What we teach and how we teach it Mathematics K-6 What we teach and how we teach it sally

Welcome Who we are: Sally Kelly - Assistant Principal Kindergarten Jann Donohue - Assistant Principal Year 2 Jodie Watson - Assistant Principal OC sally

Welcome Aims for today: Understanding of what is taught K-6 (with a focus on the number strand) Understanding of how we teach K-6 and how it has changed Give practical ways you can help your child at home sally

Syllabus Overview K-10 continuum Strands Substrands Working Mathematically: Communicating Problem Solving Reasoning Understanding Fluency jodie

Working Mathematically Communicating: Use a variety of forms to show their mathematical ideas including written, oral and graphical Problem Solving: Make choices about strategies, interpret information, model and investigate and verify answers are reasonable Reasoning: Using logical thought and actions, analyse, prove, evaluate, explain, justify, transfer learning to different contexts jodie

Working Mathematically Understanding: Build a strong foundation, understand the ‘why’ and ‘how’ of mathematics, make connections, compare and interpret information Fluency: Calculate efficiently, choose appropriate methods, recall definitions and facts, manipulate data to find solutions

Stage Statements, Outcomes and Content Early Stage 1: Kindergarten Stage 1: Year 1 and 2 Stage 2: Year 3 and 4 Stage 3: Year 5 and 6 Continuums - different instruction for different needs “The syllabus is written with the flexibility to enable students to work at different stages in different strands. For example, students could be working on Stage 4 content in the Number and Algebra strand while working on Stage 3 content in the Measurement and Geometry strand” jann

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Key Ideas Understanding is the key - students need to be able to use mental strategies and not just learn things by rote. Students need to be aware that there can be more than one way to answer a question. Opportunities at home to improve numeracy skills include budgeting, shopping, reading timetables, handling money and cooking to work out quantities. Do not do the work for them, they need to develop skills. Pinpoint the problem, ask them which strategy they would use. Learn and practise times tables; so much of stage 2 and 3 maths relies on students having fast and accurate recall. Stay positive and contact your child’s teacher when you have concerns.

How we Teach: Working mathematically Group work Flexible grouping Differentiation Why as well as how Jann

K - 2 Sally

How we teach it in the classroom Focus in on mental strategies

How we teach it in the classroom

Differentiation Emergent Counting Cannot count visible items Does not know number words Perceptual Counting Counts items using concrete materials Counts visible items to find the total Objects remain in view while counting ?Figurative Counting Visualises concealed items and counts from 1. May use fingers if concealed items are greater than 10.

Differentiation cont... Figurative Counting Visualises concealed items and counts from 1. May use fingers if concealed items are greater than 10. Counting On and Back A number takes place of a completed count e.g. 6 + 5 ; 6 and 7,8,9,10,11. Fingers may be used when counting on. When students reach the counting on and back phase they can now ?begin to work on and understand place value.

Differentiation cont... Facile Strategies Uses known facts, number structure and other non counting by ones strategies to solve number problems. E.g. Bridging to 10, 'friends of 10 and 20', compensation, doubles and near doubles, split, jump etc.

Examples of classroom games that teach mental strategies:

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Mental strategies for addition and subtraction Jump Strategy - Split Strategy - Compensation Strategy - 63 + 29; 63 + 30 = 93; subtract 1 to obtain 92 Bridging the decade - 34 + 17; 34 + 10 is 44; 44 + 7 = 51 Using patterns to extend number facts - 5 – 2 = 3; so 500 – 200 = 300

Using cards at home to help your child: Headache: Another fun game to play with your family to develop student's understanding of number and the relationship between addition and subtraction. 21: Turn two cards and add together, how many more to make 21? Change the total and the number of cards turned to make harder, or use two cards to make one 2-digit number e.g. turn over a 4, 6, 8, 6 and turn into 46 and 86.

How can I help my child at home? Look for opportunities in everyday life: Play games with cards such as 21. Play dice games using number die as well as dot die. Start asking your child to think about ways to count faster e.g. counting on, counting by 2’s, counting by 5’s. Ask addition and subtraction questions e.g. Set the table for one person and ask your child to put out enough plates for everyone. Ask them how many more were needed. Ask your child to help you work out how many more items are needed when you are shopping. "I have six apples here, how many more will I get to make 10?"

