MYP unit planner ~ Year 2: Mathemagics!

Teacher(s) Louise Fung Greaves Subject group and discipline Mathematics

Unit title Mathemagics! MYP year 2 Unit duration (hrs) 23 hours (6 weeks)

Inquiry: Establishing the purpose of the unit

Key concept Related concept(s) Global context

Form Equivalence Scientific and technical innovation

Simplification Exploration: Mathematical puzzles and tricks

Statement of inquiry

Producing equivalent forms through simplification can help clarify, solve and create puzzles and tricks.

Inquiry questions

Factual - What is a linear equation? What is the distributive law?

Conceptual - Why do we simplify forms if they are equivalent?
Debatable - Does every puzzle have a solution? Can every trick be explained?

Objectives Summative assessment

Outline of summative assessment task(s) including Relationship between summative assessment task(s)
assessment criteria: and statement of inquiry:

C: Communicating Demystifying tricks: Criterion C Demystifying tricks: Criterion C

i. use appropriate mathematical language Goal: To demonstrate key mathematical Within this unit, students will practice examining the
(notation, symbols and terminology) in both oral communication skills to explain a mathematical magic underlying mathematical structure of puzzles and tricks
and written explanations trick that uses Algebra. using Algebra. In this assessment they will use their
ii. use appropriate forms of mathematical skills to decipher a puzzle and focus on explaining their
representation to present information Role: You are a puzzle collector. approach using mathematical communication skills.
iii. move between different forms of
mathematical representation Audience: You have a blog that explains the
iv. communicate complete and coherent mathematics behind puzzles and tricks.
mathematical lines of reasoning
v. organize information using a logical Situation: You have received a puzzle/trick from one of
structure. your followers that they have asked you to decipher.
https://nrich.maths.org/thinkoftwonumbers

Product: You will present your solution to the puzzle in

a blog post, including different media formats and
 explanations of the Algebra that underlies the puzzle.

Standards: The assessment will be

completed individually in one double lesson and
a home learning session. A task-specific rubric will be
shared prior to the assessment too.  

Qualifying to be a mathemagician: Criterion A Qualifying to be a mathemagician: Criterion A

A: Knowing and understanding Goal: To demonstrate knowledge and understanding of This assessment examines the students’ knowledge
i. select appropriate mathematics when solving the learning content covered in this unit. The questions and understanding of the algebraic principles covered
problems in both familiar and unfamiliar will include a range of both familiar and unfamiliar in this unit. The concept of simplification and finding
situations situations and require students to solve problems in a equivalent forms will be addressed in many different
ii. apply the selected mathematics successfully variety of contexts. questions as students solve problems in a variety of
when solving problems contexts in increasing levels of difficulty.
iii. solve problems correctly in a variety of Role: You are a trainee mathemagician.
contexts.
Audience: The IB Mathemagician board.

Situation: In order for you to receive your

mathemagician qualification, you need to sit a written
exam that tests you on your algebraic skills.

Product: You will present your solutions in the written

paper provided. No calculators are allowed and clear
working out must be shown for all questions.

Standards: The assessment will be completed

individually during one double lesson. A task-specific
rubric will be shared prior to the assessment too.

Approaches to learning (ATL)

x. Transfer skills
In order for students to use appropriate mathematical language (notation, symbols and terminology) in both oral and written explanations, use appropriate forms of
mathematical representation to present information and move between different forms of mathematical representation, students must combine knowledge, understanding
and skills learnt in the unit to create their blog.

vii. Media literacy skills

In order for students to communicate complete and coherent mathematical lines of reasoning and organize information using a logical structure, students must
communicate information and ideas effectively using a variety of media and formats, perhaps including graphics, video clips, etc. to explain the mathematics behind their
 puzzle in their blog.

v. Reflection skills
In order for students to select appropriate mathematics when solving problems in both familiar and unfamiliar situations, apply the selected mathematics successfully
when solving problems, and solve problems correctly in a variety of contexts, students must consider content and reflect on: What did I learn today? What don’t I yet
understand? What questions do I have now?

