make and do algebra lesson plans

Brainstorming About the College Application Essay Brainstorming The most important part of your essay is the subject matter. To begin brainstorming a subject idea, consider the following points. From this brainstorming session, you may find a subject you had not considered at first. Finally, remember that the goal of brainstorming is the development of ideas -- so don't rule anything out at this stage. See if any of these questions help you with developing several ideas for your college essay. * What are your major accomplishments, and why do you consider them accomplishments? Do not limit yourself to accomplishments you have been formally recognized for since the most interesting essays often are based on accomplishments that may have been trite at the time but become crucial when placed in the context of your life. * Does any attribute, quality, or skill distinguish you from everyone else? How did you develop this attribute? * Consider your favorite books, movies, works of art, etc. Have these influenced your life in a meaningful way? Why are they your favorites?

• What was the most difficult time in your LIFE AND HOW DIDI YOU OVERCOME?

Google,Make and Do these words Make an Representation; draw

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a picture, Make a Model, Have Fun! ALGEBRA WORKS Real Numbers

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Number Line

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Number LineA number line is aninfinitely long linewhose points matchup with the real num-ber system.

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Coordinate Plane

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Dr.Henry Sampson On 6 July 1971, Dr. Sampson invented the technology which made the cell phone possible. AFRIKAAN Descendants of Noah

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Ham Cush Nimrod, Seba, Havilah, Sabtah, Raamah (sons: Sheba, Dedan), Sabteca Mizraim Ludim, Anamim, Lehabim, Naphtuhim, Pathrusim, Casluhim, Caphtorim Put No children listed. Caanan Sidon, Heth, Jebusite, Amorite, Girgashite, Hivite, Arkite, Sinite, Arvadite, Zemarite, Hamathite

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Heptagon

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180 degrees

parallel lines; 90 degrees perpendicular; adjacent; line relationships 180 degrees 1D line 2D plane 3D prism 90 degrees Across Adjacent

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Amplify Amplitude Circle

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Circumference Column Congruent

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Cone

Coordinate Plane Rise/Run Cartesian Plane The Cartesian plane is a plane (meaning that it's flat) made up of an x axis (the horizontal line) and a y axis (the vertical line).

Cartesian Coordinates Coordinates on the Cartesian plane are a set of numbers officially called "an ordered pair" that are in the form ( x , y ) ... The x guy is how far to the right or left you've counted over... and the y guy is how far up or down you've counted. cont from pg

Coordinate This is the same thing as Cartesian Coordinates... Coordinates on the Cartesian plane are a set of numbers officially called "an ordered

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pair" that are in the WHICH WAY DO WE GO?

form ( x , y )

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Cross multiply

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Cylinder

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Equation

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Equilateral Expressions FOIL

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Function

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Integers Lateral Legs

Line relationships Linear Number Line Numerator

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Operation Order of

Parallel

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Parallel lines; 90 degrees perpendicular; adjacent; line relationships

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LET’S MAKE A SLAVEThe Black slaves after receiving this indoctrinationshall carry on and will become self-refueling andself-generating for HUNDREDS of years, maybeTHOUSANDS. You must pitch the OLD black malevs. the YOUNG black male, and the YOUNG black

male againstthe OLD blackmale. Youmust use theDARK skinslaves vs. theLIGHT skinslaves, andthe LIGHT skinslaves vs. theDARK skinslaves.

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ParallelTwo lines (lying in the same plane) are parallelif they never intersect... This means that thetwo lines are always the same distance apart.

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Perimeter

Perpendicular

Point Polygon

Polyhedron Quadratic Quadrilateral Ratio; Proportion; Cross Multiply; Similar; congruent; Linear; Function; Percent;

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Decimal;

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Ray

Real Numbers Rectangle Relativity

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Rise/Run

Row /Column

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Sides

Similar

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Simplify

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Slope

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SLOPE

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Sphere

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Square

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Square area Surface area

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Symmetry Tangent Transversal Trapezoid

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Triangle

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Vertical

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Angle right Axis Column Degree 90(like a book) 180(straight Line)

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Isosceles triangle Obtuse triangle Proportion Ray Relativity a x b = c; c/a=b; c/b=a

Sides

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Scalene Vector Vertical

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Make Tables, describe in words, draw a picture, write and solve equations What ever you do, do it better than any one else. Just Make it your own. Example: The height of a tree was 7 inches in the year 2000. Each year the same tree grew an additional 10 inches. Write an equation to show the height h of the tree in y years. Let y be the number of years after the year 2000. The most literal equation might be 7 + 10y = h.

