I Have a Problem!

Here are some problems for you to think about. Have a go working them out and write your answers in the comments box. Good luck!

How many squares on the chessboard below: 

(hint: the answer is not 64 - look again)

Created by Mark Warner -  - www.teachingideas.co.uk

0

9

Problem sourced from http://nrich.maths.org/

Learning to Trade - Place Value

As a warm up, Group 1 played a place value trading game we call 'The Shark Game'. 

In the game there are worms, small fish and a shark. The aim of the game is to win the shark. In order to do that the children must roll two die and whatever number they roll i.e. 8, equates to how many worms they take. Once they have ten worms they can trade these ten for one small fish. They keep taking turns with the die, collecting worms and trading them for small fish until they get ten small fish which they can then swap for one shark and then they win the game. 

This is a great game for reinforcing the fact that in place value we must change 10 ones into 1 ten and when we have 10 tens we change it for 1 hundred. They are quick to pick up this trading aspect with ten quickly, especially if they see that the other students have more small fish!

 

Adding Fractions with Common Denominators

We have started to look at adding fractions with common denominators. This was new to my students so we have spent time previously making sure that we can identify fractions both shapes and sets and discussing in depth how the numerator is the number of parts whereas the denominator is the number of parts in the whole.

So we have now moved on to looking at adding basic fractions. The photos below show what my year 5 group began looking at today. We were using fractions cards and the students had to imagine (or touch the cards to imagine) that they were moving parts of one whole over to the other card. Once we understood that when we have created a whole (fraction) we write it as 1 (whole) and what ever is left over is also written.

So if we add 3/5 + 4/5 we need to take one part or piece from 3/5 and move it to 4/5 which now becomes 5/5's or 1 whole. We mustn't forget that there is still 2/5 left so our answer will be 1 (whole) & 2/5

Take a look at the video below (from youtube.com) which demonstrates how to add and subtract simple fractions with common denominators

Numeracy Home - School Partnership

On Wednesday the 9th April we had our annual Numeracy Home - School Partnership here at Clendon Park. 

This is an evening designed to give parents and caregivers an opportunity to learn practical ways that they can help their children with maths at home. Five teachers including myself ran stations where we showed parents (and their children) how to play maths games and use different activities to help build their maths knowledge. 

It was a very popular night and the children even got to take home a pack with all the games/activities shown so they can keep practicing with their parents at home.

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 :)

Group 2 - Fractions is a piece of cake!

Group 2 are my wonderful Year 2 and 3 group. Today we looked at fractions, from 1 whole to tenths. Its important when learning fractions that we understand that its not only shapes that can be divided into fractions but also sets.

Money, Money, Money

Group 1 had the task of figuring out over two sessions, the total value of each box of dots. There were black, white and grey dots which had values of $1, $2 and .50c. Check out the video below which shows two of the group members discussing their answers.

Below is a picture of their activity and their working out.

Group 3 Learning to problem solve

Today group 3 was given the same mathematical problem as Group 4 were given previously. However, their problem was put into a different context. As you can see from the video the group were new to problem solving so they found it hard to talk to each other at first to try to solve the problem. As the video goes on you'll see they start to communicate and work together. This is only a small snippet of the work they did. They are sure to get better and better as they become more experienced with using mathematical talk and relying on each other within the group. Please check back regulaly to see how much they progress :)

Miss Breen

The problem: On a picnic at Totara Park there are three classes with eighteen students in each class. There are only allowed to be a maximum of 60 students swimming in the pool at one time. Will all three classes be able to swim together?
(we discussed what maximum means so that the problem was accessible to all the students)

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?