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Naplan numeracy prep_bright_ideas

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Naplan numeracy prep_bright_ideas

1. 1. 2010 NAPLAN Numeracy Preparation and Bright Ideas National Assessment Program Literacy and Numeracyhttp://www.det.nt.gov.au/teachers-educators/assessment-reporting 1
2. 2. ContentsPreparing the students Key Actions 3 Interpret and unpack the language of the test questions 4 ESL support strategies 4 Strategies for answering the test questions 5 Plan of attack 5 Test instruction icons 5 Multiple choice questions 5 Short answer and calculator questions 6 Polya’s 4 step plan 7 Problem solving strategies 7 Finding out where and why students make mistakes 9 Newman’s error analysis 9 Critical questions 9Using the test and practice questions Classroom games and activities 10 Topic areas 12 Hand on learning activities 13Curriculum Ideas Work station activities 17 Number and Algebra 17 Chance and Data 18 Measurement 19 Space 20 Open-ended questions 21 Stem and leaf plots 22 Websites 23Appendix 1 – Chance Cards for the Probability Continuum 24For further information please contactEllen Herden Gay WestManager Assessment and Reporting Project Manager Numeracy AssessmentPhone: 8999 3784 Phone: 8999 3778Email: ellen.herden@nt.gov.au Email: gabrielle.west@nt.gov.auFax: 8999 4200 Fax: 8999 4200 2
7. 7. Polya’s 4 step plan To become a good problem solver, students need to have a plan or method that is easy to follow to determine what needs to be solved. The key is to have a plan which works in any mathematical problem solving situation. Polya’s 4 step plan is a useful starting point to help students develop a ‘plan of attack’ in problem solving. This will set them on the trail to develop their own successful problem solving technique. Once students find a problem solving method that suits them, they can use it in other curriculum areas and in real life problems that they encounter. Polyas four steps to problem solving 1. Understand the Calmly examine all the information in the problem. __problem Decide what information is important and what seems unimportant. Would a FIGURE or DIAGRAM help? Write down or underline all relevant information. 2. Devising a plan Have I seen a similar problem? Can I solve part of the problem? Could I organize the data into a table? Could I find a pattern? [See problem solving strategies below] 3. Carrying out the ---- Can I follow through each step of the plan? -plan Is each step correct? Can I prove it is correct? 4. Looking back Can I check the result? Does the answer make sense? Is there another way I could solve the problem? Could I use the results in a problem I have seen before? From: Polya, G. (1973) How To Solve It Princeton University Press: USA Previous years NAPLAN tests and the other practice test questions on the DET website provide teachers with useful vehicles to model problem solving using the plan outlined above. Many problems can be solved in more than one way and using a variety of problem solving strategies. Problem solving strategiesA critical skill or essential learning for working mathematically, is to be able to solve problems.Teachers need to explicitly teach the steps involved in the problem solving process:• reading or looking carefully at a problem• following a plan to analyse what is required• choosing which strategy, or strategies in combination, will help you solve the problem• checking back to see if the answer is the one required and• finally reflecting on the problem and seeing if it leads to other questions or possibilities. This last stage of the process, the ‘looking back’, may be the most important step as it provides students with an opportunity to learn from the problem.Becoming a successful problem solver is embedded in the Constructive learner and theCreative learner domains of the EsseNTial Learnings:• A Constructive learner – learns mathematics in ways that makes him or her Numerate, i.e. able to apply their mathematical knowledge appropriately in real life.• A Creative Learner – is a creative, strategic and effective problem solver. 7
11. 11. ‘Around the World’Play this game using ideas from the NAPLAN questions. • Students sit in a large circle. • One person stands behind someone in the circle. • Teacher or designated student calls out a question. • If the person standing up correctly answers first, he or she moves to stand behind the next person in the circle. The goal is to work their way around the circle. • If the person sitting down calls out the correct answer first then he or she stands up, while the person who was standing sits in their place. • Then the process begins again. Who can travel right around the entire circle (world)? • Ideas for the questions can come from the 2008 and 2009 NAPLAN test questions and practice questions on the website or real objects around the classroom such as: - large class clock or calendar - numbers and sizes of windows, doors, and chairs. - 4 big dice or 6 apples or 10 teddies etc. - a variety of containers and packages - a selection of 2D shapes and 3D objects. • Some examples of the types of questions are: Number and Algebra - There are 6 apples, I eat 2, how many are left? - How many groups of 2 teddies can I make? - Add up the numbers on the top of each dice. - Multiply the numbers on the top of each dice. - What is the next term in the number pattern shown on the dice? Space - Look at the 3D shapes, which shape has the most edges? - Name a 2D shape with 6 sides. Measurement - Look up at the clock, what was the time 2 hours ago? - The calendar on the wall shows _______ (month) - What date is the second Sunday? - Next month will start on which day of the week? - What date is 2 weeks from today? - What container would hold the least amount of water? - Which container holds closest to 2 litres? - How tall is the door, to the nearest metre? - Find something in the classroom that is taller than the desk but shorter than the door. • Questions involving times tables, multiplication, division, addition, subtraction and any other standard mental maths skills are suitable. • Another strategy is to ask the students (in pairs) to create their own questions about particular topics e.g. time questions about the class calendar or the clock. Students could be rostered on for ‘Make-up NAPLAN Questions’ sessions. http://www.det.nt.gov.au/teachers-educators/assessment-reporting/nap 11
