PSLCE Mathematics study plan

Define and distinguish place value, face value, and total value for digits up to millions and down to thousandths, writing the value of any named digit in 20 mixed numerals.

Convert fluently between standard form, expanded form, and word form for whole numbers up to 1,000,000 and for decimals to three places.

Order and compare sets of five mixed numbers and decimals using <, >, and = without a calculator, including negative integers on a number line.

Round whole numbers and decimals to any named place and state the rounding rule in your own words with two worked examples.

Classify numbers as odd/even, prime/composite, square, or multiples/factors of a given number, and list all factors of 24, 36, and 60.

Compute the lowest common multiple and highest common factor of pairs and triples of numbers using prime factorisation, showing the factor tree each time.

Apply divisibility rules for 2, 3, 4, 5, 6, 9, and 10 to test eight given numbers and justify each verdict in one sentence.

Solve four multi-step word problems involving LCM or HCF (for example, timing of recurring events or splitting into equal groups) and label the answer with units.

Perform column addition and subtraction of whole numbers up to six digits, including problems requiring borrowing across zeros.

Estimate products and quotients by rounding to convenient numbers, then check the exact answer against the estimate.

Multiply two- and three-digit numbers by one- and two-digit numbers using the standard algorithm, showing every partial product.

Divide numbers up to four digits by one- and two-digit divisors, interpreting remainders correctly in context (left over, rounded up, or as a fraction).

Apply the order of operations (brackets, then multiplication and division left to right, then addition and subtraction left to right) to 15 expressions including nested brackets.

Translate six short word problems into a single number sentence and solve them, checking with inverse operations.

Identify and correct three deliberately flawed worked calculations, naming the specific error in each.

Generate equivalent fractions and reduce fractions to simplest form using HCF, completing 20 conversions.

Add, subtract, multiply, and divide fractions and mixed numbers, converting between improper fractions and mixed numbers as needed.

Convert fluently among fractions, decimals, and percentages for common values and for any given value using division or multiplication by 100.

Solve percentage problems of the three types (find the part, find the whole, find the percent) using a unitary method and a double number line.

Order a mixed list of five fractions, decimals, and percentages by converting all to one form first.

Convert within and between metric units of length, mass, and capacity using the place-value relationship, and justify the direction of each conversion.

Solve perimeter and area problems for rectangles, squares, and composite shapes, selecting the correct unit and writing it with the answer.

Read and interpret a 12-hour and 24-hour clock, converting times in both directions, and calculate elapsed time across an hour and across midnight.

Read a bus or train timetable to answer four questions requiring departure, arrival, duration, and connection time.

Solve money problems involving change, unit price, and simple budgets, keeping two decimal places and rounding correctly.

Measure and classify angles as acute, right, obtuse, straight, or reflex, and calculate missing angles on a straight line and around a point.

Identify and draw lines of symmetry for given shapes, and state the number of lines of symmetry for common polygons.

Calculate the area of triangles and parallelograms using the correct formula, and explain why the triangle formula includes a half.

Name and describe the properties of common 2-D shapes and 3-D solids, including faces, edges, and vertices.

Plot and read coordinates in all four quadrants and describe a simple translation or reflection of a shape on a grid.

Construct a frequency table and a bar chart from a set of raw data, choosing sensible intervals and labelling both axes.

Calculate the mean, median, mode, and range of a small data set and explain which average best describes the data.

Extend a number or shape pattern, state the rule in words, and predict the 10th and 20th terms.

Write a simple algebraic expression or one-step equation for a word problem and solve it by inverse operations.

Solve two non-routine problems by working backwards or drawing a diagram, and write out the reasoning steps.

Complete two full-length timed practice papers under exam conditions and record the score for each domain.

Rank your domain scores from weakest to strongest and list the three specific error types that cost the most marks.

Rework every missed question from both papers, writing the correct method in one sentence beside each.

Rehearse a 5-minute formula and facts recall sheet (unit conversions, area formulas, averages, percentage method) from memory three times.

Build a final one-page exam-day strategy sheet covering time allocation per section and a checking routine.