Students will explore modelling partitive division of two-digit whole numbers by one and two-digit divisors.

Intentionality…

The purpose of the Day 4 activities is to reinforce key concepts from Day 1. Students will engage in a string of related problems through a math talk and will have an opportunity to complete independent purposeful practice.

The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas:

• There are two types of division;
• Partitive division is when the total quota is known (the dividend), and the number of parts or groups (the divisor) is known;
• Partitive division reveals a rate;
• In partitive division, the dividend and the divisor often have different units;
• In a quotative context, the dividend and the divisor have the same unit;
• Quotative division is when the total quota is known (the dividend), and the number per group or the rate (the divisor) is known;
• Quotative division reveals the number of copies or iterations of a rate that can be derived from the overall quota (the dividend);
• The dividend and the divisor of any division sentence represent a ratio;
• In a partitive context, the ratio is often a composed unit;
• In a quotative context, the ratio is a multiplicative comparison;
• The dividend from any division sentence can be decomposed into smaller parts to allow for friendlier division by the divisor. This strategy is known as partial quotients. (i.e.: 85 ÷ 5 = 45 ÷ 5 + 40 ÷ 5 = 9 + 8 = 17).
• The remainder can be divided by the dividend resulting in a fraction in both partitive and quotative division contexts, unless the unit is discrete and cannot be partitioned (for example, a marble or a person).