Working Mathematically wps.pearsoned.com.au A/Prof Boris Handal The Australian Curriculum http://www.ricgroup.com.au/primary/australian-curriculum-mathematics/ What is Working Mathematically? Students develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning. NSW Syllabus for the Australian Curriculum Problem solving Strategies • • • • • • • • Draw a diagram Use concrete materials Make a table Look for a pattern Think of a related problem Use symbols Act it out Make a model Draw a diagram http://www.studyzone.org/ Use concrete materials (acting it out) walnuthillhomeschool.blogspot.com Make a table https://www.youtube.com/watch?v=m_2P06RSMPk Look for a pattern www.mathwire.com - Think of a related problem Use symbols mathinthemedian.pbworks.com Make a model illuminations.nctm.org Questions to encourage problem solving (Bobis et al, p. 277) Starter questions • How many ways can you find ... ? • The answer is ... What might the question be! • What patterns can you find ... ? Questions to elicit thinking strategies • • • • • How can you group these ... ? Is there a pattern? Does that pattern help you solve the problem? How did you solve that Have you found all the answers? How do you know? Questions to justify their strategies and solutions • Is there another way to get that answer? • Why do you think that? • Which do do you think is the most effective method? Why? Questions that make the mathematics explicit ("So what? questions) • Who used a different strategy to get the same answer? How can this be? • Are everyone's answers the same? Why/why not? • How does this activity relate to the topic ... ? • How did this activity help you to understand this topic better? • Does it help you understand any other topic better? Other questions • • • • Can I check this another way? What happens if ...? How many solutions are there? How will I know when I have found them all? NSW Mathematics K–6 Number and Algebra –Stage 3 Part 1 • Read, write and order numbers of any size • State the place value of digits in numbers of any size • Record numbers of any size using expanded notation • Determine factors and multiples of whole numbers Part 2 • Recognise the location of negative numbers in relation to zero on a number line • Identify and describe prime and composite numbers • Model and describe square and triangular numbers Remember A prime number is a natural number greater than 1 that has no factor other than 1 and itself.
