. What is the probability that the three numbers **rolled** are the lengths **of** the sides **of** an obtuse **triangle**? Express your answer as **a** common fraction. Let **a**, b, c be the lengths **of** any obtuse **triangle**, with **a** < c & b < c. For the **triangle** to be obtuse, we have: a2 + b2 < c2 **and** c < **a** + b List **of** triplets meeting the criteria include: 1,1,(3,4,5,6); 1,2,(3/

four sides is **a** square. 7. **A** figure can be **a** **triangle** only if it is equilateral. 8. The angle sum **of** **a** quadrilateral is the same as its **area**. 9. The **area** **of** **a** quadrilateral can be obtained by transforming it into **a** rectangle with the same perimeter. RESEARCH **ON** SCHOOL MATHEMATİCS………… GEOMETRIC SENSE………………… The van Hieles, after years **of** extensive research, contend that **a** student develops an understanding **of** geometry by progressing/

**A** cycloid is the locus **of** **a** point **on** the rim **of** **a** circle **of** radius **a** **rolling** along **a** straight line. The cycloid was first studied by Cusa when he was attempting to find the **area** **of** **a** circle by integration. It was studied **and** named by Galileo in 1599. Department **of** Mathematics,UOM 19 April 2017 Hypocycloid The path traced out by **a** point **on** the edge **of** **a** circle **of** radius b **rolling** **on** the outside **of** **a** circle **of** radius **a**. Department **of**/

**of** this **parallelogram** is 18 inches. The value **of** x is ______. Question 4-1 What is 3 inches? Because 2x + 2x + x + x = 6x 6x = 18 x = 3 Answer 4-2 The type **of** **triangle** **and** its **area** for these coordinates: (-1, 3) (-3, -3) (1, -3) Question 4-2 What is an isosceles **triangle** with **area** **of** 12 squared units. **A**/= 9 P(red) = 1/2 = 18 P(yellow) = 6 Answer 4-5 The probability **of** **rolling** **a** number greater than 2 **on** **a** fair number cube **and** flipping **a** coin **and** getting heads. Question 4-5 What is ⅓? Because 4 = 2 x 1 = 2 = 1/

. Quick Check 6-3 Similar Figures **and** Scale Drawings PRE-ALGEBRA LESSON 6-3 Solve. 1.**Parallelogram** ABCD ~ **parallelogram** EFGH. Find the value **of** x. 2.**A** girl who is 4 feet tall casts **a** shadow that is 6 feet long. The tree next to her casts **a** shadow that is 12 feet long. How tall is the tree? 3.The scale **on** **a** map is 3 in. : 100/

had **a** height **of** 3 ft. **and** **a** width **of** 2 ft. What was the volume **of** the box? **a**.9 cubic feet b.11 cubic feet c.14 cubic feet d.24 cubic feet **A** pot **of** boiling water has **a** temperature **of** 212˚ F. What would be the temperature in Celcius? **a**.0 ˚C b.32 ˚C c.100 ˚C d.d. 212 ˚C c. 100 ˚C What the **area** **of** **a** **triangle** whose/

turn to either move your piece forward in **a** clockwise manner, or use the opportunity to move one **of** your pieces from the base to the track (by **rolling** **a** 6). 4. Be aware that you cant move **a** piece out **of** the starting **area** unless you **roll** **a** 6. If you **roll** something other than **a** 6 **and** do not have **a** piece **on** the track, then you forfeit your turn. 5. Note/

sq ft C.113 sq ft D.144 sq ft What is the minimum number **of** same-sized **triangles** as the one above that would be required to form the polygon below? 1234567891011121314151617181920 21222324252627282930 **A**.3 B.4 C.6 D.8 What is the **area** **of** the **parallelogram** shown? 1234567891011121314151617181920 21222324252627282930 **A**.185 sq ft B.230 sq ft C.2,600 sq ft D.3/

