challengeassets.pearsonglobalschools.com/asset_mgr/current/201214/...year 1 challenge workbook page...

Challenge

Framework Edition

Samplebooklet

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.

ActivityChildren 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.

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.

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?

• Relatingproblemsolvinginbookstoacontextrequireschildrento 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.

• Icanusecluestosolveproblems.• Icantakeamountsawayfrom10p.

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

Be aware Outcomes

• ChildrencanpractisemakingchoicesanddecisionsbyreadingWould you rather? by John Burningham.

Supporting resources

Summary

Y1 D1.5 Money banks

Pairs or groups working independently

Year 1 Challenge Workbook page 3

Moneybank,collectionofcoinsupto10p

Teacher notes

• Subtractone1-digitnumberfromanother • Understandsubtractionas‘takeaway’andfinda‘difference’bycounting up; use practical and informal written methods to support thesubtractionofa1-digitnumberfroma1-digitor2-digitnumberandamultipleof10froma2-digitnumber

• Solveproblemsinvolvingcounting,adding,subtracting,doublingor halving in the context of numbers, measures or money, for exampleto‘pay’and‘givechange’

• Retellstories,orderingeventsusingstorylanguage

Abacus Evolve objectives Framework objectives

2 www.pearsonschools.co.uk/abacusevolve

SubtractionD1: names of common 2D shapes; features of familiar 2D shapes; counting back 1; subtracting a 1-digit number from a ‘teens’ number Money banks D1

Tell a story to a friend that explains what the children spent their money on.

Jane Tom Isaac

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

Isaac has spent p

Who has spent the most?

Who has spent the least?

Jane has 10p in her money bank.

Tom has 1p less than Jane.

Isaac has 1p less than Tom.

3

Challenge Plan: Year 2 D1: sorting and describing 2D shapes; line symmetry; counting back in 1s, not crossing a ten; counting back in 1s, crossing a ten

• Decidingonthelineofsymmetryisimportantandchildrenneedtorealisethatthishasbeenpre-determinedbywherethepictureshave been cut.

• Icanrecogniselinesymmetry.• Icanmakesymmetricalpatternsbyfoldingandcutting.

Be aware Outcomes

Childrencanlookatpatternsandsymmetryincarwheelsin‘Watchthosewheels’:• http://nrich.maths.org/public/viewer.php?obj_id=2815


PreparationCut up some mirror card so you have one piece per pair.

Getting started ShowTextbookpage5.Explainthattheshapesareallsymmetrical,butthey have been cut in half by mistake. Make sure children understand what this means. How could you find out what is missing?

ActivityChildrenworkfromTextbookpage5.Eachchildcopiesthehalfpictures, 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 ofpaperbetweenthem.Setupabarrier(suchasabigbookoragameboard) 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 ofsymmetricalobjects.Printthepicturesandthencuttheminhalf.Children give one half to a partner to complete, then check by sticking the picture back together.

• Begintorecogniselinesymmetry• Makesymmetricalpatternsbyfoldingandcutting• Begintosketchthereflectionofasimpleshapeinamirrorline

• Identifyreflectivesymmetryinpatternsand2Dshapesanddrawlines of symmetry in shapes

• Describepatternsandrelationshipsinvolvingnumbersorshapes,make predictions and test these with examples

• Listentoothersinclass,askrelevantquestionsandfollowinstructions

Summary

What’s missing?

Individuals or pairs working independently

Year2ChallengeTextbookpage5

Paper; scissors; mirror card

Y2 D1.2



Teacher notes

Shape

What’s missing? D1

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?

1 2

These pictures are symmetrical. Half of each picture has been cut off by mistake!

Copy the pictures and draw the missing half.

5

3 4

Challenge Plan: Year 3 A1: comparing 3-digit numbers; partitioning 3-digit numbers;counting objects by grouping; counting on and back in 100s

• Childrenmaybeunfamiliarwiththeideabehindthecode-hexagonto represent changes in all directions. If necessary, go through question1together.

• Icanexploreandrecordpatternsinnumbers.• Icanrecognisegeneralpatternswhenaddingandsubtracting.

Be aware Outcomes

Growing on trees

Individuals, pairs or groups working independently

Year 3 Challenge Textbook page 7

Year 3 Challenge PCMs 1 and 2

Timer

Y3 A1.1

• Readandwritenumbersupto1000infiguresandwords• Countonin5sto100,andin50sto1000• Addandsubtractamultipleof10toandfroma3-digitnumber,

crossing100• Addandsubtractamultipleof100toandfroma4-digitnumber,

crossing1000• Extendunderstandingthatsubtractionistheinverseofaddition

• Read,writeandorderwholenumberstoatleast1000andpositionthemonanumberline;countonfromandbacktozeroinsingle-digitstepsormultiplesof10

• Addorsubtractmentallycombinationsofone-digitandtwo-digitnumbers

• Identifypatternsandrelationshipsinvolvingnumbersorshapes,and use these to solve problems

PreparationPhotocopy PCMs 1 and 2, one copy of each per child.

