using and applying/number and algebra - st. catherine's · pdf fileusing and...

Mathematics for Life Skills – Long Term Plan

Using and Applying/Number and Algebra

Topic – Properties of number (N1,3)

Objectives Basic Concepts

Levels P - 2 Verbalise numbers to 10 (1) Verbalise numbers to 100 (2) Distinguish between odd and even numbers (2) Aware of place value of HTU (2)

Levels 3 - 4 Verbalise numbers to 1000 (3) Use knowledge of place value to develop methods of computation (4)

Levels 5 - 6 Know prime numbers (5)

Topic – Order (N2,27)


Levels P - 2 Understand vocab, ‘how many/less/more/fewer/greater/some’ (1) Write and order nos to 10 (1) Write and order nos to 100 (2)

1- ‘a bit’, ‘a lot’, ‘some’ 2-‘many’, ‘more’ 3- ‘few’, ‘most’ 4- ‘fewest’, ‘less’

Levels 3 - 4 Write and order nos to 1000 (3) Order one digit decimals (3)

Levels 5 - 6

Topic – Patterns (N34)


Levels P - 2 Recognise and make repeating patterns and know how many in a repeat (1) Continue simple number patterns (1)


Explain how to find the next number in a pattern (2)

Levels 3 - 4 Explain simple number patterns and predict next number (3) Searches for patterns and tries own ideas (4)

Levels 5 - 6 Knows pattern of square and triangular numbers (5) Can describe in words the rule for the nth term of a sequence (6)

Topic – Number bonds (N6,8,9,10)


Levels P - 2 Use apparatus to add/subtract numbers to 10 (1) Solve problems of +/- up to 10 (1) Recall addition/subtraction facts to 10 (2) Add or subtract two whole numbers on a calculator (2)

Levels 3 - 4 Recall addition/subtraction facts to 20 (3) Solve problems of +/- up to two digits (3) Perform simple calculations using whole millions (3 Use addition and subtraction facts to 20 to solve problems involving larger numbers (3) Understanding equivalent functions (4)

Levels 5 - 6

Topic – Calculations


Levels P - 2 Recognise the symbols +,- and = (1) Lays out sums horizontally (1) Lays out sums vertically in the correct columns (2)

Levels 3 - 4 Add three digit numbers using paper methods including those with carrying (3)


Subtract three digit numbers using paper methods including those with decomposition (3)

Levels 5 - 6

Topic – Using and applying


Levels P - 2 Represents work with pictures (1) Represents work using simple pictures and diagrams (2)

Levels 3 - 4 Tries different approaches to a problem (3) Begins to organise work and check results (3) Uses and interprets mathematical symbols and diagrams (3) Uses a calculator appropriately (3) Finds outputs from function machines (3) Develops own strategies for problem solving (4) Uses strategies to apply mathematics to practical problems (4) Presents information and results in a clear and organised way (4)

Levels 5 - 6 Identifies and obtains necessary information before attempting problem (5) Checks results and considers whether these are sensible (5) Shows understanding by describing situations mathematically in a variety of ways (5) Makes own general statements based of own evidence and explains reasoning (5) Solves complex problems by breaking down into smaller tasks (6) Interprets and discusses information provided in a variety of forms (6) Writing explains and informs uses of diagrams (6) Gives mathematical justification for generalisations (6)


Can formulate and solve linear equations (6)

Topic – Tables (N15)


Levels P - 2

Levels 3 - 4 Recognise the need for multiplication (3) Recognise the word and symbol for division (3) Divide numbers less than 30 by numbers up to 6 (3) Understand remainders in context (3) Recall tables facts 5 x 5 and use them in division problems (3) Know times table up to 10 x 10 (4)

Levels 5 – 6 Know factors of numbers up to 100 (5)

Note: OCR objectives are in bold type OCR syllabus unit numbers are in brackets after the topic area headings. All other St. Catherine’s Mathematics Scheme of Work objectives are in regular type

Vocabulary:

Level 1: Lots of Level 2: More Level 3: Different, Between

Level 4: Less, Fewer

Digit Place value Number Hundredths Tens Units

Addition Add Plus Altogether Sum Add

Total Increase Count on Take away Subtraction Minus

Subtract More than Reduce Decrease Take from Multiply

Division Times Groups of Product Multiplication


Measures - Autumn Term 1st

Half

Topic – Length (S1,2,3,4,5)


Levels P - 2 Visually compare lengths, use and understand ‘longer/shorter than’ and ‘longest/shortest’ (1) Use a ruler to draw/measure lines in cm, mm (2) Measure lengths in m (2) Estimate the length of everyday objects (2) Know standard abbreviations for length (2) Know comparisons of length (1cm = 10mm etc.)

