents), has an inverse too, called "finding the square root." Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 …

The square root of a number, n, written

is the number that gives n when multiplied by itself. For example,

because 10 x 10 = 100

Examples

Here are the square roots of all the perfect squares from 1 to 100.

Finding square roots of of numbers that aren't perfect squares with! out a calculator

1. Estimate - first, get as close as you can by finding two perfect square roots your number is between.

2. Divide - divide your number by one of those square roots.

3. Average - take the average of the result of step 2 and the root.

4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.

Example: Calculate the square root of 10 () to 2 decimal places.

1. Find the two perfect square numbers it lies between.

Solution:
3² = 9 and 4² = 16, so lies between 3 and 4.

2. Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)

3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667

Repeat step 2: 10/3.1667 = 3.1579
Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623

Try the answer --> Is 3.1623 squa! red equa l to 10? 3.1623 x 3.1623 = 10.0001

If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.

Note: There are a number of ways to calculate square roots without a calculator. This is only one of them.

Square Root Calculator

how to find square root

Factoring the time

I stumbled upon this comic that you might enjoy... factoring the time (from xkcd.com).

help in math

And Then There Is Shape

What is a shape?

Try this. A shape is an area enclosed with edges, specific or implied. That's my definition.

I could not believe it. I checked the definition in my trusty old 1960 edition of Webster's New World Dictionary and I found garbley-gook. Then I got curious and started Googling for a definition. Same thing. Even dictionary.com has no clear definition for shape.

Aside from the definition, let's try to understand shape as it pertains to us as artists. First of all, important for artists to know is that every shape has two parts! : the space occupied by the shape and the space around the shape. You can't have one without the other. Think about it.
Above is the famous "Hare" by Albrecht Durer along side a portrait by Pat Weaver. Both have in common an acute observation of the shape itself as well as the space around the shape. That's what makes both shapes interesting to look at, even in silhouette.Look at the silhouette images in reverse. Switch your attention to the black shapes. Notice how interesting each black shape is on its own. Beyond being aware of both shape and the space around it, each artist has made these shapes interesting by careful observation of their edges and how the edges relate to both sides--the shape and its surrounding space.

But before we dwell on that, let's explo! re some nomenclature.

Since the early 20th century, shapes that occupy space have been called positive shapes whereas the space surrounding a shape is called negative space. I've always objected to these labels and I'm not alone: efforts abound to find more definitive labels, but none seem to stick. So, we will let it stay for now and use the historical labeling. (If any of you has a suggestion for how we might rename these shapes, please leave them in Comments. Thanks.)

Okay, that tells us one characteristic of shapes. The other is that they fall into two catagories--geometric shapes and organic shapes. Loosely defined, geometric shapes are those with precise edges such as a circle, square, triangle, recta! ngle and so on. Organic shapes are all the others, shapes whose edges are more random. In painting we are likely to be dealing with both.

And here is where the discussion gets tricky: we can know all this about shapes, but using shapes dynamically in our painting and drawing is a bit different from just knowing about them. So how can we make that happen?

Use acute observation and sensitive interpretation. Just that. Rather than look at a shape and ! call it a rock, for example, first look for the underlying geometric shape that forms its structure, then study intensely the variations of the edges because these variations are what create the real character of the shape.

Next, look closely at the value and textural relationship of both sides of a shape's edge. Sometimes the negative will be blending right into the positive, sometimes there is a softness between the two and sometimes there is a distinct division.

In my judgement, Charles Reid is one of the best shape-makers among our 20/21st century artists.

Charles Reid "Claire" Watercolor on paper

Reid begins each of his paintings by doing a careful contour drawing to discover and anchor the shapes and their relationships to one another. When he begins his painting, he is constantly shifting between negative and positive, sometimes causing edges between the two to be lost; other times, creating a softness between them and at others, showing distinct sharpness to the edges. What results is a lively painting that continues to invite the viewer to return to it.

