Maths Challenge Workbook for Ukg
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Transcript of Maths Challenge Workbook for Ukg
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7/30/2019 Maths Challenge Workbook for Ukg
1/16
Challenge
Framework Edition
Samplebooklet
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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
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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
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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
Supporting resources
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
4 www.pearsonschools.co.uk/abacusevolve
Abacus Evolve objectives Framework objectives
Teacher notes
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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
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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
6 www.pearsonschools.co.uk/abacusevolve
Summary
Abacus Evolve objectives Framework objectives
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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
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Year 3 Block A1 Challenge PCM 1
Growing on trees 1
1
1000
1000
AbacusEvolve
Year3Challe
ngePCMPearsonEducationLtd2009
2
100 1500
250
50
116 www.pearsonschools.co.uk/abacusevolve
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Year 3 Block A1 Challenge PCM 2
Growing on trees 2
3
1000
0
AbacusEvolve
Year3Challe
ngePCMPearsonEducationLtd2009
117
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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
Year4ChallengeTextbookpage11
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)
Abacus Evolve objectives Framework objectives
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
10 www.pearsonschools.co.uk/abacusevolve
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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
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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
Supporting resources
Summary
Egyptian multiplication
Individuals, pairs or groups working independently
Year5ChallengeTextbookpage13
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
Abacus Evolve objectives Framework objectives
12 www.pearsonschools.co.uk/abacusevolve
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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
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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
Abacus Evolve objectives Framework objectives
Summary
Y6 B1.5 Constructing triangles
A group working with an adult
Year6ChallengeTextbookpage15
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
14 www.pearsonschools.co.uk/abacusevolve
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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
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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..
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an order or call our friendly
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