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AiZ (Zones 2 & 3) Session 2 May 2010 Sue Gunningham [email protected] PROGRAM Session 1: Whole school planning for numeracy Session 2: What to teach Session 3: Using data effectively Session 4: Planning units of work AGENDA 9 - 9.30 9.30 – 10.00 Feedback: Action since S1 Recap key ideas session 1 10.00 – 11.00 Session 2 The whole school maths plan 11.00 – 11.30 MT 11.30 -1 The whole school maths plan- cont’d 1-1.30 Light Lunch 1.30 – 3.30 Session 3 Using data effectively The purpose of session 2 is for participants to: • Share progress made towards developing a whole school mathematics plan since Session 1 • Revisit the main points from Session 1 • Make sense of what to teach, when and why • Use the VELS to help plan effectively • Develop some planning resources & templates Turn and tell In pairs: 5 min “Discuss experiences you’ve had as a result of Session 1 that will advance our skills, thinking & knowledge about whole school planning” Each write 2 highlights/revelations from your own experiences Warm Up 27 34 13 52 47 17 26 43 56 79 23 54 76 98 12 76 82 61 54 29 96 56 43 58 73 58 72 44 70 14 26 83 38 46 81 11 59 37 62 51 Guiding principles for all maths lessons 1. 2. 3. 4. Explicit number fluency practice every lesson Explicit purpose for every lesson Formal structure for every lesson Students working on tasks beyond their current levels of thinking (differentiated tasks) 5. Teacher communicating high expectations and using purposeful feedback 6. Established classroom norms for working Skills AND Thinking & Reasoning “ It is important ..….(to) measure students’ ability to apply their mathematics knowledge, rather than simply their ability to remember facts and formulas” (2006 Report from the Parliamentary Inquiry into mathematics & science education Executive Summary Pxv) Skills and Thinking & Reasoning 2¾ - 1⅓ = 247 × 32 = 143 +8 765 3¾ - 1⅓ = 15/4 – 4/3 → 45/12 - 16/12 = 29/12 → 25/12 OR you could think: 2+ (1 ¾ - 1⅓ ) = 2 + (9/12 - 4/12) = 25/12 OR you could think 1⅓ (add 2/3 ) = 2 (add 1 ¾) = 3 ¾ and (2/3 + 1 ¾ = 25/12) X 200+ 40 + 7 247 × 32 30 + 2 BOY +GI RL LOVE OR 7×2 40 × 2 200 × 2 Digits 0-9 7 × 30 40 × 30 200 × 30 Some things to consider: • Planning – school, level, individual • Time allocated to maths • Mix/match of Dimensions in a week • Weighting of skill, thinking and reasoning lessons • Guiding principles: Specific lesson purpose, agreed lesson structure, number fluency, teacher expectations, degree of challenge • Differentiation- Student groupings • Assessment plan • Teacher accountability Whose plan and why? Teacher Daily Lesson Plan Teacher Weekly Plan PLT Fortnightly Plan PLT Term Plan PLT (VELS LEVEL) Annual Plan WHOLE SCHOOL PLAN (Guiding principles, Scope/sequence) Planning Format? • • • • • • Hardcopy Electronic Hyperlinked Share drive Assessment – pre/ ongoing/ post Skills, thinking and reasoning Eight models for a whole school mathematics plan 1. 2. 3. 4. 5. 6. 7. 8. Mathematician’s model Reflective model Graft-on model Replacement unit Menu model Mixed media model Thematic model Concept – Skill – Application model Morning tea yet? Planning Begin with the whole school Level 1 1. 2. 3. 4. 5. .. .. .. .. .. Level 2 Level 3 Eg NUMBER Level 4 Level 5 READY RECKONER – Number LEVEL 1 (Prep) • Number names • Counting on and back to 20 • Symbols for objects • Ordinal number • One-to one correspondence • Form equal groups • Model addition and subtraction with objects LEVEL 2 (Yrs 1/2) • Count on/back to 100 • Ordinal number • Meaning of equal • Skip count by 2,5,10 • ½ and ¼ and 1∕3 • Fact families • Number facts (shortcuts and recall) • Coins • Place value • Simple addition, subtraction, • Repeated addition as multiplication, Sharing as division • Yr 1 /2 INCIDENTAL MATHS • Place (next to, beside, in front of, behind, over and under) • Odd and even numbers • 2D shapes such as triangles, circles, squares • Cycles: day/night and the seasons • Order days, weeks, months and years • Hand claps to measure time • Longer, taller, larger, holds more and heavier • Cold, cool, warm, hot and boiling • Time