Math Teaching Guides
Practical strategies for teaching fractions, long division, multiplication tables, and core math skills to elementary students.
Teaching Guides for Math
Practical articles for classroom teachers — each guide pairs with a printable lesson on InstructorWeb.
How to Teach Fractions: A Step-by-Step Guide
A concrete-pictorial-abstract progression for teaching fractions in grades 3–6 with the misconceptions to watch for.
Curated External Resources
Fractions Teaching Resources
A curated collection of free external fractions resources from NCTM Illuminations, Math Learning Center, PBS LearningMedia, and Open Middle — visual manipulatives, lesson plans, and reasoning tasks vetted for K–6 classrooms.
How to Teach Long Division to 4th and 5th Graders
DMSB mnemonic, prerequisites, common errors, and when to use partial quotients instead of standard long division.
Multiplication Tables: Strategies Beyond Memorization
A strategy-first progression covering skip counting, arrays, doubling, the 9s trick, fluency routines, and stuck-student fixes.
Teaching Place Value
Why place value underlies every multi-digit operation, the concrete-pictorial-abstract progression that builds it, and a 5-day mini-unit.
Teaching Equivalent Fractions
Why the multiply-both rule works, the three mistakes students make, and a 4-day mini-unit that pairs with the lesson.
Teaching Order of Operations (PEMDAS)
Why PEMDAS alone leads to the most common mistake, the left-to-right rule that fixes it, and a 4-day mini-unit.
Why Students Struggle with Fractions
The five fraction misconceptions that derail elementary math, why they happen, and the diagnostic moves that fix them.
Teaching Rounding
The place-value foundation of rounding, the underline-and-look-right rule, the number-line picture, and the four places students get stuck.
Teaching Comparing Fractions
Why a bigger denominator means smaller pieces, the three comparison cases, the benchmark shortcut, and the whole-number habit that trips students up.
Teaching Adding and Subtracting Fractions
Beat the add-the-denominators error with a picture — same-size pieces add by counting; unlike denominators get renamed first. Grades 4–5.
Teaching Multiplying Fractions
The multiply-straight-across rule, why the answer gets smaller (“of” means multiply), and the area model. Grades 5–6.
Teaching Dividing Fractions
Keep-Change-Flip, what a reciprocal is, and why the answer often gets bigger. Grades 5–6.
Teaching Telling Time
The two hands, hour and half past, counting by fives, and quarter past and quarter to. Grades 1–3.
Teaching Perimeter and Area
Perimeter as the distance around, area as the space inside, area as multiplication, and plain vs. square units. Grades 3–5.
Teaching Elapsed Time
Finding how much time has passed by counting on with a number line instead of subtracting. Grades 2–4.
Teaching Multi-Digit Multiplication
Multiplying multi-digit numbers with the area model and partial products before the standard algorithm. Grades 3–5.
Teaching Skip Counting
Counting by 2s, 5s, and 10s as the bridge to multiplication, place value, time, and money. Grades 1–3.
Looking for Math Worksheets?
The math worksheet hub has printable lessons covering fractions, long division, multiplication tables, order of operations, place value, and more — all with downloadable practice and complete answer keys.