|Schemata||2A, 2A/B: Early/Mid Concrete Operations||2B: Mature Concrete Operations||2B*: Concrete Generalisation||3: Formal Operations|
|Properties of Numbers
|Add and subtract small number of objects, solve whole number problems, order and count to 100. Work out sequence backwards or forwards. Mentally add/subtract two single-digit numbers, the decades.||Know where 1,000 comes in number sequence. Can give
change from £1 coin. Use addition and subtraction to find differences between numbers up to 1,000; can handle units of 10s and 100s.
|Understand use of negative numbers in practical context. Mental addition and subtraction of two-digit numbers, or on paper any addition or subtraction of whole numbers. Enter money in f./p on calculator.||Use negative numbers in multiplication. Make estimates in calculations.|
|Properties of Numbers
|Read/write to 100, then to 1,000. Count accurately 100 objects.||Read/write multiples of 100 up to 10,000. Adding zero does not change value.||Whole number approximation of numbers with one decimal place and interpolate 10ths. Read or enter any number to 1 million. Read scale marked in 100ths, labelled in 10ths.|
|Multiplication and Division||Can double numbers up to 10. Practically knows half a set of objects. Identify halves and quarters.||Know and can use multiplication tables. Solve problems using multiplication and division. Use multiples 2, 5, 10. Practical quartering. Two inverses.||wo-digit x one digit.
0.5 = 50% =1.
Identify fractions, percentages.
|Mapping fractions onto 0-100 scale. Equivalence of fractions and decimals. Scaling as operation preserving multiplicative relations.|
|Expressions and Equations||Devise repeating patterns. Recognise use of symbol. (Can solve 3 + G = 4 for G.)||Can generate and continue a number pattern. Without enumerating intersection, can see problem of dividing pupils into those with pets and those with blue eyes. Provide many values of G & E which fit G + E = 9.||Use formulae to express words. Sets leading to bracketing. Can find member in each area of intersecting Venn. Make general statement about series (e.g. 1, 2, 4, 8 ... 'This doubles each time").||Can evaluate simple expression, e.g. wage = hours x rate/hour. Solve one-step linear equations, e.g. C x 32 = 192.|
|Functions||Sort or order a set of objects using one criterion.||Sort on two criteria, two-stage ordering, use of 2 x 2 sorting table.||Three or more successive stages of ordering. 'Function machines, interrogate and interpret data in computer database.||Linear functions as generalised number. Express a simple
|Shape and Dimensions||Identify 2D shapes. Estimate a metre by eye.||Identify common 3D shapes. Construct rectangle given dimensions. Sort 2D shapes in different ways. Read scales in units and 10ths.||Meaning of five major kinds of triangles. Order and estimate angles, know area units, understand volume.||Construct triangles, angles in triangle sum 180°. Areas of more complex figures. Use of 271 relationship in circles.|