Maths Challenge Workbook for Ukg

7/30/2019 Maths Challenge Workbook for Ukg

1/16

Challenge

Framework Edition

Samplebooklet


2/16

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 themoney 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 timeEncourage 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 intheir 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?

Relatingproblemsolvinginbookstoa contextrequireschildren

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.

Icanusecluestosolveproblems. Icantakeamountsawayfrom10p.

Challenge Plan: Year 1D1: 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 Understandsubtractionastakeawayandfindadifferenceby

counting up; use practical and informal written methods to support

thesubtractionofa1-digitnumberfroma1-digitor2-digit

numberandamultipleof10froma2-digitnumber

Solveproblemsinvolvingcounting,adding,subtracting,doublingor halving in the context of numbers, measures or money, for

exampletopayandgivechange

Retellstories,orderingeventsusingstorylanguage

Abacus Evolve objectives Framework objectives

2 www.pearsonschools.co.uk/abacusevolve


3/16

Subtraction

Money banks D1

Tell a story to a friend that explains what the childrenspent 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 hermoney bank.

Tom has 1p less thanJane.

Isaac has 1p lessthan Tom.

3


4/16

Challenge Plan: Year 2D1: sorting and describing 2D shapes; line symmetry; counting

back in 1s, not crossing a ten; counting back in 1s, crossing a ten

Decidingonthelineof symmetryisimportantandchildrenneedtorealisethatthishasbeenpre-determinedbywherethepictures

have been cut.

Icanrecogniselinesymmetry. Icanmakesymmetricalpatternsbyfoldingandcutting.

Be aware Outcomes

ChildrencanlookatpatternsandsymmetryincarwheelsinWatchthosewheels:

http://nrich.maths.org/public/viewer.php?obj_id=2815


Preparation

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

Getting started

ShowTextbookpage5.Explainthattheshapesareallsymmetrical,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

ChildrenworkfromTextbookpage5.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 thepictures, without having to copy them first.

Further extension

Ask children to work in pairs. They sit opposite each other with a pieceofpaperbetweenthem.Setupabarrier(suchasabigbookoragame

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

ofsymmetricalobjects.Printthepicturesandthencuttheminhalf.

Children give one half to a partner to complete, then check by sticking

the picture back together.

Begintorecogniselinesymmetry

Makesymmetricalpatternsbyfoldingandcutting

Begintosketchthereflectionofasimpleshape inamirrorline

Identifyreflectivesymmetryinpatternsand2Dshapesanddraw

lines of symmetry in shapes

Describepatternsandrelationshipsinvolvingnumbersorshapes,

make predictions and test these with examples Listentoothersinclass,askrelevantquestionsandfollow

instructions

Summary

Whats missing?

Individuals or pairs working independently

Year2ChallengeTextbookpage5

Paper; scissors; mirror card

Y2 D1.2



Teacher notes


5/16

Shape

Whats 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 thatthey 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


6/16

Challenge Plan: Year 3A1: comparing 3-digit numbers; partitioning 3-digit numbers;

counting objects by grouping; counting on and back in 100s

Childrenmaybeunfamiliarwiththeideabehindthecode-hexagon

to 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

Addandsubtractamultipleof 10toandfroma3-digitnumber,

crossing100 Addandsubtractamultipleof100 toandfroma4-digitnumber,crossing1000

Extendunderstandingthatsubtractionistheinverseofaddition

Read,writeandorderwholenumberstoatleast1000andposition

themonanumberline;countonfromandbacktozeroinsingle-

digitstepsormultiplesof10

Addorsubtractmentallycombinationsofone-digit andtwo-digitnumbers

Identifypatternsandrelationshipsinvolvingnumbersor shapes,and use these to solve problems

Preparation

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

Getting started

Checkthatchildrenunderstandhowthecode-hexagonbelowthetree

informs them what number to write in each space.

Activity

Children work from Textbook page 7 and record their answers on

PCMs1and2.Theyusetworulestofillinthenumbersinatree-

shaped arrangement of hexagons, and then go back and find themissing 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 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.

Teacher notes


Summary



7/16

Here is a tree of numbers.The larger numbers are at the

base and the smallest number isat the top.

The hexagon below the treeshows the rule for changingthe numbers as you move indifferent directions.

We have been given the rules formoves in two directions. We canuse these to complete the tree.

We can then complete thehexagon to show the rules forall six directions.

1 Complete the first tree on PCM 1. Time how long it takes you and writeyour 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 everyones tree look the same?

What rules did other people in the group make up?

+ 100 + 500

1000

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

Complete the diamond.What do you notice aboutthe patterns of numbers?

If you start with anothersmall number, such as 4,what patterns result?

2 5

7

Counting


8/16

Year 3 Block A1 Challenge PCM 1

Growing on trees 1

1

1000

1000

AbacusEvolve

Year3Challe

ngePCMPearsonEducationLtd2009

2

100 1500

250

50



9/16

Year 3 Block A1 Challenge PCM 2

Growing on trees 2

3

1000

0

AbacusEvolve

Year3Challe

ngePCMPearsonEducationLtd2009

117


10/16

Challenge Plan: Year 4

Somechildrenmaybeunusedtomultiplyingthreenumbers

together, and surprised by how large a product results.

Icanmultiplythreesmallnumberstogether.

Icanworkoutwhich threedigitshavebeenmultipliedtogetherto

give a product.

Icancreatepuzzlesforotherstosolve.

