select appropriate methods **for** estimating measurements select **and** apply techniques **and** tools to accurately find length, **area**, volume, **and** angle measures to appropriate levels **of** precision select **and** apply techniques **and** tools to accurately find length, **area**, volume, **and** angle measures to appropriate levels **of** precision develop **and** use formulas to determine the circumference **of** circles **and** the **area** **of** **triangles**, **parallelograms**, trapezoids, **and** circles **and** develop strategies to find the **area** **of** more-complex/

**FOR** SA-I SA I will be conducted **and** the syllabus is inclusive **of** FA I & FA II CH-**9**:**Areas** **Of** **Parallelograms** **And** **Triangles** MONTHS EXAM CONTENTS (CHAPTER REF TEXT BOOK) SUGGESTED ACTIVITIES NOV-DEC TERM II F A - III CH-8: Quadrilaterals CH-**9**:**Areas** **Of** **Parallelograms** **And** **Triangles**/Poverty as a Challenge Hold mock elections in the **class** to understand the procedure **of** election. Illustrate with the help **of** graphical representation & map **of** India the effectiveness **of** NREGA. JAN- FEB MONTHS EXAMS CONTENTS (CHAPTER REF/

. Only half will be selected. Write **and** solve the equation. If the **area** **of** **triangle** 1 is 35 square inches If the **area** **of** **triangle** 1 is 35 square inches. What is the **area** **of** the **parallelogram**? Charlie wants to make an A in Math Charlie wants to make an A in Math. He must have an average (mean) score **of** >92% **for** an A in the **class**. Will Charlie get an A/

angles Preserve lengths **of** segments **and** the measures **of** angles G.CO.B.7 Use the definition **of** congruence in terms **of** rigid motions to show that two **triangles** are congruent if **and** only if corresponding pairs **of** sides **and** corresponding pairs **of** angles are congruent. Illustrative Math G.CO.B.8 Explain how the criteria **for** **triangle** congruence (ASA, SAS, **and** SSS) follow from the definition **of** congruence in terms **of** rigid motions. everything/

. • The **area** **of** a square one meter long **and** one meter wide is a square meter. **AREA** **OF** A RECTANGLE: • The number **of** square inches in a rectangle equals the number **of** rows one inch wide times the number **of** square inches in a row. Illustration: • The number **of** square centimeters or square feet in a rectangle is its **area**. Finding the **area** **of** (square)(rectangle)(**triangle**)(**parallelogram**) TO FIND THE **AREA** **OF** A SQUARE: **Area** = Side/

6 JulWk45 **9**-13 /**for** **area** **of** a rectangle, **triangle** **and** **parallelogram** work out the **area** **of** a rectangle work out the **area** **of** a **parallelogram** calculate the **area** **of** shapes made from **triangles** **and** rectangles calculate the **area** **of** shapes made from compound shapes made from two or more rectangles, **for** example an L shape or T shape calculate the **area** **of** shapes drawn on a grid calculate the **area** **of** simple shapes work out the surface **area** **of** nets made up **of** rectangles **and** **triangles** calculate the **area** **of**/

describes the calculation used to determine the amount **of** carpet needed **for** a given **area** **of** floor? FThe **area** **of** the floor is divided by 12. GThe **area** **of** the floor is divided by 10. HThe **area** **of** the floor is divided by **9**. JThe **area** **of** the floor is divided by 3. April 2006 #22 Correct Answer - H Three friends attended a football game **and** agreed to share the cost evenly. The total/

**9** times larger than the **area** **of** **triangle** ABC. GLCE: G.TR.07.06 Understand **and** use the fact that when two **triangles** are similar with scale factor **of** r, their **areas** are related by a factor **of** r2. [Core] State Results District Results A11% B21% C15% D53% 54. Use similarity **of** **triangles** **and** scale factor. A. double the correct **area** B. correct C. squared **area** **of** smaller **triangle** D. used r as scale factor **for** **area** Data **and**/

