MYP Curriculum Map – Østerbro International School ...ish.dk/wp-content/uploads/2016/04/Mathematics-1.pdf · MYP Curriculum Map – Østerbro International School -Mathematics

MYP Curriculum Map – Østerbro International School -Mathematics

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MYP 1 - TERM 1

UNIT TITLE

MYP

OBJECTIVES

ATL SKILLS

CONCEPT

STATEMENT (Statement of

Inquiry)

UNIT

QUESTION (Inquiry

Questions)

GLOBAL

CONTEXT(S) AOI

Understanding Taking Action

Reflecting

Summative Assessment

Task(s) (Criteria)

UNIT

CONTENT

The World of Numbers

C1,2 A3

Transfer Communication

Students will understand that number systems are a representation of interactions.

Why do numbers exist?

Human Ingenuity: Students will understand that numbers are used to create solutions to problems.

Criteria A and C: Problem

solving task problems with

the knowledge of numbers

including fractions,

percentages and ratios.

Students will : Explore basic number facts such as place value both numerical and written form and placing numbers in order of value. Study ancient number systems. Develop adding, subtracting skills for decimals to hundredths Gain an understanding of how to round up and down from hundredths to millions Develop skills for adding, subtracting, multiplying and dividing positive and negative


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numbers. Gain an understanding of what prime numbers are. Gain an understanding of what multiples and factors of a number are. Gain an understanding of square numbers, square root of numbers and triangular numbers.

Let’s Speak

Algebra

B1-4 Information Literacy Students will

understand that

patterns between

variables and

relationships can

be represented

visually.

What kind of

relationships

can be

represented

visually?

Health and

Social

Education:

Students will

understand and

reflect on how

algebra helps

people to solve

complex

problems

Criterion B: Class test on

investigating patterns

using algebraic

expressions.

Students will: Develop an understanding of algebraic thinking using patterns. Learn skills in writing expressions, substitution and solving simple equations. Develop applying algebraic skills by creating graphs. Gain an understanding of collecting like terms, simplifying expression


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through canceling. Develop an understanding of sequences through counting back.

Area and

Volume

A2-3,

D1

Thinking, Collaboration Students will

understand that

area and volume

are a

representation of

place and space.

How can we

make a

difference?

Environments:

Students will

gain awareness

and reflect on

the

considerations

for the

preservation of

the

environment.

Criteria A and D:

Investigation

Students will: Investigate area of 2D shapes Investigate the surface area of 3D shapes Understand the concept of volume


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MYP 1 - TERM 2

UNIT TITLE

MYP

OBJECTIVES

ATL SKILLS

CONCEPT


Inquiry)

UNIT

QUESTION (Inquiry

Questions)

GLOBAL

CONTEXT(S) AOI


Reflecting


Task(s) (Criteria)

UNIT

CONTENT

Statistics

A1,D2 Organization Reflection

Students will understand that statistics are a powerful model to develop global perspectives.

How can data be used?

Community and Service: Students will take action on to identify methods to save threatened species.

Criteria A and D Investigation and written report on endangered animals

Statistics concepts collecting and collating data presenting data use pie graphs, bar graphs, histograms etc

Constructing Shapes

B3,C3 Reflection Students will understand that the design of models are connected to the strength of rigid shapes.

What is an effective design?

Students will understand and reflect on the processes involved in innovation, creation, development and change.

Criteria B,C: Model building

Students will: develop skills of measurng angles(acute,straight,obtuse,reflex,right) and angles in intersecting lines(complimentary,supplimentary,vertically opposite,angles in a revolution study angles in a triangle classifying triangles,quadrilaterals and cuboids


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calculations involving mixed units(m,km,cm…) use protractor,compass and set square to construct basic shapes.


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MYP 2 – Term 1

UNIT TITLE

MYP

OBJECTIVES

ATL SKILLS

CONCEPT


Inquiry)

UNIT

QUESTION (Inquiry

Questions)

GLOBAL

CONTEXT(S) AOI


Reflecting


Task(s) (Criteria)

UNIT

CONTENT

Let’s Party!