Be aware Outcomes

Triple multiplying

Pairs or groups working independently


Numbercards110;calculators(optional)

Y4 A1.4

Summary

Rehearsetheconceptofmultiplicationasdescribingan array

Understandandusethecommutativityofmultiplication

Consolidatedivisionastheinverseofmultiplication

Derive and recall multiplication facts up to 1010, the

corresponding division facts and multiples of numbers to 10 up tothe tenth multiple

Identifyandusepatterns,relationshipsandpropertiesofnumbers

or shapes; investigate a statement involving numbers and test itwith examples

Useandreflectonsomegroundrulesfordialogue (e.g.making

structured, extended contributions, speaking audibly, making

meaning explicit and listening actively)


Preparation

Prepareasetofnumbercards110,threesetsperchild.Also,

preparing a simple sheet with three boxes in a line as on the Textbook

pagemayhelptokeepchildrensrecordingneater.

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

ofthreedigits.Theyfindtheproductsandrecordthese(theydonot

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.

If you have time

Discusswiththegrouptheresultsofthesemultiplications:

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 aTheassociativelaw: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



11/16

MultiplicationA1

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 inyour group. Can you find the multipliers to make their product?

What happens if you multiply these numbers together?

2 3 4


12/16

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

Doubling3-digitnumbersmentally(particularlywhen thehundreds

digitismorethan5)canbemuchtrickierthandoubling2-digit

numbers. Encourage children to make notes to help them with the

calculation.

Icanuseanewmultiplicationmethod.

Icandoubletohelpmemultiply.

Icanestimateandcheckcalculationsusing differentmethods.

Be aware Outcomes

ThissitehasaPowerPointdemonstrationofEgyptianmultiplication(GotoFreeDownloads,then Powerpoint 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.

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 tochooseanappropriatedoublingstrategyforeachnumber.For2-digit

numbers children should be able to partition and double mentally.

Somemayalsobeabletodothisfor3-digitnumbers,ortheymay

preferamixtureofmentalstrategiesandjottings.Themethodworks

inexactlythesamewayfor3-digitnumbers.Childrencanuseother

methods 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

Usedoublingorhalvingto findnewfactsfromknownfacts

Multiplyusingcloselyrelatedfacts

Extendmentalmethodsforwhole-numbercalculations,e.g.to

multiplya2-digitby1-digitnumber(e.g.129),tomultiplyby25

(e.g.1625),tosubtractonenearmultipleof1000fromanother

(e.g.60704097)

Representapuzzleorproblembyidentifyingandrecording

the information or calculations needed to solve it; find possiblesolutions and confirm them in the context of the problem




13/16

Egyptian multiplication

Does this method work with 3-digit numbers? Make upsome 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 useddoubling.

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

B2Multiplicationand division

13

To solve 46 23, draw a table with

1 in the left-hand column and 23 in

the right-hand column. Double thenumbers in each column until thenumber in the left-hand column isgreater than 46.

1 23

2 46

4 92

8 18416 368

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 Egyptianmethod to find the answers.

1 21 36 2 31 27 3 39 52 4 53 28 5 77 43


14/16

Challenge Plan: Year 6B1: odd and even numbers; common multiples; smallest common

multiple; properties of 2D shapes; classifying quadrilaterals

Childrenwillneeddexteritytousecompassesaccurately.Check

that children are able to do this and support those that find it more

difficult.

Icanconstructtrianglesusingaruler,aprotractorandapairof

compasses.

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.Askthemtolookat the

triangles.

What information are we given about these triangles? (therightangles and the lengths of some of the sides)

Can we draw these triangles, using just this information?

Childrendrawa12cmhorizontallinehalf-waydownapieceof

paper,thenmeasureanangleof90atoneendusingaprotractor.

Theythendrawan8cmlineperpendiculartotheoriginalline,following the right angle.

Theyjointheendsof thetwolines,measurethelengthofthisline

and 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 10cm from each end of our

line, so if we join them up we will get an equilateral triangle.

Childrenjoinupthethreepointstomakeatriangle.We have drawn

triangle 2!

Childrenusetheiranglemeasurerstoconfirmthatitisan equilateral

triangle.(Eachangleis60.)

Can you think how the third triangle could be constructed?(Itcanbe

made using the compasses method, but changing the lengths.)

Childrendrawtriangle3andmeasuretheanglesto checkthatthey

haveconstructeditcorrectly.(Theinternalanglesshouldaddupto

180.)

Childrenthenexperimentwithmethodsfordrawingtriangle 4.

Remindthemtochecktheangleswhentheyhavedrawntheir

triangle.

Extra help

Children who are not confident with using compasses can practise withgeo-stripsfirst.Theyfastenoneendtothebaselineandusethehole

to draw the arc.

Teacher notes



15/16

Constructing triangles

Some triangles are impossible to construct.Try to construct these three triangles. Which one is impossibleto 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 cm

7 cm

7 cm

5 cma

b

c

ShapeB1

b

6 cm

15


16/16

Ensure your most able mathematicians are stretched

to reach their full potential withAbacus 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 weeklyAbacus Evolve

planning, or used as a stand-alone resource, the

activities provide:

Group work and opportunities for discussion topromote Speaking & Listening

Open-ended investigations and problem solvingto promote Using & Applying

A balance of breadth, depth and pace.Each Year ofChallenge includes:

A Teacher Guide

A Pupil Book (a Workbook for Year 1, and

Textbooks for Years 26)

A Challenge Module of I-Planner Online.

0845 630 22 [email protected]

www.ginn.co.uk/abacusevolve

T xti/it

T tiit

Breadth Depth Pace

Discover Practise Teaching

Investigate ProblemSolving

Game

I guid

ThIs samplebookleT conTaIns one acTIvITy from each of years 16.

Visit www..

.u/u to place

an order or call our friendly

team on 0845 630 22 22

I S B N 9 7 8 -0 - 6 02 - 5 78 9 8 -5

www.pearsonschools.co.uk

Documents

Maths Challenge Workbook for Ukg