#MathsEveryoneCan - White Rose Maths

Small Steps Guidance –Addition & SubtractionYear 7#MathsEveryoneCan

WRM – Year 7 Scheme of LearningWeek 1Week 2Week 3Week 4Week 5Week 6SequencesAutumnAlgebraic ThinkingUnderstanding andusing algebraicnotationEquality andequivalenceSpringSolving problems withmultiplication and divisionSummerLines and AnglesConstructing,measuring and usinggeometric notationWeek 8Week 9Week 10Week 11Week 12Place Value and ProportionApplications of NumberSolvingproblemswith addition& subtractionWeek 7Developing geometricreasoningPlace value andordering integers anddecimalsFraction, decimal andpercentageequivalenceDirected NumberFractional ThinkingFour operations withdirected numberAddition andsubtraction offractionsReasoning with NumberDevelopingnumbersenseSets andprobabilityPrimenumbers andproof

WRM – Year 7 Scheme of LearningSpring 1: Application of NumberWeeks 1 & 2: Solving problems with addition & subtractionWeeks 3 to 6: Solving problems with multiplication & divisionThe focus for this two weeks is building on the formal methods of addition andsubtraction students have developed at Key Stage 2. All students will look at thisin the context of interpreting and solving problems, for those for whom theseskills are secure, there will be even more emphasis on this. Problems will bedrawn from the contexts of perimeter, money, interpreting bar charts and tablesand looking at frequency trees; we believe all these are better studied alongsideaddition and subtraction rather than separately. Calculators should be used tocheck and/or support calculations, with significant figures and equationsexplicitly revisited.National curriculum content covered: use formal written methods, applied to positive integers and decimals recognise and use relationships between operations including inverseoperations derive and apply formulae to calculate and solve problems involving:perimeter construct and interpret appropriate tables, charts, and diagrams, includingfrequency tables, bar charts and pictograms for categorical data, and verticalline (or bar) charts for ungrouped numerical dataThe rest of the term is dedicated to the study of multiplication and division, soallowing for the study of forming and solving of two-step equations both withand without a calculator. Unit conversions will be the main context formultiplication by 10, 100 and 1000 and simple finding fractions and percentagesof an amount will be explored. As well as distinguishing between multiples andfactors, substitution and simplification can also be revised and extended. Againthe emphasis will be on solving problems, particularly involving area of commonshapes and the mean. Choosing the correct operation to solve a problem willalso be a focus. There will also be some exploration of the order of operations,which will be reinforced alongside much of this content next term when studyingdirected number.National curriculum content covered: use formal written methods, applied to positive integers and decimals select and use appropriate calculation strategies to solve increasinglycomplex problems recognise and use relationships between operations including inverseoperations use the concepts and vocabulary factors (or divisors), multiples, commonfactors, common multiples, highest common factor, lowest common multiple change freely between related standard units [time, length, area,volume/capacity, mass] derive and apply formulae to calculate and solve problems involving:perimeter and area of triangles, parallelograms, and trapezia (H) substitute numerical values into formulae and expressions, including scientificformulae use algebraic methods to solve linear equations in one variable (including allforms that require rearrangement) describe, interpret and compare observed distributions of a single variablethrough: the mean

WRM – Year 7 Scheme of LearningWhy Small Steps?We know that breaking the curriculum down into small manageablesteps should help students to understand concepts better. Too often,we have noticed that teachers will try and cover too many concepts atonce and this can lead to cognitive overload. We believe it is better tofollow a “small steps” approach.As a result, for each block of content in the scheme of learning we willprovide a “small step” breakdown. It is not the intention that eachsmall step should last a lesson – some will be a short step within alesson, some will take longer than a lesson. We would encourageteachers to spend the appropriate amount of time on each step fortheir group, and to teach some of the steps alongside each other ifnecessary.What We Provide Some brief guidance notes to help identify key teaching andlearning points A list of key vocabulary that we would expect teachers to draw tostudents’ attention when teaching the small step, A series of key questions to incorporate in lessons to aidmathematical thinking. A set of questions to help exemplify the small step concept thatneeds to be focussed on. These include reasoning and problem-solving questions thatare fully integrated into the scheme of learning. Dependingon the attainment of your students, you many wish to usesome or all of these exemplars, which are in approximateorder of difficulty. Particularly challenging questions areindicated with the symbol. For each block, we also provide ideas for key representationsthat will be useful for all students.In many of the blocks of material, some of the small steps arein bold. These are content aimed at higher attaining students,but we would encourage teachers to use these with as manystudents as possible – if you feel your class can access anyparticular small step, then please include it in your planning.

