Challenge - Pearson Schools

Sample booklet

Challenge

Framework Edition

Challenge Plan: Year 1

D1: names of common 2D shapes; features of familiar 2D shapes; counting back 1; subtracting a 1-digit number from a ‘teens’ number

Summary Y1

D1.5

Money banks Pairs or groups working independently Year 1 Challenge Workbook page 3 Money bank, collection of coins up to 10p

Abacus Evolve objectives

Framework objectives

• Subtract one 1-digit number from another

• Understand subtraction as ‘take away’ and find a ‘difference’ by counting up; use practical and informal written methods to support the subtraction of a 1-digit number from a 1-digit or 2-digit number and a multiple of 10 from a 2-digit number • Solve problems involving counting, adding, subtracting, doubling or halving in the context of numbers, measures or money, for example to ‘pay’ and ‘give change’ • Retell stories, ordering events using story language

Teacher notes Getting started Explain to children that they are going to work together to solve a problem about money. The problem is about a money bank – make sure they know what this is. If possible have one available for the children to look at. Activity Children work from Workbook page 3. They see pictures of three money banks with coins visible inside. They draw lines to match the money banks to three children, based on information about the amount of money each child has. Once children have done this, they work in pairs to compare their answers.

Further extension Each child is given 10p pocket money each week. How much money will each child have in their money bank next week? How many weeks will it take to save up 50p? If you have time Encourage children to talk about why they have linked the money banks in the way that they have. Do they want to change their mind having listened to their partner? Explain to children that it is okay to change your mind. Discuss with children how they might show this in their book. Encourage them not to rub out or scribble over the answer. Would you rather have 1p pocket money each day, or 10p each week?

Extra help Provide 1p coins laid out in sets to match the amounts in the three money banks. This will allow children to take away 1p to find the answer. Focus on exchanging the pennies for other coins, e.g. 2p is 2 ≠ 1p.

Be aware

Outcomes

• Relating problem solving in books to a context requires children to understand the ideas in the problem and apply them to a range of different scenarios. Using words and pictures to do this is an important skill.

• I can use clues to solve problems. • I can take amounts away from 10p.

Supporting resources • Children can practise making choices and decisions by reading Would you rather? by John Burningham.

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Subtraction

Money banks

Jane

Jane has 10p in her money bank.

Tom

Tom has 1p less than Jane.

D1

Isaac

Isaac has 1p less 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

Tom has spent

p

Who has spent the most? 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 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



• Begin to recognise line symmetry • Make symmetrical patterns by folding and cutting • Begin to sketch the reflection of a simple shape in a mirror line

• Identify reflective symmetry in patterns and 2D shapes and draw lines of symmetry in shapes • 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 Cut up some mirror card so you have one piece per pair. Getting started Show Textbook page 5. Explain that the shapes are all symmetrical, but they have been cut in half by mistake. Make sure children understand what this means. How could you find out what is missing? Activity Children work from Textbook page 5. Each child copies the half pictures, and then tries to complete them. They compare their pictures 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 symmetry. Extra help Photocopy the Textbook page so that children can complete the pictures, without having to copy them first.

Further extension 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 board) between the children, so that the barrier divides the piece of paper in two. Explain to children that they are going to pretend that the barrier is a mirror. One child draws a shape on their side of the paper 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 order to draw the reflection of the shape. This is difficult, but fun and intended to draw attention to the process of reflection. Children can check their images with a piece of mirror card when finished. If you have time Give children a digital camera and ask them to take some photos of symmetrical objects. Print the pictures and then cut them in half. Children give one half to a partner to complete, then check by sticking the picture back together.

Be aware

Outcomes

• Deciding on the line of symmetry is important and children need to realise that this has been pre-determined by where the pictures have been cut.

• I can recognise line symmetry. • I can make symmetrical patterns by folding and cutting.

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


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; 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



• Read and write numbers up to 1000 in figures and words • Count on in 5s to 100, and in 50s to 1000 • Add and subtract a multiple of 10 to and from a 3-digit number, crossing 100 • Add and subtract a multiple of 100 to and from a 4-digit number, crossing 1000 • Extend understanding that subtraction is the inverse of addition

• Read, write and order whole numbers to at least 1000 and position them on a number line; count on from and back to zero in singledigit steps or multiples of 10 • Add or subtract mentally combinations of one-digit and two-digit numbers • Identify patterns and relationships involving numbers or shapes, and use these to solve problems

Teacher notes Preparation Photocopy PCMs 1 and 2, one copy of each per child. Getting started Check that children understand how the code-hexagon below the tree informs them what number to write in each space.

If you have time 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.

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 treeshaped 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 • Children may be unfamiliar with the idea behind the code-hexagon to represent changes in all directions. If necessary, go through question 1 together.

6

Outcomes • I can explore and record patterns in numbers. • I can recognise general patterns when adding and subtracting.


Counting

Growing on trees

A1

Here is a tree of numbers. The larger numbers are at the base and the smallest number is at the top.

1000

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 all six directions.

+ 100

+ 500

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.

≠2

≠5

Complete the diamond. What do you notice about the patterns of numbers? If you start with another small number, such as 4, what patterns result?