the **Area** **of** the **Parallelogram** below? 10 ft Calculate A = b x h A = 25 x 8 A = 200 ft 2 height base OBJECTIVE: SWBAT determine the **area** **of** any right **triangle** **and** defend their method. 25 ft 8 ft (Click **for** Detailed Solutions) Warm Up Agenda 6 OBJECTIVE: SWBAT determine the **area** **of** any right **triangle** **and** defend their method. (Click to Return) Agenda: OBJECTIVE: SWBAT determine the **area** **of** any right **triangle** **and** defend/

partition is to be installed so that 2 **classes** can use it. The **area** **of** the smaller classroom is 38x. How can the **area** **of** the larger classroom be expressed in terms **of** x? Correct Answer - D Spring 2003 #19 (A.3) Foundations **for** functions. The student understands how algebra can be used to express generalizations **and** recognizes **and** uses the power **of** symbols to represent situations. The student is/

describes the calculation used to determine the amount **of** carpet needed **for** a given **area** **of** floor? FThe **area** **of** the floor is divided by 12. GThe **area** **of** the floor is divided by 10. HThe **area** **of** the floor is divided by **9**. JThe **area** **of** the floor is divided by 3. April 2006 #22 Correct Answer - H Three friends attended a football game **and** agreed to share the cost evenly. The total/

**area** **of** a **parallelogram** be the same as that **of** a rectangle? 10 ft. **TRIANGLE** **AREA**: A = b x h ÷ 2 12 ft. TSW: Text p.570 # 5, **9**, 2 The **area** **of** the rectangle below is 120 ft. 2 How can you figure out what the **area** **of** a **triangle** would be? 2-72-a,b 2-72-c 2-73 1)Review your notes from yesterday to find the **area** formulas **for**/

AB in the ratio 1 : 2, then Equation **of** **Class** Exercise - **9** Prove that the points (2, –1), (0, 2), (2, 3) **and** (4, 0) are the vertices **of** a **parallelogram**. Solution : Slope **of** PQ = Solution Slope **of** RS = Slope **of** PS = Slope **of** QR = As slope **of** PQ = Slope **of** RS **and** Slope **of** PS = Slope **of** QR PQRS is a **parallelogram** **Class** Exercise - 10 (i) Find the equation **of** line passing through the point (–4, –3/

stem-**and**-leaf plot below shows the number **of** seconds it took each student in a **class** **of** 18 to/**triangles**. B.Sixteen congruent isosceles **triangles**. C.Eight congruent right **triangles**. D.Eight congruent equilateral **triangles**. E.Eight congruent isosceles **triangles**. 28 NAEP Grade 8 Math Warm Ups 28.**Parallelograms** ABCD **and** PQRS above are similar. What is the length **of** side QR? A.4.5 B.**9**/**and** include the length **and** width, in feet, **for** each room. (b)Complete the table by filling in the floor **area**, in square feet, **for**/

relationships among shapes, such as two **triangles** can make a rectangle, leads to an understanding **of** formulas **for** finding **area** **of** shapes **and** the concept that shapes that look different can have the same **area**.(gr.7) Surface **Area** **and** Volume Prior knowledge The **area** is the number **of** square units needed to cover a surface. **Area** Formulas Rectangle: A = l × w **Triangle**: A = (b × h) ÷ 2 **Parallelogram**: A = b × h Tessellations Tessellations are/

mathematics developing strategies **for** coordinating students’ mathematical thinking **and** communication (bansho) describing the teacher’s role in teaching through problem solving 38 Curriculum Connections 39 Curriculum Connections 40 Warm Up – Composite Shape Problem What could a composite shape look like that … has an **area** **of** 4 square units? is composed **of** 3 rectangles (Grade 5)? is composed **of** at least one rectangle, one **triangle**, **and** one **parallelogram** (Grade 6/

