Big Ideas
Big Ideas
Similar shapes and objects have proportional relationships that can be described, measured, and compared.
- Sample questions to support inquiry with students:
- What characteristics make objects similar?
- How do the properties of 3D objects change in an enlargement or a reduction?
- How do the properties of 2D objects change in an enlargement or a reduction?
Optimization informs the decision-making process in situations involving extreme values.
- a mathematical analysis used to determine the minimum or maximum output for a given situation
- Sample questions to support inquiry with students:
- Can we think of a story where a conflict can be resolved through optimization?
- How can mathematics help us make decisions regarding the best course of action?
- What factors influence the decision-making process when determining an optimal solution?
- How do graphs aid in understanding a situation that is being optimized?
Logical reasoning helps us discover and describe mathematical truths.
- the process of using a strategic, systematic series of steps based on valid mathematical procedures and given statements to form a conclusion
- Sample questions to support inquiry with students:
- How can logical reasoning help us deal with problems in our everyday lives?
- How does puzzle and game analysis help us in the world outside the math classroom?
Statistical analysis allows us to notice, wonder about, and answer questions about variation.
- occurs in observation (e.g., reaction to medications, opinions on topics, income levels, graduation rates)
- Sample questions to support inquiry with students:
- How do we gather data in order to answer questions?
- How do we analyze data and make decisions?
- Can we think of a story that involves variation? How would we describe the variation?
- When analyzing data, what are some of the factors that need to be considered before making inferences?
Content
Learning Standards
Content
forms of mathematical reasoning
- logic, conjecturing, inductive and deductive thinking, proofs, game/puzzle analysis, counter-examples
angle relationships
- properties, proofs, parallel lines, triangles and other polygons, angle constructions
graphical analysis:
- using technology only
- linear inequalities
- graphing of the solution region
- slope and intercepts
- intersection points of lines
- quadratic functions
- characteristics of graphs, including end behaviour, maximum/minimum, vertex, symmetry, intercepts
- systems of equations
- including linear with linear, linear with quadratic, and quadratic with quadratic
- optimization
- using feasible region to optimize objective function
- maximizing profit while minimizing cost
- maximizing area or volume while minimizing perimeter
applications of statistics
- posing a question about an observed variation, collecting and interpreting data, and answering the question
- measures of central tendency, standard deviation, confidence intervals, z-scores, distributions
scale models
- enlargements and reductions of 2D shapes and 3D objects
- comparing the properties of similar objects (length, area, volume)
- square-cube law
financial literacy : compound interest, investments and loans
- compound interest
- introduction to investments/loans with regular payments using technology
- buy/lease
Curricular Competency
Learning Standards
Curricular Competency
Reasoning and modelling
Develop thinking strategies to solve puzzles and play games
- using reason to determine winning strategies
- generalizing and extending
Explore, analyze, and apply mathematical ideas using reason, technology, and other tools
- examine the structure of and connections between mathematical ideas (e.g., quadratics and cubic functions, linear inequalities, optimization, financial decision making)
- inductive and deductive reasoning
- predictions, generalizations, conclusions drawn from experiences (e.g., with puzzles, games, and coding)
- graphing technology, dynamic geometry, calculators, virtual manipulatives, concept-based apps
- can be used for a wide variety of purposes, including:
- exploring and demonstrating mathematical relationships
- organizing and displaying data
- generating and testing inductive conjectures
- mathematical modelling
- manipulatives such as algebra tiles and other concrete materials
Estimate reasonably and demonstrate fluent, flexible, and strategic thinking about number
- be able to defend the reasonableness of an estimated value or a solution to a problem or equation (e.g., angle size reasonableness, scale calculations and unit choice, optimal solutions)
- includes:
- using known facts and benchmarks, partitioning, applying whole number strategies to rational numbers and algebraic expressions
- choosing from different ways to think of a number or operation (e.g., Which will be the most strategic or efficient?)