3 MI/Vocab composite figure –**A** figure made up **of** 2 or more shapes Find the **area** **of** composite figures. Lesson 3 TEKS NOTES To find the **area** **of** composite figures 1.Draw lines to break the figure up into parts 2.Find the **area** **of** the parts 3.Add (or subtract) all the **areas** THE BASE **AND** THE HEIGHT MUST FORM **A** RIGHT ANGLE! **Parallelogram** **A** = bh **Triangle** **A** = ½ bh b = base h = ACTUAL/

graph shows the date each year that bluebells were first seen **a**) **On** what dates in 1993 & 1996 were bluebells first seen? /Write down all the properties **of** an equilateral, isosceles **and** right-angled **triangle** Can an isosceles **triangle** also be **a** right- angled **triangles**? If yes, what can/**area** **of** the **parallelogram**, please give correct units? 4cm Question 30 L4-6 & L5-7 Question 31 L5-7 Number **of** students that have an iPhone Number **of** students that don’t 219 **a**)What % **of** students have an iPhone? iPhone TypeNumber **of**/

. 384 cm2 d. 512 cm2 Which **of** the following formulas can be used to find the **area** **of** **a** circle? **a**. C = Pid b. C = 2(pi)r c. **A** = (pi)r2 d. D = C/(pi) Danny **rolls** two number cubes (dice), one red **and** one blue. What is the probability that he will **roll** **a** 2 **on** the red cube **and** **a** 6 **on** the blue cube? **a**. 1/6 b. 2/15 c/

**and** 90o. What is **a** 3,4,5 **triangle**? In the absence **of** this, all objects fall with the same acceleration. What is air resistance? **A** projectile must move this fast so that the curve it follows matches the curve **of** Earth. What is 8 km/s? Only this force acts **on** **a** high satellite. What is gravity? He stated that if friction were entirely absent, **a** ball **rolling** horizontally/

31 Other propositions that are needed to prove I.47 Prop. I.41 The **area** **of** **a** **triangle** is one half the **area** **of** **a** **parallelogram** with the same base **and** height. SC/NATS 1730, VIII 32 Constructions that are required to prove I.47 Prop. I.31 Given **a** line **and** **a** point not **on** the line, **a** line through the point can be constructed parallel to the first line. SC/NATS 1730/

, **and** much more available **on** my website at http://www.mathslideshows.com I have attached the list below so you can see what is available. If you teach 5 th -10 th grade this is the place for you! Please check it out! Sincerely, Amber Pasillas amberpasillas@yahoo.com http://www.mathslideshows.com **AREA** FORMULAS $30 1. **Area** **of** **a** Rectangle & Square 2. **Area** **of** **a** **Parallelogram** & **Triangle** 3. **Area** **of** **a** Trapezoid 4. **Area** **of** **a**/

-dimensional shapes. You have investigated the special properties **of** **triangles**, **parallelograms**, regular polygons **and** circles, **and** have developed tools to help you describe **and** analyze those shapes. For example, you have tools to find the interior angle **of** **a** regular hexagon, to calculate the length **of** the hypotenuse **of** **a** right **triangle**, **and** to measure the perimeter **of** **a** **triangle** or the **area** **of** **a** circle. In this Chapter, you will focus **on** three- dimensional shapes (called solids), such as/

Point **of** Intersection Measurement **and** Geometry Composite **Area** **and** Perimeter: When **a** complex shape is broken down into several different, simpler shapes which you can then use to calculate the **area** or perimeter **of** the entire shape. Example: Surface **Area**: The total **area** **of** all the faces **on** **a** 3-D figure. Example: Pyramid=**Area** **of** Base+((number **of** sides **on** base)**Area** **of** **Triangle** Example: Square Pyramid=**Area** **of** Square (l*w)+4(**Area** **of** **Triangle** (1/2(b*h)) For the **area** **of** **a** **triangle** in **a**/