1 – ‘Little’, ‘Big’

2 – ‘Long’, ‘Small’

3 – ‘Short’, ‘Longest’, ‘Smallest’

4 – ‘Longer’, ‘Smaller’, ‘Shortest’, ‘Shorter’

Levels 3 - 4 Uses standard and non-standard units for length (3) Suggest what the unit of length would be (3) Estimate measurements and check results (3) Read scales labelled with unit divisions (3) Measure in tenths of a cm (4) Chooses appropriate units and instruments (4) Use the units mm, cm, m, km (3) Recognise abbreviations for units of length (3) Calculate the perimeter and area of simple compound shapes (4) Solve simple problems involving ratios and proportion (4)

Levels 5 - 6 Knows rough metric equivalents of imperial units (5) Can convert one metric unit to another (5)


Topic – Weight (S6,7,8,9,10)


Levels P - 2 Compare and judge whether n object is more/less than 1kg (1) Use and understand terms ‘Heavier/Lighter’ and ‘heaviest/lightest’ (1) Weigh objects less than 1kg and read kitchen scales (2) Know standard abbreviations for mass (2)

1 – ‘Heavy’

2 –

3 – ‘Heaviest’, ‘Light’

4 – ‘Heavier’, Lightest’

Levels 3 - 4 Uses standard and non-standard units for mass (3) Recognise abbreviations for units of weight (3) Use units g, kg (3) Suggest what the unit of weight would be (3) Estimate measurements and check results (3) Read scales labelled with unit divisions (3) Chooses appropriate units and instruments (4)


Topic – Capacity (S11,12,13,14)


Levels P - 2 Estimate measure and compare capacities using standard units (2)

Levels 3 - 4 Uses standard and non standard units for capacity (3) Recognise abbreviations for units of capacity (3) Suggest what the unit of capacity would be (3) Estimate measurements and check results (3) Use the units l, ml (3) Read and mark a scale/dial whose divisions are labelled in


1, 2 or 5 units (3) Read a scale/dial whose divisions represent 1, 2, 5 or 10 units (3) Chooses appropriate units and instruments (4)


Note: OCR objectives are in bold type OCR syllabus unit numbers are in brackets after the topic area headings. All other St. Catherine’s Mathematics Scheme of Work objectives are in regular type Vocabulary:

Level 1: Heavy

Level 2: Long, Near

Level 3: Tall, Short, Thin, Light, Far, Level 4: Thick, Deep, Least

Length Width Height Centimetre Millimetre Metre

cm mm m Unit Measure Ruler

Standard Metric Imperial Non-standard Scale Equivalent

Convert Estimate Compare Weight Millilitres Litres

Centilitres ml l cl Kilometres Miles

Pints Inches Feet Grams Kilograms kg

g Ounces Pounds Volume Perimeter Area

Pour Capacity


Shape and Space – Autumn Term 2nd

Half

Topic – 2D and 3D shapes (S34,38,26,27,28 ,29,30,34) (D4)


Levels P - 2 Sort and classify shapes using words such as ‘flat’, ‘curved’, ‘rounded’, ‘pointed’ (1) Sort and classify objects (1) Sort and classify plane shape using words such as ‘straight’, ‘curved’, ‘sides’, ‘corners’ (2) Recognize circle, triangle, square, rectangle, hexagon (2) Understand the terms ‘square’ and ‘rectangle’ and know and use the simple properties of these shapes (2) Draw a simple plane shape using pencil and ruler only (2) Identify pictures of three-dimensional objects (2) Know simple properties of 3D shapes (3)

1 – ‘Line’, ‘Round’

2 – ‘Circle’, ‘ Flat’, ‘Square’

3 – ‘Cross’, ‘Triangle’

4 – ‘Corner’, ‘Curved’, ‘Rectangle’, ‘Straight’

Levels 3 - 4 Sort 2D and 3D shapes (3) Understand the terms ‘face’ and ‘vertex’ (3) Understand the terms ‘right angle’ and ‘parallel to’ (3) Understand what is meant by ‘cube’, ‘cuboid’, ‘cone’, ‘sphere’ (3) Know how to construct nets of cubes and cuboids (4)