For me personally, Reid's paintings are like Chopin piano works--I want to revisit them over and over again. I think that desire to keep ! looking at a art work is one of the marks of its strength and success. And when an artist is truly tuned in to the characteristics of each shape, a lot is bound to get translated into the resulting work.

Try this. Visit websites of artists like Reid, Jennifer McChristian, Richard Schmid, Carolyn Anderson, Robert Genn and others whose work is strong. List the ways they handle shapes in light of this discusssion, then try some of those techniques yourself and watch the world open up.

geometry shape definitions

Free algebra worksheets

Usually algebra textbooks provide lots of problems to practice the algebraic concepts and techniques, but some of you may still benefit from resources for free (or mostly so) printable algebra worksheets. Please see the list below, which I've originally compiled for my HomeschoolMath.net site.

Algebra worksheets

Worksheet Builder
Great and free worksheet maker software with nearly 7,000 built-in algebra and geometry questions.
www.jmap.org/JMAP_WORKSHEET_BUILDER_INSTALLATION_FILES.htm

Free Algebra Worksheets from KUTA Software
Free worksheets (PDF) for equations, exponents, inequalities, polynomials, radical & rational expressions and more.
www.kutasoftware.com/free.html

AlgebraHelp.com worksheets
Interactive worksheets that are checked online for most algebra 1 topics.
www.algebrahelp.com/worksheets/

Math.Com algebra worksheets generator
Generate worksheets for: linear equations, systems of equations, and quadratic equations.
www.math.com/students/worksheet/algebra_sp.htm

LessonCorner worksheets
These free worksheets include a few topics such as calculations with polynomials, factoring, and graphing lines.
www.lessoncorner.com/worksheets/

Algebra Fun Sheets
Worksheets that integrate algebra skills with fun activities including sudoku, word finds, riddles, color patterns, crosswords, games, matching cards, etc. A subscription is required.
www.algebrafunsheets.com

About.com Algebra Worksheets
An assorted collection of free algebra worksheets and answers. These pages are not very well organized, but they have lots of worksheets.
math.about.com/od/algebraworksheets/Algebra_Worksheets.htm

Algebra Worksheets from MathWorksheetCenter
Lots of worksheets for over 100 algebra topics. A few are free; most are accessible only by one-year a subscription.
www.mathworksheetscenter.com/mathskills/algebra/

A few fun algebra worksheets
These are for graphing linear equations and linear inequalities.

Online Math Work
Free multiple-choice worksheets for pre-algebra and algebra 1 topics. You can do them online, or copy to a word processor to print.
www.mathonlinework.com

Lastly... my own algebra worksheet collections, which aren't free but there are many free samples:

Math Mammoth Algebra 1 Worksheets Collection
A two-part collection (A and B) of 137 quality algebra worksheets covering all the topics in a typical algebra 1 curriculum. These worksheets are hand-crafted and contain lots of word problems and other variable problems. Free samples available. $11.50.
www.mathmammoth.com/worksheets/algebra_1.php

free algebra problems

The First Free Hydroponic Nutrient Calculator Program :o)

After a lot of work and effort today I have the pleasure to share with you my latest development in the area of hydroponic nutrient design and creation, a totally new and free hydroponic nutrient calculator which I programmed using Delphi. This piece of software is absolutely unique and I can guarantee that you will not find any other similar program on the internet. The piece of code I am about to release was the natural evolution of my excel spreadsheet (which comes with my free ebook) and now has a ton more features which should make hydroponic nutrient calculation for absolutely anyone a total breeze. On today's post I want to share with you this program as well as a general description of its scope, uses and improvements over the excel spreadsheet available for nutrient calculation within my ebook.