, what fraction is represented by **a** **triangle** **and** **a** trapezoid? If the rhombus is one, what number is represented by the trapezoid? 2005 Aims Education Foundation Fraction Riddles-Pattern Blocks The **area** **of** all the blocks together is the same as the **area** **of** 24 green **triangles**. Fraction Riddles-Pattern Blocks The **area** **of** all the blocks together is the same as the **area** **of** 24 green **triangles**. Three **of** the blocks together make up/

B. Prabhakaran Properties **of** the Cross Product **area** **of** **parallelogram** ab is **a** vector perpendicular to both **a** **and** b, in the direction defined by the right hand rule if **a** **and** b are parallel Multimedia System **and** Networking Lab @ UTD Slide- 28 University **of** Texas at Dallas B. Prabhakaran Example: Normal **of** **a** **Triangle** Find the unit length normal **of** the **triangle** defined by 3D points **a**, b, **and** c **a** b c Multimedia System **and** Networking Lab @ UTD/

spaces to win the game. What is the probability that Akio will **roll** **a** sum **of** at least nine **on** his next turn? Tree Problem 6 Akio **and** Tamera are playing **a** game with two number cubes, each labeled 1–6. **On** each turn, the person **rolls** both number cubes. The sum **of** the two numbers **on** top **of** the number cubes tells how many spaces that person can move the/

pattern blocks; hexagons, trapezoids, **parallelograms** **and** **triangles**. Each field’s value is based **on** its size (its fractional relationship to the whole plot **of** farm land). What part **of** the whole farm does each field represent? What would **a** fair price for each field be, based **on** its fractional value? Show **and** explain all **of** your mathematical thinking. Guided Draw an **area** model to represent each **of** the following operations. Use your/

/act-facts-**and**-formulas.pdf Relations **and** properties **of** shapes (**triangles**, rectangles, **parallelograms**, trapezoids, **and** circles), angles, parallel lines, **and** perpendicular lines. What happens when you move or change these shapes? ◦ Translations, rotations, reflections Proofs ◦ Justification, logic. Three-dimensional geometry Measurements: perimeter, **area**, **and** volume. Circles Source: http://www.erikthered.com/tutor/act-facts-**and**-formulas.pdf Lines in **a** plane What do we know about **a** **and** b in/

Q. The probability **of** **rolling** **a** 2 or **a** 4 with **a** fair die is ½ ¼ ⅓ True False Q. The probability Nicola wins **a** race is ⅓, the probability she does not win is also ⅓ **A** B C D **A** fair dice has the numbers 2, 2, 2, 2, 5 **and** 5 **on** it. The dice is **rolled**. Which arrow shows the probability **of** getting **a** 2. Impossible ½ Certain **A** B C D **A** B C D/

? Simplify. What is the formula used to find the **area** **of** **a** **triangle**? Find the **area**. 20 ft 14 ft 10 ft 8 ft Simplify. Simplify. Simplify. Christina is having dinner at **a** restaurant. She has **a** choice **of** 2 appetizers, 4 main dishes, 6 desserts **and** 4 soft drinks. How many different dinner combinations are possible? The scale used **on** **a** map is 2 cm : 5 miles. If the distance/

the number **of** faces, edges, **and** vertices **on** each three-dimensional figure. **A**. B. 6 faces12 edges8 vertices5 faces9 edges6 vertices 10-6 Three-Dimensional Figures **A** prism is **a** polyhedron with two congruent, parallel bases, **and** other faces that are all **parallelograms**. **A** prism is named for the shape **of** its bases. **A** cylinder also has two congruent, parallel bases, but bases **of** **a** cylinder are circular. **A** cylinder is not **a** polyhedron because/

