mathematics grade 10 navrachana …mathematics grade 10 navrachana international school, vadodara...

MATHEMATICS GRADE 10 Navrachana International School, Vadodara (2013-2014)

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NO. OF SESSIONS

GRADE 10 (MATHEMATICS)

ASSESSMENT OBJECTIVE (based on Assessment Criteria)

LEARNER PROFILE/ ATTITUDES

ATL SKILLS/ SUBJECT SPECIFIC SKILLS

INTERDISCIPLINARY

25 TOPIC- GEOMETRY AOI- Human Ingenuity SIGNIFICANT CONCEPTS- Geometry allows us to work out the relationships Between shapes, forms and spaces. Objects can be described and compared Using their geometric attributes. CONTENT 1. measure lines and angles 2. construct a triangle given three sides using ruler and compasses only 3. construct other simple geometrical figures from given data using protractors and set squares as necessary. 4. construct angle bisectors and perpendicular bisectors using straight edges and

CRITERIA A Knowledge and Understanding CRITERIA B Investigating Patterns

Students should be able to- (CRITERIA A) • know and demonstrate understanding of the concepts from the topic geometry. • use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts for the topic geometry. • select and apply general rules correctly in geometry to make deductions and solve problems, including those in real-life contexts. (CRITERIA B) • select and apply appropriate inquiry and

LEARNER PROFILE

Inquirer Knowledgeable Thinker Reflective

ATTITUDE Commitment

Confidence

Creativity

Curiosity

Organization Information Literacy Thinking Transfer

Physics, Geography, Art


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compasses only 5. read and make scale drawings 6. use and interpret vocabulary of triangles, quadrilaterals, circles, polygons and simple solid figures including nets

7. use the relationship between areas of similar triangles, with corresponding results for similar figures and extensions to volumes and surface areas of similar solids MYP UNIT

QUESTION- How can plane and Solid shapes are described?

mathematical problem-solving techniques in geometry • recognize patterns • describe patterns as relationships or general rules in similar figures. • draw conclusions consistent with findings • justify or prove mathematical relationships and general rules for geometry

NO. OF SESSIONS





INTERDISCIPLINARY

20 TOPIC- GEOMETRY

AOI- Human Ingenuity SIGNIFICANT

CONCEPTS-

CRITERIA A

Knowledge and Understanding CRITERIA B

Investigating Patterns

Students should be able to- (CRITERIA A) • know and demonstrate understanding of the concepts from

LEARNER PROFILE


ATTITUDE




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Geometry allows us to work out the relationships between shapes, forms and spaces. Objects can be described and compared using their geometric attributes. CONTENT 1. recognize rotational and line symmetry in two dimensions 2. know properties of triangles, quadrilaterals and circles directly related to their symmetries 3. recognize symmetry properties of the prism and pyramid 4. use the symmetry properties of circles 5. use loci and the method of intersecting loci for sets of points in two dimensions MYP UNIT

QUESTION- How can plane and solid

the topic geometry. • use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts for the topic geometry. • select and apply general rules correctly in geometry to make deductions and solve problems, including those in real-life contexts. (CRITERIA B) • select and apply appropriate inquiry and mathematical problem-solving techniques in geometry • recognize patterns in symmetry • describe patterns as relationships or general rules for

Commitment Confidence Creativity Curiosity


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shapes be described?

circle properties • draw conclusions consistent with findings • justify or prove mathematical relationships and general rules for geometry

NO. OF SESSIONS





INTERDISCIPLINARY

20 TOPIC- GEOMETRY AOI- Human Ingenuity SIGNIFICANT CONCEPTS- Geometry allows us to work out the relationships between shapes, forms and spaces. Objects can be described and compared using their geometric attributes. CONTENT 1. calculate unknown angles using the following geometrical properties: angles at a point, angles formed

CRITERIA A

Knowledge and Understanding CRITERIA B

Investigating Patterns

Students should be able to- (CRITERIA A) • know and demonstrate understanding of the concepts from the topic geometry. • use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts for the topic geometry. • select and apply

