IMPROVING NUMERACY OUTCOMES PROJECT NUMERACY ACTIVITIES .
IMPROVING NUMERACY OUTCOMES PROJECTNUMERACY ACTIVITIES ANDLESSON SEQUENCES K-10NSW DEPARTMENT OF EDUCATIONLEARNING AND TEACHING DIRECTORATE
NUMERACY FOCUS AREASSPATIALVISUALISATION,GEOMETRICREASONING ANDMAPPINGMEASUREMENTAND TIMECALCULATIONSSTATISTICS ANDPROBABILITYApplying conceptsof 3D objectsUnderstandinglengthInterpreting andanalysing dataEstimating andproblem solvingApplying conceptsof 2D shapesUnderstandingareaRepresenting datain graphsand timelinesAddition,subtraction,multiplicationand divisionApplying anglesand geometryUnderstandingmass, volumeand capacityMENTALCOMPUTATIONAND NUMERICALREASONINGUnderstandinginformation in textsUnderstandingfractions, decimals,percentages, ratesand ratiosPATTERNS ANDALGEBRAPatterning,generalisations andalgebraic reasoningUnderstandingposition, mapsand gridsInterpretingchance, eventsand probabilityUnderstanding timeUnderstandingmoney and finance2NSW Department of Education 2017 Numeracy Activities and Lesson Sequences K-10
CONTENTSIntroduction.6FRACTIONS Stage 1 The Concept of a Half.9FRACTIONS Stage 2 Understanding Fractions.12FRACTIONS Stage 2 Related Fractions.14FRACTIONS Stage 3 and 4 Adding, Subtracting and Comparing Fractions.32NUMBER Stage 2 Mathematical Problem Solving a Focus on Strategies.37NUMBER Stage 2 Mathematical Problem Solving a Focus on Language.43NUMBER Stage 2 Applying Addition and Subtraction.70NUMBER Stage 2 Problem Solving a Focus on Addition and Subtraction.75NUMBER Stage 2 Applying Multiplication and Division.79NUMBER Stage 2 Applying the Four Operations.82FRACTIONS AND DECIMALS Stage 2 and 3 Fractions and Decimal Representations.84NUMBER Stage 2 and 3 Mathematical Problem Solving a Focus on Reading.88NUMBER Stage 2 and 3 Multiplication and Division Problems.94NUMBER Stage 3 Multi-Step Problem Solving Strategies.98MONEY AND NUMBER Stage 2 Applying Whole Number Concepts and Understanding Money.105NUMBER Stage 2 Applying Whole Numbers and Understanding Place Value.109NUMBER Stage 3 Understanding Place Value.112NUMBER Stage 3 Place Value, the Four Operations and Money Problems.116FRACTIONS Stage 3 Comparing Fractions Using a Fraction wall.128FRACTIONS Stage 3 and 4 Classifying and Finding Fractions of Quantities.137DECIMALS Stage 4 Multiplying Decimals and Money Quantities.147FRACTIONS Stage 4 Comparing Fractions.158MULTI-STEP PROBLEM SOLVING Stage 2, 3 and 4 Applying the Four Operations.161PATTERNS AND ALGEBRA Stage 1 Introducing Patterns.164PATTERNS AND ALGEBRA Stage 1 Understanding Patterns.168PATTERNS AND ALGEBRA Stage 2 Identifying Patterns.171PATTERNS AND ALGEBRA Stage 2 Problem Solving Involving Pattern.173PATTERNS AND ALGEBRA Stage 2 Exploring Number Patterns.178PATTERNS AND ALGEBRA Stage 3 Patterns and Rules.182PATTERNS AND ALGEBRA Stage 3 Table of Values and the Cartesian Plane.186PATTERNS AND ALGEBRA Stage 3 Analysing and Continuing Patterns.190GEOMETRY Stage 1 Spatial Visualisation, Geometric Reasoning and Mapping.192GEOMETRY Stage 2 Understanding Geometry and Applying 2D Shapes.197GEOMETRY Stage 4 Transformations.199MEASUREMENT Stage 2 Length and 2D Shapes.206MEASUREMENT Stage 3 Understanding Measurement and Applying Length Concept.210MEASUREMENT Stage 3 Volume and Capacity.218NSW Department of Education 2017 Numeracy Activities and Lesson Sequences K-103
