Sciences, Mathematics, and Technology
Science
Modern science standards ask you to teach three dimensions together: disciplinary core ideas, science and engineering practices, and crosscutting concepts such as patterns, cause and effect, and systems. Inquiry is not a fixed six-step recipe; the productive framing is that students ask questions, plan investigations, analyze data, and argue from evidence. Distinguish hypothesis, theory, and law correctly - a theory does not graduate into a law. In lab settings, safety must be explicit: goggles and chemical handling, never tasting, proper waste disposal, and knowledge of the location of safety equipment.
Mathematics
Follow the progression: concrete-representational-abstract. Place value underpins algorithms; fractions are quantities and numbers, not simply shaded shapes; proportional reasoning is the gateway to algebra. A function assigns exactly one output to each input - vertical line test questions test exactly this. Watch for misconception items: many students believe multiplication always makes bigger and division always makes smaller, which fails for fractions. Distinguish mean, median, and mode with skewed data, and keep probability distinct from statistics.
Technology and computer science
Know algorithm, sequence, iteration, conditionals, and debugging. Binary place values double leftward. Digital citizenship covers safety, ethics, and copyright. Engineering design is iterative: define, prototype, test, redesign.
Rule of thumb
When a word problem stalls, sketch a quantity of 1 (a unit bar) and label what the numbers mean. For 1/2 divided by 1/4, ask how many quarters fit into one half - two. The model explains the invert-and-multiply rule rather than hiding it.