Can You See a Pattern?

Today both year 8 groups were asked to discuss and solve a number of Algebraic patterning tasks. These started off with basic colour patterns and gradually built up to number patterns and representations where they needed to work out the rule/formula/relationship of that sequence.

Patterning is, "critical to the development of mathematical concepts and algebraic thinking and reasoning. General mathematical processes of representation, symbolization, abstraction, generalization and proof rely on initial pattern recognition and application in a variety of shapes, counting, spatial arrays or geometric patterns" (Bobis, Mulligan & al, 2013, pg 54).

As they worked in a group, it allowed every member of the group to contribute. In Group 3, one person made a suggestion of the relationship between the first three numbers in:

1, 2, 3, 5, 8, 13, 21, __

which helped others in the group to explore that idea further which eventually ended with the discovery of the pattern and the answer.

Below is a picture of some of the tasks I used today.

Working towards Stage 7

Both year 8 groups (group 3 & 4) and my year 5 group (group 1) have been working on multiplicative strategies using arrays. Arrays are rows of objects that are used for the children to be able to see groups rather than single objects. The arrays we have been using are animal strips. Each group has started off using the strips to partition (break up) additively then they use multiplication and additive strategies to solve the answer. Using arrays also helps to correct children's misunderstanding of what multiplication looks like i.e. 6 x 3 is 6 groups of 3 whereas 3 x 6 is 3 groups of 6. Though they have the same answer, the arrays look different so using the materials helps clarify this in their minds : )

In the videos below you will see the students explaining their strategy. What the students are doing:

To solve 27 x 6, 

27 is split into 20 and 7 and these parts are multiplied then recombined, as in: 

20 x 6 = 120 

7 x 6 = 42 (or 7 x 5 = 35 and 7 x 1 = 7) 

120 + 42 = 162)

Group 1 (Mya, Heseti, Ripeka, Michael, Sacred)

Group 3 (Paul, Bethel, Teri, Faleupolu, Vera)




Group 4 (Andre, Giovanni, Losana)

Group 4 - Connecting the Pieces

Group 4 (Losana, Giovanni and Andre) have been doing a lot of problem solving lately but yesterday we needed to go back to learning about fractions so that we can see the connection between division, multiplication, decimals and percentages. 

We made fraction charts by folding paper strips into half, quarters, eights and sixteenths. We then looked at basic equivalent fractions like 1/2 which is the same as 2/4's which is the same as 4/8's etc. Then we used sets of counters to represent fractions i.e. a quarter of twelve. We even started to see how any group of objects if they are the same, can be divided equally even a word like apple can be divided into thirds ap/pl/le. Here are some pictures of us working with materials to help our understanding :)

Problem Solving

Group 1 & 4 both had problem solving questions to work on today but since they are quite new to it, it was more of an introduction on how to decode the question (what is it asking us to do?).

We also discussed the rules of the group - each member needs to ask questions of each other and use the knowledge of the group before they can ask the teacher. This teaches the students to critically examine their own thinking and helps students to cosolidate learning and learn from each other. Here is the work from today.

As you can see they made a great start : )

Group 1 (Mya, Ripeka, Michael, Sacred & Heseti)

A Prey Mantis crawled in while we were working which was perfect for the group as they could check the number of legs and add it into the solution to their problem!

Group 4 (Losana, Andre and Giovanni)

They spent a lot of time just trying to work out what the question was asking us by underlining and re-reading. It took them a little while but they got there in the end so they only just started on their problem which can be answered in many different ways. Below they began by grouping and using repeated addition. We will look at faster ways to answer this type of problem when they have run out of their own ideas. With more practice they will be unstoppable  : )

UPDATE: They solved it! check out the second photo.

The question was "In the fruit room there are some apples left over. Carol needs to share these apples out amongst three classes with eighteen students in each class. How many apples does Carol start with?

Term 1 Groups Begin

I am so excited to have begun working with my wonderful students.

I have four groups - 2 x year 8s, 1 x year 2/3 and 1 x year 5's. Here are some of these awesome kids below.

Group 1

Mya, Michael, Ripeka, Sacred, Heseti

Group 2

Serenity, Shaza, Dorothy, Sisilina

Group 4

Giovanni, Losana, Andre

Group 3

Teri, Vera, Faleupolu, Paul, Bethel