12. 12. Topic areas Individual practice questions can be separated and sorted into groups and used for review and assessment of units of work. • There are a variety of practice test questions (2004-2009) and the 2008 and 2009 NAPLAN test questions on the website to use for this activity. • Photocopy the questions onto coloured paper or card. Each band or year level can be a different colour for quick visual recognition e.g. Band 1 – green, Band 2 – blue etc. • Down load the test papers and cut up into individual questions (laminate if possible) and group them into sections like: Number and Algebra - Patterning - Money - Fractions - Operations - Equations Measurement - Length - Area - Time - Volume/capacity Chance and Data - Graphs/tables - Probability - Statistics Space - Shapes/angles - Mapping and co-ordinates. • Use questions for quiz time during and after a unit of work on these topics. • Write the answers on the back and the children can quiz each other e.g. the student who gets the correct answer can pick up the next card and ask the question. • The question cards can be left in a box or tray for students to work on individually or in small groups. • They can be used as a workstation activity for rotating maths or ‘hot potato’ sessions. • Provide students with questions that cover a range of Bands or year levels so they can find their own level of ability for a topic. Independent Time or ‘All-by-Myself-Time’ • Schedule regular times during the week when it is ‘All by myself time’ or ‘Independent Work Time’. During this period, the students must attempt a numeracy (or literacy) task without help from the teacher or their peers. Use an egg timer or stop watch and increase the period of time gradually. • This becomes an excellent Assessment as Learning opportunity as students reflect on their strengths and weaknesses. http://www.det.nt.gov.au/teachers-educators/assessment-reporting/nap 12
13. 13. Hands on learning activitiesThe following activities enable richer concept development using 2008/2009 NAPLANtest questions or practice questions as a springboard to hands-on learning activities. Patterns• Make patterns with tiles, like building a stair case.• Count the tiles and determine how many are needed for the next row, make different patterns e.g. go up 2 each time.• Create KGP 3 questions like: Draw the next line of tiles in the pattern. Numbers to 10 and numbers to 20• Use counters (a bundle of 10 or 20) and divide them into two different groups, each time record the numbers that add up to the total, e.g. separate 8 and 2 counters and record, 8 and 2 make 10 or 8 + 2 = 10, work through all the combinations.• Use blank ten frames and dice e.g. roll a 4, colour in 4 squares, use a different colour for the other 6 squares to represent the numbers that make up 10.• Use a number strip/line to 20 and put two different lots of coloured counters on the strip to represent different ways for two numbers to make 20, find all the combinations and record them.• Use counters to find the combinations of other numbers e.g. 15, 18, etc.• Create open KGP 3 tasks like: If 10 and 3 make 13 then show me another way to make 13 by writing different numbers in the spaces: ___ and ___ make 13. Grids/references• Use blank grids and draw treasure in one square/cell, follow directions to get to the treasure.• Use blank grids and write the numbers and letters down each side, place a counter in one square/cell and talk about the reference and position of that square/cell.• Create Band 1 questions like: Start at X which is in C3, move two spaces left, next go two spaces down, now go one space to the right, put a tick in this box. What is the new grid reference? Ordering• Roll two or three dice to make a 2 or 3 digit number, make four different numbers and then put the numbers in order from smallest to largest.• Use 2 digit numbers to start with and create Band 1 tasks like: Write these numbers in order from smallest to largest. 638, 386, 863, 683. ________ ________ ________ ________ Smallest Largest Place these numbers on a number line and find the difference between them. http://www.det.nt.gov.au/teachers-educators/assessment-reporting/nap 13
