mathematics grade 8 navrachana international school ... 8 math.pdf · when estimating square roots...

MATHEMATICS GRADE 8 Navrachana International School, Vadodara (2013-2014)

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NO. OF SESSIONS

GRADE 8 (MATHEMATICS)

ASSESSMENT OBJECTIVE (based on Assessment Criteria)

LEARNER PROFILE/ ATTITUDES

ATL SKILLS/ SUBJECT SPECIFIC SKILLS

INTERDISCIPLINARY

20 TOPIC- NUMBER AOI- Environment SIGNIFICANT CONCEPT- Integers, powers and roots, place value, ordering and rounding CONTENT- 1) Add, subtract, multiply and divide directed numbers 2) Estimate square roots and cube roots 3) Use positive, negative and zero indices and index laws for multiplication and division of positive integer power 4) Recognize the equivalence of 0.1, 1/10 and 10-1; multiply and divide whole numbers and decimals by 10 to the power of any positive or negative integer 5) Round numbers to the given number of decimal places or

CRITERION A Knowledge and understanding CRITERION B Investigating Patterns CRITERION C Communication in Mathematics

Students should be able to- (CRITERION A) • Know and demonstrate understanding of the concepts of directed numbers, squares and cubes • Use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts like estimation, and division by decimals • Select and apply general rules correctly to make deductions and solve problems, including those in real-life contexts (CRITERION B) • select and apply appropriate inquiry and mathematical problem-solving techniques

LEARNER PROFILE Inquirer Knowledgeable Thinker Communicator Reflective ATTITUDE- Integrity Curiosity Commitment

FOCUS ON: Organization Communication Transfer Thinking

Science


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significant figures 6) Use the order of operations, including brackets and powers MYP UNIT QUESTION- What do numbers convey?

•recognize patterns when estimating square roots and cube roots. • describe patterns as relationships or general rules when using order of operations (CRITERION C) • use appropriate mathematical language in both oral and written explanations while using the laws of indices • use different forms of mathematical representation to find square roots and cube roots. • communicate a complete and coherent mathematical line of reasoning using different forms of representations when investigating problems while using the laws of indices, and the order of operations

NO. OF GRADE 8 (MATHEMATICS)

ASSESSMENT OBJECTIVE (based on LEARNER ATL SKILLS/ INTERDISCIPLINARY


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SESSIONS Assessment Criteria) PROFILE/ ATTITUDES

SUBJECT SPECIFIC SKILLS

30 TOPIC- ALGEBRA AND SEQUENCES AOI- Human Ingenuity. SIGNIFICANT CONCEPT- Relationships can be expressed using variables and arithmetic operations of linear expressions; Patterns can be generalized. CONTENT- 1) Use index notation for positive integer powers; apply the index laws for multiplication and division to simple algebraic expressions 2) Construct algebraic expressions 3) Simplify or transform algebraic expressions by taking out single- term common factors. 4) Add and subtract simple algebraic fractions. 5) Multiplication of

CRITERION A Knowledge and understanding CRITERION B Investigating Patterns CRITERION C Communication in Mathematics CRITERION D Reflection in Mathematics

Students should be able to- (CRITERION A) • Know and demonstrate understanding of the concepts of like terms, expressions, equations, index notation • Use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts • Select and apply general rules correctly to make deductions and solve problems, including those in real-life contexts using equations, factorization (CRITERION B) • select and apply appropriate inquiry and mathematical problem-solving techniques when

LEARNER PROFILE Inquirer Knowledgeable Thinker Communicator Reflective ATTITUDE- Appreciation Enthusiasm Interdependence

FOCUS ON: Information Literacy Communication Reflection Thinking

Physics, Chemistry


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binomial by a binomial 6) Algebraic identities: (a + b)2 = a2 + 2ab + b2; (a - b)2 = a2 - 2ab + b2 a2 – b2 = (a – b)(a + b) 7) Factorization of quadratic expressions by breaking the middle term or by using algebraic identities and hence solving quadratic equations 8) Derive formulae and in simple cases ,change the subject 9) Substitute positive and negative numbers into expressions and formulae. 10) Construct and solve linear equations with integer coefficients (with and without brackets ,negative signs anywhere in the equations , positive or negative solution) 11) Solve a number problem by

factorizing expressions using the identities •recognize patterns • describe patterns as relationships or general rules using term to term rule or by describing the nth term (CRITERION C) • use appropriate mathematical language in both oral and written explanations while solving for the unknown variable • use different forms of mathematical representation • communicate a complete and coherent mathematical line of reasoning using different forms of representations when investigating problems using variables to find unknowns (CRITERION D) • explain whether their results make