One of my main objectives has always been to design and prepare my own hydroponic nutrien! t solutions and to help others do the same thing. Preparing your own solutions is not only something that gives you absolute control over the composition of the nutrients you are giving to your plants but it also allows you to make absolutely HUGE saving on commercial fertilizers. Using commercial liquid concentrated solutions the cost of a hydroponic garden is usually above 0.20 USD per gallon while if you make your own nutrients this price can drop as low as 0.01 USD per gallon. Additionally people from less developed countries where hydroponics are not very well established will be able to greatly benefit from making their own blends with this sometimes being the only way to have a hydroponic crop.
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The program I am releasing today will allow you to calculate the amount of salts you need to weight to arrive to a given hydroponic formula. The features of the program and its advantages over the spreadsheet previously available are highlighted below :

• Ability to calculate weights of salts for any given hydroponic formulation
• No need to have excel :o) any Windows platform will do.
  
• Flexibility ! Choose which salts you want to use to makeup your nutrient solution
  
• The program automatically determines which salts are better than others or pairs them up adequately if you have sever! al sources for the same nutrient
• Input the volume you want in Liters, gallons or cubic meters
• The program automatically determines if you need or don't need to prepare concentrated micro-nutrient and Fe solutions depending on the size of your reservoir
• You can also choose to add all salts directly if you have scales with the necessary precision
  
• Concentrated A+B solutions can be prepared
  
• Save your solutions ! You can easily save your recipes to a text file for later printing or reference
• Save salt selection
• Select water quality parameters
• Automatically corrects the weights of salts against your water quality analysis
  
• Example recipe obtained using the program and the list of salts I personally use (although you may change those salts for others depending on where you live)
• Automatically check for new updates
  
• And many, many more ! :o)!
  

As yo! u see, t his new program is a great leap forward in custom nutrient solution design and preparation for the average hydroponic hobbyist and small business owner. Hopefully with this program you will be able to prepare your own solutions or improve your previous calculations if you had been using the spreadsheet. I hope that you enjoy the new program and leave any feedback you have here. As always I will be glad to take into account and implement your requests :o)
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empirical formula calculator

