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Ambarvale Public School “A Hands-on Approach to Mathematics” Parent Maths Workshop Thursday 3rd September 2009 Presented by Catherine Sullivan and Mellissa Page What is Mathematics K-6? Mathematics is one of the key learning areas. * It builds upon the mathematical learning that students bring from home. * The concepts children learn in maths will be used throughout their lives. * Maths prepares students to be problem solvers. Maths is: What do I want to find out and what do I need to do? What do students learn to do? Students learn to: • Use maths in everyday contexts. • Understand what the question is asking. * Ask questions about mathematics. * Describe and explain mathematical ideas and procedures. * Choose the best methods to solve problems – this will include using calculators, written methods and mental strategies rather than just traditional pencil and paper methods. * Use calculators and computers to investigate and solve problems and retrieve and represent information. * Understand that maths is not only about numbers – it is measuring, graphing, shapes, patterns and chance. * Understand and use mathematical language. Understand that everyday words can mean something different in maths – face, odd, side, even, volume. What do students find difficult about mathematical language? What is volume? Isn’t that a control on the TV? Whole Numbers * Count forwards and backwards from any given number as well as on and off the decade. (Activity) * Automatically recognise, read, write and order numbers. * Name the number before and after a number. * Round numbers up and down when estimating. * State the place value of any digit in a number. * Recognise all coins, notes and equivalent amounts using different denominations. NOTES Addition and Subtraction * Combine groups of numbers and take part of a group away to show addition and subtraction. * Model addition and subtraction using concrete materials (counters, blocks etc). * Use mental strategies to add and subtract numbers. * Count on and back from the largest number. * Recognise and use symbols and words (+, -, plus, minus, add, subtract, takeaway, etc). * Model addition and subtraction problems using trading. (Activity) * Use doubles, near doubles, number lines, split strategy and jump strategy. (Activity) * Add and subtract numbers of any size. NOTES Multiplication and Division * Make equal rows or groups. Group and share collections equally. * Make arrays or equal groups. (Activity) * Introduce counting by 1’s, 2’s, 5’s & 10’s and begin times tables. * Repeated addition and subtraction. * Introduce symbols X and : * Counting by 3’s, 4’s, 6’s, 7’s, 8’s, and 9’s. * Commutative property of multiplication 3x7 = 7x3 * Uses known facts to figure out unknown 5x5=25, so 5x6 = 25 + 5. * Use the division symbol * Inverse relationship of multiplication and division 63 : 7 = 9 because 7x9=63 * Factors of numbers Factors of 12 are 1, 2, 3, 4, 6, 12. Multiplication and Division * Mental strategies – multiplying tens and units 7x19= (7x10) + (7x9) = 70 + 63 - doubling 23 x 4 is double 23 and double again * Recording remainders in division questions and understanding their importance in word problems. * Recording remainders as decimals and fractions 25 : 4 = 6 ¼ or 6.25 * Multiplying 3-digit and 4-digit numbers by a 1-digit number using mental and written strategies. 432 x 5 = 400 x 5 + 30 x 5 + 2 x 5 = 2000 + 150 + 10 = 2160 432 X 5 2160 Multiplication and Division * Multiplying 3-digit numbers by 2-digit numbers using the extended form (long multiplication) (activity) * Dividing a number with 3 or more digits by a single digit number using written or mental strategies (mental) (written) 341 : 341 : 4 = 340 4 : 1=4 : 4 = 85 4)341 4 = 85 4 * Multiply or divide a number by 100 or a multiple of 10. * Deciding if a number is prime or composite by finding the number of factors. 13 has two factors (1 and 13) so it is prime. 15 has more than two factors (1,3,5,15) so it is composite. NOTES Fractions and Decimals * Sharing an object by dividing it into two equal parts. * Recognise when two parts are not halves of the one whole. * Model and describe a half or a quarter of an object or a collection of objects. * Describe parts of an object or collection of objects as ‘about half’ ‘more than enough’ or ‘less than half’. * Using fraction notation for half ( ½ ) and quarter ( ¼ ) * Model, compare and represent fractions with denominators 2, 4 and 8 - describe fractions as halves, quarters and eighths - write and name fractions e.g. ¾ - place fractions on a number line (activity) - order fractions by size - count by halves and quarters e.g. ½, 1, 1 ½ , 2, 2 ½ - recognise equivalent fractions using concrete materials and diagrams. 1/2 = 2/4 Fractions and Decimals * Model, compare and represent fractions with denominators 5, 10 and 100. * Model, compare and represent decimals to two decimal places. * Use existing knowledge of place value to write and use tenths and hundredths as decimals. * Recognise that 0.1 = 1/10 * Add and subtract decimals with the same number of decimal places. * Round a number with one or two decimal places to nearest whole number. * Link common percentages to a fraction or decimal. 25% = ¼ =0.25 = 25 out of 100 NOTES Fractions and Decimals * Thirds, sixths and twelfths as part of a whole object or a collection. * Write mixed numerals as improper fractions and improper fractions as mixed numerals and show them on a number line or in diagrams. * Use models and diagrams to subtract a fraction from a whole number. 2 - ⅓ = 1⅔ * Adding and subtracting fractions with the same denominator. 5/6 + 3/6 = 8/6 = 1⅓ * Writing and reading thousandths as decimals. * Comparing and ordering decimal numbers with three decimal places. * Placing decimal numbers on a number line between 0 and 1. * adding and subtracting decimal numbers with a different number of decimal places Fractions and Decimals * Multiplying and dividing decimal numbers by single digit number and by 10, 100,1000. $2.35 x 3 = $7.05 24.76 : 100 = 0.2476 * Develop a strategy for finding equivalent fractions. multiply or divide the numerator and the denominator by the same number. 2x2 l == 2x3 3x2 = 3x3 4x2 = 4x3 l == 4/6 = 6/9 = 8/12 * Reducing a fraction to its lowest equivalent form by dividing the numerator and the denominator by a common factor. * Adding or subtracting simple fractions where one denominator is a multiple of the other. 2/3 + 1/6 = 4/6 + 1/6 = 5/6 * Multiplying simple fractions by whole numbers using repeated addition, leading to a rule. 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