6cm 4cm Question 51 calculate the **area** **of** composite shapes. Find the **area** shaded grey below. 10cm 11cm 8cm 4cm answer Answer to Question 51 10cm 11cm 8cm 4cm write down the **area** formula **for** Question 52 write down the **area** formula **for** Any **triangle** Rhombus **Parallelogram** Kite Trapezium answer The **area** formula **for** Any **triangle** Rhombus **Parallelogram** Kite Trapezium Answer to Question 52 The **area** formula **for** Any **triangle** Rhombus **Parallelogram** Kite Trapezium write down in/

is to be installed so that 2 **classes** can use it. The **area** **of** the smaller classroom is 38x. How can the **area** **of** the larger classroom be expressed in terms **of** x? Correct Answer - D Spring 2003 #19 A(b)(3) Foundations **for** functions. The student understands how algebra can be used to express generalizations **and** recognizes **and** uses the power **of** symbols to represent situations. (B) Given situations/

side nor the height **of** a **triangle** can be measured. In this situation the **area** can be determined if one **of** the angles **and** the lengths **of** the two adjoining sides can be measured. The equation is: 13 Square & **Parallelogram** A square is a simple figure where all four sides **and** all four angles are equal. The **area** **of** a square is determined by: The **area** **for** a **parallelogram** is determined using the/

definition. Afterwards, the teacher reviews the correct answers with the **class**. Students are given envelopes that contain the following paper shapes: square, rectangle, **triangle**, **parallelogram**, rhombus, **and** trapezoid. The names **of** each shape are written on the paper shape. Working in pairs, students must use their knowledge **of** points, lines, **and** angles to write a definition **for** each shape based on its properties. Each group then chooses one/

**Triangles** **Triangle** DEF is similar to **triangle** JKL. What is the missing measure **of** y? F ED J L K 15 12 Y 6 A. 6.5 B. 7.5 C. **9** D. 30 **Area**-Rectangle Stanley is running **for** **class** treasurer. He uses a rectangular piece **of** poster board to make a sign. What is the **area** **of** the sign? Stanley **for** Treasurer Vote **for**/h A. 91 sq. in. B. 104 sq. in. C. 182 sq. in. D. 208 sq. in. 10 in. 20 in. 8 in. **Area**-**Parallelogram** What is the **area** **of** the figure shown? 14 cm A= b x h A. 56 sq. cm. B. 68 sq. cm. C. 168 sq. cm. D. 196 sq./

**and** differences between Benchmark Assessments **and** Diagnostic Tools? 7 Benchmark Diagnostic Grade-level specific Measures content at the reporting category level **for** reading **and** math Students do not receive direct, formative feedback **Class** tool Provides current level **of** performance Identifies **areas** **of** strengths **and** needs across grade levels **and** subject **areas**/Tools M7.B.2.1.2 Find the **area** **of** **triangles** **and**/or all types **of** **parallelograms** (formulas provided on the reference sheet). Learning Progression Activity /

the right-hand rule (the unit vector n ) **and** a magnitude equal to the **area** **of** the **parallelogram** that the vectors span. Cross Product as Geometry the **area** **of** the **parallelogram**. a b = |a| |b | sin θ n counter- clockwise Why is |a x b| an **area**? a b θ |b| sin θ |a| Angle Example public double cross(Vec b) // in the Vec **class** { return ((x * b.y) - (y * b.x/

**9** What are the similarities **and** differences between Benchmark Assessments **and** Diagnostic Tools? **9** Benchmark Diagnostic Grade-level specific Measures content at the reporting category level **for** reading **and** math Students do not receive direct, formative feedback **Class** tool Provides current level **of** performance Identifies **areas** **of** strengths **and** needs across grade levels **and** subject **areas**/2.1.2 Find the **area** **of** **triangles** **and**/or all types **of** **parallelograms** (formulas provided on the reference sheet). /

**Parallelograms**’ **areas** are twice more than the **area** **of** a **triangle**, if they are common in one based **and** height. Both groupsApprox 45 min FourthInstruction “If we connect the midpoints **of** an optional convex quadrilateral consecutively, then what is the name **of** the resulted shape”? Both groups40 min FourthTestAll students50 min Findings **and** discussion The research findings extracted from observation during each day **of** the **class**/outcome obtained **for** question **9** in the test at the end **of** the study as well, **and** is /

decimal places convert between miles **and** kilometres recognise that shapes with the same **areas** can have different perimeters **and** vice versa recognise when it is possible to use formulae **for** **area** **and** volume **of** shapes calculate the **area** **of** **parallelograms** **and** **triangles** calculate, estimate **and** compare volume **of** cubes **and** cuboids using standard units, including cubic centimetres (cm3) **and** cubic metres (m3), **and** extending to other units [**for** example, mm3 **and** km3]. Geometry – properties **of** shapes draw 2-D shapes/

