4年级数学教学大纲

2020-06-15 12:45余昊老师
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4年级数学教学大纲

TermOne

Unit 1 (Algebra 1)

     Use mental calculationstrategies to solve number problems involving money and measures

     Explore and recordpatterns using to addition and subtraction

     Recognise and extendnumber sequences formed by counting on from any number in steps of a constantsize

     Use practical contexts togenerate sequences

     Recall quickly theaddition and subtraction facts of numbers up to 20

     Use all four operations tosolve simple number problems

     Begin to use symbols torepresent mathematical work

     Recall quickly 2, 3, 4, 5and 10 multiplication tables

     Use a rule to generateterms of a number

     Describe the rules ofsimple sequences

     Begin to explore thepositions of terms in a sequence

     Begin to understand theconcept of a function machine

Unit 2 (Number 1)

     Read and write wholenumbers to at least 1000 in figures and words

     Order whole numbers to atleast 100, then 1000, and position them on a number line

     Know what each digitrepresents, and partition 3-digit numbers into multiples of 100, 10 and 1 (HTU)

     Recall quickly additionand subtraction facts for all numbers to 20, pairs of multiples of 10 totalling100, and multiples of 100 totalling 1000

     Use mental calculationstrategies including using known number facts and place value to add mentally

     Derive quickly all numberpairs that total 100 and the related subtraction facts

     Subtract mentally usingmultiples of 10

     Use informal pencil andpaper methods to support, record or explain HTU + TU, HTU + HTU, HTU TU and HTU HTU

     Begin to use columnmethods for HTU + TU and HTU TU where the calculation can not be done mentally

     Find a small difference bycounting on

     Check results ofcalculations, understand that addition and subtraction are inverse operations,know that addition can be done in any order, or that an equivalent calculationcan be used

     Round numbers to thenearest 10 and 100 and use rounding to estimate answers

     Use rounding to estimateanswers to addition and subtraction answers

Unit 3 (Geometry and measures 1)

     Solve one-step andtwo-step problems involving measures

     Identify and estimatefractions of shapes

     Know the relationshipsbetween kilometres and metres, metres and centimetres, kilograms and grams,litres and millilitres

     Read, to the nearestdivision and half-division, scales that are numbered or partially numbered; usethe information to measure and draw to a suitable degree of accuracy

     Choose and use appropriateunits to estimate, measure, and record measurements

     Find the area of shapesdrawn on a square grid by counting squares

     Measure and calculateperimeters of rectangles

Unit 4 (Number 2)

     Recognise and comparesimple unit fractions

     Recognise fractions makingone whole

     Estimate and findfractions of shapes and numbers

     Position simple fractionson a number line

     Recognise fractions thatare several parts of a whole

     Compare simple non-unitfractions using diagrams

     Recognise simpleequivalent fractions

     Begin to find remaindersafter simple division

Unit 5 (Statistics 1)

     Use simple lists andtables to communicate findings

     Use Venn and Carrolldiagrams to sort and classify data

     Extract data from simplegraphs, charts and diagrams

     List possible outcomes

     Collect and record data

     Interpret and constructbar charts

Unit 6 (Algebra 2)

     Know that addition andmultiplication can be carried out in any order, but that order is important insubtraction and division

     Recall quickly additionand subtraction facts of numbers to

20

     Choose and use appropriatenumber operations and ways of calculating to solve problems

     Add tens and units withoutcrossing a boundary

     Recognise the use ofsymbols (such as   and   ) to stand for unknown numbers

TermTwo

Unit 7 (Geometry and measures 2)

     Recognise that a straightline is equivalent to two right angles

     Read and record thevocabulary of position, direction and movement, using the four compassdirections to describe movement about a grid

     Know that angles aremeasured in degrees and that one whole turn is 360°

     Compare and order anglesless than 180°

     Use the eight compasspoints to describe direction

     Describe and identify theposition of a square on a grid of squares

Unit 8 (Statistics 2)

     Formulate questions andpossible responses for a survey

     Determine possibleoutcomes of a survey

     Extract and interpret datafrom pictograms

     Construct pictograms wherea symbol represents a group of units

     Extract and interpret datapresented in a bar graph

     Construct a bar graph

Unit 9 (Number 3)

     Choose and use appropriateoperations to solve simple word problems and begin to explain thinking

     Understand place value andorder numbers up to 1000

     Use understanding of placevalue to multiply whole numbers by 10 or 100

     Round numbers to thenearest 10 and 100

     Recognise and interpretdecimal notation, including in the context of money

     Compare, add and subtractsimple decimals

     Recognise and use standardmetric units of length, capacity, mass and time in a range of contexts

     Add, subtract, double,halve and multiply small numbers using mental methods

     Recall quickly 2, 3, 4, 5,and 10 multiplication tables

     Use a formal writtenmethod for TU × U

     Use a calculator to solveproblems involving larger numbers and simple decimals

Unit 10 (Algebra 3)

     Explore and recordpatterns using addition and subtraction

     Explore patterns of multiplesof 2, 5 and 10, explaining the patterns and using them to make predictions

     Recognise and extendnumber sequences formed by counting on from any number in steps of a constantsize