Levels 5 - 6 Construct triangles (5) Draw nets of triangular prisms and pyramids (5) Recognise and use 2D representations of 3D objects (6) Understand and use formula for finding area, volume, circumference and perimeter (6)


Topic – Angles (S15)


Levels P - 2 Recognise angle as a measure of turn (1) Recognise right angles and angles smaller or larger than a right angle (2)

1 – ‘Little’

2 – ‘Small’, ‘Biggest’

3 – ‘Large’, ‘Smallest’

4 – ‘Smaller’, ‘Largest’

Levels 3 - 4 Recognise angles smaller or larger than a right-angle (3) Measure angles in degrees (4) Compare angles (4)

Levels 5 - 6 Draw angles to the nearest degree (5) Use language associated with angles (5) Know and use angles of quadrilaterals and other polygons (6) Solve problems using angles (6)

Topic – Position and movement (S37, 16, 39)


Levels P - 2 Understand and use the terms ‘behind’, ‘in front of’, ‘above’, ‘below’, ‘right’, ‘left’, ‘next to’ (1) Understand the terms ‘clockwise’ and ‘anticlockwise’ and the idea of quarter, half and three quarters of a turn (2)

1 – ‘by’

2 – ‘behind’, ‘in front of’, ‘next to’

3 – ‘beside’, ‘between’

4 – ‘above’, ‘below’, ‘right’, ‘left’

Levels 3 - 4 Understand and use the four points of the compass (3) Understand and use the eight points of the compass (4) Use quarter, half and three quarters of a turn (3)


Know and use clockwise and anti-clockwise (3) Use grid references and coordinates (4)

Levels 5 - 6

Topic – Pattern (S31)


Levels P - 2 Recognise and continue repeating strip patterns (1) Explain how to find/draw the next shape in a spatial pattern (1)

Levels 3 - 4 Recognise and continue simple spatial patterns and sequence (3)

Levels 5 - 6 Enlarge a shape by scale factor (6) Transform shapes (6) Devise instructions for a computer to generate and transform shapes and paths (6)

Topic – Symmetry (S32,33)


Levels P - 2 Recognise shapes which are exactly alike (1) 1 –

2 – ‘Same’

3 – ‘different’ 4 –

Levels 3 - 4 Recognise symmetry in simple plane shapes (3) Recognise rotational symmetry (3) Know that shapes have 0, 1 or more lines of symmetry (3) Understand the congruence of simple shapes (3) Understand the terms ‘reflection’, ‘reflection symmetry’ (3)


Recognise simple plane shapes or drawings that have reflection symmetry (3)

Levels 5 - 6 Know the order of rotational symmetry for given shapes (5) Know and use symmetry properties of quadrilaterals and other polygons (6) Solve problems using symmetry (6)


Vocabulary:

Level 1:

Level 2:

Flat, rounded,

circle, square,

behind, in front of,

next to,

Level 3:

Triangle,

Level 4:

Curved, pointed,

straight, corners,

rectangle, below,

above

Sides Hexagon plane regular irregular equilateral

Isosceles 2D 3D net right angle parallel

Cube cuboid cone sphere acute obtuse

Degrees right left clockwise anti-clockwise turn

Quarter half three quarters north south east

West compass repeat pattern sequence face(s)


Solid area perimeter circumference volume symbol

Order plane symmetry reflection rotation line symmetry rotation symmetry

Refection symmetry

Money – Spring Term 1st

Half

Topic – Coin recognition (N21) & Amounts of money (N22)


Levels P - 2 Recognise British coins in everyday use (1) Compare values of different coins (2) Find equivalent ways of making a given amount (2) Select coins equivalent to an amount of money up to 50p (2)

Levels 3 - 4 Select coins equivalent to an amount of money up to £5 (3) Understand fractions of money (4)

Levels 5 - 6 Use combinations of operations to solve money problems (5)

Topic – Giving change (N22)


Levels P - 2 Give change from 50p (2) Work out change for amounts up to £10 (2)

Levels 3 - 4 Give change from £5 (3)

Levels 5 - 6


Topic – Converting from to p (N23)


Levels P - 2

Levels 3 - 4 Convert from p to £ and from £ to p (3) Convert to foreign currency (4)

Levels 5 - 6 Convert between currencies (5)

Topic – Money Sums (N24)


Levels P - 2 Use real money to add and subtract amounts (2) Add amounts of money up to £25 (2)

