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Leading the Australian Curriculum: Mathematics Number and Algebra Strand Carissa Carroll Tuesday 26 February 2013

Leading the Australian Curriculum: Mathematics Number and Algebra Strand Carissa Carroll Tuesday 26 February 2013. #1. Geraldton Numeracy Strategy. Purpose of this session. Explore the mathematics of the Patterns and Algebra substrand for Years F – 7

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Leading the Australian Curriculum: Mathematics Number and Algebra Strand Carissa Carroll Tuesday 26 February 2013

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  1. Leading the Australian Curriculum: MathematicsNumber and Algebra StrandCarissa CarrollTuesday 26 February 2013 #1 Geraldton Numeracy Strategy

  2. Purpose of this session • Explore the mathematics of the Patterns and Algebra substrand for Years F – 7 • To explore the connections between the Proficiency Strands, the Content Descriptors and the Achievement Standards in Patterns and Algebra • Track the development of content for Patterns and Algebra in the primary school years

  3. Mathematics

  4. Number and algebra • Are confident, creative users and communicators of mathematics, able to investigate, represent and interpret situations in their personal and work lives and as citizens • Develop an increasingly sophisticated understanding of mathematical concepts and fluency with processes, and are able to pose and solve problems and reason in Number and Algebra, Measurement and Geometry, and Statistics and Probability • Recognise connections between the areas of mathematics and other disciplines and appreciate mathematics as an accessible and enjoyable discipline to study • (Aims: Australian Curriculum Mathematics )

  5. Six aspects of Number that are essential for Algebra • Understanding equality • Recognising the operations • Using a wide range of numbers • Understanding important properties of numbers • Describing patterns and functions • Order of operations

  6. Understanding equality • Students who interpret the equals sign as ‘work out the answer’ or ‘makes’ or ‘leaves’ may struggle to understand that both sides of the equation represent the same value • 7 x 4 = 40 ─ 12 • How do you think these misconceptions arise?

  7. Understanding equality • Today’s number sentence/expression is? • Websites and other resources • http://nrich.maths.org/5676/index?nomenu=1 • Open responses + = x

  8. Understanding equality • If this misconception is unchallenged students will be even more puzzled by 2 (d + 3) = 2d + 6

  9. Recognising the operations I have 32 children and I need to make teams with 8 children in each. How many teams will I make? Represent this problem using arithmetic, i.e. the operations.

  10. 8 + 8 + 8 + 8 = 32 32 – 8 – 8 – 8 – 8 = 0 8 x ? = 32 32 ÷ 8 = 4 I have 32 children and I need to make teams with 8 children in each. How many teams will I make?

  11. Recognising the operations • I have n children and I need to make teams with d children in each. How many teams will I make? • Represent this problem algebraically.

  12. I have n children and I need to make teams with d children in each. How many teams will I make? n ÷ d

  13. Using a wide range of numbers Students need to understand whole numbers, decimals and fractions and be able to use them in equations. This content is developed through the number and place value and the fractions and decimals sub-strands of the Australian Curriculum. 4.75 ⅓ 0.99 21 576 ¼

  14. Understanding important properties of numbers • So what properties of number are important for primary students? • Talk about the properties in your group and prepare some examples using arithmetic. • Nominate someone to share your examples and thoughts

  15. Commutative, associative and distributive properties • What does each look like when applied to algebraic terms and expressions?

  16. Commutative property 6 x 2 = 2 x 6 First Steps KU 7

  17. Distributive property The whole array represents 7 x 9 (7 rows of 9 ) The array to the left of the line shows 7 x 7 (7 rows of 7). The small array to the right of the line shows 7 x 2 ( 7 rows of 2). It can now be easily seen that 7 x 9 is the same as (7 x7 ) + ( 7 x 2) , which leads to 49 + 14 = 63 . http://nrich.maths.org/2469 Text from Nrich site article by Jenni Way First Steps KU 7

  18. Associative property Another important property of multiplication is associativity, which says that • a × (b × c) = (a × b) × c for all numbers. • We can demonstrate this with the numbers 2, 3 and 4: • 2 × (3 × 4) = (2 × 3) × 4 Associativity of multiplication ensures that the expression a × b × c is unambiguous.

  19. Understanding important properties of numbers • Builds students’ capacity for flexible computation, problem solving and reasoning. • Helps make sense! What models could help students build their understanding of these properties?

  20. Describing patterns and functions 1 2 3 4 5 What’s the rule? Explain to your partner why your rule will always work.

  21. What’s my rule? • One person thinks of a rule about numbers and the other/s take turns to guess what the rule is. • Input output Source: Access to algebra Book 1 Lowe, Johnston, Kissane, Willis 1993

  22. Pattern activity Make a matchstick pattern using squares. Position number 1 2 3 4 5 Number of matches 4 7 10 13 16 Write a rule that connects the variables to the position number. You may wish to replace the words ‘position number’ with the letter n. Source: Access to algebra Book 1 Lowe, Johnston, Kissane, Willis 1993

  23. Number pattern activity Number of matches = position number x 3 + 1 Number of matches = n x 3 + 1 (where n is the position number) Source: Access to algebra Book 1 Lowe, Johnston, Kissane, Willis 1993

  24. Writing rules where letters stand for relationships If c stands for the number of chairs in the room and t stands for the number of chair legs, which of these rules could be correct? t = c x 4 t = c ÷ 4 c = t ÷ 4 c = t x 4 c x 3 = t c = t + 4

  25. Formulas • P = 4 x L • If the sides of a square lawn are 90 metres long, what is its perimeter? (L = length of one side) • If t represents the number of metres along each side of a piece of square cloth, what does t x t stand for? Source: Access to algebra Book1 Lowe, Johnston, Kissane, Willis 1993

  26. Order of operations Who is correct ? http://www.mathgoodies.com/lessons/vol7/order_operations.html

  27. The twenty-four game • Using all four numbers 4, 6, 6 and 8, but using each number only once, there are over 60 different ways of getting the answer 24 by adding, subtracting, multiplying and dividing. • How many can you and your friends find? http://nrich.maths.org/63

  28. Order of operations The repair person charged Jenn $175 for parts and $60 per hour to repair her washing machine. If he spent 2 hours repairing the machine, how much does Jenn owe him?

  29. First Steps in Mathematics … wasn’t written for the Australian Curriculum but still great source of information and ideas to support its use

  30. Patterns & Algebra • Order the content descriptors from Foundation to year 7. • When you have finished, collect an answer sheet and compare. • Any surprises?

  31. Patterns & Algebra

  32. Looking at the Patterns and Algebra substrand • In year level groups, choose one content description from the Patterns and Algebra substrand. • Plan for a lesson, or a series of lessons, that related to the content descriptor. • Consider how the proficiencies will be developed in the lesson. • Nominate someone to describe the lesson(s) and reasons or your selection of the activities.

  33. Patterns & Algebra • On your large post it page… • Proficiencies • Content Descriptors • Focus Questions • Activities • Achievement Standard • Consider the General Capabilities & the Cross Curriculum Priorities Choose a person to report back to the group

  34. Lunch

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