.56m² or 12.57m² Categories Shape **and** Space What is the **area** **of** the **parallelogram**, given the **area** **of** the **triangle** is 36cm²? Answer 8cm 14cm Answer What is 126cm² Categories Shape **and** Space What is the measure **of** an angle supplementary to angle #1 in the diagram? Answer 39° Answer What is 141° Categories Shape **and** Space You leave **a** city **and** travel 45° **of** longitude in an westerly direction. If you/

math classrooms. We will focus **on** personal strategies **and** problem solving. Digital resources **and** activities that support teaching mathematics will be shared as well. Follow up webinar **on** "Making Meaning in Junior High Math", **on** February 3, 2011. Welcome! Where do you work? **A**. Edmonton B. Greater Edmonton **area** C. Somewhere else in Alberta D. Outside **of** Alberta Place an icon in the **area** that best describes your experience/

the castle drawbridge opening. Entering the courtyard **area**, the player meets another messenger who gives **a** scroll with instructions. Instructions **on** the next slide. To be **a** part **of** the jousting activities, you must first earn the items you will need to participate. The items you must earn are armor, **a** weapon, **a** shield, **a** helmet, **and** **a** horse. **Roll** over **and** click **on** various places in **of** the castle. You must successfully complete/

faces that are all **parallelograms**. **A** prism is named for the shape **of** its bases. **A** cylinder also has two congruent, parallel bases, but bases **of** **a** cylinder are circular. **A** cylinder is not **a** polyhedron because not every surface is **a** polygon. Course 1 10-6 Three-Dimensional Figures **A** pyramid has one polygon shaped base, **and** the other faces are **triangles** that come to **a** point. **A** pyramid is named for the/

designs Produce designs with **a** number **of** materials Zoom in **on** specific **areas** **of** designs Rotate designs Using CAM you can: Ensure each product is exactly the same as the one prior to it CAD **and** CAM can also be linked together! CAD ICT Advantages **and** Disadvantages **of** CAD **and** CAM CAD – This stands for ‘Computer Aided Design’. It’s the use **of** computers for creating drawings **and** designing products. Software/

that show at least one acute, one right, one obtuse **and** one reflex angle? Geometry Find **a** quadrilateral that can be inscribed in **a** circle **and** one that cannot Geometry It is possible to inscribe only **parallelograms** that are also rectangles Geometry I drew **a** set **of** seven **triangles**. Five were similar to one another, three were congruent, **and** two were neither similar nor congruent to any other. What/

sum **of** 7 **and** the quotient **of** x **and** 8”? **A**.7 + 8x B.7 + 8 – x C.7 – 8x D.7 + x 8 Kirsten wants to cover **a** box with newspaper **on** every side. To calculate how much newspaper she will need, she will use the formula for surface **area** **of** **a** prism/ **of** the angles inside an isosceles **triangle** measure 50° **and** 80°. What is the measure **of** the third angle? **A**.20° B.50° C.80° D.100° Which **of** these shapes could have 4 vertices **and** sides that are all different lengths? **A**.**a** **triangle** B.**a** **parallelogram** C.**a** pentagon D.**a** trapezoid **A**/

2 help you analyze the effect **of** gravity **on** the boat. For example, w 1 indicates the force necessary to keep the boat from **rolling** down the ramp, whereas w 2 indicates the force that the tires must withstand. Projections **and** Vector Components 84 Figure 11.29 Projections **and** Vector Components 85 Example 4 – Finding **a** Vector Component **of** u Orthogonal to v Find the vector component/

Pass the ball behind your legs in **a** figure **of** eight Throw up **and** catch the ball like knuckle bones **on** the back **of** your hand Pass the ball with **a** partner using two hands your left hand your right hand With **a** skipping rope can you…? Make **a** circle Make **a** square Make **a** **triangle** Make **a** rectangle Make **a** **parallelogram** Make **a** pentagon Make an octagon Make **a** semicircle Can you balance by yourself/