line for daily activity • Continue patterns • Follow instructions to place shapes and objects in familiar situations LEARNING FOCUS STATEMENTS Level 2 NUMBER Learning focus As students work towards the achievement of Level 2 standards in Number, they learn to use base 10 models (units, longs, flats and cubes) and arrays to identify, order and model the counting numbers up to1000. They create number patterns mentally, by hand and with the use of the constant addition facility of calculators. They use models and arrays to support the development of skip counting up to 100. They recognise patterns created by skip counting (for example, when counting by fours, the pattern of the ones digits is 4, 8, 2, 6, 0, 4, 8). Students perform simple addition (count on) and subtraction (count back) using numbers up to 100. They use equal groups of objects and rectangular arrays to model multiplication and equal sharing for division. Students divide geometric objects including lines, arrays and regular shapes into equal parts to develop the concept of a simple fraction as part of a whole. They learn to order money amounts in dollars and cents, form different totals using dollars and cents, and carry out simple calculations such as change from small amounts. NUMBER At 0.5 PROGRESSION POINTS •associate number names with numerals and models of numbers (counting or subitising) •draw simple symbols in place of objects(eg, B for boy) •order objects and sets (eg largest to smallest) •place a variety of objects in order from first to third •use one-to-one correspondence and numbers 1 to 10 when counting •At Level 1 •form small sets of objects from simple descriptions and make simple correspondences between those sets •count the size of small sets using the numbers 0 to 20 •use one-to-one correspondence to identify when two sets are equal in size and when one set is larger than another •form collections of sets of equal size •use ordinal numbers to describe the position of elements in a set from 1st to 10th •use materials to model addition and subtraction by the aggregation (grouping together) and disaggregation (moving apart) of objects •add/subtract by counting forward and backward using numbers from 0 to 20. •At 1.25 •order lists of small sets of numbers up to 20 •count forwards and backwards by 1 from starting points between 1 and 100 •calculate the next number when asked to add 1 or 2 to any natural number from 0 to 10 •draw diagrams to show sharing of up to 20 items •draw diagrams to show subtraction activities COUNT PLACE VALUE ADDITION AND SUBTRACTION MULTIPLICATION AND DIVISION FRACTIONS MONEY Count by 1 from any number to 100. skip count by 5 and 10 from any number to 100 skip count by 2 from any number to 50 count backwards starting from any number less than 100 read and say numbers to 99 write numerals to 99 correctly order numbers to 99 starting from any number Understands place value to 99 using materials such as bundles of 10 and single sticks perform basic addition of numbers to 20 perform basic subtraction of numbers to 20 solve real or picture problems using addition and subtraction solve basic multiplication equations solve basic division equations Can recognise and show half of a shape, object or group Can read, record and order coins to $2.00 Count by 1, 10 and 100 from any number to 100. skip count by 2, 4 and 5 from any number to 100 recognise and write numbers to 999 order numbers to 999 starting from any number Understands place value to 999 using models such as MAB recall addition and subtraction facts to 20 add 2 digit numbers with regrouping using materials such as MAB subtract 2 digit numbers with regrouping using materials such as MAB create and solve real and picture problems using a single operation Understands the concept of grouping in multiplication Understands the concept of sharing in division create and solve real and picture problems using a single operation recognise and draw simple fractions (1/2, 1/3, 1/4 ) of an object and a group of objects recognise and order money using coins and notes use coins to make various amounts in different ways GRADE3 