A new version of Symmetricon

In an earlier blog, we wrote about the visible learning effect of our Symmetricon app. Originally, we had planned for the app to have three levels but as we came to review the initial program, we felt that to include Level 3 would make it just too hard. Well, how wrong can you be?

Because of the way in which the app enables the players to ‘get it’ really quickly, we have frequently been asked if it would be possible to make it a bit more challenging. Hence the new version, in which there is a Level 3, which is based on a hexagonal design.

Writing about this also gives us a chance to point you to the feature that allows you to send your design to Facebook or a class blog or to email it to a class email address. Go to the 'Help file' and scroll to the bottom where you can select which of the social media features you want to use. That way you can accumulate a whole spectrum of symmetricon designs, which can enliven the walls of your classroom at a time when symmetry has become a hot topic.

And don’t forget that you can download a lesson plan with suggestions for using Symmetricon in the classroom.

Teaching ratio using pizza

Last week Ann ran a three day transition project across Parafield Gardens High School and its feeder primary schools. The teachers involved were open to ideas and sharing in the interests of improving understanding and continuity between primary and high school maths and pedagogy.

Each day, Ann ran a demonstration lesson which the teachers then unpacked with student work samples to guide them. On the third day, Ann took the teachers into a year 7 class to give the students a problematised situation involving ratio. The class teacher was a bit alarmed as she hadn't introduced ratio yet.

“All the better for our purposes,” thought Ann, “...we should see students struggle with the problem!” The following problem is loosely true.

The Problem

Thomas has surveyed the 18 teachers here today to find their pizza preferences.
He says that ham and pineapple, supreme and vegetarian were selected in the following ratio, 3:2:1, and that everyone would be happy if they had three eighths of a pizza. Amanda says she is going to get six pizzas two of each flavour. 

I think this is going to be a poor decision. Please work out what our pizza order should be.

The Sting

We are on a limited budget so need to buy the least number of pizzas. They are $7.50. What should we order to get the best deal?

As it turned out, the students got straight into making sense of the problem, often by drawing, as the following example shows.

Although the students had not been formally introduced to ratio, they made a great job of interpreting what the question meant. In less time than Ann thought possible, the problem was solved and the sting-in-the-tail was required. Here the students brought their own understanding of what would constitute a ‘good deal’ and many of them focused on minimising wastage.

Learning fractions out of cutting salad ingredients - it works!

Last week I was working with the year 1/2 class at Torrensville Primary School and the students were given a salad problem as we considered healthy foods.

The problem: Last night my neighbour's little boy came to visit so we made some salad.

• We chopped the veggies.
• We chopped 5 baby costs lettuces in half.
• We chopped 4 tomatoes into halves
• We chopped 3 carrots into quarters.
• We chopped 2 celery sticks into eighths.

After we had eaten the salad, Kai asked how many pieces we had made with all that chopping. I said I would ask my students to work it out for him.

The following work samples are just a few of the many solutions that the students found.

In the last sample, you can see four plates after the first working out. That little girl finished so easily that she needed the sting in the tail!

• We put the salad equally shared onto four plates - so what was on each plate?

Look closely and you will see that two lettuce halves were cut again and a quarter put onto each plate.

The students needed no assistance getting started and one child called out "Eighths means eight pieces doesn't it?" That was the only hint as such. It is amazing how easily students work with fractions if we let them work intuitively rather than try to teach adult-centred strategies.

Try it with your students and email us the results - john@naturalmaths.com.au. Have a great week!

Working with friendly numbers

The year 1s and 2 s in Lynn and Sue's class have been working with friendly numbers. Here are a couple of examples form the classroom walls. The students could chose the numbers that they wanted to work with.

Allowing the students to have such choice allows them to feel free to experiment and challenge themselves.

The students can then be engaged in differentiating the task to suit their current confidence level.

Well done Sue, Lynn and their class and to Ludig, one of the students in the class who reads this blog.