Reading for Wed/Today/Next Time FCG Chap 9 Surface Shading RB Chap Lighting 14 Review: Computing Barycentric Coordinates 2D **triangle** **area** half **of** **parallelogram** **area** from cross product **A** = P1 + P2 + P3 P1 /**A** P2 /**A** P3 /**A** ( ) = (1,0,0) (0,1,0) (0,0,1) weighted combination **of** three points [demo] 15 Review: Light Sources directional/parallel lights point at infinity: (x,y,z,0) T point/

as, "How high can you make **a** tower **of** cups?" Measure each tower **and** record their height. Skills used: engineering **and** math Build Ramps Use **a** board, sheet **of** cardboard, or small table with one side elevated to build **a** ramp. Try **rolling** **a** variety **of** objects, two at **a** time down the ramp to see which is fastest. Record your findings **on** **a** chart. Skills used: engineering **and** math. Cooking Activity Look up/

Y6: Use formula for **area** & volume **of** shapes Y6: Calculate **area** **of** **triangles** & **parallelograms** Y6: Introductory algebra & equation-solving Textbooks – anyone remember Alpha & Beta? Worksheets Games Specific number **of** days **on** **a** subject Lots **of** different methods for children to try Learn from the East – Singapore, China etc Mastery – being able to apply **a** concept to many different situations is considered mastery Using textbooks – improving independence **and** reading Use one method/

in one or more categories. Opposite sides equal in length **and** parallel Only one pair **of** parallel sides At least two angles LESS than 90 degrees (right angles) Trapezoid **Triangle** Square Rhombus Hexagon **Parallelogram** Rectangle There are 6 candy bars for 8 children to/. How many inches will each piece **of** rope be? Nicole bought 6 **rolls** **of** film for her camera Nicole bought 6 **rolls** **of** film for her camera. She was going **on** **a** hiking trip **and** planned to take **a** bunch **of** pictures. Each **roll** **of** film cost $4.82. How much/

. Determine the congruence **of** segments, angles, **and** polygons given their attributes. Subdivide **a** figure into **triangles**, rectangles, squares, trapezoids **and** semicircles. Estimate the **area** **of** subdivisions **and** combine to determine the **area** **of** the composite figure. Describe the characteristics **of** **triangles**, squares, **and** rectangles, including number **of** sides **and** number **of** angles. Compare **and** contrast attributes **of** the following quadrilaterals: **parallelogram**, rectangle, square, rhombus, **and** trapezoid. Compare the/

**of** point D? **A**. (6, 2) B. (-6,-2) C. (2, 6) D. (-2, 6) 5. Akio **and** Tamera are playing **a** game with two number cubes, each labeled 1–6. **On** each turn, the person **rolls** both number cubes. The sum **of** the two numbers **on** top **of**/ about three groups over **a** 28-year period—the number **of** licensed drivers, the number **of** registered vehicles, **and** the resident population **of** **a** certain **area**. 23. Describe one way that any two **of** the groups changed in relation to one another during **a** particular period **of** time. Name the/

-4 Algebra (handout page-10/47) **Roll** **a** die (pick from cards 1-6 or use **a** spinner) -Draw **a** picture **on** **a** coordinate plane …. -- Bring in **a** portion **of** **a** map **and** …. ---In 1990, … write an equation to model... ----Write **a** poem, song or rap …. -----Make up 5 sets **of** order pairs. Find the …. ------ Tape 2 … sticks … use this as **a** ramp …. Algebra CONCEPTUAL CATEGORY: Equations **and** Inequalities DOMAIN: Creating Equations Standard: Create/

90. What is the lowest score he could have made **on** any **of** the five tests? Unit 9 Three vertices **of** **a** **parallelogram** are at the points (0, 0), (2, 4), **and** (6, 0). What are the coordinates **of** the fourth vertex? What units would most likely be used to measure the **area** **of** **a** classroom floor? **a**.Square inches b. Square feet c.Cubic feet d. Cubic yards Carol measured/

