Math Teaching Guides
One long-form guide for each of the core operations on MathDrillSheets. Each traces the grade 1–8 progression through the Common Core standards, names the teaching strategies that hold up, and catalogues the specific mistakes that tell you a student is running a procedure they do not understand.
These were written for the original MathSheetLab library and carried over unchanged; the worksheet links now point at the matching drill sheets here. They are for teachers and parents, not students — if you want practice pages, browse the worksheets by topic.
How to Teach Addition
How to teach addition from counting on to signed rational numbers: the grade 1–8 progression, six teaching strategies, and the errors that stall students.
How to Teach Subtraction
Teaching subtraction from take-away to signed numbers: the grade 1–8 progression, borrowing across zeros, and the six error patterns that stall students.
How to Teach Multiplication
Teaching multiplication from equal groups to integer exponents: the grade 2–8 progression, times-table strategies, and the errors that stall students.
How to Teach Division
Teaching division from sharing to unit rates: the grade 3–8 progression, long division without mystery, remainders, and the errors that derail students.
How to Teach Fractions
Teaching fractions from equal shares to rational numbers: the grade 1–8 progression, why the number line matters, and the misconceptions that persist for years.
How to Teach Word Problems
Teaching math word problems without keyword tricks: the grade 1–8 progression, bar models, multi-step reasoning, and why "altogether means add" backfires.
How to Teach Mixed Operations
Teaching mixed operations and order of operations: the grade 1–8 progression, why PEMDAS misleads, and how interleaved practice builds operation sense.