South Carolina Math Kindergarten Standard K-4
The student will demonstrate through the mathematical processes an emerging sense of two- and three- dimensional geometric shapes and relative positions in space (Standards, 2012).

Instructional Goal 1
Identify two-dimensional shapes and three-dimensional shapes. Learning Objective 1: Students will take and identify foam two-dimensional shapes square, circle, triangle, and rectangle from a mystery bag with 80% accuracy. Justification: The mystery bag is used to cover the foam shapes from view. Students will need to use their sense of touch and their knowledge of the properties of the solids to identify them. Students are able to explore different orientations, sizes, and types to recognize that each shape has distinguishable characteristics. Learning Objective 2: Students will identify and record on paper three-dimensional shapes cube, sphere, and cylinder using real-world examples of the solids with 80% accuracy. Justification: Students explore these shapes using concrete models, pictures, and real world examples to generalize connections among mathematics, the environment, and other subjects. Learning Objective 3: Students will identify two out of three attributes (color, sides, size) from two-dimensional shapes square, circle, triangle, and rectangle. Justification: Students will use memorization and recognition skills to tackle these mathematical ideas. As students identify shapes and their attributes, they discuss and justify their answers to their teacher. Students understand the attributes of each shape through recognition.

Instructional Goal 2
Represent two dimensional geometric shapes.
Learning objective 1: Students will use streamers to make large size shapes in the air with 90% accuracy. Justification: Reinforcing the properties of two-dimensional geometric shapes while supporting gross motor development. The activity adds to the kinesthetic support young children need as they reinforce...

...SUPPORT FOR RIGID BODIES SUBJECTED TO THREEDIMENSIONAL FORCE SYSTEM
The first step in solving three-dimensional equilibrium problems, as in the case of two dimensions, is to draw a free-body diagram of the body (or group of bodies considered as a system)..
The reactive forces and couple moments acting at various types of supports and connections, when the members are viewed in three dimensions, are listed in Table 5–2. It is important to recognize the symbols used to represent each of these supports and to understand clearly how the forces and couple moments are developed by each support. As in the two-dimensional case, a force is developed by a support that restricts the translation of the attached member, whereas a couple moment is developed when rotation of the attached member is prevented. For example, in Table 5–2, item (4), the ball-and-socket joint prevents any translation of the connecting member; therefore, a force must act on the member at the point of connection. This force has three components having unknown magnitudes, FxFyFz Provided these components are known, one can obtain the magnitude of force. and the force’s orientation defined by the coordinate direction angles Eqs. 2–7.* Since the connecting member is allowed to rotate freely about any axis, no couple...

...Lesson Plan
Name: Geometric Solids
Content Area: Math
Grade Level: Kindergarten
Time Frame: 45 min
Prior to this lesson the students had a lesson on attributes. The children defined and identified attributes in different two-dimensionalshapes.
MA Framework Standard:
Geometry K.G
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
2. Correctly name shapes regardless of their orientations or overall size. Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).
Student Learning Objective:
CONTENT OBJECTIVE: Student will be able to identify the following geometric solids: cube, sphere, cylinder, and cone.
LANGUAGE OBJECTIVE: Student will use the following terms when identifying geometric solids: cube, sphere, cylinder, and cone.
Interdisciplinary content area: Language
Materials necessary for today’s lesson:
For Students: For Teacher
Colored Pencils or crayons -Geometric solids
Pencil -Cube, sphere, cylinder, cone
Enough sets for each group of four students to have a complete set
-Pictures of cubes, spheres, cylinders, and cones....

...
ANALYSIS
Physics has a lot of topics to cover. In the previous experiments, we discussed Forces, Kinematics, and Motions. In this experiment, the focus is all about Friction. Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction like fluid friction which describes the friction between layers of a viscous fluid that are moving relative to each other; dry friction which resists relative lateral motion of two solid surfaces in contact and is subdivided into static friction between non-moving surfaces, and kinetic friction between moving surfaces; lubricated friction which is a case of fluid friction where a fluid separates two solid surfaces; skin friction which is a component of drag, the force resisting the motion of a fluid across the surface of a body; internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation and sliding friction.
When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into heat. This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to heat whenever motion with friction occurs, for example when a...

...bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also be communicated to the offeree before it is being accepted. In addition, the acceptance has to be unqualified, unconditional and made by a positive act. In the case of Beauty and Stylish, a positive act refers to the signing of the contract. All terms of the offer must be accepted without any changes and cannot be subjected to any condition, taking effect only upon fulfillment of that condition. When Beauty and Stylish enter into the agreement, they must intend to bind and bound legally to each other by their agreement. This is the intention to create legal relations between two parties. In the meanwhile, this contract must possess consideration. A contract must therefore be a two-sided affair, with each side providing or promising to provide something of value in exchange for what the other is to provide.
Every contract, whether oral or written, contain terms. The terms of a contract set out the rights and duties of the parties. Terms are the promises and undertakings given by each party to the other. They form the substance of a contract and they specify the way in which contractual obligations are to be performed. These terms can be set out expressly or are implied into the contract by fact, trade custom or law. In the case of Beauty and Stylish, Clause 3 is an express term. The express terms of a contract are those which...