Stage 2 Stage Statement - by the end of the stage students ask questions and use efficient mental and written strategies with increased fluency to solve problems. Count, read and order numbers up to five digits Use informal and formal written and mental strategies to solve addition and subtraction problems Use mental strategies to recall multiplication facts up to 10 x 10 and related division facts Use informal written strategies for multiplication and division of two-digit numbers by one-digit numbers Represent, model and compare commonly used fractions and model, compare and represent decimals of up to two decimal places Perform simple calculations with money and solve simple purchasing problems Record , describe and complete number patterns and determine missing numbers in number sentences Estimate, measure, compare, convert and record length, area, volume, capacity and mass using informal units Read and record time in hours and minutes,convert between units of time and solve simple problems involving the duration of time Name, describe and sketch particular three-dimensional objects and two-dimensional shapes Compare angles using informal means and classify them according to their size Use a grid reference system and make simple calculations using scales on maps and plans Collect and organise data and create and interpret tables and picture and column graphs

How we teach it in the classroom Continue with strategies used in ES1 and Stage 1 - guided, modelled and independent Incorporate formal algorithm Continue to use concrete materials and give opportunities to have hands on experiences Focus on using mental strategies There is a big emphasis on language in all strands of maths

Differentiation This includes grouping to suit various levels Grouping allows for flexibility and the grouping is fluid, allowing for movement Games and discussions - how did you get the answer? Think why and question - is there another way to get the answer? We might choose 3 or 4 children to share how they arrived at the answer.

Classroom Activities Games - dice game Mabble - a maths game which is like Scrabble but it uses the four operations: addition, subtraction, multiplication and division. Points are awarded when the totals of the digits are added. There are points awarded for the actual algorithm. Addition, subtraction, multiplication and division receive 1, 2, 3 or 4 points respectively. The winner is the person with the most points.

How to help at home Playing shop Kitchen scales - estimate then weigh items Have dice at home Use pegs, cutlery, beads and other items to create patterns Put a wall measuring chart up and measure family members; plot heights and update from time to time Look at and say numbers in the environment Use different numbers as a starting point for counting - count forward or backwards from this number. Increase difficulty as child gains proficiency; count forward and backwards off the decade and in hundreds Cut fruit, pizza and similar foods into pieces and name the fraction Look at calendars - count down days to a special event When you are watching sport - discuss how the score is tallied. How long does the game go for? Is it divided into halves, quarters or is there another way it is measured Map the weather - keep a log of the week’s temperatures. Older children could keep a log of a month’s temperatures and work out the average. Look and see what time the sun rises and falls over a period of time so that they are gaining an understanding of the length of a day during the different seasons Look at recipes: discuss the use of fractions, millilitres and grams in cooking Discuss how you would double a recipe Collect Coles and Woolies catalogues - there is a lot of maths that can be derived from these Calculate change when you are shopping

Stage 3 Stage Statement Mental, written and calculator strategies for the four operations Big focus on fractions, decimals and percentages Order of operations Number patterns, prime and composite, square and triangular Four quadrants of the Cartesian plane 24 hour time, capacity, volume, converting between measurements Timezones and elapsed time Grid-reference system for maps and directional language Collect, analyse data Probability and simple chance experiments

How do we teach it in the classroom Differentiated Direct instruction for new concepts and skills Move to open ended, problem-solving contexts More formal recording/ setting out Proof and evidence Flexibility in thinking - examining more than one solution Preparation for high school mathematics

How do we teach it in the classroom WHAT'S THE PROBLEM? ‘The answer to a problem is one and a half, what might the question be?’ Description of activity Students respond to a scenario and record a variety of responses. The teacher poses the question: Students record a variety of questions, including word problems, number sentences and questions that involve more than one operation. They include the four operations in their questions.

How did you go? Grade A: https://syllabus.bostes.nsw.edu.au/assets/global/files/maths-mid-stage-3-whats-the-problem-grade- a-rania.pdf Grade B: https://syllabus.bostes.nsw.edu.au/assets/global/files/maths-end-stage-3-whats-the-problem-grade- b-ricky.pdf Grade C: https://syllabus.bostes.nsw.edu.au/assets/global/files/maths-end-stage-3-whats-the-problem-grade- c-ariel.pdf

How can I help my child at home? Explore and discuss maths in a real world context: Sports scores/ statistics Weather maps/ temperatures/ forecasts (BOM website) Cooking and recipes Shopping and catalogues Travel timetables - train, plane, bus etc Money - bank statements, bills, budgets Newspapers - statistics, number puzzles, percentages in context

Beyond Stage 3 This pentagon has three equal sides at the top and two equal sides at the bottom. Three of the angles have a measure of 130°. Figure out the measure of the angles marked x and explain your reasoning. Diagram is not accurately drawn.

Beyond Stage 3 Working with advanced Geometrical Definitions and Properties

Useful Websites: https://syllabus.bostes.nsw.edu.au/mathematics/ http://www.schoolatoz.nsw.edu.au/