Mathematics

Form 5 will extend their understanding of a variety of concepts and will be introduced to new mathematical knowledge and skills.

Below are the Primary Cambridge learning objectives that we will be working towards for the initial topics.

Learning objectives 

• Revising numbers and place value

- Know what each digit represents in whole numbers up to a
million
- Know what each digit represents in one- and two-place
decimal numbers
- Round whole numbers to the nearest 10, 100 or 1000
- Order and compare positive numbers to one million, negative numbers to an appropriate level
- Use the >, < and = signs correctly
- Estimate where four-digit numbers lie on an empty 0–10 000 number line
- Recognise the historical origins of our number system and begin to understand how it developed
- Find the difference between a positive and negative integer, and between two negative integers in a context such as temperature or on a number line

• Time

- Recognise and understand the units for measuring time (seconds, minutes, hours, days, weeks, months, years,
decades and centuries); convert one unit of time to another
- Tell the time using digital and analogue clocks using the 24-hour clock
- Compare times on digital and analogue clocks, e.g. realise
quarter to four is later than 3:40
- Use a calendar to calculate time intervals in days, weeks or months
- Calculate time intervals in days, months or years
- Appreciate how time is different in different time zones around the world

• 3D Shape

- Visualise and describe the properties of 3D shapes, e.g. faces, edges and vertices
- Recognise and make 2D representations of 3D shapes including nets.

• Addition and Subtraction

- Recall addition/subtraction facts for numbers to 20 and pairs of one-place decimals with a total of 1, e.g. 0.4 and 0.6
- Add/subtract a near multiple of 10, 100 or 1000, or a near whole unit of money, and adjust, e.g. 3127 + 4998,
5678 – 1996
- Add two and three-digit numbers with the same or different numbers of digits/decimal places

• Multiplication and division of whole numbers

- Multiply and divide any whole number from 1 to 10 000 by 10, 100 or 1000 and explain the effect
- Know and apply tests of divisibility by 2, 4, 5, 10, 25 and 100
- Use number facts to generate new multiplication facts, e.g. the 17× table from the 10× and 7× tables
- Multiply two-, three- and four-digit numbers (including sums of money) by a single-digit number and two- or
three-digit numbers by two-digit numbers
- Divide three-digit numbers by single-digit numbers,including those leaving a remainder, and divide three-digit
numbers by two-digit numbers (no remainder) including sums of money

• Measurement

- Select and use standard units of measure. Read and write to two
or three decimal places
- Convert between units of measurement (kg and g, l and ml,
m, cm and mm) using decimals to three decimal places, e.g. recognising that 1.245 m is 1 m 24.5 cm
- Interpret readings on different scales on a range of measuring instruments
- Draw and measure lines to the nearest centimetre and millimetre
- Know imperial units still in common use, e.g. the mile, and approximate metric equivalents

• Fractions

- Compare fractions with the same denominator and related denominators, e.g.3–4 with 7–8
- Recognise equivalence between fractions, e.g. between –1–
100s, 1 –10s and 1–2s
- Order mixed numbers and place them between whole numbers on a number line
- Change an improper fraction to a mixed number
- Reduce fractions to their simplest form, where this is 1–2, 1–4,3–4 or a number of fifths or tenths

Autumn 2

• Extending decimals to thousandths

- Round a number with two decimal places to the nearest tenth or to the nearest whole number

- Order numbers with up to two decimal places, including different numbers of decimal places

• Tables and Graphs

- Solve a problem by representing, extracting and interpreting data in tables, graphs, charts and diagrams,

e.g. line graphs for distance and time; a price ‘ready reckoner’ for currency conversion; frequency tables and bar

charts with grouped discrete data

- Explore how statistics are used in everyday life

• Operations on Decimals

- Multiply and divide decimals by 10 or 100 (answers up to 2 decimal places for division)

- Make and justify estimates and approximations of large numbers

- Recognise and use the equivalence between decimal and fractional forms

- Begin to convert a vulgar fraction to a decimal fraction using division

- Recall addition and subtraction facts for numbers to 20 and pairs of one-place decimals with a total of 1,

e.g. 0.4 + 0.6

- Derive quickly pairs of one-place decimals totalling 10, e.g. 7.8 and 2.2, and two-place decimals totaling 1, e.g. 0.78 and 0.22