...“Shapes On Me”
Shapes are every where
In every place I stare
Rectangle in the building
Sphere drawn on the side walk
Hexagon on the stop sign
Circle in the number nine
Triangle in the pyramids
Octagon on the jewelry box lid
Stars in the sky
Oval in Ma’am Granada’s eye
Pentagon in Washington dc
Square in my TV
Shapes are every where
In every place I look
Now I can figure out what shapes I see
If only I could find my geometry book
"On Behalf of the Sides of a Triangle"
Oh, triangle, I wish I knew why
You're known for three angles instead of three sides
Your angle's a cute part of you, I agree
But you're being obtuse if your sides you don't see
For what could be more necessarily true
Than that two sides must meet to form angles for you
And it is the length of your sides, after all
That determine if you are gigantic or small
Yes, even the straightness your sides show is key
(If two sides were curved, you'd look more like a D)
So from now on I'll boycott the triangle shape
Remove it from my geometric landscape
And some day I hope the whole world will decide
That instead of triangle, they'll call you triside
“The Geometry”
Horizontal, parallel, intersecting, perpendicular
Different widths, lengths, heights, numbers
Base times itself gives the square's area
In a circle, radius is half the...

...MATHEMATICS
SAMPLE TEST PAPER (SEMSTER II)
CLASS VI
Class:6
Time :2hrs
Max Mks:45
No of pages: 3
General Instructions:
All questions are compulsory.
Questions 1to 4 carry 1mark each.
Questions 5to 7 carry 2mark each.
Questions 8 to 12 carry 3mark each.
Questions 13 to17 carry 4 mark each.
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1. Rohit has 8 blue balls, 5 red balls and 12 yellow balls. What is the ratio of blue and yellow
balls?
2. Name the side, vertices ad diagonals of given figure.
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3. How many right angles do you make if you start facing south and turns clockwise to east.
4. Construct a line segment having length of 2a
5. Write the number of sides and angles of below figures
6. Draw the mirror image of the given letter
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7. Find the perimeter of the rectangle with l= 3.m-6m B= 2.6m
8. Draw a line segment XY of any length. Now,without measuring it , draw a copy of XY
9. Given RS = 2.3 draw AB such that the length of XY is thrice of RS verify by measurement.
10. Find the perimeter of a regular octagon with sides 12.8 cm.
11. Find the No of faces, No of corners, No of edges of a cuboid
12. Measure each of the marked angle with the help of protractor
13. Prove that a square is a rhombus with all its angles at right angles.
14. Draw a rough sketch of a pentagon and draw all it diagonals. How many diagonals can you
draw
15. Draw a...

...Understanding of the Concept of a Three-Dimensional Cubes
and Surface Area in the Classroom
Written by Vanessa Kinsey
There are several uses in our daily lives that involve calculating the area of objects or places. Many of these daily recurring calculations require using acquired skills to figure out the area of three-dimensional objects. When introducing the concept of surface area to 5th and 6th grade students, they need to first know what three-dimensional objects look like and understand what the definition is, or the difference between a two-dimensional and a three-dimensional object. Through the use of manipulatives, instructing the students to change a two-dimensional piece of paper into a three-dimensional object, the students should gain a better understanding of the concept. It is helpful for students to create and hold a cube to fully understand what a three-dimensional cube looks like. Once students gain an understanding of the concept of a three-dimensional cube, they will be able to understand the concept of finding its surface area with ease.
To introduce the concept of surface area, I will begin reviewing the concept of finding the area of a two-dimensional object such as a...

...D.A.V. PUBLIC SCHOOL, THANE. 2012-13 WORKSHEET :10 TOPIC: CIRCLES&TANGENTS SUB: MATHEMATICS.
STD: X
1. Three circles are described touching each other at two places externally. If the sides of
the triangle are 4cm, 6 cm and 8 cm, find the radii of circles. 2. In the given figure, circles with centres O and O’ touch internally at point A. AB is a chord of bigger circle intersecting the smaller one at C. If the smaller circle passes through the centre of the bigger circle , then P.T AC = CB.
B A
A
O
b
B
C .O'
3. A Quadrilateral ABCD is drawn so that D = 90° . BC = 38 cm . CD = 25 cm. A circle is inscribed in the quadrilateral and it touches the sides AB , BC ,CD & DA
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at P,Q, R & S respectively. If, BP = 27 cm , find the radius of the inscribed circle.
D C
4. ABC is an isosceles triangle in which AB= AC, is circumscribed about a circle. Show that BC is bisected at the point of contact. 5. Prove that the intercept of a tangent between two parallel tangents to a circle , subtends a right angle at the centre of the circle. Draw suitable figure. 6.’O’ is the centre of a circle. AB is a chord and AT is the tangent at A. If AOB = 100°. then find BAT .
O
A
T B
A 7. In the figure, OP is equal to diameter of the circle.
P
Prove that ABP is an equilateral triangle.
O
8. A circle touches all the four sides of a ABCD whose sides are AB = 6cm, BC = 9cm, CD = 8cm. Find the length of...

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