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# Primary Maths resource Abacus Evolve Challenge for Gifted and more able pupils

## on Mar 18, 2010

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Take a look at our free Abacus Evolve Challenge Sample Booklet for you to try before you buy! This booklet is aimed to give you a taster of Abacus Evolve Challenge, which is perfect for stretching ...

Take a look at our free Abacus Evolve Challenge Sample Booklet for you to try before you buy! This booklet is aimed to give you a taster of Abacus Evolve Challenge, which is perfect for stretching your gifted and more able Primary Maths pupils.

This sample booklet contains one activity from each of years 1-6, and the supporting page from the Teacher Guide. The Teacher Guide page includes a summary of the unit, the Abacus Evolve objectives, the Primary Maths Framework objectives, teacher notes and guidance on common errors and misconceptions.

Topics covered in the sample booklet include:
Year 1: Names and features of familiar 2D shapes, subtracting a 1-digit number from a ‘teens’ number
Year 2: Sorting and describing 2D shapes, line symmetry
Year 3: Comparing and Partitioning 3 digit numbers, counting on and back in 100s
Year 4: Whole numbers to 10 000, dividing whole numbers
Year 5: Multiplication, doubling and halving
Year 6: Odd and even numbers, classifying quadrilaterals

To find out more, or order your free demo CD, simply visit us at www.pearsonschools.co.uk/aechallenge

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## Primary Maths resource Abacus Evolve Challenge for Gifted and more able pupilsDocument Transcript