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Right Angle

Acute Angle

Quadrilaterals

Triangular Prism

Prism

Cone

Sphere

Cube

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Multiplication of Polynomials Multiplication of a Polynomial by a Monomial To multiply a polynomial by a monomial, use the distributive property: multiply each term of the polynomial by the monomial. This involves multiplying coefficients and adding exponents of the appropriate variables.

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6x –2 This is NOT a polynomial term... ...because the variable has a negative exponent. 1/x2 This is NOTa polynomial term... ...because the variable is in the denominator. sqr t(x) This is NOTa polynomial term... ...because the variable is inside a radical. 4x2 This IS a polynomial term....because it obeys all the rules. cont on pg<None> this

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Table of Formulas For Geometry A table of formulas for geometry, related to area and perimeter of triangles, rectangles, cercles, sectors, and volume of sphere, cone, cylinder are presented. Right Triangle and Pythagora's theorem Pythagora's theorem: The two sides a and b of a right triangle and the hypotenuse c are related by a 2 + b 2 = c 2 Right Triangle Area and Perimeter of Triangle Triangle Perimeter = a + b + c There are several formulas for the area. If the base b and the corresponding height h are known, we use the formula Area = (1 / 2) * b * h.

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If two sides and the angle between them are known, we use one of the formulas, depending on which side and which angle are known Area = (1 / 2)* b * c sin A Area = (1 / 2)* a * c sin B Area = (1 / 2)* a * b sin C . If all three sides are known, we may use Heron's formula for the area. Area = sqrt [ s(s -‐ a)(s -‐ b)(s -‐ c) ] , where s = (a + b + c)/2. Area and Perimeter of Rectangle Rectangle Perimeter = 2L + 2W Area = L * W Area of Parallelogram Area = b * h Area of Trapezoid Trapezoid Area = (1 / 2)(a + b) * h Circumference of a Circle and Area of a Circular Region CircleCircumference = 2*Pi*r Area = Pi*r 2 Arclength and Area of a Circular Sector Sector Arclength: s = r*t Area = (1/2) *r 2 * t where t is the central angle in RADIANS. Volume and Surface Area of a Rectangular Solid Sector Volume = L*W*H Surface Area = 2(L*W + H*W + H*L) Volume and Surface Area of a Sphere Sphere Volume = (4/3)* Pi * r 3 Surface Area = 4 * Pi * r 2 Volume and Surface Area of a Right Circular Cylinder Volume = Pi * r 2 * h Surface Area = 2 * Pi * r * h Volume and Surface Area of a Right Circular Cone right cone

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Volume = (1/3)* Pi * r 2 * h Surface Area = Pi * r * sqrt (r 2 + h

Here are a couple WLA/ART examples of what square root means

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Scientific Notation Scientific notation is a way to write a number as the product of a number between 1 and 10 and a multiple of 10. Examples:

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2)

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number of sides name 3 equilateral triangle 4 square 5 pentagon 6 hexagon 7 heptagon 8 octagon 9 nonagon 10 decagon 11 undecagon

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12 dodecago

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Simple Polynomial Multiplication (page 1 of 3) Sections: Simple multiplication, "FOIL" (and a warning), General multiplication

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There were two formats for adding and subtracting polynomials: "horizontal" and "vertical". You can use those same two formats for multiplying polynomials. The very simplest case for polynomial multiplication is the product of two one-‐term polynomials. For instance: * Simplify (5x2)(–2x3) I've already done this type of multiplication when I was first learning about exponents, negative numbers, and variables. I'll just apply the rules I already know: (5x2)(–2x3) = –10x5 The next step up in complexity is a one-‐term polynomial times a multi-‐term polynomial. For example: * Simplify –3x(4x2 – x + 10) To do this, I have to distribute the –3x through the parentheses: –3x(4x2 – x + 10) = –3x(4x2) – 3x(–x) – 3x(10)

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= –12x3 + 3x2 – 30x The next step up is a two-‐term polynomial times a two-‐term polynomial. This is the simplest of the "multi-‐term times multi-‐term" cases. There are actually three ways to do this. Since this is one of the most common polynomial multiplications that you will be doing, I'll spend a fair amount of time on this. * Simplify (x + 3)(x + 2) The first way I can do this is "horizontally"; in this case, however, I'll have to distribute twice, taking each of the terms in the first parentheses "through" each of the terms in the second parentheses: Copyright © Elizabeth Stapel 2006-‐2008 All Rights Reserved (x + 3)(x + 2) = (x + 3)(x) + (x + 3)(2) = x(x) + 3(x) + x(2) + 3(2)