Grade 7 Math Curriculum

7th Grade Annual Curriculum Plan with Activities
Day of Instruction	Performance Indicator	Description	Technology Oriented Activity
1	7.N.1	Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, and irrational numbers)	Comparing Numbers http://321know.com/g7_41gx1.htm
2	7.N.2	Recognize the difference between rational and irrational numbers (e.g., explore different approximations of)	Number Practice Game http://www.softschools.com/quiz_time/math/arithmetic/theme2.html
3	7.N.3	Place rational and irrational numbers (approximations) on a number line and justify the placement of the	Placing numbers on a  number line http://www.mathsframe.co.uk/placenumbers.swf
4	7.N.17	Classify irrational numbers as non-repeating/non-terminating decimals	Irrational numbers http://en.wikipedia.org/wiki/Irrational_number
5	7.S.1	Identify and collect data using a variety of methods	Qualitative data collection http://people.uwec.edu/piercech/ResearchMethods/Data%20collection%20methods/DATA%20COLLECTION%20METHODS.htm
6	7.S.1	Identify and collect data using a variety of methods	Primary data collection methods http://brent.tvu.ac.uk/dissguide/hm1u3/hm1u3text3.htm
7	7.S.1	Identify and collect data using a variety of methods
8	7.S.4	Calculate the range for a given set of data	Statistical Range for a set http://321know.com/g7_518x3.htm
9	7.S.5	Select the appropriate measure of central tendency	Basic statistical mean http://321know.com/sta418x5.htm
10	7.N.13	Add and subtract two integers (with and without the use of a number line)	Integer lesson http://www.mathgoodies.com/lessons/vol5/intro_integers.html
11	7.N.13	Add and subtract two integers (with and without the use of a number line)	Integers Quiz http://www.softschools.com/quiz_time/math/arithmetic/theme2.html
12	7.N.13	Add and subtract two integers (with and without the use of a number line)	Subtracting Number ball game http://www.sheppardsoftware.com/mathgames/Numberballs_subtraction/numberballsSubtraction.htm
13	7.N.12	Add, subtract, multiply, and divide integers	Adding integers http://www.mathgoodies.com/lessons/vol5/addition.html
14	7.N.12	Add, subtract, multiply, and divide integers	Subtracting integers http://www.mathgoodies.com/lessons/vol5/subtraction.html
15	7.N.12	Add, subtract, multiply, and divide integers	Multiplying integers http://321know.com/g7_310mx.htm
16	7.N.12	Add, subtract, multiply, and divide integers	Dividing integers http://321know.com/g7_55_di.htm
17	7.N.12	Add, subtract, multiply, and divide integers	Math Mah Jong game http://www.sheppardsoftware.com/mathgames/mahjongMath.html
18		TEST
19	7.N.8	Find the common factors and greatest common factor of two or more numbers	Factorize game http://www.shodor.org/interactivate/activities/FactorizeTwo/
20	7.N.9	Determine multiples and least common multiple of two or more numbers	Least common multiple calculator http://wims.unice.fr/wims/wims.cgi?module=tool/popup.en&search=lcm
21	7.N.10	Determine the prime factorization of a given number and write in exponential form	Factorization in exponential form http://www.eduplace.com/math/mathsteps/5/b/index.html
22	7.N.11	Simplify expressions using order of operations (Note: Expressions may include absolute value and/or integral exponents greater than 0.)	Order of Operations game http://www.shodor.org/interactivate/activities/OrderOfOperationsFou/ Calculating using order of operations http://321know.com/pro73cx0.htm
23	7.N.14	Develop a conceptual understanding of negative and zero exponents with a base of ten and relate to fractions and decimals (e.g., 10-2 = .01 = 1/100)	Evaluating exponents of negaive numbers http://321know.com/exp-int-eval-exp.htm
24	7.A.2	Add and subtract monomials with exponents of one	Evaluating exponents http://321know.com/exp-eval-exp.htm
25	7.A.2	Add and subtract monomials with exponents of one	Arithemetic Four game http://www.shodor.org/interactivate/activities/ArithmeticFour/
26	7.A.2	Add and subtract monomials with exponents of one	Math game http://www.sheppardsoftware.com/mathgames/arithmetic/arithmetic.htm
27	7.N.4	Develop the laws of exponents for multiplication and division	Exponent Quiz Game http://www.softschools.com/quiz_time/math/exponents/theme6.html
28	7.N.4	Develop the laws of exponents for multiplication and division	Multiplication game http://www.softschools.com/quiz_time/math/properties/theme50.html
29	7.N.4	Develop the laws of exponents for multiplication and division
30	7.N.15	Recognize and state the value of the square root of a perfect square (up to 225)	Square root video http://www.mathplayground.com/mv_square_root.html