Levels 3 - 4 Add, subtract and order sums of money, using a calculator where necessary (3) Understand and use different representations of money as they appear on a calculator (3) Add, subtract, multiply and divide decimals with a calculator in the context of money eg personal and household finance (3) Use all four operations to solve word problems (3) Solve money questions involving times and divide (4)

Levels 5 - 6 Solve money questions using long multiplication and long division (5) Find percentages of money (5) Solve reverse percentage problems (6) Solve percentage problems such as increase/decrease and inflation (6) Use a calculator for reverse percentage problems (6)


Note: OCR objectives are in bold type OCR syllabus unit numbers are in brackets after the topic area headings. All other St. Catherine’s Mathematics Scheme of Work objectives are in regular type Vocabulary:

Level 1: Lots of

Level 2: Level 3: Difference, nearest

Level 4: Less than

Pounds pence £ p decimal equivalent

1p 2p 5p 10p 50p £1

change count up greater than > < inverse operation

total bill receipt estimate even convert

exchange currency denomination discount sale percentage

increase decrease inflation

Handling Data – Spring Term 2nd

Half

Topic – Gathering Information (D1,D2) Filling in tables (D3)


Levels P - 2 Sort and classify objects (1) Can demonstrate criteria (1) Construct and interpret tally charts (2)

Levels 3 - 4 Extract information from printed lists (3)


Read simple bus or rail timetables and other common two-way tables (3) Complete an order form to buy a selection from a page in a catalogue (3)

Levels 5 - 6

Topic – Venn/Carroll Bar graphs, pictograms and Tallies (D4,D5,D6)


Levels P - 2 Sort and classify objects (1) Can demonstrate criteria (1) Complete a tally chart from given data (2) Construct and interpret tally charts (2) Tally outcomes of events (2) Construct a bar chart or pictogram from a given data (2) Record results in simple tables, block graphs and diagrams to communicate findings (2)

Levels 3 - 4 Design a data collection sheet (3) Make or use a frequency table for a set of data (3) Construct bar charts and pictograms to communicate gathered information (3) Can collect discrete data and record on frequency table (4) Can construct and interpret line diagrams (4)

Levels 5 - 6 Understands that different outcomes may come from repeating an experiment (5) Deals with two experiments and identifies all possible outcomes using tables and diagrams (6) Collects and records continuous data choosing appropriate class intervals to create frequency tables (6)


Constructs pie charts (6)

Topic – Interpretation (D7)


Levels P - 2

Levels 3 - 4 Interpret frequency diagrams (including bar graphs, ‘stick graphs’, pictogram) or pie charts, perhaps using a key (3) Interpret information from bar charts and pictograms (3) Can understand and use mode and median (4) Can group data and represent it in frequency diagrams (4) Can interpret frequency diagrams (4)

Levels 5 - 6 Understands and uses the mean of discrete data (5) Compares two simple distributions using range and average (5) Interprets graphs and diagrams and draws conclusions (5) Construct and interpret frequency diagrams (6) Draw conclusions from scatter diagrams and has basic understanding of correlation (6)

Topic – Probability


Levels P - 2 Place events in order of likelihood and use appropriate words to identify the chance of an event happening (2)

Levels 3 - 4 Distinguish between fair and unfair (3) Understand the idea of ‘evens’ and say whether events ate more or less likely than this (3) Understand and use a range of vocabulary associated with 2-

1- 2- More 3- 4- Less


probability (4)

Levels 5 - 6 Find and justify probabilities (5) Understands and uses probability scale from 0 to 1 (5) Uses the knowledge that the probability of all outcomes amounts to 1 (6)

Note: OCR objectives are in bold type OCR syllabus unit numbers are in brackets after the topic area headings. All other St. Catherine’s Mathematics Scheme of Work objectives are in regular type.

