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Friday, 30 August 2013

A new series of 10 books written by Ann have just been released by Pascal Press. 

Over the next few days, we’ll give you an overview of the series, and where better to start than with the two books on Addition and Subtraction.

Those of you who know our parent books will not be surprised to see that these two books follow a logical developmental sequence that takes the child from counting on through doubles and rainbow facts to bridge through 10 and number splitting using a variety of representations, such as chunking. By the way, did you know that Ann has been called the Chunking Queen – a well-deserved title!

The Addition and Subtraction books also introduce the two important representations of chunking and empty number line. 

In the examples blow, the chunking diagram for 25 +36 has been given a new look and the empty number line for the subtraction 45 – 26 shows how number splitting makes sense of the subtraction process.

The series has been designed for the parent market, but we feel sure that you will find lots in them that will give you inspiration for your strategy lessons. For details, go to:

Thursday, 29 August 2013

Blast off

To tie in with the book week theme, we again refer to year one teacher. Sonia Dittman from Seaview Primary School who challenged her students to create shape rockets using 16 shapes. She says many students enjoyed deciding on blast off times and measuring that they forgot to punt the shapes. Never mind, the results are striking!

Notice how students were able to differentiate the activity by selecting which time to show on the clocks as well as what and how to measure.

The display in the library was eye catching and again put maths right in the picture, which is where it belongs.  

Wednesday, 28 August 2013

Art and maths combine

Sonia Dittman of Seaview Primary School challenged her year one students to make a combination of spiders and insects with a number of legs that came as close to 40 legs they could get.

Checkout the art works that resulted, which also brightened up the school hallway. Sonia’s awesome room combines maths and art – or should I say collide in imaginative and engaging ways!

Tuesday, 27 August 2013

Children's Book Week wrap up

As Children’s Book Week ends for another year, we’d like to sum up our favourite books we shared throughout the week. As you would expect, they have a maths influence. Let’s begin with ‘Bean Thirteen’ by Matthew McElligott; ‘Me Counting Time, From Seconds to Centuries’ by Joan Sweeney’ ‘How to Land a Jumbo Jet: A Visual Exploration of Travel Facts, Figures and Ephemera’ by Joan Sweeny; ‘Seeing Symmetry’ by Loreen Leedy; ‘The Very Blue Thingamajig’ by Narelle Oliver (one of my all time favourites); ‘Do You Wanne Bet? Your Chance to Find Out About Probability’ by Jean Cushman. 

These books are beautifully illustrated while containing lots of practical and engaging problems that enable fun and meaningful learning. 

And speaking of books, our ‘Back to Basics’ series is also now available, which you can purchase via our website http://www.pascalpress.com.au/back-to-basics/.  

Monday, 26 August 2013

Spatial Awareness Workshop

This is what happened when Ann challenged participants at Saturday’s Spatial Awareness Workshop to create a pyramid with 100 cubes. Creativity was required to ensure that all 100 cubes were used. The planning, discussion and engagement are clear to see. 

Imagine doing this with a class of students. The spatial thinking, planning, reasoning and construction that ensue as a result of the problem solving will lead to enhanced spatial awareness.

The main message of the day was that visual and spatial reasoning develop from hands on experimentation and obstruction not from the flat and fixed shapes on the page.

If you like the blocks or the activities then check out the website www.naturalmaths.com.au where you will find the book, ‘Hands on Activities with Blocks’ and blocks to accompany it. 

Tuesday, 13 August 2013

Continuing Ed

I was in the McLaren Vale yesterday where teachers came to Day 3 of the professional development program that I am running for the SA Department of Education. Here you see the teachers sharing the students’ work samples in response to the problematised situation of Activity 9, Problem Solving at Level 3, in a Stephanie Alexander kitchen that the school has established.

Observing how students tackle a maths problem and their mathematical thinking were the topics of this part of the day.

Congratulations to the participating teacher and their commitment to continuing their own learning.

Monday, 12 August 2013

Because You Can!

I love to get into classrooms to do demo lessons or to co- teach. I have been in Canberra all last week and have had opportunities to try out the Show Bags problem (see the blog below) in various guises with students in Grades 1, 2, 3 and 4. The results were interesting and informative.
Students respond well to being challenged when they are in an environment that values risk taking and sharing of ideas rather than right answers and where students are able to invent their own approaches to a problem. These children have a ‘because you can’ attitude to maths that enables them to get going on a challenge rather than shy away from engaging with difficulties that the challenge presents.

Grade 1

For the Grade 1s I reduced the number of show bags to 4 and chose some different quantities for the items:
4 bouncey balls
6 balloons
3 dice
10 counters
5 sticks of chalk
We did not get to the Sting in the Tail part of the problem but reflected on several of the student strategies, how they worked, how some of them ‘saved brain space’ and how they were each related mathematically to each other.
Some students simply added the number of items initially not realising that they had to fill 4 bags each time. The range was as expected very wide with some students drawing pictures and counting all or counting on . Some combined pictures and chunking as shown below for the bouncey balls.

Note how the secret code makes the thinking visible. In this instance we see that a double followed by a count on was used for the solution to 4 lots of 4 bouncey balls. Using tallies was also used to find the number of bouncey balls:
Other strategies included using skip counting sequences (often by counting on each time), using known facts, (e.g., double 4 is 8, double it again is 16) and in a few instances 4 × 5 = 20 and so 4 × 10 = 40.