LEARNER PROFILE


ATTITUDE Commitment Confidence Creativity Curiosity




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within parallel lines, angle properties of regular polygons, angles in a semi-circle, angle between the tangent and radius of a circle

2. know angle properties of irregular polygons 3. angle properties related to circle segments MYP UNIT QUESTION- How can plane and solid shapes be described?

general rules correctly in geometry to make deductions and solve problems, including those in real-life contexts. (CRITERIA B) • select and apply appropriate inquiry and mathematical problem-solving techniques in geometry • recognize patterns in symmetry • describe patterns as relationships or general rules for circle properties • draw conclusions consistent with findings • justify or prove mathematical relationships and general rules for geometry

NO. OF SESSIONS





INTERDISCIPLINARY

25 TOPIC- CRITERIA A Students should LEARNER Organization Physics, Geography


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MENSURATION AOI- Environment SIGNIFICANT CONCEPTS- Perimeter and area of two-dimensional shapes, Surface area and volume of solids CONTENT 1. carry out calculations involving the perimeter and area of a rectangle and triangle, the circumference and area of a circle, the area of a parallelogram and a trapezium, the volume of a cuboids, prism and cylinder and the surface area of a cuboids and a cylinder 2. solve problems involving the arc length and sector area as fractions of the circumference and area of a circle, the surface area and volume of a sphere, Pyramid and cone.

Knowledge and Understanding CRITERIA B Investigating Patterns CRITERIA D Reflection in Mathematics

be able to- (CRITERIA A) • know and demonstrate understanding of the concepts for mensuration. • use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts for mensuration. • select and apply general rules correctly in geometry to make deductions and solve problems, including those in real-life contexts for mensuration. (CRITERIA B) • select and apply appropriate inquiry and mathematical

PROFILE Inquirer Knowledgeable Thinker Reflective ATTITUDE Confidence Creativity Curiosity Interdependence

Information literacy Thinking Transfer Reflection


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MYP UNIT QUESTION- When and how do you measure perimeter, area and volume in real world?

problem-solving techniques in mensuration. • recognize patterns of 2D shapes • describe patterns as relationships or general rules of 3D shapes • draw conclusions consistent with findings • justify or prove mathematical relationships and general rules for solids (CRITERIA D) • explain whether the results in mensuration make sense in the context of the problem • explain the importance of surface area and volume of 3d shapes in connection to real life where


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appropriate • justify the degree of accuracy in calculating the area and volume where appropriate • suggest improvements to the method when necessary for mensuration topic.

NO. OF SESSIONS





INTERDISCIPLINARY

20 TOPIC- TRIGONOMETRY AOI- Human Ingenuity SIGNIFICANT CONCEPTS- Pythagoras theorem, sine, cosine and tangent ratios for a right triangle, sine, cosine of an obtuse angle, area of a triangle, solving a triangle CONTENT 1. interpret and use three figure

CRITERIA A Knowledge and Understanding CRITERIA B Investigating Patterns CRITIERIA C Communication in Mathematics CRITERIA D Reflection in Mathematics

Students should be able to- (CRITERIA A) • know and demonstrate understanding of the concepts for trigonometry. • use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations,

LEARNER PROFILE Inquirer Knowledgeable Thinker Communicator Reflective

ATTITUDE Confidence Creativity Curiosity Interdependence

Organization Information Literacy Thinking Transfer Collaboration Communication Reflection

Physics


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bearings measured clockwise from north 2. apply Pythagoras' theorem and the sine, cosine and tangent ratios for acute angles to the calculation of a side or an angle of a right angled triangle 3. solve trigonometrically problems in two dimensions involving angles of elevation and depression MYP UNIT QUESTION- How does knowing the basic trigonometry ratios simplify Finding distances and angles?

including those in real-life contexts for trigonometry. • select and apply general rules correctly in geometry to make deductions and solve problems, including those in real-life contexts for trigonometry. (CRITERIA B) • select and apply appropriate inquiry and mathematical problem-solving techniques in trigonometry. • recognize patterns for different triangles and application of Pythagoras theorem. • describe patterns as relationships or general rules for sine, cosine and tangent ratios for