Vocabulary: Pictogram Data Bar Graph Frequency Graph Tally

Survey Table Interval Interpret Mean Mode

Plot Range Collect Record Median Diagrams

Present findings Database Groups Recording Pie Chart Scattergram

Fraction Best fit Chart Scale Investigation Chance

Likely Unlikely Certain Probability Even Impossible


Time – Summer Term 1st

Half

Topic – Calendars (S22,23)


Levels P - 2 Knows basic calendar facts (2)

Levels 3 - 4 Know and use basic calendar facts including common abbreviations (3) Use a calendar (3)

Levels 5 - 6

Topic – Telling the time – digital and analogue (S17,18,19)


Levels P - 2 Read analogue clocks to the nearest 15 minutes (2) Read digital clocks correctly (2)

1- 2- 3- nearest 4- before, after

Levels 3 - 4 Recognise different representations of the same time (3) Read analogue clocks in 5 minute intervals (3) Use a.m. and p.m. (3) Use the 24 hour clock (3) Use a.m./p.m. or 24-hour clock times and convert between the two systems (3)

Levels 5 - 6

Topic – Timings (S20,21)



Levels P - 2 Use clocks and watches to time events (2)

Levels 3 - 4 Estimate time lapses of a minute (3) Know 60 seconds = 1minute and 60 minutes = 1 hour (3) Work out starting times, finishing times and intervals, up to one hour, for times given in multiples of 10 minutes (3)

Levels 5 - 6

Topic – Timelines and timetables (S24)


Levels P - 2

Levels 3 - 4 Use a timeline to calculate intervals of time (3) Read simple timetables (3) Read and use a simple timetable such as those used by railway companies at stations (3)

Levels 5 - 6


Vocabulary:

Level 1: again, now Level 2: today, after, soon, Level 3:always, yesterday, before, later

Level 4: early, late, tomorrow

Time Clock Watch O’clock Half past Quarter past

Minutes past Quarter to Minutes to Hour Minutes Second

Hand Analogue Digital a.m. p.m. Midday Noon


24-hour Hundred-hours Day Morning Afternoon Midnight

Evening Night Week Weekend Fortnight Month

Year Leap year Century Millennium Monday Tuesday

Wednesday Thursday Friday Saturday Sunday January

February March April May June July

August September October November December Season

Spring Summer Autumn Winter Calendar Date

Timetable Arrive Depart

Fractions, Decimals and Percentages – Summer Term 2nd

Half

Topic – Fractions (N31) Dividing in halves and quarters


Levels P - 2 Recognise simple unit fractions and use them to find fractions of shapes and quantities (2) Understand fraction notation and represent simple fractions in diagrams (2) Recognise the relationship between halving and doubling (2) Use doubling and halving mental strategies to solve simple problems (2)

Levels 3 - 4 Recognise fractions that are several parts of a whole, and mixed numbers (3)


Recognise tenths expressed as fractions (4)

Levels 5 - 6 Use a fraction as an operator to find fractions of quantities (5)

Topic – Fractions (N32,33) Equivalent fractions and ordering


Levels P - 2 Use and understand the language of simple fractions in appropriate contexts (2) Calculate simple fractions of quantities (2) Recognise simple unit fractions and use them to find fractions of shapes and quantities (2) Order simple fractions (2)

Levels 3 - 4 Compare and order simple fractions (3)

Levels 5 - 6

Topic – Fractions (N32,33) Division relationships


Levels P - 2 Recognise the relationship between halving and doubling (2) Use doubling and halving mental strategies to solve simple problems (2)

Levels 3 - 4 Know and use halving as the inverse of doubling (3) Find remainders after division (3)

Levels 5 - 6

Topic – Decimals



(N27,28,29)

Levels P - 2

Levels 3 - 4 Order one digit decimals (3) Add and subtract simple decimals (3) Recognise the decimal notation for tenths and hundredths (3) Use decimal notation for tenths and hundredths (4) Order a mixed set of numbers with up to three decimal places (4) Relate fractions to division and to their decimal representations (4)

Levels 5 - 6

Topic – Decimals (N30)


Levels P - 2 Know decimal representations for simple quantities (2)

Levels 3 - 4 Add and subtract decimals on a calculator (3) Multiply and divide a decimal by a whole number (3) Use a calculator to find equivalent decimals (3)

Levels 5 - 6 Carry out multiplication and division of numbers involving decimals (5)

Topic – Percentages


Levels P - 2 Know percentage representations for simple quantities (2)

Levels 3 - 4 Know that a percentage is a number of parts in every hundred (3) Use a calculator to find percentages (4)

Levels 5 - 6 Understand percentage as the number of parts in every hundred


and find simple percentages of small quantities (5)


Vocabulary:

Fraction Whole Half Quarter Numerator Denominator

Equivalent Mixed Top-heavy Share Proper Improper

Common Cancel Divide Remainder Decimal Point

Place Tenth Hundredth Column Digit Convert

Recurring Percentage Proportion Ratio Symbol

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