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Year 10 Mathematics (MYP 4)

Units

Mint units are the ones studied so far

Orange units are the ones we are working on now

10.1 Sequences - under construction

10.1 Sequences - under construction

Statement of inquiry: How can we be sure a pattern will keep working?

Lessons in this unit
10.1.1 Represent a sequence as a picture, a table, a graph and an algebraic rule - under construction10.1.2 Determine the general rule of a sequence built by shifting a known pattern, e.g. one less than the square numbers - under construction10.1.2b Find the general rule of a quadratic sequence using second differences - under construction10.1.3 Determine the general rule of an arithmetic sequence, and solve to find u₁ and d - under construction10.1.4 Determine the general rule of a geometric sequence, and solve to find u₁ and r - under construction10.1.5 Work backwards from given terms to find u₁, d, r or n - under construction10.1.6 Use the equal-difference and equal-ratio properties to solve for an unknown in a sequence’s terms - under construction10.1.7 Write and use the recursive definition of arithmetic and geometric sequences - under construction

10.1 Practice Homework Booklet (PDF)

Revise this unit:10.1 Revision slides10.1 Flash cards10.1 Quizzes10.1 Revision notes10.1 Revision slides as text
Approaches to learning
Communication

I can show my maths thinking clearly by setting out my work neatly and using maths symbols correctly.

I can explain my ideas in different ways, not just give an answer, but also explain why it works.

Self-management

I can use my time wisely and practise independently by choosing helpful resources to support my learning of mathematics.

Community engagement
  • We build a classroom community where we help and support each other
  • We share our methods and explain our thinking to each other, so that everyone learns
  • We talk openly about maths anxiety and encourage each other to keep trying
  • We learn from other students, and we can help others through peer tutoring
Global context and inquiry questions

Global context: Scientific and Technical Innovation Key concepts: Generalisation, Patterns, Representation

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10.2 Exponents and Indices - under construction

10.2 Exponents and Indices - under construction

Statement of inquiry: Why keep an answer exact when a calculator gives a decimal?

Lessons in this unit
10.2.1 Apply the index laws to positive and zero indices - under construction10.2.1b Apply the index laws to negative and fractional indices - under construction10.2.2 Solve equations by writing both sides with the same base and comparing exponents - under construction10.2.3 Solve exponential equations where the exponent itself is an algebraic expression - under construction10.2.4 Understand what a surd is and simplify surds, then multiply surds, expand brackets and collect like surds - under construction10.2.4b Rationalise a denominator using the conjugate - under construction10.2.5 Work with sequences whose terms are written as surds - under construction

10.2 Practice Homework Booklet (PDF)

Revise this unit:10.2 Revision slides10.2 Flash cards10.2 Quizzes10.2 Revision notes10.2 Revision slides as text
Approaches to learning
Communication

I can show my maths thinking clearly by setting out my work neatly and using maths symbols correctly.

I can explain my ideas in different ways, not just give an answer, but also explain why it works.

Self-management

I can use my time wisely and practise independently by choosing helpful resources to support my learning of mathematics.

Community engagement
  • We build a classroom community where we help and support each other
  • We share our methods and explain our thinking to each other, so that everyone learns
  • We talk openly about maths anxiety and encourage each other to keep trying
  • We learn from other students, and we can help others through peer tutoring
Global context and inquiry questions

Global context: Scientific and Technical Innovation Key concepts: Equivalence, Representation, Simplification

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MYP assessment criteria

How assessment works

  • There are 4 assessment criteria in the MYP
  • Assessment dates are shared on ManageBac with at least 1 week's notice
  • Assessments are marked and given back within 2 weeks
  • You take your assessment home, complete an error analysis in green pen, get it signed by a parent or guardian and return it to your teacher
  • You are assessed at least twice on each criterion during the year

Criterion marking

  • Each criterion has 2 to 5 strands. You must meet each strand to reach a level
  • To reach a level, you must also have met ALL the levels before it

The levels are shown at the start of each line. Level 1 is the lowest and level 8 is the highest