Year 7 Spring Term 1 Application of NumberCountObjects to 100Key RepresentationsExemplificationConcrete, pictorial and abstractrepresentations are an important part ofdeveloping students’ ���𝒄𝒄 84Tens100Ones?Number lines are particularly useful forboth addition and subtraction andprovide a good model of mentalmethods.?True or False? 𝑎𝑎 𝑏𝑏 𝑑𝑑 𝑐𝑐Hundreds45?121The column methods are sometimesnot understood by students and aretherefore prone to error. Linking theseformal methods to the use of placevalue counters and/or base 10 blocksillustrating exchanges is very useful.

Year 7 Spring Term 1 Application of NumberAddition and SubtractionSmall StepsProperties of addition and subtractionMental strategies for addition and subtractionUse formal methods for addition of integersUse formal methods for addition of decimalsUse formal methods for subtraction of integersUse formal methods for subtraction of decimalsChoose the most appropriate method: mental strategies, formal written or calculatorSolve problems in the context of perimeterSolve financial maths problems

Year 7 Spring Term 1 Application of NumberAddition and SubtractionSmall StepsSolve problems involving tables and timetablesSolve problems with frequency treesSolve problems with bar charts and line chartsAdd and subtract numbers given in standard formHdenotes higher strand and not necessarily content for Higher Tier GCSEH

Year 7 Spring Term 1 Application of NumberCountObjectsto 100 & subtractionPropertiesof additionExemplar QuestionsNotes and guidanceList all the additions and subtractions that these diagrams show.What other models could you use?37Students will know from earlier study that addition andsubtraction are inverses, and that addition is commutativebut subtraction is not. This step reinforces these conceptsand the associated language and encourages multiplerepresentations of calculations to deepen understanding. Itis useful to extend this to algebraic expressions and also touse the associative law to simplify calculations.Key 5610733Number LineInverseKey questionsIf we know 𝑥𝑥 𝑦𝑦 𝑧𝑧, what other addition facts do weknow? What subtraction facts do we know?What’s the easiest way to add a list of numbers like this:6 8 4 7 2 3?How could a number line help us to find the differencebetween, say, 186 and s bar model illustrates that7 3 3 7We say addition is commutative.Generalise the above exampleusing this second bar model.Is subtraction commutative?Why, or why not?17 26 14 17 26 1417 26 14 17 26 1443 14 17 4057 57This example shows thataddition is associative.Which is the easiest way to findthe sum of the three numbers?Why?Marcel says that addition and subtraction are inverse operations.Use examples and diagrams to explain what this means.

Year 7 Spring Term 1 Application of NumberCountto 100MentalObjectsstrategiesExemplar QuestionsNotes and guidanceHere are some ways of working out 78 96This small step looks at ways students can develop theirflexibility and efficiency in mental addition and subtractioncalculations. Increased flexibility in their choice of strategyis developed through regular discussion and comparisonof different approaches. The use of part-whole modelsand number lines to illustrate methods will help students’understanding.Key vocabularyBridgingDifferenceCompensationCount OnPartitionNumber bondsKey questionsMake up an example where number bonds to 10 and 100are useful to perform mental calculations.How does adding the same number to both parts of asubtraction affect the difference?Find three ways to mentally calculate 700 43878 96 2 280 9494 8017478 9696 7896 4 74100 7417478 9678 90 6168 617478 9670 90 8 6160 1417478 9678 100 4178 417478 96 4 474 100174Which strategies do you prefer and why?How would you work out each of these mentally?386 9957 6489 25478 9678 2 9480 94174694 238How does this number line show that 93 37 90 34?34 35 36 3790 91 92 93What strategies would you use to work out these subtractions mentally?786 29997 29852 13181 544378 2402000 18646502 1601

Year 7 Spring Term 1 Application of NumberCountto adding100 integersFormalObjectsmethods:Exemplar QuestionsTensNotes and guidanceOnesFor students who are confident with the formal method ofaddition, this small step will provide practice and revision.Students who find this more challenging should have theopportunity to revisit with concrete materials alongside theformal method to develop their understanding. Key vocabularyComplete these calculations.Column MethodPlace ValueExchangePlaceholderCarryingKey questionsWhy do we start column addition with the column on theright?When and why do we exchange in column addition?Is the column method always the best way to solve anaddition problem? What addition calculationis illustrated here?What exchange needs tobe done to complete thecalculation?Compare this to theformal written methodfor adding two integers.HTOHTOHTO187207386542643215 What are the similarities and differences between the calculations?Estimate the answers to these calculations and then use the columnmethod of addition to find the actual answers.2634 more than 180035172 sixty-seven thousand485 000 six hundred and seven thousand850 000 added to half a million7648 372 5063