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constructing and solving a linear equation. 12) Solve a simple pair of simultaneous linear equations by eliminating one variable 13) Solve problems using simultaneous equations 14) Expand the product of two linear expressions of the form (x± n) and simplify the corresponding quadratic expressions 15) Understand and use inequalities signs (<,>, ≤, and ≥); construct and solve linear inequalities in one variable; represent the solution set on a number line. 16) Generate terms of a sequence using term to term and position-to term rules. 17) Derive an expression to describe the nth term

sense in the context of the problem while solving for the unknown variable, or generating a sequence • explain the importance of their findings in connection to real life where appropriate • justify the degree of accuracy of their results where appropriate • suggest improvements to the method when necessary, while solving for the unknown variable, or generating a sequence


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of an arithmetic sequence MYP UNIT QUESTION- How do we solve problems?

NO. OF SESSIONS





INTERDISCIPLINARY

20 TOPIC- MEASUREMENT, MOTION AND TRANSFORMATION AOI- Environment SIGNIFICANT CONCEPT- Length, Mass, Capacity, Compound measure and Motion, Position and Movement CONTENT- 1) Solve problems involving measurements in a variety of contexts. 2) Solve problems involving average speed 3) Use compound measures to make comparisons in real life contexts e.g. travel graph and


Students should be able to- (CRITERION A) • Know and demonstrate understanding of the concepts of length, mass, capacity, motion and transformations • Use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts while using length, mass, capacity and motion • Select and apply general rules correctly to make deductions and solve problems,

LEARNER PROFILE Knowledgeable Communicator Thinker Inquirer ATTITUDE- Curiosity Interdependence

FOCUS ON: Organization Information Literacy Communication Thinking Transfer

Science, Art, Humanities


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value of money 4) Tessellate triangles and quadrilaterals and relate to angle sums and half turn rotations ;know which regular polygons tessellate , and explain why others will not 5) Use the coordinate grid to solve problems involving translations ,rotation ,reflection and enlargements 6) Transform two-dimensional shapes by combinations of rotation, reflection and translations; describe the transformation that maps an object onto its image. 7) Enlarge two-dimensional shapes, given a centre and positive integer scale factor; identify the scale factor of an enlargement as the ratio of the lengths of any two corresponding line segments.

including those in real-life contexts (CRITERION B) • select and apply appropriate inquiry and mathematical problem-solving techniques while inter-converting units of length, mass, capacity and motion •recognize patterns when working with transformations • describe patterns as relationships or general rules (CRITERION C) • use appropriate mathematical language in both oral and written explanations when describing transformations • use different forms of mathematical representation • communicate a complete and coherent mathematical line of reasoning using different forms of representations when


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8) Recognize that translation, rotation and reflection preserve length and angle and map object on to congruent images, and that enlargements preserve angle but not length. 9) Know what is needed to give precise description of a reflection, rotation, translation or enlargement. MYP UNIT QUESTION- How are measurements an integral part of life?

investigating problems of length, mass, capacity and motion (CRITERION D) • explain whether their results make sense in the context of the problem while working with length, mass, capacity and motion and transformations • explain the importance of their findings in connection to real life where appropriate • justify the degree of accuracy of their results where appropriate • suggest improvements to the method when necessary

NO. OF SESSIONS





INTERDISCIPLINARY

20 TOPIC- FRACTIONS, RATIO AND PROPORTION AOI- Human Ingenuity

CRITERION A Knowledge and understanding CRITERION B Investigating

Students should be able to- (CRITERION A) • Know and demonstrate understanding of the

LEARNER PROFILE Knowledgeable Risk taker Thinker

FOCUS ON: Organization Transfer Thinking Information

Science, Humanities


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SIGNIFICANT CONCEPT- Fractions, Decimals, Percentages, Ratio and Direct Proportion

CONTENT- 1) Consolidate writing a fractions in its simplest form by cancelling common factors 2) Add, subtract, multiply and divide fractions, interpreting division as multiplicative inverse, and cancelling common factors before multiplying and dividing. 3) Solve problems involving percentage changes, including simple problems involving personal or household finance, e.g. simple interest, discount, profit-loss and tax 4) Recognize when fractions or percentages are needed to compare different quantities 5) Compare two ratios; interpret and use ratio in a range of contexts 6) Recognize when two quantities are directly proportional; solve