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= x2 + 3x + 2x + 6 = x2 + 5x + 6 This is probably the most difficult and error-‐prone way to do this multiplication. The "vertical" method is much simpler. First, think back to when you were first learning about multiplication. When you did small numbers, it was simplest to work horizontally, as I did in the first two polynomial examples above: 3 Å~ 4 = 12 But when you got to larger numbers, you stacked the numbers vertically and, working from right to left, took one digit at a time from the lower number and multiplied it, right to left, across the top number. For each digit in the lower number, you formed a row underneath, stepping the rows off to the left as you worked from digit to digit in the lower number. Then you added down. For instance, you would probably not want

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to try to multiply 121 by 32 horizontally, but it's easy when you do it vertically: 121 Å~ 32 = 3872 You can multiply polynomials in this same manner, so here's the same exercise as above, but done "vertically" this time: * Simplify (x + 3)(x + 2) I need to be sure to do my work very neatly. I'll set up the multiplication: multiplication ...and then I'll multiply: multiplicationIf you want to use FOIL, that's fine, but (warning!) keep its restriction in mind: you can ONLY use it for the special case of multiplying two binomials. You can NOT use it at ANY other time! * Simplify (x – 4)(x – 3) multiplication So the answer is: x2 – 7x + 12 Using FOIL would give:

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"first": (x)(x) = x2 "outer": (x)(–3) = –3x "inner": (–4)(x) = –4x "last": (–4)(–3) = +12 product: (x2) + (–3x) + (–4x) + (+12) = x2 – 7x + 12 * Simplify (x – 3y)(x + y) multiplication So the answer is: x2 – 2xy – 3y2 Using FOIL would give: "first": (x)(x) = x2 "outer": (x)(y) = xy "inner": (–3y)(x) = –3xy "last": (–3y)(y) = –3y2 product: (x2) + (xy) + (–3xy) + (–3y2) = x2 – 2xy – 3y2 Let me reiterate what I said at the beginning: "FOIL" works ONLY for the specific and special case of a two-‐term expression times another two-‐term expression. It does NOT apply in ANY other caseA figure can represent

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several types simultaneously Lines Adjacent Ver tex Ray Straight line 180 degrees Y Longi tude Lines Meridians Ver tical 0-‐180 east west Up down X Latitude Lines paral lels horizontal N nor th S south Left/ Right N/S 0-‐ 90Lines • Copy a line segment • Perpendicular bisector of a line segment • Divide a line segment into n equal segments • Perpendicular to a line at a point on the line • Perpendicular to a line from an external point • Perpendicular to a ray at its endpoint • A parallel to a line through a point Angles • Copy an angle • Bisect an angle • Construct a 30° angle

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• Construct a 45° angle • Construct a 60° angle • Construct a 90° angle (right angle) • Constructing 75° 105° 120° 135° 150° angles and more An obtuse angle is one which is more than

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90° but less thanType of Angle Description Acute Angle an angle that is less than 90° Right Angle an angle that is 90° exactly Obtuse Angle an angle that is greater than 90° but less than 180° 6 Straight Angle an angle that is 180° exactl y Reflex Angle an angle that is greater than 180°Like terms 7ac + ac = 8c 7ac =-‐ ac = 6ac 4 apples + 1 apple = 5 apples Cylinder s prism Rectangles plane Two dimensional planes Three dimensional prisms 1 dimensional vec tor a signed number•

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Angles associated with polygons • Exterior angles of a polygon • Interior angles of a polygon • Relationship of interior/exterior angles • Polygon central angle Named polygons • Tetragon, 4 sides Pentagon, 5 sides • Hexagon, 6 sides • Heptagon, 7 sides • Octagon, 8 sides • Nonagon Enneagon, 9 sides

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• Decagon, 10 sides • Undecagon, 11 sides

Introduction: Ks-‐3 Geometry is a construction of object according to our desired given measurement. Ks-‐3 Geometry has the collection of object it should be triangle, circle, parallelogram, etc. Each object in Ks-‐3 geometry has some properties. The topic includes in Ks-‐3 Geometry is 2D shapes, 3D shapes, Introduction to transformations, Angles, Polygons, Symmetry, Circles, Pythagoras' theorem etc. 2D and 3D Geometry: Two dimensional: These shapes are always flat which has the four sides and four corners. There are different kinds of quadrilaterals are square, rhombus, quadrilateral etc. Three Dimensional: 3d shapes have 3-‐dimensions depth, width and length. The important shapes in 3D are sphere, cube, cone, cylinder etc. It also includes Prisms and pyramids, Polygon: Polygons are the 2D shapes. It has sum of the exterior anglesare 360°.