14. 14. Number Patterns, Sequencing and Algebra• Use the 100 grid and create/colour in number sequences/patterns.• Practise whisper or skip counting, emphasise specific numbers and whisper all other numbers, count backwards as well as forwards 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 . . .• Use coloured counters to emphasis patterns.• Start with tally marks or bundles of sticks to count in fives.• Create Band 1 to Band 4 tasks as follows: Band 1 Write the next number in this sequence 15, 20, 25, 30, Band 2 Write the next number in this sequence 9, 8.5, 8, 7.5, Band 3 Write the next number in this sequence 400 000, 8 000, 160, Band 4 Write the next number in this sequence 1.5, 1.0, 0.5, 0, – 0.5,• Make a pattern of triangles with paddle pop sticks. Count the number of triangles and the number of paddle pop sticks needed. Discuss the pattern and create Band 1 questions like There is a pattern in the way these triangles are made. How many sticks would you need to make the next triangle?• Make a list of values – number of triangles with number of paddle pop sticks.• Create Band 3 questions like s=2t+1 Fill in the missing values. How many sticks are needed to make 10 triangles, . . . . . 100 triangles?• Create Band 4 questions like Which rule describes how many sticks s are needed for t triangles? Brackets and Order of Operations• Use small cards with brackets, equals and algorithm signs such as ( ) = + – x ÷ < > 2 and digit cards from 0 to 9 to create a variety of equations. Review the BODMAS rules: B Brackets first O Orders (i.e. Powers, exponents, indices and square roots, etc.) DM Division and Multiplication (left to right) AS Addition and Subtraction (left to right)• Show how equations with the same numbers can have different answers: 2 + 5 x 3 = 17 (2 + 5) x 3 = 21 30 ÷ 5 x 3 = 18 30 ÷ (5 x 3) = 2 5 x 2 2 = 20 (5 x 2) 2 = 100 http://www.det.nt.gov.au/teachers-educators/assessment-reporting/nap 14
15. 15. Calendars• Use a current calendar to read dates and days regularly.• Students draw the current month from scratch, without looking at the calendar or use a blank calendar and fill it in.• Teacher asks questions like Band 1 What is the name of this month? How many days in a week? How many days/ weeks in this month? Band 2 Write the date of the second Tuesday in May. Write the date that is 2 weeks after this date. The month is _ _ _ _ _ _ _ _ _ _ _ _ _ Use horizontal Monday and vertical Tuesday calendars Wednesday Thursday Friday Saturday Sunday 2D Shape Patterns• Cut out a 2D shape and trace around it, move it, trace around it again and make a continuous pattern.• Cut out several copies of the one shape and stick them onto paper to make a pattern.• Trace or stick the shape in different ways in a continuous pattern, by flipping it, sliding it, or turning it.• Talk about the language of flipping, sliding, or turning the shape and how the shape looks the same or different. Use the words reflect, translate and rotate for older students.• Create activities like Band 2 Redraw the shape below to show that it has been flipped to the right. Band 3 Rotate this shape by 180 degrees. 3D Objects – nets and cross sections• Draw a net of a 3D shape, cut it out, fold it to see if it works.• Draw a variety of nets and see if your buddy can work out what 3D object it is.• Make as many different nets of a cube as possible – there are 11, can you find them all?• Make some 3D objects with plasticine or play dough. Use fishing line to cut through the objects and make as many different cross sectional shapes as possible. These shapes can be used to make interesting patterns and designs. http://www.det.nt.gov.au/teachers-educators/assessment-reporting/nap 15
16. 16. Money• Make different combinations of an amount of money, say \$3.85 or \$42.• Talk about how many different ways you can make these amounts.• Use real or play money to add and take away amounts.• Use real or play money to work out change from \$2, \$5, \$10, \$20 etc.• Make use of junk mail e.g. calculate the cost of a loaf of bread, a carton of milk and a dozen eggs, then work out the change from \$10 (\$20 or \$50).• Role play shopping to practice counting out amounts of money, adding and subtracting amounts, and giving change out from \$10, \$20 or \$50.• Create questions and tasks such as Band 1 What is the total value of these coins? Band 2 Show two different ways of making \$4.25. The cost of a CD was \$15.85. What was the change from \$20?• Using money to help with the understanding of percentage – interest, discounts and price increases. Junk mail and advertisements are useful for these activities.• Partitioning amounts of money into percentage parts with questions like Band 4 What is \$10 as a percentage of \$40? A skate board is normally \$85. Work out the new price after a discount of 20%. Spinners• Talk and ask questions about the chance of events occurring What number are we most likely/least likely to spin up? Why? Why not?• Make an easy spinner (a sharp pencil held vertically with its point in the centre of the spinner surface, flick a paper clip around the lead end).• Make spinners with coloured parts of the circle e.g. ½ red, ¼ blue, 1/8 yellow, and 1/8 green. Discuss what could happen, where the spinner might land and how often. What colour/number are we most likely/least likely to spin? Why? Why not?• Record outcomes of spins using tally marks, graph results and create questions like Band 2 Write the number that is most likely to come up on this spinner. Band 4 What is the chance that the spinner will land on …? Chance and Data• Use a variety of different objects e.g. cards, stickers, stamps, marbles, to set up groups in bags and containers. Work out the probability of selecting items from these sets.• Use the probability cards in Appendix 1 to teach the specific language of chance.• Place 12 counters in a sock or bag – 3 different colours. Next shake the sock and take a counter out without looking. The pupils tally the colour and the counter is replaced in the sock. Continue sampling the counters until you have a representative/fair sample. Pupils are told there are 12 counters in the sock, from that and the results, they have to estimate how many of each colour there are. http://www.det.nt.gov.au/teachers-educators/assessment-reporting/nap 16