This is an activity in which the students are able to explore division using models and manipulatives. Students will discover that when a quantity is divided by another amount, the solution can be written as a fraction where the numerator is the original quantity is the numerator and the denominator is number of groups the quantity is being divided into.
For example, If 4 pizzas are shared equally amount nine people, students should be able to state that each person get’s 4/9 of a pizza.
- Use of manipulatives & models: Students should use cut out manipulatives to model each scenario. They will use scissors, rulers, or folding to divide the items into equal amounts. This will allow students to build a concrete understanding of the process of division when the answer is a fraction.
- Exploration & discovery: Students should work with their peers to model each scenario and discover that the dividend in the problem is the same as the denominator in the solution and that the divisor in the problem is the same as the numerator in the solution.
- Collaboration: Students should work in small groups or partners to work with the manipulatives and discuss their findings
On page one, students are asked to identify what patterns they notice about their solutions and the number of items being divided and the number
of groups the items are being divided into. Students will identify this pattern at different times throughout the problem set. Tell students that they
should answer that question when they feel confident in their answer. Students should use the manipulatives or models to solve all of the problems
in the table (a-j) even if they can solve them without the models or manipulatives early on. This will ensure students are building a deep understanding
of the concept and of division involving fractions. Once students have a good understanding of the concept, they should work
on answering the questions on the right side of the page without a model or manipulatives. Some of these problems will require students to simplify
their answer, which may be easier for some students to recall than others. Talk about the difference between the problems in which students got an improper fraction and what that means in context to the scenario. Show students with the models what it looks like to have an improper fraction
rather than a fraction less than one. Encourage students to do as much as they can on their own or with their small group or partner, but emphasize that it is ok if they do not get all of the answers on their own. Use a document camera to model tricky problems for the class if necessary, or to model new problems if students need more practice.
Note that there are several different ways that the manipulatives and models can be divided to answer each question. If some students are struggling
with the concept of how to divide the objects into equal parts, consider pulling a small teacher led group.