Using pictures of monkeys and some beans to feed the monkeys the students discussed various ways to share the beans with the monkeys. Remembering to remind the students that you want to have a fair way of sharing the beans. After providing some time for the students to think about what they would do, Jo gave them the beans and asked them to share their thinking with the others. Being sure to stop and have the students explain their thinking allowed her to see which stage of thinking they were at while they solved the problem.
ex. If you have 2 monkeys and 8 beans how many monkeys would each monkey get?
If they are able to easily answer this question, raise the number of beans they are sharing. Once again provide thinking time prior to having them share their reasoning with their buddy. Then, if doubles are going well, move them on to 3s, etc.
Moving to Fractions using Equal Groups
Instead of saying 3 monkeys shared 12 beans, move students to understanding that this is 1/3 of the beans. This achieved first by showing them 3 fractions (1/2, 1/3, 1/4) and asking which would be used for this problem. Which fraction would be use to make 3 equal groups?
Using Repeat Addition
With another groups of year 3 students, we moved onto solidifying basic facts without using skip counting. Using the animal strips, make up a word problem.
ex. Farmer Jo has 6 fields and she has 5 snails in each field. How many snails does she have altogether?
How could we write this as a multiplication problem? What if we combined the fields to 3? Then, we would have 3 groups of 10. After doing a few similar problems, ask how many groups of 10s we have compared to groups of 5. See if they are able to understand that making groups of 10 creates 1/2 the number of groups.
Deriving Basic Multiplication Facts
Using games to practise "rote" learning of facts after discussing with the class how you could find the product using what you already know about the basic "benchmark" facts (1, 2, 5 and 10).