- Use place value and number facts to add or subtract two digit whole numbers and to add or subtract three-digit

multiples of 10 and pairs of decimals, e.g. 560 + 270; 2.6+ 2.7; 0.78 + 0.23

- Add/subtract near multiples of 1 when adding numbers with one decimal place, e.g. 5.6 + 2.9, 13.5 – 2.1

- Double quickly any two-digit number, e.g. 78, 7.8, 0.78; derive corresponding halves

- Add two- and three-digit numbers with the same or different numbers of digits/decimal places Add or subtract numbers with the same and different numbers of decimal places, including amounts of money

• 2D Shapes

- Classify different polygons and understand whether a 2D shape is a polygon or not

- Identify and describe properties of quadrilaterals (including the parallelogram, rhombus and trapezium) and classify using parallel sides, equal sides, equal angles

• Perimeter

- Measure and calculate the perimeter and area of rectilinear shapes

- Calculate perimeter and area of simple compound shapes that can be split into rectangles

• Multiples and Factors

- Find factors of two-digit numbers Find some common multiples, e.g. for 4 and 5

- Recognise odd and even numbers and multiples of 5, 10, 25, 50 and 100 up to 1000

- Recognise prime numbers up to 20 and find all prime numbers less than 100

• More Multiplication and Division

- Multiply pairs of multiples of 10, e.g. 30 × 40, or multiples of 10 and 100, e.g. 600 × 40

- Multiply near multiples of 10 by multiplying the multiple of 10 and adjusting

• Angles

- Estimate, recognise and draw acute and obtuse angles and use a protractor to measure to the nearest degree

- Check that the sum of the angles in a triangle is 180°, for example, by measuring or paper folding; calculate angles in a triangle or around a point

- Predict where a polygon will be after one reflection, where the sides of the shape are not parallel or perpendicular to the mirror line, after one translation or after a rotation through 90° about one of its vertices

• Percentages 

- Understand percentage as parts in every 100 and express 1–2, 1–4, 1–3, 1 –10, –1–100 as percentages

- Solve simple percentages of shapes and whole numbers

Spring 1

• Mass

- Select and use standard units of measure. Read and write to two and three decimal places
- Convert between units of measurement (kg and g, l and ml, cm and mm) using decimals to three decimal places, e.g. recognising that 1.245m is 1m 24.5cm 
- Recognise and use decimals with up to three places in the context of measurement

• Probability

- Use the language associated with probability to discuss events, to assess likelihood and risk, including those with equally likely outcomes

• Revising Co-ordinates

- Read and plot co-ordinates in all four quadrants

- Predict where a polygon will be after one reflection, where the sides of the shape are not parallel or perpendicular to the mirror line, after one translation or after a rotation through 90° about one of its vertices

• Extending division and multiplication methods

- Multiply pairs of multiples of 10, e.g. 30 × 40, or multiples of 10 and 100, e.g. 600 × 40 

- Multiply by halving one number and doubling the other, e.g. calculate 35 × 16 using 70 × 8

- Multiply two-, three- and four-digit numbers (including money) by a single digit number and two- or three-digit numbers by two-digit numbers

- Divide three-digit numbers by single digit numbers, including those leaving a remainder, and divide three-digit numbers by two-digit numbers (no remainder) including sums of money

- Give an answer to a division as a mixed number, and a decimal (with divisors of 2, 4, 5, 10 or 100)

- Know and apply the arithmetic laws as they apply to multiplication (without necessarily using the terms

commutative, associative and distributive)

• Ratio and proportion

- Solve simple problems involving ratio and proportion

• More multiplication

- Use place value and multiplication facts to multiply/divide mentally, e.g. 0.8 × 7, 4.8 ÷ 6
- Multiply near multiples of ten by multiplying the multiple of ten and adjusting

• More graphs; summary statistics

- Solve a problem by representing, extracting and interpreting data in tables, graphs, charts and diagrams,

e.g. line graphs for distance and time; a price ‘ready reckoner’ for currency conversion; frequency tables and bar charts with grouped discrete data

- Find the mode and range of a set of data from relevant situations, e.g. scientific experiments

- Begin to find the median and mean of a set of data

- Explore how statistics are used in everyday life

• Patterns and basic algebra

- Count on and back in fractions and decimals, e.g. 1–3s, 0.1s and repeated steps of whole numbers (and through zero)

- Recognise and extend number sequences

- Make general statements about sums, differences and multiples of odd and even numbers