skip count by 2, 3, 4 and 5 from any number to 100 Understands whole number place value to at least 9 999 count, read, write and order numbers to at least 9 999 recall automatically basic number facts using addition and subtraction Add 2 digit numbers with renaming e.g. 45 + 49 = subtract 2 digit numbers with regrouping e.g. 95 – 48 = recall multiplication and division facts within the 2, 3, 4, 5 and 10 times tables multiply 2 digit numbers by a single digit number e.g. 39 x 4= divide 2 digit numbers by a single digit number e.g. 39 ÷ 4 = solve worded problems using basic written computations read, write, compare and order decimal fractions to 1 decimal place name and compare simple common fractions Can solve simple addition and subtraction problems involving money GRADE 4 skip count by any number from 2 to 10 at least to 100 Understands whole number place value to at least 99 999 count, read, write and order numbers to at least 99 999 recall automatically basic number facts using addition and subtraction Add 2 and 3 digit numbers with renaming e.g. 498 + 524 = subtract 2 and 3 digit numbers with regrouping e.g. 435 – 148 = solve worded problems using a variety of strategies recall multiplication and division facts up to 10 x 10 times tables divide 2 and 3 digit numbers by a 1 digit divisor e.g. 439 ÷ 4= solve worded problems using a variety of strategies read, write, compare and order decimal fractions to 2 decimal places Understands decimal place value to hundredths name simple common fractions and identify equivalent fractions Can do basic calculations with money GRADE5 generate and investigate simple number patterns and sequences count, read, write and order numbers up to 1 000 000 Understands whole number place value up to 1 000 000 Has automatic response of basic addition, subtraction, multiplication and division facts add 3, 4 and 5 digit numbers with renaming eg. 5 498 + 3 524 = subtract 3, 4 and 5 digit numbers with regrouping eg 6 435 – 4 148 = use rounding off and estimation to verify calculations solve word problems involving whole numbers, decimals and fractions Has automatic response of basic addition, subtraction, multiplication and division facts multiply 2 and 3 digit numbers by 1 and 2 digit numbers eg 309 x 43 = divide 3 and 4 digit numbers by 1 digit divisor eg 5 439 ÷ 4= use rounding off and estimation to verify calculations solve number sentences involving a number of operations eg (9 x 8) + (5 x 6) = solve word problems involving whole numbers, decimals and fractions compare and order common fractions and find equivalents of common faction using models count, read, write and order decimal numbers to at least hundredths Understands decimal place value to at least hundredths Understands the relationship between simple common fractions and decimal fractions add and subtract decimal numbers and common fractions with the same denominator solve word problems involving whole numbers, decimals and fractions GRADE 6 Can generate and investigate complex number patterns and sequences Can identify multiples, factors and prime numbers Can count, read, write and order numbers up to 1 000 000 Understands whole number place value up to 1 000 000 Can count, read, write and order decimal numbers to thousandths Understands decimal place value to thousandths Has automatic response of basic addition and subtraction facts Can add 4, 5 and 6 digit numbers with renaming eg. 423,328+ 526,135 = Can subtract 4, 5 and 6 digit numbers with regrouping eg 523,638 – 176,379= Can use rounding off and estimation to verify calculations Can construct, verify and solve number sentences eg (9 x 8) + (5 x □) =200-98 Has automatic response of basic multiplication and division facts Can multiply 4, 5 and 6 digit numbers by 1 and 2 digit numbers eg 309 x 43 = Can divide 4, 5 and 6 digit numbers by 1 digit divisor eg 445 439 ÷ 4 2= Can use rounding off and estimation to verify calculations Can construct, verify and solve number sentences eg (9 x 8) + (5 x □) =200-98 Can compare and order common fractions and find equivalents of common factions Can add and subtract decimal numbers and