List of topics in Unit 1 - Foundation.

Knowledge Organisers linked to some topics.

Higher topics are below these - Foundation knowledge is also needed for Higher.

 

1.1.1     read and write whole numbers of any magnitude expressed in figures or words

1.1.2     round whole numbers to the nearest 10, 100, 1000, etc

1.1.3     understand place value of whole numbers and those written in decimal form

1.1.4     round decimals to the nearest whole number or a given number of decimal places

1.1.5     round numbers to a given number of significant figures

1.1.6     understand, use and order directed numbers

1.1.7     decide whether to round up or down, as appropriate, in a problem

1.1.8     check methods and solutions using appropriate strategies

1.2.1     the common properties of numbers, including knowledge of odd, even, integers, multiples, factors, primes

1.2.2     the meaning of the terms square, square root, cube and cube root.

1.3.1     the notation for positive integral indices

1.4.1     how to find equivalent fractions

1.4.2     the equivalences between fractions, decimals and percentages

1.4.5     simplify fractions

1.4.6     express one number as a fraction or percentage of another

1.4.7     find a fraction or percentage of a quantity

1.4.8     calculate fractional and percentage changes (increase and decrease)

1.4.9     understand and use multipliers

1.4.10  solve problems with repeated proportional changes

1.4.11  calculate using ratios in a variety of situations

1.5.1     understand and use number operations and the relationships between them, including inverse operations and the hierarchy of operations

1.5.2     add, subtract, multiply and divide whole numbers, including large whole numbers

1.5.3     add, subtract, multiply and divide decimals, fractions and negative numbers

1.5.5     use a calculator efficiently and effectively, including:

1.5.5(a)     order of operations

1.5.5(b)     addition, subtraction, multiplication and division.

1.5.5(c)     square, cube and other powers

1.5.5(d)     square root and cube root

1.5.5(e)     brackets

1.5.5(f))     other appropriate functions

1.6.1     round an answer to a reasonable degree of accuracy in light of the context

1.6.2     recognise that measurement is approximate and that a measurement expressed to a given unit is in possible error of half a unit

1.6.5     premature rounding in problems involving multiple steps may affect the accuracy of the final answer

1.7.1     interpret and use mathematical information presented in written or visual form, including infographics, schedules, tables, timetables, calendars and charts

1.7.2     create plans and schedules

1.7.3     use, interpret and produce Venn diagrams

1.8.1     carry out calculations involving knowledge of money; pounds (£) and pence

1.8.2     understand the basic principles of personal / household finance and enterprise in order to solve problems relating to, for example:

1.8.2(a)      wages and salaries, including payslips

1.8.2(b)      taxation, including income tax and National Insurance

1.8.2(c)      savings and investments

1.8.2(d)      loans / repayments

1.8.2(e)      mortgages

1.8.2(f)      appreciation / depreciation

1.8.2(g)      budgeting

1.8.2(h)      bank statements

1.8.2(i)      utility bills

1.8.2(j)      mobile phone and other bills

1.8.2(k)      VAT

1.8.2(l)      best buys

1.8.2(m)      price comparison

1.8.2(n)      finance schemes, including buying by instalments

1.8.2(o)      discount / price increase

1.8.2(p)      buying and selling

1.8.2(q)      profit and loss

1.8.2(r)      travel including foreign currencies, exchange rates and commission

1.8.3     recognise the difference between simple and compound interest and be able to perform calculations with both, using efficient calculation methods and including the use of multipliers

2.1.1     understand the basic conventions of algebra

2.1.2     substitute positive and negative whole numbers, fractions and decimals into simple formulae and expressions written in words or in symbols

2.1.3     recognise the definitions of the terms equation, expression and formula and be able to distinguish between them.

2.1.5     form and simplify expressions

2.1.6     collect like terms

2.1.7     expand expressions – single bracket

2.2.1     form, manipulate and solve linear and other simple equations with whole number and fractional coefficients

3.1.1     Geometric terms, including:

3.1.1(a)      point, line and plane

3.1.1(b)      horizontal, vertical, diagonal

3.1.1(c)      midpoint

3.1.1(d)      parallel and perpendicular

3.1.1(e)      clockwise and anticlockwise turns

3.1.1(f)      acute, obtuse, reflex, right angle, straight angle, full turn

3.1.1(g)      exterior, interior angles

3.1.1(h)      faces, edges and vertices

3.1.2     Vocabulary and essential properties of 2-D shapes, including:

3.1.2(a)      triangles - scalene, isosceles, equilateral, right-angled

3.1.2(b)      quadrilaterals - square, rectangle, parallelogram, rhombus, kite, trapezium

3.1.2(c)      polygons – including pentagon, hexagon, octagon, regular and irregular