DATA Stage 2 Displaying Data.220DATA Stage 2 and 3 Displaying and Interpreting Data.222DATA Stage 2 and 3 Interpreting and Displaying Data.230CHANCE Stage 3 Understanding Chance and Events.240DATA Stage 3 and 4 Displaying Data, Sector Graphs.243DATA Stage 4 Interpreting and Representing Data Variables.245DATA Stage 4 Understanding Statistical Surveys and Data Collection.261DATA Stage 4 Variables, Data Analysis and Surveys.267PROBABILITY Stage 4 Understanding Probability.289PROBABILITY Stage 4 Statistics and Probability Across the Curriculum.293Numeracy Across the CurriculumKEIRA HIGH SCHOOLPROBLEM SOLVING Stage 3 and 4.306KURRI KURRI HIGH SCHOOLCOMPARING SIZE OF COUNTRIES Stage 4 LOTE .327COLOUR MIXING RATIOS Stage 4 CAPA.333KING RICHARD III DOT PLOTS Stage 4 HSIE.338DATA PERSPECTIVE ON SOURCES Stage 4 English.343DATA BERTIE BOTT’S GRAPHING Stage 4 Science.345FRACTIONS AND DECIMALS POISONOUS POTIONS Stage 4 Science.347DECIMALS Stage 4 Operating with Decimals.349FRACTIONS Stage 4 Operating with Fractions.351MEASUREMENT Stage 4 Converting Units.353PERCENTAGES Stage 4 Operating with Percentages.355TIME ZONES Stage 4 Calculating Time.357LITHGOW HIGH SCHOOLDOT PLOTS Stage 4 Analysing and Interpreting Data.359TRANSLATIONS IN THE CARTESIAN PLANE Stage 4.368ALGEBRAIC TECHNIQUES Stage 4 Algebraic Expressions.379MULWAREE HIGH SCHOOLRATES AND RATIOS Stage 4 Unit Pricing.387RATES AND RATIOS Stage 4 Comparing Units.390RATES AND RATIOS Stage 4 Best Buys.392NAREENA HIGH SCHOOLMONEY Stage 3 Money Addition and Subtraction.3974NSW Department of Education 2017 Numeracy Activities and Lesson Sequences K-10
TAREE HIGH SCHOOLFRACTIONS Stage 3 and 4 Understanding Fractions.399VOLUMES Stage 3 Investigating Volume of Prisms.403RATIO Stage 3 and 4 Proportional Thinking.408WINGHAM HIGH SCHOOLDECIMALS Stage 4 Decimal Relay.410DATA Stage 4 Calculating Mean.412PERCENTAGES Stage 4 Calculating Price Increase and Decrease.414GEOMETRIC FIGURES Stage 4 Reflection, Rotation and Translation.416GALSTON HIGH SCHOOLNUMERACY GUIDE 1 Stage 4 Fractions, Decimal and Percentage.418NUMERACY GUIDE 2 Stage 4 Examples of Fractions, Decimal and Percentage.420NUMERACY GUIDE 3 Stage 4 Spatial Visualisation, Geometric Reasoning and Mapping.422NUMERACY GUIDE 4 Stage 4 Measurement and Time Calculations.427NUMERACY GUIDE 5 Stage 4 Mental Computation and Numerical Reasoning.433FITNESS TESTING – GRAPHICAL REPRESENTATION AND DATA ANALYSIS Stage 4 PDHPE.436SMOKING CALCULATIONS – APPLYING ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISIONStage 4 PDHPE.438ATHLETICS – UNDERSTANDING AND APPLYING LENGTH CONCEPTS Stage 4 PDHPE.440RISKY SITUATIONS - UNDERSTANDING AND APPLYING LENGTH CONCEPTS Stage 4 PDHPE.442HEALTHY EATING PLAN - INTERPRETING AND ANALYSING DATA Stage 4 PDHPE.444PARTICIPATION IN SPORT AND RECREATION INTERPRETING AND ANALYSING DATA Stage 4 PDHPE.446APPLICATION OF MEASUREMENT – MEASUREMENT Stage 4 TAS.448PENCIL BOX - APPLYING CONCEPTS OF ANGLES, GEOMETRY AND 2D SHAPES Stage 4 TAS.450CHICKEN SAUSAGE ROLLS - APPLYING ADDITION, SUBTRACTION, MULTIPLICATION, DIVISION, APPLYINGFRACTIONS AND DECIMALS Stage 4 TAS.452JAPAN UNDER THE SHOGUNS – CONSTRUCTING TIMELINES Stage 4 HSIE.454UNDERSTANDING CONTOUR LINES – SPATIAL VISUALISATION, GEOMETRIC REASONING AND MAPPINGStage 4 HSIE.456TESTING REACTION TIME – INTERPRETING AND ANALYSING DATA, CALCULATING MEAN AND INVESTIGATINGOUTLIERS Stage 4 Science.458CALCULATING DOSAGE – MASS VOLUME, RATES AND RATIO Stage 4 Science and Agriculture.462FEEDING AND GROWING PIGS; SLAUGHTER AND SELLING – DISPLAYING AND INTERPRETING DATAStage 4 Science and Agriculture.464OIL BURNER – MEASUREMENT AND VOLUME Stage 4 Visual Arts.468CALCULATING DISTANCE USING RATIO SCALE ON A MAP – MAPPING, SCALE AND RATIO Stage 4 HSIE.471CROOKWELL HIGH SCHOOLISNIP EQUIVALENT FRACTIONS Stage 3 and 4.473NSW Department of Education 2017 Numeracy Activities and Lesson Sequences K-105