Patterns CRITERION C Communication in Mathematics CRITERION D Reflection in Mathematics

concepts of fractions, decimals and percentages • Use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts • Select and apply general rules correctly to make deductions and solve problems, including those in real-life contexts when working with fractions, decimals and percentages (CRITERION B) • select and apply appropriate inquiry and mathematical problem-solving techniques when working with fractions, decimals and percentages •recognize patterns • describe patterns as relationships or general rules (CRITERION C) • use appropriate mathematical language in both oral and written explanations • use different forms of

Open Minded Reflective ATTITUDE- Appreciation Creativity Commitment

Literacy Reflective


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problems involving proportionality, e.g. converting between different currencies.

MYP UNIT QUESTION- Why do we need to represent the same number in different forms?

Why do we need to compare quantities?

mathematical representation • communicate a complete and coherent mathematical line of reasoning using different forms of representations when investigating problems when working with fractions, decimals and percentages (CRITERION D) • explain whether their results make sense in the context of the problem • explain the importance of their findings in connection to real life where appropriate • justify the degree of accuracy of their results where appropriate • suggest improvements to the method when necessary.

NO. OF SESSIONS





INTERDISCIPLINARY

10 TOPIC- CALCULATIONS AND MENTAL STRATEGIES AOI- Human Ingenuity SIGNIFICANT

CRITERION A Knowledge and understanding CRITERION B Investigating Patterns

Students should be able to- (CRITERION A) • Know and demonstrate understanding of the

LEARNER PROFILE Knowledgeable Thinker Inquirer ATTITUDE-

FOCUS ON: Communication Reflection Thinking


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CONCEPT- Mental methods for performing different operations CONTENT- 1) Solve word problem mentally. 2) Divide by decimal by transforming to divisions by an integer 3) Multiply by decimals, understanding where to position the decimal point by considering equivalent calculations. 4) Extend mental methods of calculations, working with decimals, fractions, percentages and factors, with jottings where appropriate 5) Consolidate use of rules of arithmetic and inverse operations to simplify calculations 6) Recognize the effects of multiplying and dividing by numbers between 0

CRITERION C Communication in Mathematics CRITERION D Reflection in Mathematics

concepts • Use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts • Select and apply general rules correctly to make deductions and solve problems, including those in real-life contexts (CRITERION B) • select and apply appropriate inquiry and mathematical problem-solving techniques •recognize patterns • describe patterns as relationships or general rules (CRITERION C) • use appropriate mathematical language in both oral and written explanations • use different forms of mathematical representation • communicate a

Enthusiasm Interdependence Respect


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and 1 MYP UNIT QUESTION- How to choose the correct method to solve a word problem? How to perform different operations mentally?

complete and coherent mathematical line of reasoning using different forms of representations when investigating problems when working with fractions, decimals and percentages (CRITERION D) • explain whether their results make sense in the context of the problem while creating their own patterns • explain the importance of their findings in connection to real life where appropriate • justify the degree of accuracy of their results where appropriate • suggest improvements to the method when necessary.

NO. OF SESSIONS





INTERDISCIPLINARY


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20 TOPIC- HANDLING AND PROCESSING DATA AOI- Health and Social Education SIGNIFICANT CONCEPT – Planning and collecting data, Processing and Presenting data, Interpreting and discussing result CONTENT- 1) Suggest a question to explore using statistical methods; identify the sets of data needed, how to collect them, sample sizes and degree of accuracy 2) Identify primary or secondary sources of suitable data 3) Design, trial and refine data collection sheets 4) Collect and tabulate discrete and continuous data, choosing suitable equal class intervals where appropriate 5) Calculate statistics


Students should be able to- (CRITERION A) • Know and demonstrate understanding of the concepts of graphs, tables, averages • Use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts using the data collected through a survey • Select and apply general rules correctly to make deductions and solve problems, including those in real-life contexts (CRITERION B) • select and apply appropriate inquiry and mathematical problem-solving techniques •recognize patterns in the data collected with the problem in question • describe patterns as

LEARNER PROFILE Inquirer Knowledgeable Communicator Risk taker Thinker Open minded Reflective ATTITUDE- Integrity Tolerance Commitment Confidence Creativity

