Making 1000 Count!

Madonna Pianegonda, Catholic Education Office Archdiocese of Canberra and Goulburn

In my role as Curriculum Officer Numeracy P-6, I am often asked to model inquiry lessons in schools. Making 1000 (Maths300 Lesson 49) is a valuable choice which can be differentiated depending upon the students involved. While the Maths300 lesson plan recommends Year levels 1, 2, 3, I have also used this lesson with students in Years 4 - 6.
The lesson concentrates on counting which, for younger students, involves unitary counting strategies. However, it also affords the opportunity to transition to counting in collections (Count Me in Too, LFIN). In particular, it reinforces the idea that 'ten of these make one of those': a construct underpinning our entire number system and place value.

In Years 4 - 6 the content can be differentiated to look also at the Number and Measurement Strands in the Mathematics Curriculum. In the Number Strand, there is the opportunity to extend the lesson by asking students, "What fraction or percentage (of the whole) a layer in the 1000 cube may be?" For example the top layer is 1/10 or 10% of the whole (1000). This can lead to formal number sentences in Years 5 and 6. That is, 100 = 10% of 1000, or three layers is 300 = 3/10 of 1000 or 30%. The remaining layers must be 70%, etc.

For the Measurement Strand the lesson lends itself to discuss area and volume. The rectangular shape of the 100 x 10 lengths can be calculated formally or informally. (Counting the 10 towers = 1000 square Unifix cubes or, more formally, 100 Unifix cubes x 10 Unifix cubes = 1000 square Unifix cubes.) Equally the cube can be used to calculate volume in the same manner informally or formally.

Having modelled this lesson in many schools and to many different year groups, it is a lesson which always engages the students. Of interest is the different ways in which students begin making the snake; usually with a flourish of students rushing forward making many little snakes in the beginning. A question about how many snakes were to be made, usually brings students back to a more collaborative approach. Additionally the constraint that the snake be exactly 1000 Unifix cubes long forces students to devise some way of counting as they construct.


Using a 10 tower as a counter.

Many different snakes begin the lesson.

This is determined by the students and therefore many different solutions evolve. It may be that a certain coloured Unifix cube is used for every 10th cube or a 10 tower is used as a ruler to count. The curlier the snake the more inaccurate the latter count strategy is - something the students quickly realise.

One Extraordinary Class


Worker bees!
I would like to relate my experience with a particular class whose teacher had attended Working Like A Mathematician (WLAM) Professional Learning and used this pedagogy and those experiences extensively in her lessons. While the students had not been exposed to Making 1000 before, they were used to mathematical thinking, working in groups, justifying, reasoning and checking their answers. To my surprise (and delight), these students did not rush to make many different snakes. Instead this Year 2/3 class chose to discuss how they would attempt the task. It was decided before any construction, that the snake would be assembled in towers of 10 Unifix cubes of identical colour. That way, as one student commented, the count at the snake's construction would be easier. It was decided also that there would be 'worker bees' who constructed the towers and then another working group who built the snake. No work commenced until roles were determined and strategies were agreed upon.

Even the tried and true question during construction (near the 850 cube stage) about "How long is the snake at this point?" could be answered easily. Students had used pointers along the snake to determine the count at various places. This was to stop the need to count from the very beginning "in case of a mistake", one student said.

The normally rushed lesson to model this in an hour was calm, organised and over in 35 minutes! These fantastic mathematicians understood the problem, planned a strategy to start the problem, carried out their plan and had a way of checking the result (Working Mathematically Process).


Towers of 10 in identical colours...

 

...Which leads to a very different looking 1000 rectangle from previously modelled lessons shown above.

Calculating Changes ... is a division of ... Mathematics Centre