• Sample booklet Challenge Framework Edition
• Subtraction Money banks D1 Jane Tom Isaac Jane has 10p in her Tom has 1p less than Isaac has 1p less money bank. Jane. than Tom. Draw lines to join each child to their money bank. Each child had 10p to start with. How much money has each child spent? Jane has spent p Who has spent the most? Tom has spent p Who has spent the least? Isaac has spent p Tell a story to a friend that explains what the children spent their money on. 3
• D1: sorting and describing 2D shapes; line symmetry; counting Challenge Plan: Year 2 back in 1s, not crossing a ten; counting back in 1s, crossing a ten Summary Y2 D1.2 What’s missing? Individuals or pairs working independently Year 2 Challenge Textbook page 5 Paper; scissors; mirror card Abacus Evolve objectives Framework objectives • Begin to recognise line symmetry • Identify reflective symmetry in patterns and 2D shapes and draw • Make symmetrical patterns by folding and cutting lines of symmetry in shapes • Begin to sketch the reflection of a simple shape in a mirror line • Describe patterns and relationships involving numbers or shapes, make predictions and test these with examples • Listen to others in class, ask relevant questions and follow instructions Teacher notes Preparation Further extension Cut up some mirror card so you have one piece per pair. Ask children to work in pairs. They sit opposite each other with a piece of paper between them. Set up a barrier (such as a big book or a game Getting started board) between the children, so that the barrier divides the piece of Show Textbook page 5. Explain that the shapes are all symmetrical, but paper in two. Explain to children that they are going to pretend that the they have been cut in half by mistake. Make sure children understand barrier is a mirror. One child draws a shape on their side of the paper what this means. How could you find out what is missing? and as they are drawing it they describe it to their partner. The second child has to follow the instructions, reversing them in their head, in Activity order to draw the reflection of the shape. This is difficult, but fun and Children work from Textbook page 5. Each child copies the half intended to draw attention to the process of reflection. Children can pictures, and then tries to complete them. They compare their pictures check their images with a piece of mirror card when finished. with a partner, and talk about what methods they used. They check their pictures by holding a piece of mirror card along the line of If you have time symmetry. Give children a digital camera and ask them to take some photos of symmetrical objects. Print the pictures and then cut them in half. Extra help Children give one half to a partner to complete, then check by sticking Photocopy the Textbook page so that children can complete the the picture back together. pictures, without having to copy them first. Be aware Outcomes • Deciding on the line of symmetry is important and children need • I can recognise line symmetry. to realise that this has been pre-determined by where the pictures • I can make symmetrical patterns by folding and cutting. have been cut. Supporting resources Children can look at patterns and symmetry in car wheels in ‘Watch those wheels’: • http://nrich.maths.org/public/viewer.php?obj_id=2815 4 www.pearsonschools.co.uk/abacusevolve
• Shape What’s missing? D1 These pictures are symmetrical. Half of each picture has been cut off by mistake! Copy the pictures and draw the missing half. 1 2 3 4 Fold a piece of paper in half. Draw half a picture on one side. Give the piece of paper to your partner. They complete the drawing. How can you check that they have drawn it correctly? 5
• A1: comparing 3-digit numbers; partitioning 3-digit numbers; Challenge Plan: Year 3 counting objects by grouping; counting on and back in 100s Summary Y3 A1.1 Growing on trees Individuals, pairs or groups working independently Year 3 Challenge Textbook page 7 Year 3 Challenge PCMs 1 and 2 Timer Abacus Evolve objectives Framework objectives • Read and write numbers up to 1000 in figures and words • Read, write and order whole numbers to at least 1000 and position • Count on in 5s to 100, and in 50s to 1000 them on a number line; count on from and back to zero in single- • Add and subtract a multiple of 10 to and from a 3-digit number, digit steps or multiples of 10 crossing 100 • Add or subtract mentally combinations of one-digit and two-digit • Add and subtract a multiple of 100 to and from a 4-digit number, numbers crossing 1000 • Identify patterns and relationships involving numbers or shapes, • Extend understanding that subtraction is the inverse of addition and use these to solve problems Teacher notes Preparation If you have time Photocopy PCMs 1 and 2, one copy of each per child. Children will find it useful to discuss their patterns. Often children will have different insights that combine to give all of them a better picture. Getting started Check that children understand how the code-hexagon below the tree informs them what number to write in each space. Activity Children work from Textbook page 7 and record their answers on PCMs 1 and 2. They use two rules to fill in the numbers in a tree- shaped arrangement of hexagons, and then go back and find the missing four rules. Ask the group to start the puzzle at the same time, starting a timer as they do so. As each child finishes, they write their time, to the nearest half minute, in the star at the top of the tree. Children then compare their trees. They should notice how the patterns work in all six directions, and recognise that inverse rules apply for opposite directions. They should also notice that hexagons to the left or right of each other are affected by a combination of the rules. Children then complete a second tree, before going on to make up their own rules for two more trees. Be aware Outcomes • Children may be unfamiliar with the idea behind the code-hexagon • I can explore and record patterns in numbers. to represent changes in all directions. If necessary, go through • I can recognise general patterns when adding and subtracting. question 1 together. 6 www.pearsonschools.co.uk/abacusevolve