common fractions with different denominators Can multiply and divide simple common fractions Understands the relationship between common fractions and decimal fractions and percentages Can solve word problems involving whole numbers, decimals and fractions YEAR 7 Shows an understanding of prime numbers, prime factors, powers and square roots Can round off and estimate answers to written computations Uses correct order of operations to solve number sentences Applies reasoning strategies to solve problems Can multiply whole numbers and decimals by 3 digit numbers Can divide decimal numbers and measurements by single digit whole numbers Can round off and estimate answers to written computations Uses an appropriate sequence of operations to sole word problems Uses correct order of operations to solve number sentences Applies reasoning strategies to solve problems Can compare and order common and decimal fractions, percentages and ratios Adds and subtracts decimals with different numbers of decimal places Adds and subtracts common fractions with different denominators Can multiply and divide simple common fractions Finds fractions and percentages of quantities eg. Find 25% of $48 Can solve word problems related to common fractions Applies reasoning strategies to solve problems GRADE PREP GRADE 1 GRADE 2 Year 5 overview Topics Term 1 Term 2 Place value Addition and subtraction Multiplication and division Patterns and structure Equivalence and equations Measurement Data Space Major focus Minor focus Incidental Term 3 Term 4 VELS 2.5 – 4.0 Structure Number patterns **#**#**? 3, 6, 9, ? The equals sign Properties of numbers Odd, even, prime, square, etc + is inverse of – Associative Law (7+3)+ 2 = 7 + (3+2) (a+b)+c= a+(b+c) (2×3)× 5=2 × (3×5) (a×b)× c = a×(b× c) × is inverse of ÷ Distributive law of multiplication 5×(3+4)=(5×3)+(5×4) a×(b+ c)= (a×b)+(a×c) Combining number properties (Shortcuts) Combining number properties (Shortcuts) 24 × 13 = 20 10 3 68 ÷ 4 = (40 ÷ 4) + (28 ÷ 4 ) 4 Venn diagrams Intersection of multiples of 4 & multiples of 6 VELS 3.0 – 5.0 Space Lines Polygons Tessellate vertical, horizontal parallel, curved, perpendicular 2D shapes, names, features, symmetry tangrams Angles Prisms Transformations flip, rotate, measure, supplementary, complementary, internal, corresponding 3D shapes, names, features, faces edges vertices reflect Reduce/Enlarge Nets Maps scale, grids, scale, ratio compass directions, grid references, networks Visualisation orientation Year 7 Space Number Progression Points 4.25 June Yr 7 4.50 Dec Yr 7 DECIMALS, PERCENTAGES, FRACTIONS. (Term 1 wks 1-2) -----------------------------------SPECIAL NUMBERS: primes, composites, factors, multiples, squares & square roots. Estimating √of other numbers. (Term 2 wks 2-3) DIRECTED NUMBER Introduction to directed number (Term 2 wk 9). -----------------------------------POWERS of 10 Division & multiplication by powers of 10, with estimation. Simplifying ratio, 2 : 5 = 1 : 2.5 (Term 3 wk 1) RATIO (Term 3 wks 2-3) Progression Points 4.25 June Yr 7 4.50 Dec Yr 7 CO-ORDINATE GRAPHS (1st quadrant) mapping. (Term 1 wks 3-4) ---------------------------------2D SHAPES, triangles, & angles., quadrilaterals, tessellation, transformations. (Term 2 wks 4-5) ---------------------------------LINES & ANGLES Properties of angles & lines, congruent shapes.(Term 3 wks 4-5) NETS 3D solids, sorting, nets Solids to nets and vice versa for polyhedron & interpolation between labeled co-ordinates (Term 4 wks 5-6). Interpretation of Mathematics VELS & Progression Points Measurement, chance & data Progression Points 4.25 June Yr 7 4.50 Dec Yr 7 PERIMETER, AREA, VOLUME Estimating & measuring perimeter & area of rectangles, basic volume, capacity, temperature (Term 1 wks 5-7) -----------------------------------CHANCE & DATA: probabilities for chance outcomes, simulate chance events, multiple event experiments & calculate and interpret measures of centrality (mean, median, mode) and data spread (range). (Term 2 wks 6-8) -----------------------------------CIRC, AREA, VOLUME Perimeter & area of triangles & parallelograms, area of