Multiplication and Division to Three Digits
Multi-digit multiplication in Grade 5 extends to three-digit numbers and two-digit multipliers. 234 x 6 = (200x6) + (30x6) + (4x6) = 1200+180+24 = 1404. Division with remainders introduces a new decision: when the quotient is not a whole number, what does the remainder mean in context? 17 students need to cross a river in canoes that hold 3 people. 17/3 = 5 remainder 2: you need 6 canoes, not 5. The context determines whether to round up or down.
Three-digit multiplication
234 x 6: decompose 234 = 200+30+4. Multiply each part: 200x6=1200, 30x6=180, 4x6=24. Add: 1200+180+24=1404. The area model shows this as a rectangle split into three sections. For two-digit multipliers: 47 x 23 = 47x20 + 47x3 = 940 + 141 = 1081. The distributive property scales to any number of digits.
Division with remainders
127/5: 5x25=125, remainder 2. So 127/5 = 25 remainder 2, or 25 r2. The interpretation depends on context. Sharing cookies: 25 each with 2 left over (remainder stays). Cutting ribbon: 25 pieces with 2 cm left (useful but unusable). Needing boxes: 26 boxes (round up because the 2 remaining items need a box). The mathematics is the same; the context determines the answer.
Real-world multi-step problems
A First Nations community is planning a feast. 234 adults and 78 children will attend. Each table seats 6 people. How many tables? Total: 234+78=312. Tables: 312/6=52. If the hall has 50 tables, is there room? No: 52 > 50. How many extra tables are needed? 52-50=2 more tables. Multi-step problems connect addition, division, and comparison in one coherent context.