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right angles • draw conclusions consistent with findings in trigonometry. • justify or prove mathematical relationships and general rules calculation of a side or an angle of a right angled triangle (CRITERIA C) • use appropriate mathematical language in both oral and written explanations in trigonometry. • use different forms of mathematical representation in trigonometry. • communicate a complete and coherent mathematical line of reasoning using different forms of representation when


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investigating problems in trigonometry. (CRITERIA D) • explain whether the results in trigonometry make sense in the context of the problem • explain the importance of Pythagoras theorem, trigonometrical ratios in connection to real life where appropriate • justify the degree of accuracy in calculating the area of triangle and angle or length of side in triangle where appropriate • suggest improvements to the method when necessary for trigonometry.


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NO. OF SESSIONS





INTERDISCIPLINARY

20 TOPIC- TRIGONOMETRY AOI- Human Ingenuity SIGNIFICANT CONCEPTS- Pythagoras theorem, sine, cosine and tangent ratios for a right triangle, sine, cosine of an Obtuse angle, area of a triangle, solving a triangle. CONTENT 1. extend sine and cosine functions to angles between 90° and 360° 2. solve problems using the sine and cosine rules for any triangle and formula for area of triangle 3. solve simple trigonometrically problems in three dimensions

CRITERIA A Knowledge and Understanding CRITERIA B Investigating Patterns CRITIERIA C Communication in Mathematics CRITERIA D Reflection in Mathematics

Students should be able to- (CRITERIA A) • know and demonstrate understanding of the concepts for trigonometry. • use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts for trigonometry. • select and apply general rules correctly in geometry to make deductions and solve problems, including those in

LEARNER PROFILE Inquirer Knowledgeable Thinker Communicator Reflective

ATTITUDE Confidence Creativity Curiosity Interdependence

Organization Information Literacy Thinking Transfer Collaboration Communication Reflection

Physics


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including angle between a line and a plane MYP UNIT QUESTION- How does knowing the basic trigonometry ratios simplify finding distances and angles?

real-life contexts for trigonometry. (CRITERIA B) • select and apply appropriate inquiry and mathematical problem-solving techniques in trigonometry. • recognize patterns for sine and cosine functions • describe patterns as relationships or general rules types of triangle and application of sine rule and cosine rule to it • draw conclusions consistent with findings for trigonometry • justify or prove mathematical relationships and general rules for solving trigonometrically problems in


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three dimensions (CRITERIA C) • use appropriate mathematical language in both oral and written explanations in trigonometry. • use different forms of mathematical representation in trigonometry. • communicate a complete and coherent mathematical line of reasoning using different forms of representation when investigating problems in trigonometry. (CRITERIA D) • explain whether the results in trigonometry make sense in the context of the problem • explain the


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importance of Pythagoras theorem, trigonometrical ratios in connection to real life where appropriate • justify the degree of accuracy in calculating the area of triangle and angle or length of side in triangle where appropriate • suggest improvements to the method when necessary for trigonometry.

NO. OF SESSIONS





INTERDISCIPLINARY

20 TOPIC-TRANSFORMATIONS AOI- Human Ingenuity SIGNIFICANT CONCEPTS- Understanding of different types of transformations, use

CRITERIA A Knowledge and Understanding CRITERIA B Investigating Patterns CRITIERIA C Communication

Students should be able to- (CRITERIA A) • know and demonstrate understanding of the vectors concepts.

LEARNER PROFILE Inquirer Knowledgeable Thinker Reflective ATTITUDE Commitment Confidence

Organization Information literacy Thinking Transfer

Physics


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of matrices and vectors to describe transformations CONTENT 1. describe a translation by using a vector 2. add vectors and multiply a vector by a scalar 3. calculate the magnitude of a vector 4. represent vectors by directed line segments 5. use the sum and difference of two vectors to express given vectors in terms of two coplanar vectors 6. use position vectors MYP UNIT QUESTION: How vectors and matrices can be used to describe Transformations?

in Mathematics

• use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts for the topic transformation and vectors. • select and apply general rules correctly in vectors to make deductions and solve problems, including those in real-life contexts. (CRITERIA B) • select and apply appropriate inquiry and mathematical problem-solving techniques in vectors • recognize patterns in transformations using vectors

Creativity Curiosity Tolerance.


