Students will explore contexts that involve ratio and the ratio’s related rates. Students will continue to use models to reveal the rate through partitive division.

Intentionality…

In today’s math talk and purposeful practice, students will solve problems involving partitive division. Students will examine sample solutions in an effort to name the strategy and/or model, and offer an alternative strategy.

Some of the big ideas that may emerge through this task include:

• Partitive division is one of the two structures of division;
• In partitive division, the dividend is the quota and the divisor is the number of parts or groups;
• When dividing partitively, the quotient reveals a rate, how many per part (or the quota per group);
• The quotient can be expressed as any fraction equivalent to the dividend over the divisor;
• The number of partitions determines the fraction unit and gives the quantity its name (i.e.: partitioning a whole into 5 parts creates “5 fifth” parts);
• Different denominators can be used to represent equivalent quantities;
• Rate reasoning involves dividing one part of a ratio by the other through partitive division in order to reveal a rate.