Model with mathematics in situational contexts
- use mathematical concepts and tools to solve problems and make decisions (e.g., in real-life and/or abstract scenarios)
- take a complex, essentially non-mathematical scenario and figure out what mathematical concepts and tools are needed to make sense of it
- including real-life scenarios and open-ended challenges that connect mathematics with everyday life
Think creatively and with curiosity and wonder when exploring problems
- by being open to trying different strategies
- refers to creative and innovative mathematical thinking rather than to representing math in a creative way, such as through art or music
- asking questions to further understanding or to open other avenues of investigation
Understanding and solving
Develop, demonstrate, and apply mathematical understanding through play, story, inquiry, and problem solving
- includes structured, guided, and open inquiry
- noticing and wondering
- determining what is needed to make sense of and solve problems
Visualize to explore and illustrate mathematical concepts and relationships
- create and use mental images to support understanding
- Visualization can be supported using dynamic materials (e.g., graphical relationships and simulations), concrete materials, drawings, and diagrams.
Apply flexible and strategic approaches to solve problems
- deciding which mathematical tools to use to solve a problem
- choosing an appropriate strategy to solve a problem (e.g., guess and check, model, solve a simpler problem, use a chart, use diagrams, role-play)
- interpret a situation to identify a problem
- apply mathematics to solve the problem
- analyze and evaluate the solution in terms of the initial context
- repeat this cycle until a solution makes sense
Solve problems with persistence and a positive disposition
- not giving up when facing a challenge
- problem solving with vigour and determination
Engage in problem-solving experiences connected with place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures
- through daily activities, local and traditional practices, popular media and news events, cross-curricular integration
- by posing and solving problems or asking questions about place, stories, and cultural practices
Communicating and representing
Explain and justify mathematical ideas and decisions in many ways
- use mathematical arguments to convince
- includes anticipating consequences
- Have students explore which of two scenarios they would choose and then defend their choice.
- including oral, written, visual, use of technology
- communicating effectively according to what is being communicated and to whom
Represent mathematical ideas in concrete, pictorial and symbolic forms
- using models, tables, graphs, words, numbers, symbols
- connecting meanings among various representations
Use mathematical vocabulary and language to contribute to discussions in the classroom
- partner talks, small-group discussions, teacher-student conferences
Take risks when offering ideas in classroom discourse
- is valuable for deepening understanding of concepts
- can help clarify students’ thinking, even if they are not sure about an idea or have misconceptions
Connecting and reflecting
Reflect on mathematical thinking
- share the mathematical thinking of self and others, including evaluating strategies and solutions, extending, posing new problems and questions
Connect mathematical concepts with each other, other areas, and personal interests
- to develop a sense of how mathematics helps us understand ourselves and the world around us (e.g., daily activities, local and traditional practices, popular media and news events, social justice, cross-curricular integration)
Use mistakes as opportunities to advance learning
- range from calculation errors to misconceptions
- by:
- analyzing errors to discover misunderstandings
- making adjustments in further attempts
- identifying not only mistakes but also parts of a solution that are correct
Incorporate First Peoples worldviews, perspectives, knowledge, and practices to make connections with mathematical concepts
- by:
- collaborating with Elders and knowledge keepers among local First Peoples
- exploring the First Peoples Principles of Learning (http://www.fnesc.ca/wp/wp-content/uploads/2015/09/PUB-LFP-POSTER-Princi…; e.g., Learning is holistic, reflexive, reflective, experiential, and relational [focused on connectedness, on reciprocal relationships, and a sense of place]; Learning involves patience and time)
- making explicit connections with learning mathematics
- exploring cultural practices and knowledge of local First Peoples and identifying mathematical connections
- local knowledge and cultural practices that are appropriate to share and that are non-appropriated
- Bishop’s cultural practices: counting, measuring, locating, designing, playing, explaining (http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/abishop.htm)
- Aboriginal Education Resources (www.aboriginaleducation.ca)
- Teaching Mathematics in a First Nations Context, FNESC (http://www.fnesc.ca/resources/math-first-peoples/)