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NSW Curriculum and Learning Innovation Centre

NSW Curriculum and Learning Innovation Centre. Pattern & Number Structure The Companion Mathematics Challenge. Peter Gould, Group Leader, Mathematics and Numeracy Chris Francis, Leader, Numeracy. A problem.

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NSW Curriculum and Learning Innovation Centre

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  1. NSW Curriculum and Learning Innovation Centre • Pattern & Number Structure • The Companion Mathematics Challenge Peter Gould, Group Leader, Mathematics and Numeracy Chris Francis, Leader, Numeracy

  2. A problem Many of the questions students encounter in day-to-day lessons do not provide a sense of what it is like to engage in mathematical thinking. Indeed, some students see mathematics as being only about finding the correct answers to large quantities of questions that are not particularly challenging.

  3. A problem This lack of challenge has led to the recommendation that …greater emphasis be given to providing students with frequent exposure to higher-level mathematical problems rather than routine procedural tasks, … with increased opportunities for students to discuss alternative solutions and explain their thinking. (p. xii) Australian National Numeracy Review Report (2008)

  4. Finding problems

  5. The mathematics challenges The Mathematics Challenges aim to develop an appreciation of: i.The design of mathematics problems that help to develop mathematical reasoning. The problems in both the Red dragonfly mathematics challenge and the Companion mathematics challenge highlight mathematical patterns, and the conditions under which the patterns arise.

  6. The mathematics challenges ii.The value of specific methods of reasoning in the problem solving process. These methods of reasoning are part of mathematics and can strengthen students’ mathematical dispositions to investigate mathematical challenges.

  7. The mathematics challenges The Companion mathematics challenge provides a range of problems carefully linked to the problem types introduced in the Red dragonfly mathematics challenge. Often the problems share the same number in both books.

  8. From a problem to a lesson

  9. Bug ate the calculation mushi insect kui eat zan from Keisan (calculation) mushikuizan

  10. Bug ate the calculation • In a bug-ate-the-calculation problem blank squares or cards stand in place of specific digits. • This problem type can be applied to a range of problems, such as subtracting a 2-digit number from a 3-digit number.

  11. Bug ate the calculation In Stage 2 students use mental and written strategies, including the formal written algorithm, to solve addition and subtraction problems involving numbers up to four digits. NS2.2

  12. Bug ate the calculation 3 What could the question have been? Is there more than one answer?

  13. What if the answer to the subtraction was 1? Bug ate the calculation 5 What could the question have been? Is there more than one answer? How many answers are there?

  14. Bug ate the calculation How do you know? 2 What could the question have been? Is there more than one answer? How many answers are there?

  15. Red dragonfly mathematics challenge What number should be in each square? (1) Replace the same letters with the same numbers to make a correct sum. What do you get?

  16. Companion mathematics challenge Task • Draft a lesson plan to support students’ reasoning in solving the problem, What number should be in each square? (1)

  17. Developing students’ reasoning • Reflecting on your own strategies and reasoning to solve the problem • Ensuring all students understand the question • Knowing how to begin the lesson • Asking the right questions to promote logical pathways for reasoning • Anticipating responses • Moving student strategies beyond “guess and check” • Managing differing ability levels NSW Curriculum and Learning Innovation Centre

  18. Bug ate the calculation Choose digits (0 to 9) to complete the calculation. 1 2 Multiply three-digit numbers by two-digit numbers using the extended form (long multiplication) NS3.3 x 3 7 8 4 6 3 0 4 4 4

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