FOCUS ON: Information Literacy Communication Reflection Collaboration Transfer

Humanities, Science, PE, IT


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and select those most appropriate to the problem 6) Select, draw and interpret diagrams and graphs, including frequency diagrams for discrete and continuous data, line graphs for time series, scatter graphs to develop understanding of correlation and back-to-back stem-and-leaf diagrams 7) Interpret tables, graphs and diagrams and make inferences to support or cast doubt on initial conjectures; have a basic understanding of correlation. 8) Compare two or more distributions; make inferences, using the shape of the distributions and appropriate statistics. 9) Relate results and conclusions to the original question. MYP UNIT

relationships or general rules (CRITERION C) • use appropriate mathematical language in both oral and written explanations while interpreting the collected data • use different forms of mathematical representation • communicate a complete and coherent mathematical line of reasoning using different forms of representations when investigating problems. (CRITERION D) • explain whether their results make sense in the context of the problem after interpreting and analyzing the data • explain the importance of their findings in connection to real life where appropriate • justify the degree of


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QUESTION- What stories do data tell?

accuracy of their results where appropriate • suggest improvements to the method when necessary.

NO. OF SESSIONS





INTERDISCIPLINARY

20 TOPIC- GEOMETRY AOI- Human Ingenuity SIGNIFICANT CONCEPT – Shapes and Geometric reasoning, Pythagoras Theorem, Area and Volume, Circle, Cylinder and Prism CONTENT- 1) Calculate the interior or exterior angle of any regular polygon; prove and use the formulae for sum of the interior angles of any polygon; prove that the sum of the exterior angles of any polygon is 360. 2) Solve problems


Students should be able to- (CRITERION A) • Know and demonstrate understanding of the concepts of geometry, Pythagoras theorem, area and volume • Use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts when working out problems on Pythagoras theorem, area and volume • Select and apply general rules correctly to make deductions

LEARNER PROFILE Inquirer Knowledgeable Communicator Risk taker Thinker ATTITUDE- Integrity Tolerance Commitment Confidence Creativity


Science


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using properties of angles, of parallel and intersecting lines, and of triangles, other polygons and circles, justifying inferences and explaining reasoning with diagrams and text. 3) Analyze three-dimensional shapes through plans and elevations. 4) Draw three-dimensional shapes on isometric paper. 5) Identify reflection symmetry in three dimensional shapes. 6) Use a straight edge and compasses to construct the perpendicular from a point to a line and the perpendicular from a point on a line and to inscribe squares, equilateral triangles, and regular hexagons and octagons in a circle. 7) Know and use Pythagoras theorem to solve two- dimensional problems

and solve problems, including those in real-life contexts (CRITERION B) • select and apply appropriate inquiry and mathematical problem-solving techniques when working with geometry, Pythagoras theorem, area and volume •recognize patterns • describe patterns as relationships or general rules when using geometric reasoning (CRITERION C) • use appropriate mathematical language in both oral and written explanations while reasoning out geometric problems • use different forms of mathematical representation • communicate a complete and coherent mathematical line of reasoning using


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involving right-angled triangles. 8) Convert between metric units of area and volume 9) Know and use the relationship 1cm2 = 1ml. 10) Know that land area is measured in hectares (ha), and that 1hectare=10000m2; convert between hectares and square meters. 11) Solve problems involving the circumference and area of circles, including by using the π key of a calculator. 12) Calculate lengths, surface areas and volumes in right-angled prisms and cylinders 13) Round numbers to a given number of decimal places or significant figures ; use to give solutions to problems to an appropriate degree of accuracy

different forms of representations when investigating problems on Pythagoras theorem, area and volume (CRITERION D) • explain whether their results make sense in the context of the problem after completing the task on area and volume • explain the importance of their findings in connection to real life where appropriate • justify the degree of accuracy of their results where appropriate • suggest improvements to the method when necessary.


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MYP UNIT QUESTION- How can geometry be used creatively in real life situations?