• Counting Growing on trees A1 Here is a tree of numbers. 1000 The larger numbers are at the base and the smallest number is at the top. The hexagon below the tree shows the rule for changing the numbers as you move in different directions. We have been given the rules for moves in two directions. We can use these to complete the tree. We can then complete the hexagon to show the rules for + 100 + 500 all six directions. 1 Complete the first tree on PCM 1. Time how long it takes you and write your time, to the nearest half minute, in the star on top of your tree. Does everyone’s tree look the same? 2 Complete the next tree on PCM 1. It has different rules! 3 Complete the two trees on PCM 2. Make up your own rules for these trees. What rules did other people in the group make up? Copy this diamond pattern onto squared paper. Write 1 in the bottom box. Complete the diamond. What do you notice about ≠2 ≠5 the patterns of numbers? If you start with another small number, such as 4, what patterns result? 7
• Year 3 Block A1 • Challenge PCM 1 Abacus Evolve Year 3 Challenge PCM © Pearson Education Ltd 2009 Growing on trees 1 1 1000 1000 1100 1100 1500 1500 2 1000 �50 1000 �250 �50 �250 116 www.pearsonschools.co.uk/abacusevolve
• Year 3 Block A1 • Challenge PCM 2 Abacus Evolve Year 3 Challenge PCM © Pearson Education Ltd 2009 Growing on trees 2 3 1000 1000 0 0 117
• A1: whole numbers to 10 000; partitioning into Th, H, T and U; Challenge Plan: Year 4 multiplication as repeated addition; dividing whole numbers Summary Y4 A1.4 Triple multiplying Pairs or groups working independently Year 4 Challenge Textbook page 11 Number cards 1–10; calculators (optional) Abacus Evolve objectives Framework objectives • Rehearse the concept of multiplication as describing an array • Derive and recall multiplication facts up to 10 ≠ 10, the • Understand and use the commutativity of multiplication corresponding division facts and multiples of numbers to 10 up to • Consolidate division as the inverse of multiplication the tenth multiple • Identify and use patterns, relationships and properties of numbers or shapes; investigate a statement involving numbers and test it with examples • Use and reflect on some ground rules for dialogue (e.g. making structured, extended contributions, speaking audibly, making meaning explicit and listening actively) Teacher notes Preparation If you have time Prepare a set of number cards 1–10, three sets per child. Also, Discuss with the group the results of these multiplications: preparing a simple sheet with three boxes in a line as on the Textbook 2 ≠ 5 ≠ 6 2 ≠ 6 ≠ 5 5 ≠ 2 ≠ 6 5 ≠ 6 ≠ 2 page may help to keep children’s recording neater. 6 ≠ 2 ≠ 5 6 ≠ 5 ≠ 2 All the products are 60. Does this work for other sets of three numbers Activity in different orders? Why is this? Children work from Textbook page 11. They multiply sets of three digits and find the products. Information Children then use number cards to make their own multiplications Children may recognise that any set of three digits will always give the of three digits. They find the products and record these (they do not same product. This may give insight into two laws of arithmetic: reveal the multipliers to other children). They then swap sheets and find The commutative law: a ≠ b = b ≠ a the multipliers that would make each product. The associative law: a ≠ (b ≠ c) = (a ≠ b) ≠ c. Together these laws mean that any three numbers multiplied in any Further extension order give the same overall product. Using calculators, children can extend their range of multiplying up to 9 ≠ 9 ≠ 9 to produce further, more challenging puzzles. Others in the group use calculators to deduce the digits that have been multiplied. Be aware Outcomes • Some children may be unused to multiplying three numbers • I can multiply three small numbers together. together, and surprised by how large a product results. • I can work out which three digits have been multiplied together to give a product. • I can create puzzles for others to solve. 10 www.pearsonschools.co.uk/abacusevolve
• Multiplication Triple multiplying A1 What happens if you multiply these numbers together? 1 2 3 4 Now try with these multiplications. 2 4 ≠ 2 ≠ 4 = 3 2 ≠ 5 ≠ 2 = 4 5 ≠ 3 ≠ 1 = Find the possible missing multipliers. 5 ≠ ≠ 4 = 40 6 ≠ 3 ≠ = 36 7 ≠ ≠ = 105 8 Choose any three digit cards and find their product. Show your working. Write out the product (but not the multipliers). Swap with someone in your group. Can you find the multipliers to make their product? What always happens to the product if … • one of the three digits chosen is a 2? • one of the three digits chosen is a 5? • one digit is even and another is a 5? 11
• B2: multiplication; doubling and halving; coordinates; names Challenge Plan: Year 5 and properties of 2D shapes Summary Y5 B2.2 Egyptian multiplication Individuals, pairs or groups working independently Year 5 Challenge Textbook page 13 Calculators (optional) Abacus Evolve objectives Framework objectives • Use doubling and halving to help multiply • Extend mental methods for whole-number calculations, e.g. to • Use doubling or halving to find new facts from known facts multiply a 2-digit by 1-digit number (e.g. 12 ≠ 9), to multiply by 25 • Multiply using closely related facts (e.g. 16 ≠ 25), to subtract one near multiple of 1000 from another (e.g. 6070 ≠ 4097) • Represent a puzzle or problem by identifying and recording the information or calculations needed to solve it; find possible solutions and confirm them in the context of the problem Teacher notes Preparation Further extension Familiarise yourself with the Egyptian multiplication method by looking Children could use the Egyptian multiplication method to work out the at Textbook page 13. calculations from Activity B2.1. Getting started Ask children to practise doubling some random numbers before they start the activity. Activity Children work from Textbook page 13. They learn about the Egyptian number system and the Egyptian method for multiplication. This method involves doubling and children should be encouraged to choose an appropriate doubling strategy for each number. For 2-digit numbers children should be able to partition and double mentally. Some may also be able to do this for 3-digit numbers, or they may prefer a mixture of mental strategies and jottings. The method works in exactly the same way for 3-digit numbers. Children can use other methods or a calculator to check their answers. Be aware Outcomes • Doubling 3-digit numbers mentally (particularly when the hundreds • I can use a new multiplication method. digit is more than 5) can be much trickier than doubling 2-digit • I can double to help me multiply. numbers. Encourage children to make notes to help them with the • I can estimate and check calculations using different methods. calculation. Supporting resources This site has a PowerPoint demonstration of Egyptian multiplication (Go to Free Downloads, then Powerpoint Shows): • http://www.numeracysoftware.com/xm.html 12 www.pearsonschools.co.uk/abacusevolve