C1-2,D1-2

Organization Collaboration

Students will understand that interaction is vital so systems function.

How do we keep to a budget?

Community and Service: Students will gain awareness, reflect and take action on planning an event to improve socializing in class.

Criteria C and D: Planning a class dinner with a predetermined budget.

Students will: learn converting fractions into decimals and vice versa learn converting decimals to percentages order fractions by writing them with a common denominator perform various operations of fractions. Develop an understanding of the equivalence of fractions, decimals and percentages. Learn to perform calculations such as percentage of a number Extend their understanding to


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real world by working on percentage increase and decrease in a variety of situations. Improve their understanding of ratio and extend t to proportion, reduce the ratio to its simplest form, recognize links with fractions notation.

Algebra A1-3,C3

Communication, Collaboration: Students will productively participate in group work and contribute to group’s learning.

Students will understand that mathematical systems are a model to solve problems

How do I use methods of algebra in analyzing real life situations?

Human Ingenuity: Students will reflect on the benefits of mathematical language.

Criterion A: Students will analyze the problem given and show a solution to it step by step.

Students will: Begin to distinguish the different roles played by letter symbols Know that the algebraic operations follow the same conventions and order as arithmetic operations Will learn to simplify linear expressions by collecting like terms; multiply a


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single term over a bracket. Will start using graphs and setup equations

Maximizing

our space

B4-5

Thinking Students will understand that measurements function to solve problems.

How can we use what we know?

Environments: Students will show understanding of the role our environments play in our lives.

Criterion B: Area usage (Creation of a seating plan)

Students will: Use units of measurement to estimate, calculate and solve problems in everyday contexts involving length, area ,volume, capacity, mass, time, angle Know and use the formula for the area, surface area and volume of simple 3D shapes such as cuboids.


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MYP 2 - TERM 2

UNIT

TITLE

MYP

OBJECTIVES

ATL SKILLS

CONCEPT

STATEMENT

(Statement of

Inquiry)

UNIT

QUESTION

(Inquiry

Questions)

GLOBAL CONTEXT(S)

AOI Understanding Taking Action

Reflecting


Task(s) (Criteria)

UNIT

CONTENT

Statistics C3,D3

Reflection, Information literacy

Students will understand that statistical patterns help us change the world we live in.

How can mathematics help to communicate the health of a society?

Health and Social Education: Students will show awareness and understanding of ourselves and others including issues such as disease.

Criteria C and D: Report on a global issue

Students will: Able to analyse the data given by looking at the mean, median, mode and range.

Pythagoras

Theorem

A1-2,B1-3

Transfer Students will understand that designs are represented through creative constructions.

In what way is mathematics involved in architecture and design? Where do we see mathematics around us?

Human Ingenuity: Students will show awareness and reflect on the impact of human creations

Criterion A and B: Class test

Students will: Develop further geometrical reasoning in lines, angles and shapes by learning to distinguish between conventions, definitions and derived properties


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Apply their reasoning and solve problems using properties of angles, parallel and intersecting lines, triangles and polygons Apply their skills to find interior and exterior angles of a quadrilaterals, pentagons and hexagons. Develop understanding of Pythagoras Theorem and use it in familiar and unfamiliar situations


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MYP 3 - TERM 1

UNIT TITLE

MYP

OBJECTIVES

ATL SKILLS

CONCEPT

STATEMENT

(Statement of

Inquiry)

UNIT

QUESTION

(Inquiry

Questions)

GLOBAL CONTEXT(S)


Reflecting


Task(s) (Criteria)

UNIT

CONTENT

Number A2:use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar situations, including those in real-life contexts A3: select and apply general rules correctly to make deductions and solve problems, including those in real-life contexts. B1:select and apply appropriate inquiry and mathematical problem-solving

Communication Information Thinking

Students will understand that patterns of numbers are key to understanding how the world functions.