Action: Teaching and learning through inquiry

Content Learning process

Algebraic rules and expressions Learning experiences and teaching strategies

● Review their understanding of using letters and
symbols to form algebraic expressions that Prior learning
represent relationships between variables Students should be familiar with basic use of letters and symbols to represent variables, algebraic notation
● Review algebraic notation rules rules and solving simple one and two-step linear equations. Throughout this unit, a topic checklist/journal will
● Define key terms such as coefficients, monomials be used to encourage students to practice their reflection (ATL) skills and review their understanding. This
and polynomials will then be an opportunity to record their reflections and make the progression of learning more tangible.
● Simplify expressions by collecting like terms
Algebraic rules and expressions
● Substitute values into expressions
This part of the unit forms the underlying algebraic understanding that is required for the rest of the unit when
further algebraic manipulation is performed. As students will have different levels of prior knowledge,
Linear Equations common misconceptions will also be discussed so that students can deepen their conceptual understanding
● Recognize linear equations with one unknown of what equivalence, simplification and the algebraic rules mean; and in particular address the conceptual
● Solve linear equations (including difficult fractional inquiry question: “Why do we simplify forms if they are equivalent?”. Definitions of key terms are also crucial
and negative coefficients) by “balancing scales” here as for the rest of the unit the students will be expected to use the terms in their explanations (in
and by using inverse operations particular the following C assessment).
● Solve linear equations with brackets (by using
Linear equations & self-directed learning
inverse operations) With reference to the SOI, students will be introduced to various algebraic puzzles and tricks in which they
● Solve linear equations with unknowns on both sides have to develop their knowledge of solving different types of linear equations of increasing difficulty. To allow
(including simple algebraic fractions) for better differentiation, scaffolding and individual support, students will work through a series of tasks so
● Apply knowledge of solving linear equations to that the learning is “flipped” and they will “discover” the skill through videos and/or inquiry tasks. (In particular,
problems in real-life contexts, such as calculating a variety of media platforms (ATL: Media literacy) will be used so students can experience this in preparation
for their C assessment). The skills practice activities in class and for home learning will be decided by the
discounts with the use of a multiplier
student so that they reinforce their own learning. When each task is completed, students can use their
reflection journal to review their understanding and produce an answer to the factual inquiry question: “What
The laws of indices/exponents is a linear equation?”.
 ● Review and use terms such as “base number” and
“exponents/indices/powers” to describe numbers of Laws of indices/exponents - Short investigation tasks
the form an In this section, students will follow the inquiry continuum (criterion B strands) to establish and verify the laws
of indices. Using the familiar strands will reinforce the investigation process and how we verify and justify the
● Understand and apply the addition law of
relationships. To review their understanding of the laws, a series of true, false and maybe cards will be used
exponents: am x an = am+n frequently as starters and plenaries to consolidate how the laws work and what they mean.
● Understand and apply the power law of exponents:
(am)n = amn Use of exponents in standard form will require some focus as students may need reminding of what standard
● Understand and apply the multiplication law of form is. Using real-life contexts for this section will help students identify the use of standard form and better
exponents: (ab)n = an x bn grasp the size of numbers which are usually presented in standard form.
● Understand and apply the division law of
Algebraic multiplication & visual representations
exponents: am / an = am-n
Algebraic multiplication will be taught using the concept of area (ATL: Transfer) and answer this unit’s factual
● Understand that a zero exponent equals 1 inquiry question: “What is the distributive law?”. Students will be encouraged to develop a more visual
● Understand that negative exponents represent representation/model to multiplication, in particular using the grid method and algebra tiles, so that it is clear
reciprocal values and apply this to solve problems what happens when we perform algebraic multiplication and why we would need to factorize expressions
● Apply the use of positive and negative exponents in when dividing. The derivation of the difference of two squares and perfect squares will enable early
standard form to describe very large and small discussions on polynomials of order of 2, i.e. quadratics.
numbers
Formative assessment
● Perform operations and calculations with numbers
in standard form
Diagnostic quiz
Algebraic multiplication Students will begin this unit with mixed levels of understanding. In order to gauge their confidence, and also
conceptual understanding, students will be given an initial quiz that can address common misconceptions
● Review multiplication of monomials
and identify their prior knowledge.
● Apply the distributive law of multiplication to expand
single and double brackets 5 Quick questions
● Identify and apply the properties of expressions After each section of the unit is completed, students will regularly complete a collection of 5 quick questions
which are a difference of two squares to practice their recall and application of the algebraic techniques. This will help to again address common
● Identify and apply the properties of expressions misconceptions and identify areas that require review when more detail revision occurs.
which are perfect squares
Differentiation
● Divide monomials by identify factors that “cancel”
● Factorize expressions when dividing polynomials Skills practice and groupings
The activities and skills practice will be presented in various levels of difficulty. Using visual representations of
Common Core State Standards: 7.EE.1-3, 4a; 8.EE.1, 3-4
the algebraic manipulation will help explain the concepts and negate misconceptions. Groupings in this unit
CNC: Grade 7 Book 1 Ch3 & 5, Grade 7 Book 2 Ch1
will be based on ability. This will help direct the level of instruction and the variety of tasks provided in
MYP 2: Ch4
practices.

Possible extension topics:

● Research the history of Algebra
● What about powers of 0, in particular 0^0?
 ● The binomial expansion (for expanding (a+b) n with n>0)

Resources

● Mathsbox and Mathspad activities

● Standards units
● Tarsia puzzles
● Nrich investigations:
○ Using symbols and letters - Letter land: https://nrich.maths.org/850
○ Linear equations and tricks - Your number was: https://nrich.maths.org/7216
○ Indices: https://nrich.maths.org/public/topic.php?group_id=5&code=48#results
○ Algebraic multiplications - Shape Products: https://nrich.maths.org/13079
○ The distributive law - Seven Up: https://nrich.maths.org/687
● Mangahigh

Reflection: Considering the planning, process and impact of the inquiry

Prior to teaching the unit During teaching After teaching the unit

Students will have mixed confidence in starting this

unit. Some students will be able to perform the
algebraic manipulations with ease, whereas there will
be some students who struggle to grasp the rules of
algebra and understand why they are so. By providing
a reflection journal, this should help identify and record
the individual strengths and weaknesses of the
students’ understanding and help formulate the pace
and level of progression of the unit.