Getting startedCheckthatchildrenunderstandhowthecode-hexagonbelowthetreeinforms them what number to write in each space.

ActivityChildren work from Textbook page 7 and record their answers on PCMs1and2.Theyusetworulestofillinthenumbersinatree-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.

If you have timeChildren will find it useful to discuss their patterns. Often children will have different insights that combine to give all of them a better picture.

Teacher notes


Summary


Here is a tree of numbers. 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 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.

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.

Growing on trees A1

Does everyone’s tree look the same?

What rules did other people in the group make up?

+ 100 + 500

1000

Copy this diamond pattern onto squared paper. Write 1 in the bottom box.

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?

≠ 2 ≠ 5

7

Counting

Year 3 Block A1 • Challenge PCM 1

Growing on trees 1

1

1000

1100 1500

1000

�250

�50

Ab

ac

us Evolve

Yea

r 3 Ch

allen

ge PC

M ©

Pearso

n Ed

uca

tion

Ltd 2009

2

1000

1100 1500

1000

�250

�50


Year 3 Block A1 • Challenge PCM 2

Growing on trees 2

3

1000

0

Ab

ac

us Evolve

Yea

r 3 Ch

allen

ge PC

M ©

Pearso

n Ed

uca

tion

Ltd 20091000

0

117

Challenge Plan: Year 4

• Somechildrenmaybeunusedtomultiplyingthreenumberstogether, and surprised by how large a product results.

• Icanmultiplythreesmallnumberstogether.• Icanworkoutwhichthreedigitshavebeenmultipliedtogetherto

give a product. • Icancreatepuzzlesforotherstosolve.

Be aware Outcomes

Triple multiplying

Pairs or groups working independently


Numbercards1–10;calculators(optional)

Y4 A1.4

Summary

• Rehearsetheconceptofmultiplicationasdescribinganarray• Understandandusethecommutativityofmultiplication• Consolidatedivisionastheinverseofmultiplication

• Derive and recall multiplication facts up to 10 ≠ 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple

• Identifyandusepatterns,relationshipsandpropertiesofnumbersor shapes; investigate a statement involving numbers and test it with examples

• Useandreflectonsomegroundrulesfordialogue(e.g.makingstructured, extended contributions, speaking audibly, making meaning explicit and listening actively)


PreparationPrepareasetofnumbercards1–10,threesetsperchild.Also,preparing a simple sheet with three boxes in a line as on the Textbook pagemayhelptokeepchildren’srecordingneater.

ActivityChildren 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 ofthreedigits.Theyfindtheproductsandrecordthese(theydonotreveal 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.

If you have timeDiscusswiththegrouptheresultsofthesemultiplications:2 ≠ 5≠ 6 2 ≠ 6 ≠5 5≠ 2 ≠6 5≠ 6 ≠ 2 6 ≠ 2 ≠5 6≠5≠ 2All 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 sameproduct.Thismaygiveinsightintotwolawsofarithmetic:Thecommutativelaw:a≠ b = b ≠ a Theassociativelaw:a≠(b≠ c) =(a≠ b) ≠ c. Together these laws mean that any three numbers multiplied in any order give the same overall product.

Teacher notes

A1: whole numbers to 10 000; partitioning into Th, H, T and U; multiplication as repeated addition; dividing whole numbers


Multiplication A1

11

Triple multiplying

What always happens to the product if … • oneofthethreedigitschosenisa2?• oneofthethreedigitschosenisa5?• onedigitisevenandanotherisa5?

1

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 happens if you multiply these numbers together?

2 3 4

Challenge Plan: Year 5 B2: multiplication; doubling and halving; coordinates; namesand properties of 2D shapes

• Doubling3-digitnumbersmentally(particularlywhenthehundredsdigitismorethan5)canbemuchtrickierthandoubling2-digitnumbers. Encourage children to make notes to help them with the calculation.

• Icanuseanewmultiplicationmethod.• Icandoubletohelpmemultiply.• Icanestimateandcheckcalculationsusingdifferentmethods.

Be aware Outcomes

ThissitehasaPowerPointdemonstrationofEgyptianmultiplication(GotoFreeDownloads,thenPowerpoint Shows):http://www.numeracysoftware.com/xm.html•


Summary

Egyptian multiplication

Individuals, pairs or groups working independently


Calculators(optional)

Y5 B2.2

Preparation Familiarise yourself with the Egyptian multiplication method by looking at Textbook page 13.

Getting started Ask children to practise doubling some random numbers before they start the activity.