• Multiplication Egyptian multiplication and division B2 The Ancient Egyptians used symbols to represent numbers: 1 10 100 1000 10 000 100 000 1 000 000 There was no symbol for zero. They had to draw several of each symbol for each number. For example, 213 would be written as Have a go at writing some other numbers using the Ancient Egyptian symbols. The Egyptians had their own way of solving multiplications. They used doubling. 1 23 To solve 46 ≠ 23, draw a table with 2 46 1 in the left-hand column and 23 in 4 92 the right-hand column. Double the 8 184 numbers in each column until the number in the left-hand column is 16 368 greater than 46. 32 736 64 1472 Find the numbers in the left-hand column that total 46. 32 + 8 + 4 + 2 = 46 Add together the corresponding numbers in the right-hand column. 736 + 184 + 92 + 46 = 1058 Check your answer using another method or with a calculator. Estimate the answers to the following calculations then use the Egyptian method to find the answers. 1 21 ≠ 36 2 31 ≠ 27 3 39 ≠ 52 4 53 ≠ 28 5 77 ≠ 43 Does this method work with 3-digit numbers? Make up some calculations with 3-digit numbers and try it out! 13
• B1: odd and even numbers; common multiples; smallest common Challenge Plan: Year 6 multiple; properties of 2D shapes; classifying quadrilaterals Summary Y6 B1.5 Constructing triangles A group working with an adult Year 6 Challenge Textbook page 15 Rulers; protractors; pairs of compasses; plain paper; geo-strips (optional) Abacus Evolve objectives Framework objectives • Y6-7 Construct a triangle given two sides and the included angle • Y6-7 Construct a triangle given two sides and the included angle Teacher notes Getting started line, so if we join them up we will get an equilateral triangle. Check that children are confident in accurately using a ruler, a • Children join up the three points to make a triangle. We have drawn protractor and a pair of compasses. triangle 2! • Children use their angle measurers to confirm that it is an equilateral Activity triangle. (Each angle is 60°.) • Children work from Textbook page 15. Ask them to look at the triangles. • Can you think how the third triangle could be constructed? (It can be • What information are we given about these triangles? (the right made using the compasses method, but changing the lengths.) angles and the lengths of some of the sides) • Children draw triangle 3 and measure the angles to check that they • Can we draw these triangles, using just this information? have constructed it correctly. (The internal angles should add up to 180°.) • Children draw a 12 cm horizontal line half-way down a piece of paper, then measure an angle of 90° at one end using a protractor. • Children then experiment with methods for drawing triangle 4. • They then draw an 8 cm line perpendicular to the original line, Remind them to check the angles when they have drawn their following the right angle. triangle. • They join the ends of the two lines, measure the length of this line and measure each angle. Extra help • Ask children to mark these measurements on the drawing. We have Children who are not confident with using compasses can practise with drawn triangle 1! geo-strips first. They fasten one end to the base line and use the hole to draw the arc. • Children then draw a 10 cm horizontal line, leaving about 12 cm of space above it. • Children use a ruler to open a pair of compasses to 10 cm. • They place the point of the compass at one end of the line and draw a quarter circle from the other end of the line. They repeat this from the other end of the line. • Where the circle marks cross is exactly 10 cm from each end of our Be aware Outcomes • Children will need dexterity to use compasses accurately. Check • I can construct triangles using a ruler, a protractor and a pair of that children are able to do this and support those that find it more compasses. difficult. 14 www.pearsonschools.co.uk/abacusevolve
• Shape Constructing triangles B1 Draw these four triangles using the measurements shown. Measure all the angles. 1 2 8 cm 12 cm 10 cm 3 4 7 cm 7 cm 7 cm 5 cm 11 cm 8 cm Some triangles are impossible to construct. Try to construct these three triangles. Which one is impossible to construct? Why? 7 cm 5 cm b b 13 cm 13 cm 6 cm a 12 cm 5 cm c 7 cm 6 cm 15
• Ensure your most able mathematicians are stretched to reach their full potential with Abacus Evolve Challenge. Containing a wide range of enrichment and extension activities that add a fourth level of differentiation above that found in other programmes, Challenge encourages children to develop their thinking skills and attain a deeper level of mathematical understanding. Visit www.pearsonschools. Easily integrated into your weekly Abacus Evolve co.uk/abacusevolve to place an order or call our friendly planning, or used as a stand-alone resource, the team on 0845 630 22 22 activities provide: • Group work and opportunities for discussion to promote Speaking & Listening • Open-ended investigations and problem solving to promote Using & Applying • A balance of breadth, depth and pace. Each Year of Challenge includes: • A Teacher Guide • A Pupil Book (a Workbook for Year 1, and Textbooks for Years 2–6) • A Challenge Module of I-Planner Online. ThIs sample bookleT conTaIns one acTIvITy from each of years 1–6. Icon guide Type of extension/enrichment Breadth Depth Pace Type of activity Discover Practise Teaching Investigate Problem Game Solving www.pearsonschools.co.uk www.ginn.co.uk/abacusevolve 0845 630 22 22 enquiries@pearson.com I S B N 978-0-602-57898-5 9 780602 578985