7

Growing on trees 1 1

1000 1000

1100 1100 1500 1500

2

1000 �50 �250

1000

�50

�250

116


Abacus Evolve Year 3 Challenge PCM © Pearson Education Ltd 2009

Year 3 Block A1 • Challenge PCM 1

Abacus Evolve Year 3 Challenge PCM © Pearson Education Ltd 2009

Year 3 Block A1 • Challenge PCM 2

Growing on trees 2 3

1000 1000

0 0

117

A1: whole numbers to 10 000; partitioning into Th, H, T and U; 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)



• Rehearse the concept of multiplication as describing an array • Understand and use the commutativity of multiplication • Consolidate division as the inverse of multiplication

• Derive and recall multiplication facts up to 10 ≠ 10, the corresponding division facts and multiples of numbers to 10 up to 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 Prepare a set of number cards 1–10, three sets per child. Also, preparing a simple sheet with three boxes in a line as on the Textbook page may help to keep children’s recording neater. Activity Children work from Textbook page 11. They multiply sets of three digits and find the products. Children then use number cards to make their own multiplications of three digits. They find the products and record these (they do not reveal the multipliers to other children). They then swap sheets and find the multipliers that would make each product. Further extension 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 • Some children may be unused to multiplying three numbers together, and surprised by how large a product results.

10

If you have time Discuss with the group the results of these multiplications: 2 ≠ 5 ≠ 6 2 ≠ 6 ≠ 5 5 ≠ 2 ≠ 6 5 ≠ 6 ≠ 2 6 ≠ 2 ≠ 5 6≠5≠2 All the products are 60. Does this work for other sets of three numbers in different orders? Why is this? Information Children may recognise that any set of three digits will always give the same product. This may give insight into two laws of arithmetic: The commutative law: a ≠ b = b ≠ a The associative law: a ≠ (b ≠ c) = (a ≠ b) ≠ c. Together these laws mean that any three numbers multiplied in any order give the same overall product.

Outcomes • I can multiply three small numbers together. • I can work out which three digits have been multiplied together to give a product. • I can create puzzles for others to solve.


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 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)



• Use doubling and halving to help multiply • Use doubling or halving to find new facts from known facts • Multiply using closely related facts

• Extend mental methods for whole-number calculations, e.g. to multiply a 2-digit by 1-digit number (e.g. 12 ≠ 9), to multiply by 25 (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 Familiarise yourself with the Egyptian multiplication method by looking at Textbook page 13.

Further extension Children could use the Egyptian multiplication method to work out the 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 digit is more than 5) can be much trickier than doubling 2-digit numbers. Encourage children to make notes to help them with the calculation.

• I can use a new multiplication method. • I can double to help me multiply. • I can estimate and check calculations using different methods.

Supporting resources This site has a PowerPoint demonstration of Egyptian multiplication (Go to Free Downloads, then Powerpoint Shows): • http://www.numeracysoftware.com/xm.html

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Multiplication and division

Egyptian multiplication

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.

To solve 46 ≠ 23, draw a table with 1 in the left-hand column and 23 in the right-hand column. Double the numbers in each column until the number in the left-hand column is greater than 46.

1 2 4 8 16 32 64

23 46 92 184 368 736 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 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)



• 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 Check that children are confident in accurately using a ruler, a protractor and a pair of compasses. Activity • Children work from Textbook page 15. Ask them to look at the triangles. • What information are we given about these triangles? (the right angles and the lengths of some of the sides) • Can we draw these triangles, using just this information? • 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. • They then draw an 8 cm line perpendicular to the original line, following the right angle. • They join the ends of the two lines, measure the length of this line and measure each angle. • Ask children to mark these measurements on the drawing. We have drawn triangle 1!

line, so if we join them up we will get an equilateral triangle. • Children join up the three points to make a triangle. We have drawn triangle 2! • Children use their angle measurers to confirm that it is an equilateral triangle. (Each angle is 60°.) • Can you think how the third triangle could be constructed? (It can be made using the compasses method, but changing the lengths.) • Children draw triangle 3 and measure the angles to check that they have constructed it correctly. (The internal angles should add up to 180°.) • Children then experiment with methods for drawing triangle 4. Remind them to check the angles when they have drawn their triangle. Extra help Children who are not confident with using compasses can practise with 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 • Children will need dexterity to use compasses accurately. Check that children are able to do this and support those that find it more difficult.

14

Outcomes • I can construct triangles using a ruler, a protractor and a pair of compasses.


Shape

Constructing triangles

B1

Draw these four triangles using the measurements shown. Measure all the angles. 1

2

8 cm

10 cm

12 cm

3

4 7 cm

7 cm

5 cm

7 cm

8 cm

11 cm

Some triangles are impossible to construct. Try to construct these three triangles. Which one is impossible to construct? Why?

7 cm 5 cm 13 cm

13 cm a

bb 6 cm 12 cm

c

5 cm

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. Easily integrated into your weekly Abacus Evolve planning, or used as a stand-alone resource, the 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.

Visit www.pearsonschools. co.uk/abacusevolve to place an order or call our friendly team on 0845 630 22 22

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

Discover

Practise

Teaching

Investigate

Problem Solving

Game

Type of activity

www.pearsonschools.co.uk www.ginn.co.uk/abacusevolve 0845 630 22 22 [email protected] I S B N 978-0-602-57898-5

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780602 578985