How can life be without numbers?

Approaches to learning: Students will understand and reflect on thinking mathematically by analyzing problems and applying techniques solving problems

Criteria A and B A:End of unit assessment task (e.g. Diagnostic Tests) B: A proportional flip: Students will use an Assessment Grid to understand the idea of proportion B:Investigation: Jobs in the careers section of a newspaper

Recognize and use correct order of operations Work with and convert between fractions, decimals, percentages and ratios Round numbers to a given number of significant figures Approximate numbers and estimate answers Find the unknown amount in a proportion statement and solve


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techniques B2: recognize patterns B3:describe patterns as relationships or general rules B4: draw conclusions consistent with findings B5: justify or prove mathematical relationships and general rules.

proportional problems Work with inverse proportion and solve associated problems Solve problems involving different forms of income Calculate extra payments and income Calculate deductions from income Calculate taxable income and the tax payable on an income Set up and work with a budget Work through problems involving spending money – best buys, lists and change Work through problems involving sales tax Solve problems on different ways of paying


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for items Solve problems on profit and income

Algebra I A2 B1, B3


Most problems can be identified and represented algebraically.

Are problems so difficult to solve?

Approaches to learning: Students will understand how to think analytically and logically and apply problem solving skills.

Criteria A, C and D A: End of unit assessment task (e.g. Diagnostic Tests) D: The history of algebra: Students will find out about the early history of algebra. C: Investigation:

Multiplying and dividing

by powers of 10: Students

will look for a connection

between questions and

answers and then fill in

the rules at the end of the

investigation.

Translate sentences into algebraic expressions Substitute into an algebraic expression Simplify algebraic expressions Work with algebraic fractions Simplify expressions with grouping symbols Understand and work with binomial products including special binomial products Revise, understand and apply the basic index laws Understand the meaning of a negative index and solve


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associated problems Work with, apply and understand fractional indices Use and interpret standard (scientific) notation (form) Scientific notation and the calculator The real number system Surds Addition and subtraction of surds Multiplication and division of surds Binomial products Rationalizing the denominator Recognize equivalent equations Solve equations with grouping symbols Solve equations involving fractions Apply equations to the solution of


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problems Understand the need for and the application of inequations Changing the subject of a formula Solve an equation after substituting into a formula Solve problems written literally Solve problems using formulae Factorize algebraic expressions including: common factors, grouping in pairs, difference of two squares/cubes, quadratic trinomials Simplify algebraic fractions Calculate the distance between two points on the coordinate axes Calculate the midpoint of an


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interval on the coordinate axes Calculate the gradient of a line on the coordinate axes Construct the graph of a line given its equation Apply the gradient-intercept form of a straight line:

cmxy

Find the equation of a straight line given a point on the line and its gradient Find the equation of a straight line given two points on the line Understand and apply the rules for parallel and perpendicular lines on the coordinate axes Solve simultaneous equations algebraically


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Use simultaneous equations to solve problems

MYP 3 - TERM 2

UNIT TITLE

MYP

OBJECTIVES

ATL SKILLS

CONCEPT

STATEMENT

(Statement of

Inquiry)

UNIT

QUESTION

(Inquiry

Questions)

GLOBAL CONTEXT(S)


Reflecting


Task(s) (Criteria)

UNIT

CONTENT

Algebra II

C1,C2 D1,D2


Students will understand that problems can be represented so we can make a generalization

How can problems be represented using symbols and in diagrams?

