Multiplicative Reasoning Demonstration You will need: 20 blocks (that will represent sweets, guinea pigs, chocolates and books), 4 circles, 3 squares and 10 counters. Demonstration on the carpet: The teacher reads the partitive problem: There are four children and we are going to share 12 sweets fairly among them. The teacher chooses four circles to represent four pretend-children and lays them out on the carpet. The teacher invites a child to share the counters as pretend-sweets. Then the teacher asks: if we share them fairly, how many will each one get? The child shares and answers the question. This demonstration is repeated one with one more partitive problem: There were three houses and we need to put 15 guinea pigs in the houses. We want to distribute them equally so that no house is more crowded than the other houses. The teacher invites a child to come out and suggests that the rectangles are the pretend-houses and the counters the pretend-guinea pigs. The child is encouraged to solve the problem but if necessary the teacher gives guidance: “Three houses and 15 guinea pigs. How many squares do you need? How many counters do you need? How do you find out how many to put in each house so they all have the same number of guinea pigs?”

The teacher proceeds in the same way to demonstrate the quotitive problem: We are going to have a party and we have 15 chocolates. Each child that comes to the party will get three chocolates. How many children can we invite? The teacher invites a child to act out the story. Quotitive problems are more difficult than partitive problems for children at this age level and more prompting may be required for the children to act out the story. The teacher encourages the child to work out the solution and to take 15 counters to be the pretend chocolates. If the child is stuck, the teacher takes three counters, puts one circle in front of the counters, and says: here, three chocolates for this child. So this child can come to the party. The teacher then asks the child to carry on. If the child doesn't do anything, the teacher encourages the child to take three more pretend-chocolates and one more child who can come to the party. The teacher encourages the child to distribute all the chocolates like this. At the end, the teacher repeats the question: “So, how many children can come to the party? This demonstration is repeated with another quotitive problem: We are preparing bags with books to sell at the school fair. We need to put two books in each bag. We have 18 books. How many bags can we fill?

To print and cut to use as materials. One copy of this page per 2 children.

There are four children and we are going to share 12 sweets fairly among them. How many will each one get?

There were three houses and we need to put 15 guinea pigs in the houses. We want to distribute them equally so that no house is more crowded than the other houses. Three houses and 15 guinea pigs. How many squares do you need? How many counters do you need? How do you find out how many to put in each house so they all have the same number of guinea pigs?”

We are going to have a party and we have 15 chocolates. Each child that comes to the party will get three chocolates. How many children can we invite?

We are preparing bags with books to sell at the school fair. We need to put two books in each bag. We have 18 books. How many bags can we fill?