INTRODUCTIONThis resource contains a collection of numeracy activities and teaching sequences to enhance andimprove student outcomes in numeracy. All the activities were implemented in classrooms and studentsshowed significant improvement in numeracy outcomes. Students were pre-tested and post-testedusing NAPLAN questions and extended response questions. Students were asked to explain how theysolved the problems and explain thinking strategies. Student work samples were analysed and thedata used to inform and guide teaching. The syllabus areas covered by the activities were areas wherestudents performed below state average in NAPLAN and teachers identified as common problem areas.THE TEACHING AND LEARNING CYCLEWhat doI wantmy studentsto learn?ongoingongoingAssessing andrecordingPlanning andprogrammingHow do Iknow whenmy studentsget there?egClassroompracticeHow willmy studentsget there?ongoingntiouaalveReportingQualityteaching &assessingWhere aremy studentsnow?eionatluvantioualvaionatluvaeExplicit and systematic teaching and learning will best occur when teachers follow the process articulated by the teachingand learning cycle. The teaching and learning cycle represents the four stages that occur in the design and deliveryof classroom tasks that incorporate an outcomes-based approach. The cycle has no start or end point, with each stepinforming the next. It is the process of gathering data and reflection that indicates where in the cycle you are operating.ongoinASSESSMENTAssessment is an essential component of the teaching and learning cycle. Assessment enables teachers to gatherevidence and make judgements about student achievement. Assessment for learning and assessment of learningmay be used individually or together and formally or informally.The principles of assessment for learning and assessment as learning have some common elements. Assessmentfor learning and assessment as learning incorporate: self-assessment and peer assessment strategies for studentsto actively monitor and evaluate their own learning feedback, together with evidence, to help teachers and studentsdecide whether students are ready for the next phase of learning or whether they need further learning experiencesto consolidate their knowledge, skills and understanding.Assessment for learning and assessment as learning approaches, in particular, help teachers and students to know ifcurrent understanding is a suitable basis for future learning. Teachers, using their professional judgement in a standardsreferenced framework, are able to extend the process of assessment for learning into the assessment of learning.6NSW Department of Education 2017 Numeracy Activities and Lesson Sequences K-10
TEACHING AND LEARNING SEQUENCEThe teaching and learning sequences of activities inthis resource includes assessment of prior knowledge,explicit teaching strategies and learning activities tointroduce, develop and consolidate concepts.Explicit teaching and learning strategies havebeen differentiated into: modelled guided independentAssessment for/of learningAssess students’ learning to determine their currentlevel of knowledge and skills and provide them withpurposeful feedback.PlanningPlan a lesson or series of lessons based onassessment and clearly focus planning on whatneeds to be taught and how it is taught.Modelled teaching is mainly teacher-regulated andinvolves explicit or direct