ActivityChildren 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 chooseanappropriatedoublingstrategyforeachnumber.For2-digitnumbers children should be able to partition and double mentally. Somemayalsobeabletodothisfor3-digitnumbers,ortheymaypreferamixtureofmentalstrategiesandjottings.Themethodworksinexactlythesamewayfor3-digitnumbers.Childrencanuseothermethods or a calculator to check their answers.

Further extension Children could use the Egyptian multiplication method to work out the calculations from Activity B2.1.

Teacher notes

• Usedoublingandhalvingtohelpmultiply• Usedoublingorhalvingtofindnewfactsfromknownfacts• Multiplyusingcloselyrelatedfacts

• Extendmentalmethodsforwhole-numbercalculations,e.g.tomultiplya2-digitby1-digitnumber(e.g.12≠9),tomultiplyby25(e.g.16≠25),tosubtractonenearmultipleof1000fromanother(e.g.6070≠4097)

• Representapuzzleorproblembyidentifyingandrecordingthe information or calculations needed to solve it; find possible solutions and confirm them in the context of the problem



Egyptian multiplication

Does this method work with 3-digit numbers? Make up some calculations with 3-digit numbers and try it out!

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.

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

B2Multiplication and division

13

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.

1 232 464 928 18416 36832 73664 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

Challenge Plan: Year 6 B1: odd and even numbers; common multiples; smallest commonmultiple; properties of 2D shapes; classifying quadrilaterals

• Childrenwillneeddexteritytousecompassesaccurately.Checkthat children are able to do this and support those that find it more difficult.

• Icanconstructtrianglesusingaruler,aprotractorandapairofcompasses.

Be aware Outcomes

• Y6-7 Construct a triangle given two sides and the included angle • Y6-7 Construct a triangle given two sides and the included angle


Summary

Y6 B1.5 Constructing triangles

A group working with an adult


Rulers;protractors;pairsofcompasses;plainpaper;geo-strips(optional)

Getting started Check that children are confident in accurately using a ruler, a protractor and a pair of compasses.

Activity• ChildrenworkfromTextbookpage15.Askthemtolookatthe

triangles. • What information are we given about these triangles? (theright

angles and the lengths of some of the sides) • Can we draw these triangles, using just this information?

• Childrendrawa12cmhorizontallinehalf-waydownapieceofpaper,thenmeasureanangleof90°atoneendusingaprotractor.

• Theythendrawan8cmlineperpendiculartotheoriginalline,following the right angle.

• Theyjointheendsofthetwolines,measurethelengthofthislineand measure each angle.

• Askchildrentomarkthesemeasurementsonthedrawing.We have drawn triangle 1!

• Childrenthendrawa10cmhorizontalline, leaving about 12 cm of space above it.

• Childrenusearulertoopenapairof compassesto10cm.

• Theyplacethepointofthecompassatoneend ofthelineanddrawaquartercirclefromtheother 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

line, so if we join them up we will get an equilateral triangle. • Childrenjoinupthethreepointstomakeatriangle.We have drawn

triangle 2!• Childrenusetheiranglemeasurerstoconfirmthatitisanequilateral

triangle.(Eachangleis60°.)

• Can you think how the third triangle could be constructed?(Itcanbemade using the compasses method, but changing the lengths.)

• Childrendrawtriangle3andmeasuretheanglestocheckthattheyhaveconstructeditcorrectly.(Theinternalanglesshouldaddupto180°.)

• Childrenthenexperimentwithmethodsfordrawingtriangle4.Remindthemtochecktheangleswhentheyhavedrawntheirtriangle.

Extra helpChildren who are not confident with using compasses can practise with geo-stripsfirst.Theyfastenoneendtothebaselineandusetheholeto draw the arc.

Teacher notes


B1: odd and even numbers; common multiples; smallest commonmultiple; properties of 2D shapes; classifying quadrilaterals Constructing triangles

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

Draw these four triangles using the measurements shown.

Measure all the angles.

1

3

2

4

8 cm

12 cm 10 cm

7 cm 7 cm

11 cm

7 cm 5 cm

8 cm

12 cm

6 cm

13 cm 13 cm

5 cm7 cm

7 cm

5 cma

b

c

ShapeB1

b

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.

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.

0845 630 22 [email protected]

www.ginn.co.uk/abacusevolve

Type of extension/enrichment

Type of activity

Breadth Depth Pace

Discover Practise Teaching

Investigate ProblemSolving

Game

Icon guide

ThIs sample bookleT conTaIns one acTIvITy from each of years 1–6.

Visit www.pearsonschools.co.uk/abacusevolve to place an order or call our friendly

team on 0845 630 22 22

I S B N 978-0-602-57898-5

9 7 8 0 6 0 2 5 7 8 9 8 5

www.pearsonschools.co.uk

challengeassets.pearsonglobalschools.com/asset_mgr/current/201214/...year 1 challenge workbook page...

Documents