NO. OF SESSIONS





INTERDISCIPLINARY

20 TOPIC- FUNCTIONS AND GRAPHS AOI- Environment SIGNIFICANT CONCEPT – Linear functions and Graphs CONTENT- 1) Find the inverse of linear functions. 2) Construct tables of the values and plot the graphs of linear functions , where y is given implicitly in terms of x 3) Rearranging the equations into the form y = mx + c 4) Know the significance of m and find the gradient of a straight line graph 5) Find the appropriate solutions

CRITERION A Knowledge and understanding CRITERION B Investigating Patterns CRITERION C Communication in Mathematics

Students should be able to- (CRITERION A) • Know and demonstrate understanding of the concepts of linear functions • Use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts • Select and apply general rules correctly to make deductions and solve problems, including those in real-life contexts when solving simultaneous



Humanities, Science


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of a simple pair of simultaneous linear equations by finding the point of intersections of their graphs 6) Use systematic trial and improvement methods to find approximate solutions of equations such as x2 + 2x = 20. 7) Construct functions arising from real life problems 8) Draw and interpret their graphs 9) Use algebraic methods to solve problems involving direct proportion, relating solutions to graphs of the equations. MYP UNIT QUESTION- How can graphs help solve problems?

equations and using graphs (CRITERION B) • select and apply appropriate inquiry and mathematical problem-solving techniques when solving simultaneous equations and reading graphs •recognize patterns • describe patterns as relationships or general rules (CRITERION C) • use appropriate mathematical language in both oral and written explanations • use different forms of mathematical representation • communicate a complete and coherent mathematical line of reasoning using different forms of representations when investigating problems on simultaneous equations


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(CRITERION D) • explain whether their results make sense in the context of the problem • explain the importance of their findings in connection to real life where appropriate • justify the degree of accuracy of their results where appropriate • suggest improvements to the method when necessary.

NO. OF SESSIONS





INTERDISCIPLINARY

20 TOPIC- BEARINGS AND DRAWINGS AOI- Environment SIGNIFICANT CONCEPT – Bearings, Scale drawings, locus of point CONTENT- 1) Use bearings (angles measured clockwise from north) to solve problems involving distance and

CRITERION A Knowledge and understanding CRITERION B Investigating Patterns CRITERION D Reflection in Mathematics

Students should be able to- (CRITERION A) • Know and demonstrate understanding of the concepts of Bearings • Use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations,



Science, Humanities


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directions. 2) Make and use scale drawings and interpret maps. 3) Find by reasoning the locus of a point that moves at a given distance from a fixed point, or at a given distance from a fixed straight line MYP UNIT QUESTION- Where am I?

including those in real-life contexts while working out the bearing of one place from another • Select and apply general rules correctly to make deductions and solve problems, including those in real-life contexts (CRITERION B) • select and apply appropriate inquiry and mathematical problem-solving techniques while working out the bearing of one place from another •recognize patterns • describe patterns as relationships or general rules when working with scale drawings and locus (CRITERION D) • explain whether their results make sense in the context of the problem • explain the importance of their findings in connection to real life where


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appropriate • justify the degree of accuracy of their results where appropriate • suggest improvements to the method when necessary.

NO. OF SESSIONS





INTERDISCIPLINARY

20 TOPIC- SETS AND PROBABILITY AOI- Environment SIGNIFICANT CONCEPT – Set Theory, Probability, mutually exclusive events, sample space CONTENT- 1) Concept of set and the elements of sets 2) Find the union and intersection of the sets 3) Represent the sets and the set operations using Venn diagrams 4) Know that the sum of probabilities of all mutually exclusive


Students should be able to- (CRITERION A) • Know and demonstrate understanding of the concepts of set theory and probability • Use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts • Select and apply general rules correctly to make deductions and solve problems, including those in real-life contexts



Humanities


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outcomes is 1 and use this when solving problems 5) Find and record all outcomes for two successive events in a sample space diagram. 6) Understand relative frequency as an estimate of probability and use this to compare outcomes of experiments in a range of contexts. MYP UNIT QUESTION- How does math help to predict outcomes?

(CRITERION B) • select and apply appropriate inquiry and mathematical problem-solving techniques while finding experimental probability •recognize patterns • describe patterns as relationships or general rules while comparing theoretical and experimental probability (CRITERION C) • use appropriate mathematical language in both oral and written explanations • use different forms of mathematical representation while solving problems on probability • communicate a complete and coherent mathematical line of reasoning using different forms of representations when investigating problems using the


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Venn diagram (CRITERION D) • explain whether their results make sense in the context of the problem • explain the importance of their findings in connection to real life where appropriate • justify the degree of accuracy of their results where appropriate • suggest improvements to the method when necessary.

mathematics grade 8 navrachana international school ... 8 math.pdf · when estimating square roots...

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