31	7.N.16	Determine the square root of non-perfect squares using a calculator	Square root game http://www.softschools.com/math/games/squareroot_practice.jsp
32	7.N.18	Identify the two consecutive whole numbers between which the square root of a non-perfect square whole number less than 225 lies (with and without the use of a number line)
33	7.N.5	Write numbers in scientific notation	Scientific notation calculator http://www.calculatorsoup.com/calculators/math/scientificnotation.php
34	7.N.6	Translate numbers from scientific notation into standard form	Converting from scientific notation http://321know.com/nam-g6_71gx1.htm
35	7.N.7	Compare numbers written in scientific notation	Converting to scientific notation http://321know.com/nam-g6_71fx1.htm
36	7.A.1	Translate two-step verbal expressions into algebraic expressions	Algebra Quiz http://www.softschools.com/math/games/algebra_practice.jsp
37	7.A.1	Translate two-step verbal expressions into algebraic expressions	Two variable expressions http://321know.com/equ723x3.htm
38	7.A.1	Translate two-step verbal expressions into algebraic expressions	Algebra Number Ball Game http://www.sheppardsoftware.com/mathgames/Numberballs_algebra_I/numberballsAlgebraI.htm
39	7.A.1	Translate two-step verbal expressions into algebraic expressions
40		TEST
41	7.A.3	Identify a polynomial as an algebraic expression containing one or more terms	Algebra II ball game http://www.sheppardsoftware.com/mathgames/Numberballs_algebra_II/numberballsAlgebraII.htm
42	7.A.3	Identify a polynomial as an algebraic expression containing one or more terms
43	7.A.4	Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation	Make 24 game http://www.sheppardsoftware.com/mathgames/make24/make24.htm
44	7.A.4	Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation	Expressions with two variables http://321know.com/equ723x3.htm
45	7.A.4	Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation
46	7.A.4	Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation
47	7.A.4	Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation
48	7.A.7	Draw the graphic representation of a pattern from an equation or from a table of data	Pattern game http://www.shodor.org/interactivate/activities/PatternGenerator/
49	7.A.7	Draw the graphic representation of a pattern from an equation or from a table of data	Pascals triangle game http://www.shodor.org/interactivate/activities/ColoringMultiples/
50	7.A.7	Draw the graphic representation of a pattern from an equation or from a table of data
51	7.A.7	Draw the graphic representation of a pattern from an equation or from a table of data
52	7.S.6	Read and interpret data represented graphically (pictograph, bar graph, histogram, line graph, double line/bar graphs or circle graph)	Graphing activity http://www.shodor.org/interactivate/activities/Sequencer/
53	7.S.6	Read and interpret data represented graphically (pictograph, bar graph, histogram, line graph, double line/bar graphs or circle graph)	Bar Graph tool http://www.shodor.org/interactivate/activities/BarGraph/
54		TEST
55	7.A.8	Create algebraic patterns using charts/tables, graphs, equations, and expressions
56	7.A.8	Create algebraic patterns using charts/tables, graphs, equations, and expressions
57	7.A.8	Create algebraic patterns using charts/tables, graphs, equations, and expressions
58	7.A.8	Create algebraic patterns using charts/tables, graphs, equations, and expressions
59	7.A.10	Write an equation to represent a function from a table of values	Two variable function pump game http://www.shodor.org/interactivate/activities/TwoVariableFunction/
60	7.A.10	Write an equation to represent a function from a table of values	Data flyer game http://www.shodor.org/interactivate/activities/DataFlyer/
61	7.A.10	Write an equation to represent a function from a table of values
62	7.G.10	Graph the solution set of an inequality (positive coefficients only) on a number line (See 7.A.5)	Solving Inequality video http://www.mathplayground.com/howto_InequalitiesA.html
63	7.G.10	Graph the solution set of an inequality (positive coefficients only) on a number line (See 7.A.5)
64	7.G.10	Graph the solution set of an inequality (positive coefficients only) on a number line (See 7.A.5)
65	7.M.4	Draw central angles in a given circle using a protractor (circle graphs)	Circle crossword puzzle http://www.mathgoodies.com/puzzles/crosswords/icircle2.html
66	7.M.4	Draw central angles in a given circle using a protractor (circle graphs)	Protractor video http://www.mathplayground.com/mv_using_protractor.html