simple composite shapes. Calculations of time – elapsed and duration. (Term 3 wks 6-7) TIME & SPEED (Term 3 wk 9) CHANCE & DATA:- two event experiments, represent univariate data as stem – leaf, bar charts & histograms. (Term 4 wks 1-2) Structure Progression Points 4.25 June Yr 7 4.50 Dec Yr 7 INTRODUCTION TO ALGEBRA. (Term 1 wks 8-9) (Term 2 wks 1) ------------------------------------BACK TRACKING Introduction to back tracking and inverse operations, Venn Diagrams & Karnaugh maps. (Term 2 wks 10 -11) ------------------------------------LINEAR EQUATIONS & GRAPHING, using table of values & inverse operations. Term 3 wk 8) EQUATIONS & INEQUATIONS Solving inequations, rearrange simple formulas, distributive law. (Term 4 wks 3-4 Working Mathematically Progression Points 4.25 June Yr 7 4.50 Dec Yr 7 Develop generalizations, find patterns, identify relevant variables, use spreadsheets. (all year) Incorporate in a project, explain mathematical relationships by extending patterns. ( all year) . RATIO At SSC we have a different number of students at each year level Yr Level No of students 7 68 8 72 9 76 10 52 11 44 12 50 2 /7 DECIMALS How many ways can you make the calculator show 12.34 without pressing the decimal button? FOLIO CARDS a)Represent this data in ratio form b)Represent the above in simplest ratio form c)Represent each Yr level as a fraction of the total school population 3 /7 4 /7 ESTIMATION MASS In the film ‘Local Hero’ a man says he will pay $1 for every grain of sand he can hold in one hand. a)Estimate how much money he will pay. b)Justify your answer (use text, mathematical calculations and/or diagrams) a) Find three things that are bigger than a potato but lighter. Describe how the items are ‘bigger’ than the potato using mathematical terms (eg width, length, circumference, etc) a)Find two objects that have the same mass but are different sizes. Describe their sizes using mathematical terms (eg perimeter, area, length, etc). b)I weighed an item in the classroom that was between ¾ kg and 1 kg. What might the item have Suggested Year 10 Course Outline Term 1 ( 9 weeks) 2 weeks- Mathematical Structure (Bills, interest, inflation, sets) * activity: Telephone call costs pg8 Heinemann 2 weeks- Surds 2 weeks- Indices * activity: The von Koch snowflake (pg69 Heinemann) Dry Cleaning VELS task (pg79) 1 week- Scientific Notation and Exponential relationships. 2 weeks- Expanding in Algebra * activity: Proving Generalisations (pg 114) The Firefighter’s Ladder (pg 115) Term 2 ( 11 weeks) 2 weeks- Factorisation in Algebra 3 weeks- Measurement (Time and time zones, Perimeter, Area, TSA, Volume Density and Capacity) *activity: Pizza Prices (pg 175) Project (Design your own Can) 2 weeks- Linear Equations *activity: Lost in the desert (pg 232),CAS investigation (pg240) 2 weeks- Simultaneous Equations and Inequations *activity: The tourist railway (pg 265) 2 weeks- Year 10’s on work experience. Term 3 (10 weeks) STAGES OF LEARNING “Building Breadth and Depth” 5-8. In these years students progress beyond the foundations and their literacy and numeracy becomes more developed. An expanded curriculum program provides the basis for in depth learning within all domains in the strand. LEVEL 4 PROGRESSION POINTS & STANDARDS 3.25 ½ way Grade 5 LEARNING FOCUS Students extend their understanding of whole numbers, fractions and decimals. They use patterns and arrays to develop understanding of multiples (including lowest common multiple), factors (including highest common factor), prime and composite numbers. They recognise and use simple powers (for example, 23 = 8). Students investigate and use equivalent forms of common fractions. They order fractions and decimals and locate them on a number line. They investigate temperature and other contexts to develop the concept of negative numbers. They explore ideas of ratio (as a comparison) and percentage (comparing to 3.5 End demonstrate understanding of whole numbers up to millions and decimals to hundredths using models, including number lines estimate the results of whole number or decimal calculations mentally by using near whole numbers and