     Use a rule to generateterms of a number sequence

     Begin to explore theposition of terms in a sequence

     Solve number problemsusing all four operations

     Begin to understand theconcept of a function machine

     Begin to express simplefunctions in words

     Find outputs of simplefunctions

     Describe and identify theposition of a square on a grid of squares

     Begin to read and plotcoordinates in the first quadrant

     Extract and interpret datapresented in bar graphs

     Begin to plot simplestraight-line graphs

Unit 11 (Geometry and measures 3)

     Use mathematical names forcommon 3-D and 2-D shapes

     Sort shapes and describesome of their features

     Classify and describe 3-Dand 2-D shapes

     Classify polygons asregular or irregular

     Reason about shapes, explainingmethods and thinking

     Solve mathematicalproblems or puzzles involving shapes

Unit 12 (Number 4)

     Recognise and understandunit fractions (hundredths)

     Understand fractions whichare several parts of a whole (hundredths)

     Begin to understandpercentage as the number of parts in

100

     Understand and usepercentages

     Find simple fractions ofwhole number amounts

     Use multiplication anddivision to solve word problems

     Solve word problemsinvolving money and measures

     Use a calculator for calculationsinvolving money

     Begin to use ideas ofsimple proportion

     Develop calculator skillsand use a calculator effectively

TermThree

Unit 13 (Algebra 4)

     Understand therelationship between addition and subtraction, and between multiplication anddivision

     Know that addition andmultiplication can be carried out in any order but subtraction and divisioncannot, and use this to perform mental calculation strategies

     Recognise the use ofsymbols (such as   and   ) to stand for unknown numbers and completecalculations using mental recall and a range of calculation strategies

     Begin to representexpressions using symbols

Unit 14 (Geometry and measures 4)

     Read and record thevocabulary of position, direction and movement, using compass directions todescribe movement about a grid

     Recognise horizontal andvertical lines

     Describe and identify theposition of a square on a grid of squares

     Know that angles aremeasured in degrees and that one whole turn is 360°

     Identify and sketch linesof symmetry in simple shapes

     Recognise shapes with nolines of symmetry

     Draw and complete shapeswith reflective symmetry and draw the reflection of a shape in a mirror linealong one side

     Derive and recall doublesof all numbers to 20 and corresponding halves

     Use understanding of placevalue to multiply whole numbers by 10 or 100

     Use understanding of placevalue to multiply and divide numbers to 1000 by 10 or 100 (whole numberanswers), and relate this to scaling up or down

     Solve one-step andtwo-step problems involving measures, choosing and carrying out appropriatecalculations

     Read scales and measureand draw to a suitable degree of accuracy

     Find the area ofrectilinear shapes drawn on a square grid by counting squares

     Draw rectangles andmeasure and calculate their perimeters

Unit 15 (Statistics 3)

     Use frequency tables torepresent results

     Answer a question byidentifying what data to collect

     Organise and present datain tables, diagrams, tally charts and bar charts

     Interpret data in barcharts

Unit 16 (Number 5)

     Know what a square numberis

     Recognise square numbersup to 10 × 10

     Use a calculator to workout and check simple multiplication calculations

     Develop calculator skillsrequired to calculate with powers

     Understand what a factoris

     Be able to find factorpairs

     Begin to understand what aprime number is

     Mentally recall 2, 5 and10 times tables

     Use the term multiple

Unit 16 (Number 5) continued

     Find multiples of familiarnumbers

     Recognise multiples of 2,5 and 10 up to 1000

     Know and extend knowledgeof the 2, 5 and 10 times tables

     Explore patterns ofmultiples of 2, 5 and 10, explain the patterns, and use them to makepredictions

     Understand therelationship between division and multiplication

     Recall multiplicationfacts for 2, 5 and 10 times tables and corresponding divisibility rules

     Recognise that fractionsmake one whole

     Add two simple fractions

     Recognise simple fractionsequivalent to one half

     Use simple fractions incontext

     Add and subtract 2-digitwhole numbers, and numbers with one decimal, in the context of measures

     Multiply TU × U

     Find half or quarter oflengths

     Understand therelationship between division and repeated subtraction

     Solve one- and two-stepword problems involving multiplication and division

     Understand why divisionproblems often have remainders

     Round remainders up ordown depending on context

Unit 17 (Algebra 5)

     Recognise and extendnumber sequences formed by counting on or back in steps of equal size

     Add and subtract mentallycombinations of 1- and 2-digit numbers

     Derive and recallmultiplication facts for the 2, 3, 4, 5, 6 and 10 times tables

     Solve one- and two-stepproblems involving numbers, money or measures

     Use positive and negativenumbers in context and position them on a number line

     State inequalities usingthe symbols < and >

     Use knowledge of numberoperations and corresponding inverses

     Derive and record relatedmultiplication and division number sentences

Unit 18 (Geometry and measures 5)

     Relate 2-D shapes and 3-Dsolids to drawings of them

     Use a set square to drawright angles and to identify right angles in 2-D shapes

     Describe, visualise,classify, draw and make 2-D and 3-D shapes

     Classify and describe 3-Dand 2-D shapes referring to properties

     Represent the informationin a puzzle or problem using numbers, images or diagrams; use these to find asolution and present it in context, including units of measure whereappropriate

     Identify patterns andrelationships involving numbers or shapes, and use these to solve problems

     Make shapes, eg constructpolygons by paper folding