67	7.M.4	Draw central angles in a given circle using a protractor (circle graphs)	Circle graph tool http://www.shodor.org/interactivate/activities/CircleGraph/
68	7.A.5	Solve one-step inequalities (positive coefficients only) (See 7.G.10)	Soving inequalities http://321know.com/equ725x7.htm
69	7.A.5	Solve one-step inequalities (positive coefficients only) (See 7.G.10)
70	7.A.5	TEST
71	7.G.10	Graph the solution set of an inequality (positive coefficients only) on a number line (See 7.A.5)	Graphing linear inequalities http://www.purplemath.com/modules/syslneq.htm
72	7.G.10	Graph the solution set of an inequality (positive coefficients only) on a number line (See 7.A.5)
73	7.G.10	Graph the solution set of an inequality (positive coefficients only) on a number line (See 7.A.5)
74	7.S.2	Display data in a circle graph	Interactive circle word search http://www.mathgoodies.com/puzzles/wordsearch/icircle_ws.html
75	7.S.2	Display data in a circle graph	Circumference video http://www.mathplayground.com/mv_circumference.html
76	7.S.2	Display data in a circle graph	Circle graph tool http://www.shodor.org/interactivate/activities/CircleGraph/
77	7.S.3	Convert raw data into double bar graphs and double line graphs	Bar Graph tool http://www.shodor.org/interactivate/activities/BarGraph/
78	7.S.3	Convert raw data into double bar graphs and double line graphs	Multi bar graph tool http://www.shodor.org/interactivate/activities/MultiBarGraph/
79	7.S.3	Convert raw data into double bar graphs and double line graphs
80	7.G.1	Calculate the radius or diameter, given the circumference or area of a circle	Area of Circle video http://www.mathplayground.com/mv_area_circles.html
81	7.G.1	Calculate the radius or diameter, given the circumference or area of a circle	Circumference of a circle http://321know.com/g7_612x7.htm
82		TEST
83	7.G.2	Calculate the volume of prisms and cylinders, using a given formula and a calculator	Volume of prism video http://www.mathplayground.com/mv_volume_prisms.html
84	7.G.2	Calculate the volume of prisms and cylinders, using a given formula and a calculator	Polygon Video http://www.thefutureschannel.com/dockets/hands-on_math/inventing_with_polygons/index.php
85	7.G.2	Calculate the volume of prisms and cylinders, using a given formula and a calculator	Volume of a cylinder http://321know.com/exp79_x5.htm
86	7.G.2	Calculate the volume of prisms and cylinders, using a given formula and a calculator	Volume rectangular prism http://321know.com/g79_vox6.htm
87	7.M.2	Convert capacities and volumes within a given system	Volume triangular prism http://321know.com/g79_vox1.htm
88	7.M.2	Convert capacities and volumes within a given system	Volume sphere http://321know.com/g79_vox7.htm
89	7.M.2	Convert capacities and volumes within a given system	Volume pyramid http://321know.com/g79_vox5.htm
90	7.G.3	Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones, and pyramids)	Interactive crossword puzzle - easy http://www.mathgoodies.com/puzzles/crosswords/icircle1.html
91	7.G.3	Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones, and pyramids)	Shape inlay game http://www.mathplayground.com/shape_inlay.html
92	7.G.3	Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones, and pyramids)	Volume of cones http://www.mathplayground.com/mv_volume_cones.html
93	7.G.3	Identify the two-dimensional shapes that make up the faces and bases of three-dimensional shapes (prisms, cylinders, cones, and pyramids)	Shape Explorer game http://www.shodor.org/interactivate/activities/ShapeExplorer/
94	7.A.6	Evaluate formulas for given input values (surface area, rate, and density problems)	Surface area of a cube http://321know.com/exp79_x2.htm#section2
95	7.A.6	Evaluate formulas for given input values (surface area, rate, and density problems)	Density solver http://www.sartep.com/chem/chartsandtools/densitysolver.cfm
96	7.A.6	Evaluate formulas for given input values (surface area, rate, and density problems)	Surface are of a prism http://321know.com/g79_sux3.htm
97	7.G.4	Determine the surface area of prisms and cylinders, using a calculator and a variety of methods	surface area of cylinder http://321know.com/g79_sux2.htm
98	7.G.4	Determine the surface area of prisms and cylinders, using a calculator and a variety of methods	Surface Area game http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/
99	7.G.4	Determine the surface area of prisms and cylinders, using a calculator and a variety of methods	Surface area calulator - online http://www.csgnetwork.com/surfareacalc.html
100	7.G.4	Determine the surface area of prisms and cylinders, using a calculator and a variety of methods
101	7.M.11	Estimate surface area	Estimator quiz http://www.shodor.org/interactivate/activities/EstimatorQuiz/