One student used the 2s to get to the 4s by doubling his answer to 2 × 4 for 4 × 4 and later used his answer to 4 × 10 to find 4 × 5 by halving. This is an early indicator that multiplicative thinking and proportional reasoning are beginning to naturally develop as part of being given the opportunity to grapple with a challenging situation.

Grade 2

The responses in the Grade 2s was similar but here the number of show bags was increased 7 and I added 25 paper clips to the list of items for the show bag.
One student looked at the 25s and said he knew three 25s was 75 so double it is 150 and 25 more is 175. The distributive property was used by several students who worked out 7 × 25 by first working out 7 × 20 and then 7 × 5 and adding the two products
Another student wasn’t sure what 7 × 3 dice would be, but quickly worked out 7 × 2 by doubling then simply added one more 7 for 7 × 3, knowing that that was a fast strategy.
These indicators of deep understanding are always exciting to see and, when students are invited to share them in their own terms with the class, are often contagious.

Grades 3 and 4

There were still some students who did not recognise that this was a multiplication problem initially and as teachers we need to ensure that students can recognise the appropriate operation for a given problem. Often this is experiential and students need many more experiences interpreting and possible writing their own problems.
Some students were still using counting, skip counting and repeated addition strategies. For these students it is important to help them make connections between repeated addition and multiplicative strategies. Often students do not make these connections easily. One student, given the 26 lots of 25 paper clips as a sting, knew that 4 × 25 was 100. The 26 was split into 2 + 24 because 24  = 6 × 4 which gives 24 × 25 = 6 × 4 × 25 = 6 × 100 = 600 and another 2 lots of 25 is 650.

It is only by offering challenging problems that we can get windows into what the students do know, what they can do as well as how they do it.
Hope you have tried the problems too. Simply adapt them to your students.

P.S. By the way we did need an extra sting. We had to quickly come up with realistic prices for each of the packets so that the Year 1 teacher would know how much it was all going to cost.

Thursday, 8 August 2013

What do you get at the EKKA?

The EKKA is the Royal Queensland Show which is held annually at the Brisbane Exhibition Ground. Breeders show off their farm animals, the best jam or the best cake is judged, not to mention the fashion parades, dancing dogs and the rides and of course the show bags. So here is a show bag problem. Ann has tried this problem out in Canberra and found that the numbers chosen made for some very revealing information about the ?Year 3-4 class that she was working with..

Show Bags

My friend the /Grade 1 teacher is going to make show bags with her class. They are going to swap them with the class next door. The class has to make 26 show bags.
This is what they have decided to put into each bag:
2 bouncey balls
5 balloons
3 dice
10 counters
4 sticks of chalk
My friend wants to know how many of each item she needs to buy ready for the show bags. I said you would work it out for her. She also wondered how many items they would be packing altogether.

Sting in the Tail

Bouncey balls come in packets of 10.
Balloons come in packets of 10 as well.
Dice come in packets of 6. Counters come in bags of 50.
Chalk comes in boxes of 12 sticks.
How many packets of each item will she need to buy?

While on the subject of show bags, what a hot topic for some data collection.

What should be in a Perfect Show Bag?

What 6 things would you like to have in your perfect show bag?
Are these the same or different to things that the rest of the class would like in their show bag?
How could you decide what to put into a show bag for the boys/girls in your class?
How could you decide what to put into a show bag that suited the whole class?
What data/information will you need to collect to be sure that you have made the best decisions?
Think about how to present your information clearly to the class to see if they agree.

If you try thin idea out, expect it to last for more than one lesson, but do send us your ideas with supporting data and we may put it on the blog for others to see. Who knows maybe a manufacturer would listen and next year you might have the perfect show bag.

Monday, 5 August 2013

The Story of the Lesson

When a parent asks “What did you do in school today?” it is not uncommon for the answer to be along the lines of “not much”. Holding a reflection at the end of a maths lesson makes it much more likely that the answer will be fuller than that, and there is one technique that almost guarantees that the question will be met by a full and interesting account of what was being learned in today’s maths lesson.
At one of my PD sessions in South Australia Lynn from Lake Windermere Primary School liked my examples of students being asked to tell the story of the lesson. She decided to find out what stories her students would tell and so she gave them paper which they folded into quarters which gave them spaces for different parts of the lesson. The students were asked to draw and write the story of the number line maths lesson. As you will see from the samples below her students were able to retell the story of the lesson clearly and highlight the parts that were special to them.

The first sample shows Lynn in her chair and the students on the carpet as she introduces the lesson.
The second sample focuses on some of the pedagogical moves that Lynn used, first some mental warm ups then the introduction of the rule that the numbers on the number line should be evenly spaced. The students had time to work and then came back to the carpet for the reflection where they were able to share and ‘teach’ others about what they had learnt.

It must have been very gratifying to Lynn to be able to get this window into how her students perceived the lesson as well as to know that she certainly had a very strong story thread through her lesson.
I have been asking many of the classes that I have worked with this year to tell the story of the lesson and it is interesting and informative to hear what they say. I would recommend this as a reflection tool from time to time.