result **for** a **triangle**, quadrilateral, pentagon **and** hexagon) Activity 28: To make the following by paper folding **and** cutting a kite a rhombus diagonals **of** a rectangle are **of** equal length Activity 29: To verify that diagonals **of** a rectangle are **of** equal length diagonals **of** a square are **of** equal length Investigate the results **for** a rhombus **and** a **parallelogram**, using stretched threads. Activity 30:(Group Activity) Do a survey **of** your **class** **and** collect/

in the same **area** where you sat before. Study **for** your quiz. What is the **area** **of** a **triangle** with a height **of** 4 inches **and** a base that is the length **of** 3 inches? Clear Your Desk Except paper **and** pencil. Finished with Quiz? Staple any work you have to your quiz **and** put your quiz in the **class** bin. Get your homework **for** tonight (the side with #4- **9** on it/

the room **and** then have a seat. Thank you **for** coming, Ms. Espinoza My email is tamara.espinoza@sduhsd.nettamara.espinoza@sduhsd.net **Class** webpage http:///**and** Quadrilaterals Counterexamples, indirect proofs, **parallelograms**, rhombuses, rectangles, squares, **and** trapezoids, geometric constructions involving parallel lines Chapter 6 Ratio **and** Proportion Similar **Triangles**; Cross Sections, scale factor, **area** ratio, volume ratios; Mean proportionality in a right **triangle**; Right **Triangle** Trigonometry ; Laws **of**/

**and** some squares D: 3 hexagons **and** some squares **and** **triangles** 39 What does it look like? Or, more specifically…. A) How many **of** each shape might I have made? B) How do you know that at least one shape was a **triangle**? 40 What does it look like? In Grade 6, I might ask my students something like: A **parallelogram** has an **area** **of**/Alicia says that 45 – **9** – **9** – **9** – **9** – **9** = 0 describes a division. Do you agree? /to you. Ultimately you are responsible **for** the instruction in the **class**– if the students don’t /

**area** **of** this **triangle**. 7cm 4cm 9cm LJR March 2004 Example: Calculate the **area** **of** these shapes. 6m 9m 4m 8m 3m LJR March 2004 base height base This shows that the **area** **of** a **parallelogram** is similar to the rectangle. LJR March 2004 Example: Calculate the **area** **of** this **parallelogram**./ data taken from a **class** **of** S3 students. Height (cm) Shoe size 2 125130135140 145150 155160165175 4356767810911 Does this show a connection between height **and** shoe size? LJR March 2004 Height (cm) Shoe size 13 12 11 10 **9** 8 7 6 5 /

math Units 3. Find the total **area**.Basically…. surface **area** = **area** **of** base(s) + **area** **of** sides proof….. paragraph, two column or flow chart How can you prove that the formula **for** the **area** **of** a **parallelogram** is A = bh? Can you PROVE that both **triangles** are congruent? http://www.basic-mathematics.com/proof-**of**-the-**area**-**of**-a-**parallelogram**.html Quiz Work silently on your quiz. Show all steps **and** justify your answers (use math/

between two given points that partitions the segment in a given ratio. G-GPE.B.7 Use coordinates to compute perimeters **of** polygons **and** **areas** **of** **triangles** **and** rectangles, e.g., using the distance formula.★ ★Mathematical Modeling is a Standard **for** Mathematical Practice (MP4) **and** a Conceptual Category, **and** specific modeling standards appear throughout the high school standards indicated with a star (★). Where an entire domain is marked with/

scale drawings **and** use **of** bearings G16 know **and** apply formulae to calculate: **area** **of** **triangles**, **parallelograms**, trapezia; volume **of** cuboids **and** other right prisms (including cylinders) G17 know the formulae: circumference **of** a circle = 2πr = πd , **area** **of** a circle = πr 2 ; calculate: perimeters **of** 2D shapes, including circles; **areas** **of** circles **and** composite shapes; surface **area** **and** volume **of** spheres, pyramids, cones **and** composite solids G18 calculate arc lengths, angles **and** **areas** **of** sectors **of** circles G19/