Multiplication Tables

Two books in the 'Back to Basics' series,  'Multiplication Tables', Ann has written cover multiplication tables.

Let’s dip inside and have a look at what makes these two books so special.

Ann has taken the thinking-teachers' approach to helping children become masters of their multiplication tables and starts by giving them a vocabulary with which they can describe the strategies that they might use to work out an unknown fact.
 
In the second book, Ann shows how to use tallies to work out one of those troublesome multiplication facts:

With games and ‘beat the calculator’ activities, these books are full of bright new ideas for helping children over the multiplication tables hurdle. For more information, visit www.pascalpress.com.au/back-to-basics/

Bridging through ten and one hundred

Sue Carey and Lynn Smart, year 1/2 teachers at Torrensville Primary School have been working on bridging through ten and one hundred.

The photos below show the examples that the students made using Kidpix.

Around the classroom posters made by the students as shown below are on display. In these two classes the students differentiate for themselves by choosing the numbers that they want to work with. As you can see from the second photo below, the class drips with student produced maths materials.

Sue said her whole display used to be literacy but now their are tons of maths every where around the room.
Watch out or more from Sue and Lynn later in the week.

A problem solving mathematical journey

Rita Romano from Lefvre Peninsular Primary School keeps an A3 sized maths journal for her class.

Every maths lesson is recorded with photos and/or student work. It tells the story of the mathematical journey that her class is taking. Parents love it, the students love it and use it as a resource during their problem solving.

Rita did my favourite lesson where a large number of paddle pop sticks are dumped on the floor. Students estimate how many and then find their own ways into counting.

It makes magnitude of large numbers visible and leads to students really understanding why base ten is so important. Rita gave me permission to show case these three pages from her book. I am hoping for more at a later date.

Read and enjoy. Thanks Rita!

About Time!

A new series of 10 books written by Ann have just been released by Pascal Press. Last week we gave you a preview of the Addition and Subtraction books, this week we’ll start with the book about Time.

In the early sections of the book, Ann emphasizes the difference between the hour and minute hands by introducing the hour hand alone before showing both hands on the clock face. 


What times are showing on these clock faces?

A gentle introduction to the past the hour and to the hour times is also featured as the research into children’s abilities with time show these to be common stumbling blocks. The book also relates the digital clock to the analogue clock as well as setting the scene for understanding calendars.

This book in the series matches well with our new package called Telling the Time, that is described at

http://naturalmaths.com.au/kt_Time.php

The sections on Calendars also match well with one of our IWB programs, Calendars, which you can preview at  http://naturalmaths.com.au/kt_iwb_Calendars.php

How a shopping list for Snow White helps students with problem solving

Darienne Crickmar of Victor Harbour R - 7 School has been doing problematised situations with her reception students. Her latest problem was related to Snow White and the Seven Dwarfs. Snow White had to make a shopping list for their dinner. They each wanted: 

• 2 sausages
• 3 carrots
• 5 potatoes
• 10 peas.

When the children started solving the problem they decided that Snow White needed to eat as well, hence 8 plates of food. The following work samples have been annotated by Darienne after she interviewed the children about their solution strategies. One of the samples is incomplete but it shows what a child who has only been at school for a few weeks can do. Notice how clever Darienne has been in her selection of numbers, counting by twos, fives and tens is part of the curriculum.

Doing it in a problem solving situation leads to purposeful skip counting not simply rote counting. Enjoy. Thank you Darienne for an interesting problematised situation.

What a joke!

Recently I was in the year 4/5 class at Angaston Primary School where I noticed maths joke posters displayed across the wall. I told the teacher, Michelle Goudie that I thought they were very funny and very well done. Last week when she was part of the DECD Day 3 (maths) with me she handed me a spiral bound book of the posters.

So Michelle thank you very much. With permission I have included just a few of the posters. I hope you enjoy these as much as I do.