Written by Libby Foley

The Reasoning Proficiency Strand in the Australian Curriculum is so much more than just explaining thinking. Students reason mathematically when they analyse, evaluate, infer, generalise, justify, compare and contrast. Students can then make statements to communicate ideas, utilising the language of mathematics. One of reSolve’s reasoning-rich and versatile teaching resource is the Attribute Train lesson sequence. The sequence is designed for Foundation students but can be easily adapted for other year levels.

The purpose of the sequence is to build students’ ability to observe the similarity and differences of objects based on attributes. The sequence begins by looking at the attributes of colour and shape and then introduces a third attribute of size. Students are asked to determine what an object might look like when one or two of its attributes are changed. All lesson resources are provided, however, you may like to use attribute blocks if they are available at your school.

Pre-teaching

In the Attribute Train lesson sequence students use objects, undertake mathematical thinking and make statements to communicate their mathematical ideas. Naming, describing and classifying are important skills in the development of mathematic vocabulary, and they are the beginning of students’ understanding of mathematical proof. So I think it is crucial to spend time interacting with the vocabulary before getting into the first lesson.

There is a lot of fun to experience with the dramatics of interacting with the new word attribute. For example, saying it loudly (loud crowd mode), quietly (spy mode), silently (ninja mode), slowly, quickly, like a robot etc. The teacher can then put on their imaginary binoculars, look around the room, and choose someone to examine and take notice of their attributes e.g. Summer - one of her attributes is glasses. Can everyone see Summer’s glasses in their binoculars? Who has a similar attribute and has glasses? How are your glasses similar? How are they different? Who has a different attribute? Summer also has the attribute of blonde hair etc. This sort of activity reinforces the language of similar and different. Students compare and contrast, and develop their understanding of the key vocabulary they will use in the lesson sequence. Now is also a good time to create class definitions for the words and use examples (words or pictures) from the binoculars activity.

Lesson 1: Attribute Train

This task asks students to use a set of attribute cards to create an attribute train. The cards use the attributes of colour and shape. One shape is chosen as the start of the train and each subsequent card added must change just one attribute at a time. Students use their cards to make the longest train that they can. Three additional challenges are then presented to the students. I printed a train and carriages for the class train.

Challenge 1

Can you create an attribute train that is 7 blocks long, starting with a red square and ending with a yellow square?

Challenge 2

This attribute train uses all of the blocks from one complete set. Can you place the remaining blocks in the blank squares to complete the train, changing one attribute each time?

Challenge 3

Can you create a circular attribute train that starts and ends with a blue circle?

Lesson 2: Train Challenge

This resource extends on the first task in the sequence by adding the additional attribute of size. The game ‘Train Challenge’ has students play against each other to create trains using three attributes. The lesson concludes by looking at a hypothetical game and considers the most strategic moves that can be made by each player.

Activity Adaptations

The concept of identifying and discussing similarities and differences in shape attributes carries on throughout the curriculum. Attribute trains and comparison activities can be adapted for any age. I am a primary school teacher so some of the adaptations I have played with include:

• Compare and contrast shapes using sorting circles or hoops. Separate hoops have different attributes. The circles do not have to overlap. This is a good starting point for discussion, limited shapes and the introduction of ‘what if…’ I would do this activity in the pre-teaching lesson sequence.
• Investigate types of triangles
• Investigate quadrilaterals
• Compare everyday objects and their 3D object counterparts
• Compare nets to 3D objects
• Incorporate understanding of enlargement/reduction of figures, line or rotational symmetry, transformations, geometric reasoning (types of angles or size of angles), combining/splitting shapes. There is a lot of vocabulary that will come out, as well as areas of misconception.

Final Words

reSolve tasks open themselves to many pathways and opportunities for discovery. My advice is to give students time. Time to think, explore, discuss, share ideas, question, build vocabulary and understanding of concepts, and to make connections. This also gives the teacher time to investigate student thinking, identify areas of misconception, ask enabling or extending prompts, facilitate success for all leaners, and make plans for further learning experiences. Do not feel like you have to rush to get through all of lesson 1 in one day. I don’t think I have since beginning this journey in 2017. Finally, and most importantly, enjoy the wonder of maths with your students.