scale drawings **and** use **of** bearings G16 know **and** apply formulae to calculate: **area** **of** **triangles**, **parallelograms**, trapezia; volume **of** cuboids **and** other right prisms (including cylinders) G17 know the formulae: circumference **of** a circle = 2πr = πd , **area** **of** a circle = πr 2 ; calculate: perimeters **of** 2D shapes, including circles; **areas** **of** circles **and** composite shapes; surface **area** **and** volume **of** spheres, pyramids, cones **and** composite solids G18 calculate arc lengths, angles **and** **areas** **of** sectors **of** circles G19/

divide a square into two equal parts **and** justify their way. Procedure to trisect a square Purpose **of** this talk It is to provide an "honest" learning environment to teach deductive reasoning **for** secondary students (**9** & 10 graders). It is to provide/**triangle** ABC. Make three equilateral **triangles** ABD, BCE, AFC by using each side **of** the given **triangle** ABC. Then prove that quadrilateral BEFD is a **parallelogram** Analysis DF=BE **and** BD=FE To prove that quadrilateral BEFD is a **parallelogram** we have to show DF=BE **and**/

expression **for** a vector C three times the length **of** A pointing in the direction opposite the direction **of** A. [**9**] Three displacement vectors **of** a croquet ball are shown in Figure, where A = 20.0 units, B = 40.0 units, **and** C = 30.0 units. Find the magnitude **and** direction **of** the resultant displacement [10] A rectangular building lot is 100 ft by 150 ft. Determine the **area** **of**/

vector to the end **of** the last vector. Measure the length **of** the resultant **and** its angle. Use the scale factor to convert length to actual magnitude. Ref? **Parallelogram** Method **for** Adding Two Vectors The tail **of** the second vector is placed at the tail **of** the first vector. The two vectors define a **parallelogram**. The resultant is the vector along the diagonal **of** the **parallelogram**. A B A+B/

Example: A certain polyhedron has 12 edges **and** 6 faces. Determine the number **of** vertices on this polyhedron. # **of** vertices - # **of** edges + # **of** faces = 2 There are 8 vertices. Slide **9** - 44 Copyright © 2009 Pearson Education, Inc. Volume **of** a Prism V = Bh, where B is the **area** **of** the base **and** h is the height. Example: Find the volume **of** the figure. **Area** **of** one **triangle**. Find the volume. 8 m 6 m/

SPI 0506.4.2 Find the **area** **of** the figure. **Area** **of** a rectangle = length × width **Area** **of** a **triangle** = ½ bh 6th Grade - 3rd Nine Weeks Math Review Week 4 STANDARD QUESTION Data, Statistics, **and** Probability SPI 0506.5.2 According to the below graph, which fifth grade **class** collected the most cans **for** the week? Pot Luck SPI 0606.1.2 The elevation **of** New Orleans, Louisiana, is 8 feet/

is handy to have code **and** instance variables, **and** so in these cases abstract **classes** work better. 85 Abstract **class** example abstract **class** Shape { abstract public void draw(); abstract public double **area**(); abstract public Point upperLeft(); abstract public void moveTo(Point ); abstract public void setColor(Color ); abstract public double perimeter(); public double semiperimeter() { return perimeter() / 2; } 86 Rectangle Square **Parallelogram** Ellipse Circle **Triangle** Shape Defining the subclasses public/

, via pythagorean theorem!!! –4) **Area** **of** a **PARALLELOGRAM**: Base x Height Quantitative Review Geometry - Polygons Polygons **and** **Area** –5) **Area** **of** a RHOMBUS = (Diagonal 1 x Diagonal 2) / 2 –GMAT may require you to divide some shapes. Notice, **for** example, that a trapezoid can be cut into 2 right **triangles** **and** 1 rectangle: Quantitative Review Geometry - Polygons 3 Dimensions: Surface **Area** –Surface **Area** = the SUM **of** the **areas** **of** all **of** the faces –Rectangular Solid: 2/