102	Why Does Goldman Need A Fed Exemption For VaR Calculations? Lately the topic of Goldman's VaR has taken on significant prominence, not least because as Zero Hedge disclosed yesterday, it hit a record high. The implications for this were large enough that even Bloomberg picked up on this story. Many readers raised questions of how is it even remotely possible for the company to have a VaR in the low-mid $200 MM ballpark, yet to post a record number of $100MM+ trading days in Q1; Zero Hedge is willing to wager that the upcoming 10-Q release will demonstrate another record number of $100MM+ days in the just closed quarter as well.How is that possible? The clue may come from a February 5 letter by the Federal Reserve to Goldman CAO Sarah Smith. The letter had come in response to GS requests for "temporary exemptions from the application of certain aspects of the Board's Market Risk Rules for state member banks and bank holding companies and the Board's general risk-based capital rules for bank holding companies." Basically thr! ough the end of 2009 Goldman is basically using non-traditional. SEC approved VaR models as can be seen here: GSGI has requested that (1) through December 31, 2009, GSGI and Bank be permitted to use certain Value-at-Risk ("VaR") models approved by the SEC... to determine their capital requirements for specific risk under the Market Risk Rules; (2) through December 31, 2009, GSGI and Bank be permitted to use methods approved by the SEC to determine their capital requirements under the Market Risk Rules for those trading assets, including distressed debt and restricted stock investments that the SEC did not require to be included in the VaR-based models of GSGI and Bank; and (3) GSGI be allowed to use methods approved by the SEC to calculate risk-based capital requirements for its nonfinancial equity investments that are subject to the Board's Credit Risk Capital Rules. The letter goes into detail explaining why a bank needs to follow a MRR VaR me! thodology. Yet what is not made clear is i) why does Goldman n! eed almo st a full year of alternative VaR calculation and MRR exemption and ii) what is the protocol for the SEC to enforce VaR compliance when Goldman's ultimate regulator is the Federal Reserve. The exemption raises critical questions not only with regard to the validity of the company's indicate VaR, but also downstreaming capital requirement reports. Zero Hedge would be remiss to point out that a very close relationship between the most critical financial company in the world and the most discredited regulator (SEC) does not bode well for confidence in this critical risk indicator, which as many have pointed out, is clearly the main metric by which to measure not only the performance, but the risk capacity of the world's largest government-backstopped hedge fund. Mr. Canaday, Mr. Van Praag - the floor is, again, yours. In your absence, Zero Hedge will, and encourages it readers to, contact Mr. Homer Hill at the Federal Reserve Bank Of New York at (212) 720-2164 to provide additi! onal clarity on the matter. Sphere: Related Content Bookmark this post with: Print this post calculations based on stp and methods Subscribe to: Posts (Atom) Followers Blog Archive ▼  2010 (32) ▼  August (32) Direct Instruction, Part 1 How to calculate square roots without a calculator... Factoring the time And Then There Is Shape Free algebra worksheets The First Free Hydroponic Nutrient Calculator Prog... Grade 7 Math Curriculum Why Does Goldman Need A Fed Exemption For VaR Calc... A Seasonal Sales Shift: For Bargain Hunters, Retai... Private Label Food and Beverages in the U.S. now a... Graphing - Standard Form of the Equation 101 Physics Solvers now available in the App Store! Teaching Fractional Arithmetic Visually Solving Systems of Partial Differential Equations ... #6 Math error discussion (Coordinate Geometry) Struck A Chord Rutgers Graduate Student Finds New Prime-Generatin... Pythagorean auctions and other Pythagorean excitem... Application of Derivatives FREE PRE ALGEBRA HELP Pre algebra help Free algebra worksheets Strang's Linear Algebra: homework Video Solution and Discussion of Twitter SAT Proba... Math Hep, Homework help, Algebra Help Review of Carnegie Learning's Cognitive Tutor Alg... 20 Free Online Education Resources for Middle Scho... Work Problem 5 Trigonometry - Tangent, SOHCAHTOA Free Geometry Help Good Confirmation Gift - Ask.com Mathway: Precalculus Problem Solver About Me mathqa48 View my complete profile Simple theme. Powered by Blogger.