3.1.2(d)      circles - radius, diameter, tangent, circumference, chord, arc, sector, segment

3.1.3     Vocabulary and essential properties of 3-D shapes including cube, cuboid, cylinder, prism, pyramid, cone, sphere, tetrahedron

3.2.1     measure and accurately draw:

3.2.1(a)      a straight line

3.2.1(b)      a circle or arc of a circle

3.2.1(c)      an angle of any size

3.3.1     read and interpret scales

3.3.2     use and interpret maps

3.3.3     interpret and produce scale drawings; scales may be written in the form 1 cm represents 5 m, or 1:500

3.3.4     understand 3-figure bearings and use this knowledge to interpret and draw bearings

3.4.1     recall and use the following angle properties:

3.4.1(a)      sum of angles at a point

3.4.1(b)      sum of angles on a straight line

3.4.1(c)      opposite angles at a vertex

3.4.1(d)      alternate, corresponding and interior angles within parallel lines

3.4.1(e)      sum of angles in a triangle

3.5.1     Time:

3.5.1(a)      Notation for 12- and 24-hour clock

3.5.1(b)      Seconds in a minute, minutes in an hour, hours in a day, days in a week and months in a year

3.5.2     Metric Units:    Standard metric units for length, mass and capacity and the relationships between them

3.5.3     carry out calculations involving time

3.5.4     convert between units of time

3.5.5     carry out calculations involving different time zones

3.5.6     make sensible estimates of metric measurements in everyday situations, recognising the appropriateness of units in different contexts

3.5.7     convert between the following metric and Imperial units: km - miles; cm, m - inches, feet; kg - lb; grams - ounces; litres - pints, gallons - the appropriate metric to imperial equivalences will be given to learners

3.5.8     recall and use compound measures for speed and fuel consumption. Units include: m/s, km/h, mph and mpg

3.6.1     2-D shapes:

3.6.1(a)      Estimate of the area of an irregular shape drawn on a square grid

3.6.1(b)      Perimeter and area of a square, rectangle, triangle, parallelogram, trapezium, circle, semicircle and a composite shape

3.6.3     3-D shapes:

3.6.3(a)      Surface area, cross-sectional area, volume and capacity of a cube, cuboid, prism, and a composite solid

3.6.3(b)      Cross-sectional area, volume and capacity of a cylinder

4.1.1     understand and use the statistical problem solving process: specify the problem/planning; collect, process and represent data; interpret and discuss results, including limitations of data and anomalies

4.1.2     specify and test hypotheses, taking account of the limitations of the data available

4.1.3     design and criticise questions for a questionnaire, including notions of fairness and bias

4.1.4     consider the effect of sample size and other factors that affect the reliability of data and conclusions drawn

4.1.8     group discrete or continuous data into class intervals of equal or unequal widths

4.2.1     construct and interpret pictograms, bar charts and pie charts for qualitative data and for discrete quantitative data

4.2.2     construct and interpret vertical line diagrams for discrete data

4.2.3     construct line graphs for the values of a variable at different points in time; understand that intermediate values in a line graph may or may not have meaning

4.2.21  recognise that graphs may be misleading

4.2.22  look at data to find patterns and exceptions

4.2.23  draw inferences and conclusions from summary measures and data representations, relate results back to the original problem

 

 

List of topics in Unit 1 - Higher.

Knowledge Organisers linked to some topics.

Foundation content also needed for Higher.

 

1.3.2     the notation for zero and negative indices

1.3.6     convert ordinary numbers into and out of standard form

1.3.7     use numbers written in standard form

1.4.12  solve numerical problems involving direct and inverse proportion

1.4.13  find the original quantity given the result of a proportional change

1.5.5     use a calculator efficiently and effectively, including:

1.5.5(g)     standard form

1.6.3     determine the upper and lower bounds of numbers expressed to a given degree of accuracy

1.6.4     calculate the upper and lower bounds in the addition, subtraction, multiplication and division of numbers expressed to a given degree of accuracy

1.8.4     perform calculations involving multiple rates

1.8.5     calculate, use and apply Annual Equivalent Rate (AER) when comparing financial products

1.8.6     calculate, use and apply Annual Percentage Rate (APR) when comparing financial products, including mortgages

1.9.6        use pi in exact calculations

3.5.10  convert between units of area and volume

3.6.3     3-D shapes:

3.6.3(c)      Surface area of a cylinder

3.6.3(d)      Surface area, volume and capacity of a sphere, cone, pyramid and a compound solid

4.1.9     specify the data needed and consider potential sampling methods

4.1.10  understand, describe and use different sampling techniques – i.e. random, systematic and stratified sampling