Human Ingenuity: Students will develop mathematical models and formulae to describe real life phenomena

Criteria C, D: D:Students will explore the application of mathematical knowledge in industrial and technological developments C: Diagnostic Test on equations, Inequations and Formulae

Recognize equivalent equations Solve equations with grouping symbols Solve equations involving fractions Apply equations to the solution of problems Understand the need for and the application of inequations Changing the subject of a


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formula Solve an equation after substituting into a formula Solve problems written literally Solve problems using formulae Factorize algebraic expressions including: common factors, grouping in pairs, difference of two squares/cubes, quadratic trinomials Simplify algebraic fractions Calculate the distance between two points on the coordinate axes Calculate the midpoint of an interval on the coordinate axes Calculate the gradient of a line


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on the coordinate axes Construct the graph of a line given its equation Apply the gradient-intercept form of a straight line:

cmxy

Find the equation of a straight line given a point on the line and its gradient Find the equation of a straight line given two points on the line Understand and apply the rules for parallel and perpendicular lines on the coordinate axes Solve simultaneous equations algebraically Use simultaneous equations to solve problems


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Geometry A1 B4 C2

Collaboration Thinking

Geometric representations help us to think logically

How can logic be used to deduce facts about the shapes in our world?

Environments: Students will discover regular polygons and reflect on how they can be put together.

Criterion C: Investigation: On a computer students will create an Excel sheet where they will make calculations by using formulas.

Use deductive reasoning in numerical exercises Solve polygons Use deductive reasoning in non-numerical exercises Solve congruent triangles Prove two triangles congruent Use congruent triangles to find unknown sides and angles Use deductive geometry and triangles Use deductive geometry and quadrilaterals Use Pythagoras’ Theorem and its converse. Solve area, perimeter and surface area. Solve volumes of prisms and cylinders Solve volumes of composite solids Use practical


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applications of measurement Understand an introduction to vectors Understand column vectors and vector operations Understand magnitude of a vector Solve problems using vectors

Trigonometry C1

Communication, Thinking


How is trigonometry use?


Criterion C: By using a calculator, students will find unknown sides and angles

Label sides of right triangles and the trigonometric ratios Use the calculator with trigonometry Find unknown sides and angles using trigonometry Apply trigonometry to practical problems

Statistics B4, D3

Information literacy, Reflection

Students will understand that statistical patterns help us change the world we live in.

How can statistics improve our world?

Environments: Students will show understanding of the role our environments

Criteria D: Investigation: Write a report on a diagram

Display the median, range and inter-quartile range of a set of data in a box and whisker


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play in our lives. plot Find the standard deviation of a set of data. Use measures of the center and measures of spread to compare sets of data. Organize outcomes of compound events Solve dependent and independent events Use probability using tree and dot diagrams Use probability using tables and Venn diagrams Solve simulation experiments


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MYP 4 - TERM 1

UNIT TITLE

MYP

OBJECTIVES

ATL SKILLS

CONCEPT


Inquiry)

UNIT

QUESTION (Inquiry

Questions)

GLOBAL

CONTEXT(S) AOI


Reflecting


Task(s) (Criteria)

UNIT

CONTENT

Coordinate Geometry

A1,2 B1-3

Information literacy, Thinking, Transfer

Students will

understand that

systems and

patterns can be

represented

visually.

How do the

expressions and

diagrams help

us solve

problems?

Human

Ingenuity

Students will

gain an aware -

ness of and

reflect on

measurements,

shapes and

space.

Criteria A,B: Class Test

Calculate the distance between two points on the coordinate axes Calculate the midpoint of an interval on the coordinate axes Calculate the gradient of a line on the coordinate axes Construct the graph of a line given its equation Apply the gradient-intercept form of a straight line:

cmxy

Find the equation of a straight line given a point on the line and its gradient Find the equation of a straight line given two points on the line Understand and apply the rules for parallel and perpendicular lines on the coordinate axes Graph inequalities on


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the coordinate axes

Simultaneous Equations and

Graphs of Physical

Phenomena

C1,2 D1,2

Collaboration, Communication,

Reflection

Students will understand that mathematical models have connections to other disciplines

How can I show my understanding in a graph?

Environments: The students will understand and reflect on how investigating physical events can be expressed as graphs

Criteria C,D: Power point Presentation: Simultaneous physical

events and

interpretation of

Solve simultaneous equations graphically Solve simultaneous equations algebraically Use simultaneous equations to solve problems Interpret and construct Distance/Time graphs Relating graphs to physical phenomena

Deductive Geometry

B3-5 C1,2

Thinking, Transfer

Students will understand that relationships between shapes and models can help us solve problems

How can we quantify the different characteristics of solid shapes?