151 152 153 154 155 156 157 158 159 Find the perimeter. 160 161 Find the **area** **of** the **parallelogram**. 162 163 164 165 166 167 168 169 Bonnie, Jason, Melda, Kenji, Tanya **and** Darren form **a** chess club. They each want to play one game with every other member **of** the club. How many games will be played? A16 B36 C6 D15 Tammy is selling/

very close links to the Church **and** surrounding community. Around 40% **of** pupils attend from outside our immediate **area** which means there are **a** wide diversity **of** socio-economic home backgrounds. Around 40% **of** pupils attend from outside our immediate **area** which means there are **a** wide diversity **of** socio-economic home backgrounds. Number **on** **roll**: 110 + 13 place Nursery (smaller than national average) Number **on** **roll**: 110 + 13 place Nursery (smaller than/

, **and** **a** rectangle (like your notebook paper). **Roll** the rectangle **and** place the two circles one **on** each end **and** you have just formed **a** cylinder. Pyramid **A** pyramid is **a** three-dimensional shape with one polygonal base **and** lateral sides that are all **triangles** that/**a** rectangle that is “wrapped around” the circular faces at the ends. **A** cone is **a** three-dimensional shape with **a** circular base **and** **a** vertex opposite the base Surface **Area** The surface **area** **of** **a** space figure is the total **area** **of** all the faces **of**/

formula for **area** & volume **of** shapes Y6: Calculate **area** **of** **triangles** & **parallelograms** Y6: Introductory algebra & equation-solving Science KS1 Some physics topics moved to KS2 only: Light & Dark; Sound; Forces; Electricity Care for animals/others/environment removed No requirement to make predictions or fair tests Reduce requirement to know life processes Changing materials with heat moves to KS2 Drugs as medicines removed Y1: Naming **of** plants **and** animals/

the perimeter **of** **a** square measuring 3 inches **on** each side? Back to Board Geometry What is the **area** **of** **a** **parallelogram** with **a** base **of** 8 meters **and** **a** height **of** 15 meters? Back to Board Geometry What is the circumference **of** **a** circle with **a** radius **of** 7 feet? Back to Board Geometry What is the **area** **of** **a** **triangle** with **a** base **of** 13 inches **and** **a** height **of** 19 inches? Back to Board Probability What is the probability **of** landing **on** “yellow” **on** **a** spinner/

, converting measurements **of** … volume… from **a** smaller unit **of** measure to **a** larger unit, **and** vice versa, using decimal notation to up to three decimal places New content recognise when it is possible to use formulae for **area** **and** volume **of** shapes New content calculate the **area** **of** **parallelograms** **and** trianglesNew content find unknown angles in any **triangles**, quadrilaterals, **and** regular polygons New content illustrate **and** name parts **of** circles, including radius, diameter **and** circumference **and** know that/

graph. Based **on** this graph, which set **of** numbers is the closest to the total **area** **of** the five Great Lakes? **A**. between 70,000 **and** 80,000 square miles B. between 80,000 **and** 90,000 square miles C. between 90,000 **and** 100,000 square miles D. between 100,000 **and** 110,000 square miles index 39. Points R **and** T are the midpoints **of** the sides **of** **triangle** QSU, as/

without learning something. Confucius Do you remember this? Spiral Review **Area** **of** **a** **Parallelogram** Hands **on** Practice: **Parallelogram** Cut Ups AIMS book- **Area** Formulas for **Parallelograms**, **Triangles**, **and** Trapezoids: page 9 Practice finding **AREA** **of** **parallelograms** Answers… More Practice… Answers. Problem Solving… Spiral Review… **Area** **of** **Triangles**… Hands **on** Practice: **Triangle** Cut Ups AIMS book-**Area** Formulas for **Parallelograms**, **Triangles**, **and** Trapezoids: page 25 Where there is matter, there is geometry." -- Johannes/

measures make simple conversions between units, using decimals use side or edge lengths to find the perimeters **and** **areas** **of** rectangles, **parallelograms**, **and** **triangles** **and** the volumes **of** cuboids sort two- **and** three-dimensional shapes into classes, considering the relationships between the classes **and** justifying the decisions made identify **and** describe the features **of** shapes or patterns that change or do not change under transformation create or identify nets for rectangular prisms/

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