Fractions of sets

This term I am focusing on Fractions, Decimals and Percentages with my students. The students are started to see the connection and relationship between these three areas i.e. that 0.2 is the same as 20% which is the same as 1/5. They are also learning how to simplify fractions and about equivalency at the same time.

So on Monday we started using paper strips to work out the fraction of a certain number of chocolate bars each person would get.

Example:
Miss Breen has 4 Chocolate bars left over at the end of the school term. She wants to share them out with the 5 children that were the best helpers that week. How much chocolate will each child get?

The paper strips helped the students to think about the chocolate bars as wholes before they broke them up into fractions and shared them out. We had a few tries, much trial and error before they began to realise that it was a good idea to start by breaking each whole paper strip into the number of people from each problem.

Once the students understood that each problem related to parts of a whole we moved onto the fractional equations. The students were still free to draw pictures but they began to use multiplication and division as a way to work out their answers.

Here are some photos from this week, of the students from all my groups working on these types of problems.

p.s. I let my kids draw on the tables with Whiteboard markers, it makes for a great working space :-)

Is There Another Way?

My students have been working very hard with me ever since they started their groups a few weeks ago. We have spent some time learning what Multiplication looks like as an array, using Animal Strips. I use this material as it is an excellent way for the students to see what the groups are made up of i.e. 9 is made up of 5 and 4, 8 is made up of 5 and 3 etc and it moves them away from counting in ones or skip counting and towards looking at groups of/sets of/lots of instead. While my students are still getting a grasp of their multiplication facts, using this materials enables them to break down the numbers into the Multiplication tables they do already know like 5 and 3 or 5 and 2 and 2 (4). 

This leads them into learning the strategies of Place Value Partitioning (breaking up the tens and ones) and Rounding and Compensating (rounding to the nearest ten and then subtracting the groups you added in the beginning). As my students generally have some knowledge of written strategies like algorithms, we look at those as well, which I teach them can be another tool to check their answer with but it should be one of many ways they know how to solve a problem.

Below are some photos of my year 7 & 8's - Group 8 (Trinaye, Michaela, Katelyn, Aisea, Harrison & Jerome) working with these Animal Strips to develop their understanding of Multiplication and related strategies; followed by a problem solving session where they needed to extract what the questions were asking them and then use their knowledge of these strategies to solve each problem. They were able to demonstrate all three strategies and are becoming much better at identifying the maths question within all the 'words' of each problem.

These questions were taken from the Mathematics Assessment Resource Banks (ARBS) Copyright 2011 Ministry of Education, Wellington, New Zealand.

The first question for example is: 

"Hohepa worked in a store for 16 hours a week for 7 weeks over Christmas. Show how to work out how many hours he worked over that time"