### ***Practice 1 - Partial Quotients*** ![[Pasted image 20260421141949.png]] Partial quotients is an alternative division algorithm in which students subtract multiples of the divisor from the dividend in chunks rather than performing the standard long division algorithm all at once. Students choose any multiple they know, subtract it, and keep track of partial answers until nothing remains to divide. |Pros|Cons| |---|---| |Reduces cognitive demand by allowing students to work at their own level of fact knowledge.|Less efficient than the standard algorithm for students who have mastered it.| |Builds conceptual understanding of division as repeated subtraction.|Some students struggle to organize work across multiple steps.| |Highly accessible for students with disabilities or gaps in fact fluency.|Not always accepted on standardized assessments that require a standard algorithm.| **** ### ***Practice 2 - Fact Family Instruction*** ![[Pasted image 20260421142013.png]] Fact family instruction teaches students to see multiplication and division as inverse operations by grouping related facts together — for example, 4 × 6 = 24, 6 × 4 = 24, 24 ÷ 6 = 4, and 24 ÷ 4 = 6. Students learn that knowing one fact in the family gives them access to all four. |Pros|Cons| |---|---| |Reduces the number of new facts students need to memorize independently.|Students must have a solid understanding of multiplication before fact families are meaningful.| |Builds number sense and understanding of inverse operations.|Some students find the visual representation of fact families confusing without scaffolding.| |Connects multiplication and division instruction naturally.|Requires explicit instruction — students rarely discover the inverse relationship on their own.|