Mathematics
Core concepts
Know number concepts and place value, the four operations and their properties, fractions, decimals and percentages, ratio and proportion, measurement, geometry, patterns and algebra, data handling, and simple probability. Understand the CPA sequence (concrete, pictorial, abstract) and the role of manipulatives. Know the difference between conceptual understanding, procedural fluency, strategic competence and reasoning, and understand why error analysis matters. Be familiar with the number line, base-ten blocks, place-value charts, and the meaning of the equals sign as balance rather than "answer comes next".
Traps
Common traps include treating a misconception as carelessness. For example, a child who writes 0.5 is smaller than 0.25 because 25 is bigger than 5 is applying whole-number reasoning to decimals. Another trap is confusing area and perimeter, or using the wrong unit conversion, such as forgetting that one square metre is 10,000 square centimetres. Questions often test the order of operations, so remember brackets, then orders, then division and multiplication, then addition and subtraction. Do not confuse factors with multiples, or mean with median.
Worked example
A question gives 3 + 4 × 2 and asks for the value. Rule of thumb: multiplication before addition, so 4 × 2 = 8, then 3 + 8 = 11, not 14. If a learner answers 14, the diagnosis is a precedence error, not a fact error, so reteach order of operations with worked examples.
Application
Use manipulatives and number lines to build meaning, then move to symbols; always ask learners to explain their reasoning and to check answers by estimation.