steve lomax @maxthemaths - swindon teaching schools · teaching for mastery in mathematics key...
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Steve Lomax@MaxTheMaths
@GLOWMathswww.glowmathshub.com
www.kangaroomaths.com
www.kangaroomaths.com >Kenny’sPouch>SchemesofWork
TeachingforMasteryinMathematicsKeyCharacteristics
+A‘Theme’iselaboratelydesignedandtaughtusingasequenceof‘KeyLearningPoints’
+Intelligentpracticeisusedtofocusondevelopingconceptualunderstanding,practise thethinkingprocesswithincreasingcreativityandavoidmechanicalrepetition.
+Examplesandtasksarecarefullydesignedusingvariationtheory:- ConceptualVariation(Knowledge)Positive- WhatitisNegative- Whatit’snot- ProceduralVariation(Process)Applying todifferentcontextsSolvingproblemsMakingconnections
+Possiblesolutionsshared,explainedanddiscussedtodeepenunderstanding.Theanswerisonlythebeginning.
ere's theanswer,what’sthequestion?
oyouagree?ActiveArgument/Cognitiveconflict:Yes/No,True/False,Always/Sometimes/Never
xplicit useofmisconceptionsandmistakes
hemissingsymbols/digits‘EmptyBox’questions
robingQuestions(i.e. Showme,andanother,andanotherthatno-onewillhaveConvinceme,What's the same,what'sdifferent?)
Theanswerisonlythebeginning
count inmultiplesof6,7, 9,25and1000
find 1000more or lessthan agiven number
count backwardsthrough zeroto include
negative numbers
recognise theplacevalue ofeachdigit
ina four-digitnumber
(thousands, hundreds, tens,andones)
order andcompare numbersbeyond 1000
identify, represent andestimate numbersusing differentrepresentations
round anynumberto thenearest10, 100or1000
solve number and practicalproblems
that involve alloftheabove andwithincreasingly largepositive numbers
read Roman numerals to100 (I toC)and know
thatover time, thenumeralsystem changed to includetheconcept of zero and
place value
addand subtractnumbers with up to4digits
using theformal written
methods ofcolumnaraddition and subtraction
where appropriate
estimate anduseinverse operationstocheckanswerstoacalculation
solve addition and subtractiontwo-step problems in contexts,deciding which operations and
methods touseandwhy
recall multiplication anddivision facts formultiplicationtables up to12× 12
useplacevalue, knownandderived factstomultiply
anddivide mentally, including:multiplying by0and1;dividing by1;multiplyingtogether threenumbers
recognise andusefactorpairs andcommutativity
inmental calculations
multiply two-digit and three-digit numbers byaone-digitnumber using formalwritten
layout
solve problems involving multiplyingandadding, includingusingthedistributive lawto
multiply twodigit numbers byonedigit, integerscalingproblemsand
hardercorrespondenceproblemssuchasnobjectsareconnectedtomobjects
recognise andshow,using diagrams,families of
common equivalentfractions
solve comparison, sumanddifference problems
using informationpresented in bar
charts, pictograms, tablesandother graphs
interpret andpresentdiscrete and
continuous datausing appropriate graphicalmethods, including barcharts and time graphs
plot specified pointsanddraw sidestocomplete agiven polygon
describe movementsbetween positions as
translations ofagiven unit to the
left/right and up/down
describe positions ona2-Dgridas
coordinates inthe first quadrant
complete a simplesymmetric figurewith respect toa
specific line of symmetry
identify lines ofsymmetry in2-Dshapes
presented in differentorientations
identify acuteandobtuse angles andcompare
andorder angles
up to two right angles bysize
compare andclassifygeometric shapes, includingquadrilaterals and triangles,based on their properties
andsizes
solve problems involvingconverting fromhours tominutes;
minutes toseconds; years tomonths;
weeks todays
read, write and convert timebetween analogue and
digital 12- and24-hour clocks
estimate, compare andcalculate different
measures,including money
inpounds and pence
find theareaofrectilinear shapes bycounting
squares
measure and calculate theperimeter ofa
rectilinearfigure (including squares)incentimetres and metres
Convert betweendifferent units ofmeasure[forexample, kilometre tometre;hour tominute]
solve simple measureandmoney problems
involvingfractions anddecimals
to two decimal places.
compare numbers with thesame number ofdecimalplaces up to two decimal
places
round decimals withone decimal placeto thenearestwhole number
find theeffectofdividingaone- or two-digit number by
10and100,identifying the
value of thedigitsin the answer asones, tenths
andhundredths
recognise andwrite decimalequivalentsto¼,½, ¾
recognise andwrite decimalequivalents
ofanynumberof tenths orhundredths
addand subtractfractions with thesame denominator
solveproblems involving increasinglyharder fractions to
calculatequantities, andfractions todividequantities,includingnon-unit fractionswhere theanswer isawhole
number
count upanddown inhundredths; recognise that
hundredthsarise when
dividing anobject byonehundred anddividing tenths
by ten
www.kangaroomaths.com >Kenny’sPouch>SchemesofWork
The first part of a framework for assessing without levels: a maximum of
13 mastery indicators each year are chosen to represent the most important
skills that students need to acquire in order to make progress in their
mathematics
Alongside the mastery indicators, essential knowledge lists the facts
that students need to know in order to make progress in their
mathematics
www.kangaroomaths.com >Kenny’sPouch>SchemesofWork
Potential KEY LEARNING POINTS.
www.kangaroomaths.com >Kenny’sPouch>SchemesofWork
www.kangaroomaths.com >Kenny’sPouch>Assessment
www.kangaroomaths.com >Kenny’sPouch>Assessment
BAM!