instruction in new learning, thefocus of which is informed by assessment information.Students can say, I have learned something new.Guided teaching involves supporting student practicewhere students take increasing control of new learning.Students can say, I will have a go by myself, but I mightneed some help.Independent teaching involves supporting students toconsolidate, transfer and apply new learning. Students cansay, I know how to do it and when, where and why to use it.Each of the lessons may have a mixture of modelled,guided and independent activities. Some lessons aremore explicit and involve mainly modelled activities,some may focus on independent activities where theteacher plays the role of a facilitator.Learning activities and tasks have been differentiated toinclude introductio
2 NSW Department of Education 2017 Numeracy Activities and Lesson Sequences K-10 MENTAL COMPUTATION AND NUMERICAL REASONING Understanding information in texts Estimating and problem solving
Practical Numeracy is a course run from S1-S3. The Practical Numeracy course will help to develop the numeracy skills you will use in your practical STEM subjects. The numeracy skills you will use in Practical Numeracy are the same skills you will be using in all your other STEM subjects. These are called transferable skills.
level of proficiency in functional (a) literacy and (b) numeracy skills. The target age group for this indicator is the population of 15 years and older. This report recommends that the literacy and numeracy indicators be based upon the definitions of literacy and numeracy used in the OECD’s PIAAC adult skill assessment program.
Practise 4 Times Tables you wearing your hat by and/or Fitness Practise 11 Times Tables and/or Fitness Practise 3 Times Tables and/or Fitness Practise 7 Times Tables Numeracy Ninjas Session 1 Week 10 Numeracy Ninjas Week 10 Session 2 Numeracy Ninjas Week 10 Session 3 Wellbeing Numeracy Nin
level of literacy and numeracy of young children, particularly those from the hardest-to-reach families. Early childhood professionals have traditionally concentrated their literacy and numeracy efforts on programming for children’s spoken development and focused on the development of number. For instance, we often plan to
Learning Pathways in Numeracy: Addressing Early Numeracy Skills Except where otherwise noted, content in this document is licensed by the Office of Superintendent of Public Instruction under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
of the components. In total, we found 29 appropriate or informative frameworks applicable to adult numeracy. From these documents and from our understanding of the existing body of related research, we propose three major components that form and construct adult numeracy: 1. Context — the use and purpose for which an adult takes on a task with
Numeracy Professional Skills Practice Test 1 This is a practice test adapted from Department for Education practice tests which can be . 75% of pupils achieved 52% or more in Test A. 20 25 30 35 40 45 50 55 60 65 70 Test A Test B) www.sigma 25 -network.ac.uk Numeracy Professional Skills Test1.
2 Annual Book of ASTM Standards, Vol 06.03. 3 Annual Book of ASTM Standards, Vol 14.03. 4 Reagent Chemicals, American Chemical Society Specifications, American Chemical Society, Washington, DC. For suggestions on the testing of reagents not listed by the American Chemical Society, see Analar Standards for Laboratory Chemicals, BDH Ltd., Poole, Dorset, U.K., and the United States Pharmacopeia .