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I Two-‐ and Three-‐Dimensional Geometry Essential content for elementary teachers 1. Develop an understanding of basic geometric concepts including: point, line, plane, space, line segment, betweenness, ray, angle, vertex, parallelism, perpendicularity, congruency, similarity, simple closed curve, Pythagorean relationship. 2. Identify types of angles including acute, right, obtuse, straight, reflex, vertical, supplementary, complementary, corresponding, alternate interior, and alternate exterior. 3. Recognize and define common geometric shapes. 1. Two-‐dimensional geometric shapes 1. Triangles: be able to classify by sides (equilateral, scalene, isosceles)

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and classify by angle (right, acute, obtuse) 2. Quadrilaterals (trapezoid, parallelogram, rectangle, square, rhombus, kite): identify characteristics and relationships among these shapes 3. Polygons, regular polygons 4. Circle 2. Three-‐dimensional geometric shapes 1. Polyhedra (prisms, pyramids), regular polyhedra (Platonic solids): connecting polyhedra to polygons, nets 2. Cylinder, cone, sphere Essential content for students K-‐3 1. Analyze characteristics and properties of two-‐ and three-‐dimensional geometric shapes and develop mathematical

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arguments about geometric relationships.8 1. Two-‐dimensional geometric shapes 1. Recognize, name, build, draw, compare, and sort shapes. 2. Describe attributes and parts of shapes: circle, rectangle, square, triangle, parallelogram (sides and vertices); locate interior (inside) and exterior outside) angles. 3. Compare shapes made with line segments (polygons) and identify congruent and similar geometric shapes. 4. Identify right angles in polygons. 5. Investigate and predict the results of putting together and taking apart shapes. 2. Three-‐dimensional geometric shapes 1. Recognize, name, build, draw, compare, and sort shapes: sphere (ball), cone,

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cylinder (can), pyramid, prism (box), cube. 2. Describe attributes and parts of shapes: identify faces, edges, vertices (corners). 3. Sort using similar attributes (curved surfaces, flat surfaces). 4. Investigate and predict the results of putting together and taking apart shapes. 2. Develop vocabulary and concepts related to two-‐ and three-‐dimensional geometric shapes. 1. Two-‐dimensional shapes: angle, circle, congruency, line segment, parallelogram, polygon, rectangle, similarity, square, triangle 2. Three-‐dimensional shapes: cone, cube, cylinder, edge, face, prism, pyramid, sphere, vertices Essential content for students grades 4-‐5 1. Maintain and expand on concepts introduced in primary grades. 2. Analyze characteristics and properties of

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two-‐ and threedimensional geometric shapes and develop mathematical arguments about geometric relationships.9 1. Two-‐dimensional geometric shapes 1. Identify, compare, and analyze attributes of shapes, and develop vocabulary to describe the attributes. 1. Angles (right, acute, obtuse, straight) 2. Circles (diameter, radius, center, arc, circumference) 3. Lines (parallel, intersecting, perpendicular) 4. Line segments 5. Polygons (vertex, side, diagonal, perimeter); classification by number of sides (quadrilaterals, pentagon, hexagon) 2. Classify shapes according to their properties. 1. Triangles (classify by angles and sides)

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2. Quadrilaterals (square, rectangle, parallelogram, rhombus, trapezoid, kite) 3. Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes. 4. Explore and identify congruence and similarity. 5. Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions. 2. Three-‐dimensional geometric shapes 1. Identify shapes (cylinder, cone, sphere, pyramid, prism). 2. Apply terms (face, edge, vertex). 3. Classify shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids. 4. Investigate, describe, and reason about the results of subdividing, combining,

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and transforming shapes. • Dodecagon, 12 sides

make and do algebra lesson plans

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d line

d plane

horizontal line

vertical line

cartesian coordinates

degrees parallel lines

x axis

y axis