problem solving strategies
In the Australian Curriculum, the general capabilities encompass the knowledge, skills, behaviours and dispositions that, together with curriculum content in each learning area and the cross-curriculum priorities, will assist students to live and work successfully in the twenty-first century.
There are seven general capabilities:
In the Australian Curriculum: Mathematics, general capabilities are identified wherever they are developed or applied in content descriptions. They are also identified where they offer opportunities to add depth and richness to student learning through content elaborations.
Problem Solving and developing appropriate problem solving strategies are vital for students to work towards these general capabilities, as well as the specific numeracy strands of:
Number and Algebra, Measurement and Geometry, and Statistics and Probability.
Literacy is an important aspect of mathematics. Students develop literacy in mathematics as they learn the vocabulary associated with number, space, measurement and mathematical concepts and processes. This vocabulary includes synonyms (minus, subtract), technical terminology (digits, lowest common denominator), passive voice (If 7 is taken from 10) and common words with specific meanings in a mathematical context (angle, area). They develop the ability to create and interpret a range of texts typical of Mathematics ranging from calendars and maps to complex data displays.
Students use literacy to understand and interpret word problems and instructions that contain the particular language features of mathematics. They use literacy to pose and answer questions, engage in mathematical problem solving, and to discuss, produce and explain solutions.
Students develop capability in critical and creative thinking as they learn to generate and evaluate knowledge, clarify concepts and ideas, seek possibilities, consider alternatives and solve problems. Critical and creative thinking are integral to activities that require students to think broadly and deeply using skills, behaviours and dispositions such as reason, logic, resourcefulness, imagination and innovation in all learning areas at school and in their lives beyond school.
Students develop critical and creative thinking as they learn to generate and evaluate knowledge, ideas and possibilities, and use them when seeking solutions. Engaging students in reasoning and thinking about solutions to problems and the strategies needed to find these solutions are core parts of the Mathematics curriculum.
Students are encouraged to be critical thinkers when justifying their choice of a calculation strategy or identifying relevant questions during a statistical investigation. They are encouraged to look for alternative ways to approach mathematical problems, for example, identifying when a problem is similar to a previous one, drawing diagrams or simplifying a problem to control some variables.
There are seven general capabilities:
- Literacy
- Numeracy
- Information and communication technology (ICT) capability
- Critical and creative thinking
- Personal and social capability
- Ethical understanding
- Intercultural understanding.
In the Australian Curriculum: Mathematics, general capabilities are identified wherever they are developed or applied in content descriptions. They are also identified where they offer opportunities to add depth and richness to student learning through content elaborations.
Problem Solving and developing appropriate problem solving strategies are vital for students to work towards these general capabilities, as well as the specific numeracy strands of:
Number and Algebra, Measurement and Geometry, and Statistics and Probability.
Literacy is an important aspect of mathematics. Students develop literacy in mathematics as they learn the vocabulary associated with number, space, measurement and mathematical concepts and processes. This vocabulary includes synonyms (minus, subtract), technical terminology (digits, lowest common denominator), passive voice (If 7 is taken from 10) and common words with specific meanings in a mathematical context (angle, area). They develop the ability to create and interpret a range of texts typical of Mathematics ranging from calendars and maps to complex data displays.
Students use literacy to understand and interpret word problems and instructions that contain the particular language features of mathematics. They use literacy to pose and answer questions, engage in mathematical problem solving, and to discuss, produce and explain solutions.
Students develop capability in critical and creative thinking as they learn to generate and evaluate knowledge, clarify concepts and ideas, seek possibilities, consider alternatives and solve problems. Critical and creative thinking are integral to activities that require students to think broadly and deeply using skills, behaviours and dispositions such as reason, logic, resourcefulness, imagination and innovation in all learning areas at school and in their lives beyond school.
Students develop critical and creative thinking as they learn to generate and evaluate knowledge, ideas and possibilities, and use them when seeking solutions. Engaging students in reasoning and thinking about solutions to problems and the strategies needed to find these solutions are core parts of the Mathematics curriculum.
Students are encouraged to be critical thinkers when justifying their choice of a calculation strategy or identifying relevant questions during a statistical investigation. They are encouraged to look for alternative ways to approach mathematical problems, for example, identifying when a problem is similar to a previous one, drawing diagrams or simplifying a problem to control some variables.
Some problems to try and solve:
1. What is the value of n that makes the sentence true?
1 x 2 x 3 x 4 x 5 = 8 x n
Extension problem:
What is the value of n if 1 x 2 x 3 x 4 x 5 x 6 x 7 = 10 x 12 x n?
2. A, B and C are different digits.
If 1287 x C = ABBA, then what is the value of ABBA x C?
3. If Fran piles her stickers in groups of 8, there are 3 left over. If she piles them instead in groups of 10, there are 3 left over. If she piles them instead into groups of 12, there are 3 left over. Fran has fewer than 1000 stickers.
What is the greatest number of stickers Fran could have?
ANSWERS:
1. n = 15
Strategies you could have used were:
Extension problem
n = 42
2. 63 063
Strategies you could have used were:
3. 963
Strategies you could have used were:
1. What is the value of n that makes the sentence true?
1 x 2 x 3 x 4 x 5 = 8 x n
Extension problem:
What is the value of n if 1 x 2 x 3 x 4 x 5 x 6 x 7 = 10 x 12 x n?
2. A, B and C are different digits.
If 1287 x C = ABBA, then what is the value of ABBA x C?
3. If Fran piles her stickers in groups of 8, there are 3 left over. If she piles them instead in groups of 10, there are 3 left over. If she piles them instead into groups of 12, there are 3 left over. Fran has fewer than 1000 stickers.
What is the greatest number of stickers Fran could have?
ANSWERS:
1. n = 15
Strategies you could have used were:
- Balance the equation by finding the missing factors
- Compute using arithmetic
Extension problem
n = 42
2. 63 063
Strategies you could have used were:
- Make an educated guess and check (trial and error)
- Make a list of multiples of 1287
3. 963
Strategies you could have used were:
- Start with zero piles of 3 stickers left over and count up by the LCM
- Use your understanding of divisibility to narrow down your options.