ACriterion A: Knowing and understandingKnow it and use it

Criterion A is usually given as a traditional maths test. You are assessed on 3 strands

You should be able to

  1. select appropriate mathematics when solving problems in both familiar and unfamiliar situations
  2. apply the selected mathematics successfully when solving problems
  3. solve problems correctly in a variety of contexts

Strand i The student is able to select appropriate mathematics when solving …

Levels 1–2simple problemsinfamiliar situations
Levels 3–4more complex problemsinfamiliar situations
Levels 5–6challenging problemsinfamiliar situations
Levels 7–8challenging problemsin bothfamiliar and unfamiliar situations

Strands ii and iii are the same at every level, because strand i is about how complex and how familiar the problems are

Strand ii The student is able to apply the selected mathematics successfully when solving these problems

Strand iii The student is able to generally solve these problems correctly in a variety of contexts

BCriterion B: Investigating patternsSpot it and explain it

Criterion B is usually an investigation that you are guided through, to explore a new pattern or idea. You are assessed on 3 strands, but strand iii is only assessed at levels 5 to 8

You should be able to

  1. select and apply mathematical problem-solving techniques to discover complex patterns
  2. describe patterns as general rules consistent with findings
  3. prove, or verify and justify, general rules

Strand i The student is able to …

Levels 1–2apply, with teacher support,mathematical problem-solving techniques to discoversimple patterns
Levels 3–4applymathematical problem-solving techniques to discoversimple patterns
Levels 5–6select and applymathematical problem-solving techniques to discovercomplex patterns
Levels 7–8select and applymathematical problem-solving techniques to discovercomplex patterns

Strand ii The student is able to …

Levels 1–2state predictions consistent with patterns
Levels 3–4suggest general rules consistent with findings
Levels 5–6describe patterns as general rules consistent with findings
Levels 7–8describe patterns as general rules consistent with correct findings

Strand iii The student is able to …

Levels 5–6verify the validity of these general rules
Levels 7–8prove, or verify and justify, these general rules
CCriterion C: CommunicatingSay it clearly

Criterion C is usually assessed together with another criterion. You are assessed on 5 strands, but strand iii is only assessed at levels 5 to 8 and strand v is not assessed at levels 1 to 2

You should be able to

  1. use appropriate mathematical language (notation, symbols and terminology) in both oral and written explanations
  2. use appropriate forms of mathematical representation to present information
  3. move between different forms of mathematical representation
  4. communicate complete, coherent and concise mathematical lines of reasoning
  5. organise information using a logical structure

Strand i The student is able to …

Levels 1–2use limitedmathematical language
Levels 3–4use some appropriatemathematical language
Levels 5–6usually use appropriatemathematical language
Levels 7–8consistently use appropriatemathematical language

Strand ii The student is able to …

Levels 1–2use limited forms of mathematical representation to present information
Levels 3–4use appropriate forms of mathematical representation to present information adequately
Levels 5–6usually use appropriate forms of mathematical representation to present information correctly
Levels 7–8use appropriate forms of mathematical representation to consistently present information correctly

Strand iii The student is able to …

Levels 5–6usually move between different forms of mathematical representation
Levels 7–8move effectively between different forms of mathematical representation

Strand iv The student is able to …

Levels 1–2communicate through lines of reasoning that are difficult to interpret
Levels 3–4communicate through lines of reasoning that are complete
Levels 5–6communicate through lines of reasoning that are complete and coherent
Levels 7–8communicate through lines of reasoning that are complete, coherent and concise

Strand v The student is able to …

Levels 3–4adequately organise information using a logical structure
Levels 5–6present work that is usually organised using a logical structure
Levels 7–8present work that is consistently organised using a logical structure
DCriterion D: Applying mathematics in real-life contextsUse it in real life

Criterion D is usually a problem to be solved using maths set in a real-world context. You think about both the maths and the context, with analysis. You are assessed on 5 strands, but strands iii, iv and v are not assessed at every level

You should be able to

  1. identify relevant elements of authentic real-life situations
  2. select appropriate mathematical strategies when solving authentic real-life situations
  3. apply the selected mathematical strategies successfully to reach a solution
  4. justify the degree of accuracy of a solution
  5. justify whether a solution makes sense in the context of the authentic real-life situation

