The brain is constantly looking for and making connections. Learning mathematics within contexts and making connections relevant to learners can validate past experiences and prior knowledge, and increase students’ willingness to participate and be actively engaged. Mental Mathematics and Estimation [ME] Mental mathematics is a combination of cognitive strategies that enhance flexible thinking and number sense. It is calculating mentally and reasoning about the relative size of quantities without the use of external memory aids. Mental mathematics enables students to determine answers and propose strategies without paper and pencil. It improves computational fluency and problem solving by developing efficiency, accuracy, and flexibility. Estimation is a strategy for determining approximate values of quantities, usually by referring to benchmarks or using referents, or for determining the reasonableness of calculated values. When estimating, students need to know what strategy to use, when to use it, and how to use it. Estimation is used to make mathematical judgements and develop useful, efficient strategies for dealing with situations in daily life. Problem Solving [PS] Learning through problem solving should be the focus of mathematics at all grade levels. When students encounter new situations and respond to questions of the type, “How would you ...?”, “Can you ...?”, or “What if ...?”, the problem solving approach is being modelled. Students develop their own problem-solving strategies by being open to listening, discussing, and trying different strategies. In order for an activity to be problem-solving based, it must ask students to determine a way to get from what is known to what is sought. If students are given ways to solve the problem, it is not problem solving but practice. A true problem requires students to use prior learning in new ways and contexts. Problem solving requires and builds depth of conceptual understanding and student engagement. Problem solving is a powerful teaching tool that fosters multiple and creative solutions. Creating an environment where students actively look for and engage in finding a variety of strategies for solving problems empowers students to explore alternatives and develops confidence, reasoning, and mathematical creativity. Reasoning [R] Mathematical reasoning helps students think logically and make sense of mathematics. Students need to develop confidence in their abilities to reason and explain their
travel themes. [C, CN, ME, R, V] Create, solve, and verify the reasonableness of solutions to questions that involve the use of a formula. Analyze solutions to questions that involve formulae to verify the preservation of equality, correct if necessary, and explain the reasoning. Solve, with or without the use of technology, questions that involve the application of a formula that: does not require manipulation does require manipulation. Sample Formulae: volume and capacity, surface area, slope and rate of change, primary trigonometric ratios, finance charges, and income. Goals: Number Sense, Logical Thinking, Spatial Sense, Mathematics as a Human Endeavour Outcomes [FM20.2 and WA20.2] M21.2 Demonstrate understanding of numerical reasoning and problem solving strategies by analyzing puzzles and games. [C, CN, PS, R] Indicators Make conjectures by observing patterns and identifying properties, and justify the reasoning. Observe and analyze errors in solutions to puzzles or in strategies for winning games to identify and correct errors, if necessary, and explain the reasoning. Solve questions that involve numerical reasoning.