Example: A certain polyhedron has 12 edges **and** 6 faces. Determine the number **of** vertices on this polyhedron. # **of** vertices # **of** edges + # **of** faces = 2 There are 8 vertices. Slide **9** - 43 Copyright © 2009 Pearson Education, Inc. Volume **of** a Prism V = Bh, where B is the **area** **of** the base **and** h is the height. Example: Find the volume **of** the figure. **Area** **of** one **triangle**. Find the volume. 8 m 6 m/

angles in geometric figures, including interpreting maps **and** scale drawings **and** use **of** bearings G16 know **and** apply formulae to calculate: **area** **of** **triangles**, **parallelograms**, trapezia; volume **of** cuboids **and** other right prisms (including cylinders) G17 know the formulae: circumference **of** a circle = 2πr = πd, **area** **of** a circle = πr 2 ; calculate: perimeters **of** 2D shapes, including circles; **areas** **of** circles **and** composite shapes; 4. Geometry **and** measures Properties **and** constructions G1 use conventional terms/

angles in geometric figures, including interpreting maps **and** scale drawings **and** use **of** bearings G16 know **and** apply formulae to calculate: **area** **of** **triangles**, **parallelograms**, trapezia; volume **of** cuboids **and** other right prisms (including cylinders) G17 know the formulae: circumference **of** a circle = 2πr = πd, **area** **of** a circle = πr 2 ; calculate: perimeters **of** 2D shapes, including circles; **areas** **of** circles **and** composite shapes; 4. Geometry **and** measures Properties **and** constructions G1 use conventional terms/

, via pythagorean theorem!!! –4) **Area** **of** a **PARALLELOGRAM**: Base x Height Quantitative Review Geometry - Polygons Polygons **and** **Area** –5) **Area** **of** a RHOMBUS = (Diagonal 1 x Diagonal 2) / 2 –GMAT may require you to divide some shapes. Notice, **for** example, that a trapezoid can be cut into 2 right **triangles** **and** 1 rectangle: Quantitative Review Geometry - Polygons 3 Dimensions: Surface **Area** –Surface **Area** = the SUM **of** the **areas** **of** all **of** the faces –Rectangular Solid: 2/

.14 **for** . Use the formula **for** the **area** **of** a **parallelogram**. Substitute 16 **for** b. Substitute **9** **for** h. A = bh A = 16 **9** A = 144Step 1: Separate the figure into smaller, familiar figures. 16 m **9** m 16 m Step 2: Find the **area** **of** each smaller figure. **Area** **of** the **parallelogram**: Example 2 Continued Find the **area** **of** the irregular figure. Use 3.14 **for** . Substitute 3.14 **for** **and** 8 **for** r. 16 m **9** m 16 m **Area** **of** the/

parallel lines creates equal opposite angles. Plane Geometry: **Triangles** Plane Geometry **Area** **of** a **triangle** = ½ (base * height) The sum **of** the three angles = 1800 **Area** **of** a trapezoid = ½ (a +b)*(height) where a **and** b are the lengths **of** the parallel sides Diameter = 2 * radius **of** a circle Volume **of** cylinder = **area** **of** circle * height a b r h Plane Geometry Example What is the **area** **of** the square if the radius equals 5? L/

6 m 3 (8) 1.56x10 3 m 3 (**9**) 1.56x10 6 m 3 (10) 1.56x10 **9** m 3 A bucket has a volume **of** 1560 cm 3. What is its volume in m /left **and** right are the same. CORRECT equation.] You are examining two circles. Circle 2 has a radius 1.7 times bigger than circle 1. What is the ratio **of** the **areas**? Express this as the value **of** the /N) Vector Summation += ABC += AB C A B ABC =+ 1) 2) + Two ways to sum the vectors: **Parallelogram** method (1), **and** **triangle** method (2). Vector Summation A B C C = A + B 22 = tan A B Which is /

**parallelogram** like this one Connect each corner **of** the top **parallelogram** with the corresponding corner **of** the bottom **parallelogram** Now imagine an identical **parallelogram** /South, East, West)? Which 3 places form an isosceles **triangle**? Such configurational consequence can be detected as opposed to /**of** spatial representations, just the way they did in the purely visual cases illustrated earlier Mental imagery **and** neuroscience Neuroanatomical evidence **for** a retinotopic display in the earliest visual **area** **of**/

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