Strand i The student is able to …

Levels 1–2identify some of the elements of the authentic real-life situation
Levels 3–4identify the relevant elements of the authentic real-life situation
Levels 5–6identify the relevant elements of the authentic real-life situation
Levels 7–8identify the relevant elements of the authentic real-life situation

Strand ii The student is able to …

Levels 1–2apply mathematical strategies to find a solution to the authentic real-life situation, with limited success
Levels 3–4select, with some success, adequate mathematical strategies to model the authentic real-life situation
Levels 5–6select adequate mathematical strategies to model the authentic real-life situation
Levels 7–8select appropriate mathematical strategies to model the authentic real-life situation

Strand iii The student is able to …

Levels 3–4apply mathematical strategies to reach a solution to the authentic real-life situation
Levels 5–6apply the selected mathematical strategies to reach a valid solution to the authentic real-life situation
Levels 7–8apply the selected mathematical strategies to reach a correct solution to the authentic real-life situation

Strand iv The student is able to …

Levels 5–6explain the degree of accuracy of the solution
Levels 7–8justify the degree of accuracy of the solution

Strand v The student is able to …

Levels 3–4discuss whether the solution makes sense in the context of the authentic real-life situation
Levels 5–6explain whether the solution makes sense in the context of the authentic real-life situation
Levels 7–8justify whether the solution makes sense in the context of the authentic real-life situation

Approaches to learning

Approaches to learning (ATL) are the skills that help you learn anything, in maths and everywhere else. The MYP groups them into five categories, and we practise them in every unit.

Thinking

Ask what if

Critical thinking, creative thinking and transfer.

Spot patterns and connections, ask what if, and use an idea you learned in one place to solve a problem somewhere new.

Communication

Share your ideas

Sharing ideas clearly, in different ways.

Show your maths thinking clearly by setting out your work neatly and using maths symbols correctly. Explain your ideas in different ways, not just the answer but why it works.

Social

Work with others

Working well with others.

Work with a partner or group, listen to other methods, and explain your thinking to help someone else.

Self-management

Keep going, reflect

Organisation, staying positive and reflecting.

Use your time wisely and practise independently by choosing helpful resources, such as videos and worked examples. Keep going when it is hard, and reflect on what to do differently.

Research

Find and check

Finding and using information well.

Find useful examples and explanations, check where they come from, and decide whether they are reliable.

The IB learner profile

IB learners strive to be:

Inquirers

We nurture our curiosity, developing skills for inquiry and research. We know how to learn independently and with others. We learn with enthusiasm and sustain our love of learning throughout life.

Knowledgeable

We develop and use conceptual understanding, exploring knowledge across a range of disciplines. We engage with issues and ideas that have local and global significance.

Thinkers

We use critical and creative thinking skills to analyse and take responsible action on complex problems. We exercise initiative in making reasoned, ethical decisions.

Communicators

We express ourselves confidently and creatively in more than one language and in many ways. We collaborate effectively, listening carefully to the perspectives of other individuals and groups.

Principled

We act with integrity and honesty, with a strong sense of fairness and justice, and with respect for the dignity and rights of people everywhere. We take responsibility for our actions and their consequences.

Open-minded

We critically appreciate our own cultures and personal histories, as well as the values and traditions of others. We seek and evaluate a range of points of view, and we are willing to grow from the experience.

Caring

We show empathy, compassion and respect. We have a commitment to service, and we act to make a positive difference in the lives of others and in the world around us.

Risk-takers

We approach uncertainty with forethought and determination; we work independently and cooperatively to explore new ideas and innovative strategies. We are resourceful and resilient in the face of challenges and change.

Balanced

We understand the importance of balancing different aspects of our lives (intellectual, physical and emotional) to achieve well-being for ourselves and others. We recognise our interdependence with other people and with the world in which we live.

Reflective

We thoughtfully consider the world and our own ideas and experience. We work to understand our strengths and weaknesses in order to support our learning and personal development.

Useful links