Human Ingenuity: The students will understand how to apply area and perimeter formulae in practical situations

Criteria B,C : Oral Test

Use deductive reasoning in numerical exercises Solve polygons Use deductive reasoning in non-numerical exercises Solve congruent triangles Prove two triangles congruent Use congruent triangles to find unknown sides and angles Use deductive geometry and triangles Use deductive geometry and quadrilaterals Use Pythagoras’ Theorem and its converse.

Measurement C1-3 D1,4

Communication And transfer

Students will understand that

How can we find the

ATL: Students will

Criteria C,D: Investigation:

Solve area, perimeter and surface area.


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models are a representation of real life creations

volume? understand, take action and reflect on their thinking analytically and logically to apply problem solving skills

Wallpapering rooms, Skirting board and perimeter

Solve volumes of prisms and cylinders Solve volumes of composite solids Use practical applications of measurement

MYP 4 - TERM 2

UNIT TITLE

MYP

OBJECTIVES

ATL SKILLS

CONCEPT


Inquiry)

UNIT

QUESTION (Inquiry

Questions)

GLOBAL

CONTEXT(S) AOI

Understanding

Taking Action Reflecting


Task(s) (Criteria)

UNIT

CONTENT

Trigonometry and Vectors

A 1-3 C 1,3

Thinking, Transfer Students will understand that models and patterns can be used to solve problems

Where are angles in everyday life?

ATL: Student will understand and reflect on thinking analytically and logically to apply problem solving skills

Criteria A,C: Oral Test

Label sides of right triangles and the trigonometric ratios Use the calculator with trigonometry Find unknown sides and angles using trigonometry Apply trigonometry to practical problems Understand an introduction to vectors Understand column vectors and vector operations Understand magnitude of a vector


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Solve problems using vectors

Statistics and

Probability

A 1,2 C 1,2

Organization, information literacy

Students will understand that statistics can change our perspective on life

In what ways can we use statistics?

Health and social education: Student will gain an awareness of usage of statistics in community health issues.

Criteria A,C: Survey: Sport, smoking and health

Find the inter-quartile range of a set of data Display the median, range and inter-quartile range of a set of data in a box and whisker plot Find the standard deviation of a set of data. Use measures of the center and measures of spread to compare sets of data. Organize outcomes of compound events Solve dependent and independent events Use probability using tree and dot diagrams Use probability using tables and Venn diagrams. Solve simulation experiments

Logic

A 2,3 B 2,3,5

Thinking, Transfer

Students will understand that Statements are created to form logical systems

How do I make my statements make sense?

Human ingenuity: Student will understand and reflect on using a table to represent the truth of statements

Criteria A,B: Class Test: Revision Assignment

Understand and use the ideas behind propositions Combine statements to make compound propositions Translate between word and logic statements Use truth tables to evaluate when compound statements are true and to establish the logical equivalence of statements Work with and build conditional statements.

Numbers B 1-5 D 1,2

Communication Thinking

Students will understand that

What would life be without

Community and Service:

Criteria B , D Spreadsheet:

Find the unknown amount in a proportion statement and


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patterns of numbers are key to understanding how the world functions.

numbers? Students will understand how the government earns revenue for local spending

Budgeting

solve proportional problems Work with inverse proportion and solve associated problems Solve problems involving different forms of income Calculate extra payments and income Calculate deductions from income Calculate taxable income and the tax payable on an income Set up and work with a budget Work through problems involving spending money best buys, lists and change Work through problems involving sales tax Solve problems on different ways of paying for items Solve problems on profit and income

MYP Curriculum Map – Østerbro International School ...ish.dk/wp-content/uploads/2016/04/Mathematics-1.pdf · MYP Curriculum Map – Østerbro International School -Mathematics

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