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• describe patterns as relationships or general rules for vectors. • draw conclusions consistent with findings for translations • justify or prove mathematical relationships and general rules for vectors. CRITERIA C) • use appropriate mathematical language in both oral and written explanations in vectors • use different forms of mathematical representation in vectors • communicate a complete and coherent mathematical line of reasoning using different forms of representation


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when investigating problems in vectors

NO. OF SESSIONS





INTERDISCIPLINARY

25 TOPIC- TRANSFORMATIONS AOI- Human Ingenuity SIGNIFICANT CONCEPTS- Understanding of different types of transformations, use of matrices and vectors to describe transformations CONTENT 1. display information in the form of a matrix of any order 2. calculate the sum and product of two matrices 3. calculate the product of a matrix and a scalar quantity 4. use the algebra of 2x2 matrices

CRITERIA A Knowledge and Understanding CRITERIA B Investigating Patterns CRITIERIA C Communication in Mathematics

Students should be able to- (CRITERIA A) • know and demonstrate understanding of the matrices Concept. • use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts for the topic transformation and matrices. • select and apply general rules correctly in

LEARNER PROFILE Inquirer Knowledgeable Thinker Reflective ATTITUDE Commitment Confidence Creativity Curiosity Tolerance.


Physics


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including the zero and identity 2x2 matrices 5. Calculate the determinant and inverse of non-singular matrix A. MYP UNIT QUESTION: How vectors and matrices can be used to describe Transformations?

matrices to make deductions and solve problems, including those in real-life contexts. (CRITERIA B) • select and apply appropriate inquiry and mathematical problem-solving techniques in matrices • recognize patterns in transformations using matrices • describe patterns as relationships or general rules for matrices • draw conclusions consistent with findings for matrices • justify or prove mathematical relationships and general rules for matrices (CRITERIA C) • use appropriate


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mathematical language in both oral and written explanations in matrices • use different forms of mathematical representation in matrices • communicate a complete and coherent mathematical line of reasoning using different forms of representation when investigating problems in matrices

NO. OF SESSIONS





INTERDISCIPLINARY

25 TOPIC- TRANSFORMATIONS AOI- Human Ingenuity SIGNIFICANT CONCEPTS- Understanding of different types of transformations, use of matrices and

CRITERIA A Knowledge and Understanding CRITERIA B Investigating Patterns CRITIERIA C Communication in Mathematics

Students should be able to- (CRITERIA A) • know and demonstrate understanding of the transformations concept. • use

LEARNER PROFILE Inquirer Knowledgeable Thinker Reflective ATTITUDE Commitment Confidence Creativity Curiosity



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vectors to describe transformations CONTENT 1. reflect simple plane figures in horizontal or vertical lines 2. rotate simple plane figures about the origin, vertices or mid-points of edges of the figures, through multiples of 90 3. construct given translations and enlargements of simple plane figures 4. recognize and describe reflections, rotations, translations and enlargements 5. use reflection, rotation, translation, enlargement, shear, stretching and their combinations 6. Identify and give precise descriptions of transformations connecting given figure. 7. Describe

appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts for the topic transformation and matrices. • select and apply general rules correctly in transformations to make deductions and solve problems, including those in real-life contexts. (CRITERIA B) • select and apply appropriate inquiry and mathematical problem-solving techniques in transformations • recognize patterns in transformations like reflection,

Tolerance


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transformations using coordinates and matrices. MYP UNIT QUESTION: How vectors and matrices can be used to describe Transformations?

rotation shear and stretch. • describe patterns as relationships or general rules for transformations using matrices • draw conclusions consistent with findings for transformations and matrices • justify or prove mathematical relationships and general rules for transformations (CRITERIA C) • use appropriate mathematical language in both oral and written explanations in transformations • use different forms of mathematical representation in transformations • communicate a complete and coherent mathematical


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line of reasoning using different forms of representation when investigating problems in transformations

mathematics grade 10 navrachana …mathematics grade 10 navrachana international school, vadodara...

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