# 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

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

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

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

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