known facts such as 3.1 x 8 is about 3 x 8 = 24 multiply a whole number by a single digit divide a whole number by a single digit, expressing remainder as a whole number or fraction in context, such as decimal remainder for many metres each use brackets to show order of operations in simple cases, such as calculate (3 + 4) x 5 = 35 understand subtraction as both “take away” and “difference between” choose multiplication or division rather than repeated addition or subtraction, such as finding how many 20ml doses in a 300ml bottle of medicine by division find equivalent fractions, multiples and fractions of fractions, such as twice one sixth or half of one third perform simple addition and subtraction with fractions using fraction models, including linear models. use physical models and number lines to compare, rename and identify decimals, such as 3.2 is 32 tenths. create and describe patterns using calculators, including sets of multiples and squares TEACHING & LEARNING TOOLS & STRATEGIES ASSESSMENT TOOLS / TASKS / EVIDENCE Week 1 Monday Tuesday Warm up How many more to 10? Count on Launch Focus: Model +, - with material Activity: Big Book ‘Ten in the Bed’ Focus: Begin with larger number for addition Activity: Which number is bigger? 100 chart, objects Explore Use 10 frame and 2 different coloured counters to make 10 (6 + 4 =10) Order number pairs Use a mirror to check 3+4=4+3 Use 10 frame and one set of counters to calculate what’s been taken away (10- 3 =7) Use counters to create addition algorithms 7 + 4 =11 13 = 2 + 4 + 5 + 2 Card game in pairs, biggest number wins the pair of cards Place a straw between counters to prove 7=3+4 7=4+3 Use your own 100 chart and count on from the bigger number 4 + 23 7 + 15 Use counters to create subtraction algorithms 14 – 3 = 11 Write your own algorithms that use 2 diff numbers, the bigger first and total > 20 Create related +,- algorithms 7+ 4 = 11 4+ 7 = 11 11 – 4 = 7 11 -7 = 4 Summarise Share in groups One highlight per group Add a fact to the fact wall Tch highlight few MATHEMATICS / UNIT PLANNER–VELS Level 4 Term 2 Year 2007 Year Level 5 Dimension – Number Focus: Decimals Standards: * Comprehend the size and order of small numbers (to thousandths). * Model decimals. * Place integers, decimals and common fractions on a number line. •Use decimals, ratios and percentages to find equivalent representations of common fractions (for example, 3/4 = 9/12 = 0.75 = 75% = 3 * Add, subtract, and multiply decimals (2 decimal places) and apply these operations in practical contexts, including the use of money. * Use estimates for computations and apply criteria Vocabulary: average, calculate, decimals, decimal point, decade, estimate, fractions, hundredths, nought, numeral, ones, percentages, Pre- Assess tasks DEECD Fractions & Decimals Interview Qs XXX - XXXXX Activity one Use placevalue knowledge to read, write and order negative whole numbers and decimal numbers from thousandths Measuring heights Students measure and record each other’s height in decimal form then order the measurements from shortest to tallest. Do this the first day of each month throughout the year noting growth. Materials required : Tape measures Activity: In pairs, measure and record each other’s height. Record measurements in decimal form (1.34 m). When completed, the class orders the heights from shortest to tallest. Extension: XXXXXXXXXXXXX Assessment Ask chn the difference in height between themselves and another child. Eg1.34 m and 1.56m MATHS TERM PLANNER GRADE 5 AND 6 TOPIC NUMBER Recognise and use simple powers Devise and use mental and written methods to add and subtract decimals MISCONCEPTIONS List some of these as key points ASSESSMENT Diagnostic: (Should include aspects of the Indicators of Progress) EXPLICIT LEARNING GOALS INDICATORS OF PROGRESS & DEVELOPMENTAL OVERVIEWS Formative: Summative: VOCABULARY TEACHING APPROACHES Modelled Maths Lessons Shared Maths Lessons Guided Maths Lessons LEARNING ACTIVITIES 1. 2. 3. ASSESSMENT & REFLECTION RESOURCES & LINKS Whole School Assessment Plan VELS Level 1 Level 2 Level 3 Level 4 Term 1 Term 2 Term 3 Term 4