Robot Navigation Games

Here are some ideas for teaching mathematical outcomes in the location, direction and movement topic in the strand of space:

S1.2 Students follow and give simple directions to move through familiar environments and located and place objects in those environments.

S2.2 Students interpret and create simple maps, plans and grids to follow and give directions, and to locate or arrange places or objects.

The learning sequence:

Step 1: Discuss the directional terms such as forwards, backwards, left and right, to assess children's understandings of those terms.




Set 2: Set up a grid using hula-hoops. Place an object, e.g. teddy-bear in one of the hoops, then ask a child-volunteer to be a robot, who can only move by recieving directions from their robot master.




The robot master can be you (the teacher) to begin with. The robot master's role is to give directions to the robot, so that the robot can navigate through the hula-hoop grid in order to rescue the teddy-bear. The directions should include position language such as "Move forward one step. Take one step the right. Then move forward two steps. Then take one step the left." and so forth.

You can introduce other complications to make the game more difficult, e.g. mark some of the hoops as being "lava hoops" which the robot cannot pass through. The robot master must navigate the robot to the teddy-bear without going through the lava spots.



The next step in the learning sequence is to ask the children to map out the route which they have taken. It is a good idea to provide the children with pre-drawn grids so that they can concentrate on the mathematical aspects of mapping.




After the children have completed their maps ask them to use their maps to describe the route to their friends as they follow the directions either on the grid or on a blank grid/map.

It is important to remember that the concept of space concerns more than just shapes - it includes developing understandings about direction, location and movement too.

Robot Navigation the boardgame:




I turned this game into a boardgame to help children visualise what they are doing now that they have experienced moving in differnt directions. It was also designed as a resource to teach the children about more complex directional language, such as "anti-clockwise" and "clockwise".

Aim: For each player to navigate their robot to the pot of gold (symbolised by the yellow spot).

How to play:
Each player is given 4 position cards (yellow) and 4 step cards (green) at the beginning of the game.




Players can only move their robot by playing step cards and/or position cards, e.g. a player may play one “to the left” position card and one “1 step” step card to move a robot one step to the left.

changes to


Robots can also rotate using position cards, e.g. a quarter-turn clockwise, half-turn anti-clockwise etc. But rotation cards cannot be used in conjunction with a step card, i.e. if a player rotates his/her robot, they must wait till the next turn to move the robot steps in any direction.


changes to
(after playing "quater-turn anticlockwise" card)

Each player must replace the cards they play by picking up another card from the deck.

Red spots symbolise lava hot-spots which must be avoided.

If another robot is blocking the path a player planned to take, they cannot land on, or pass through that space.

If a robot cannot make a valid move, that player may choose to discard one position or step card and pick up a new one.

Who am I? (With shapes)

Teaching focus:

I love a good game of who am I. There are so many variations one can have. Here's one with shapes. The teaching focus is for students to focus on identifying and recognising attributes of shapes.

From our workshop discussions in week 8 and 9, we discussed how the more helpful learning sequence for shapes is to introduce 3D shapes before 2D shapes as 2D shapes are less tangible than 3D shapes. By learning about 3D shapes first, introducing 2D shapes becomes easier because you can explain how 2D shapes are used to dsecribe the faces of 3D shapes, thereby helping them to see the connection between the two seemingly different concepts.

How to play:

(Basic level)

• Display the 3D shapes on the floor in front of a small group of children
• Describe some attributes of a particular shape (e.g. This shape can slide but it cannot roll. It has six faces. None of them are curved. All the faces look exactly the same. It has 12 sides, all of which are the same length.)
• Have a child volunteer pick out the shape he or she thinks you are describing
• Ask the child to pick a shape. This can be from another set of shapes inside a box or opaque bag so that the child can have a look at the shape in order to describe it properly without anyone else noticing which shape it is.

(Medium level)

• Play the same game as before but have the child describe the shape by visualising it in his/her mind
• Alternatively, play a similar game with just two players
• Provide each player with one set of 3D shapes and a photograph of one of those shapes
• Have the students try to guess the shape on the other person's photograph by asking yes/no questions, E.g. Does your shape have six faces?

(Medium level)

• Play celebrity heads with shapes
• Stick a picture of a shape on the child volunteer's forehead (or a headband displaying the picture)
• Have the volunteer ask yes/no questions about their shape while the rest of the class answers them
• The aim of the game is for the volunteer to guess the shape by identifying it from a pile or saying the name of the shape (keep in mind naming the shape may take the focus away from describing attributes)

Shape Story Video

The main idea/teaching focus this resource can be used for is to provide children with an interesting context for describing and identifying attributes of shapes.

They can conduct real-life investigations, researching questions such as "What do the shapes look like from differnt perspectives?" "Which shapes can roll?" "Which shapes can slide?" "What constitute a shape?"

This video can be watched a few times. The first time you may watch it the whole way through and discuss specific bits that stood out to the students. The second time, you may like to watch a small segment and conduct an investigation (with a bucket of the shapes) before watching the second part.

Disclaimers:
Please take note to mention that the 2D shapes shown in these images are not actually 2D because they have a thickness.

Also with younger children do not worry about naming shapes so much - you may like to call the shapes by their first names or just pick a shape out of a pile to talk about it. Even a simple activity such as getting the young childrern to identify "Which shape is Shaphia?" out of a pile of unpainted geometric shapes could be a good learning experience to get children to identify and describe attributes. "Why do you think she would be that shape?"

If I were to produce it again, I would probably do it on an animation program so that the shapes move as they talk, and I will try to write a story that is not as corny as this one. I would probably think twice about the bit about fat shapes and flat shapes too as it does contribute to the misconception concerning 2D shapes.

Week 9 Workshop I - Tangrams

What are tangrams?
Tangrams are a type of ancient Chinese geometric puzzle which contains seven pieces, made up of two large triangles, one medium triangle, two small triangles, one square and one rhomboid (or parallelogram) (Bohning & Althouse, 1997). These pieces can be assembled in different ways so as to make shapes such as...

A square...



A rectangle...



A triangle...



A trapezium...



A parallelogram...



And lots of other shapes e.g. birds, boats, etc.

What do you learn by working with tangrams?
According to Bohning and Althouse (1997), explorations with tangrams assist children’s skills development with “geometry vocabulary, shape identification, classification, discovering relationships between and among the pieces...recognising and appreciating geometry in their natural world.” (p.240).

In week 9’s workshop, through our explorations with tangrams I came to a deeper appreciation of how these skills may be developed. The use of geometry vocabulary was obvious as those of us present in our class tried desperately to assemble the shapes, in particular, the square shape. For example, in the spirit of collaboration, those of us who successfully assembled the square coached those of us who were less successful in our attempts, often by using location and direction terminology such as flip, slide and rotate. Furthermore, the names or the attributes of the shapes were also used to explain where they should go, for example, “Put the little two little triangles next to the square, but rotate the one on the right so that its longest side is on the edge”.

In terms discovering the relationships among the pieces, we discussed how each of the shapes was made up of certain numbers of the smaller triangle. For example, the square is made up of two of the smaller triangle, and the big triangle is made up of four smaller triangles. Therefore, in terms of area, the big triangle is actually equivalent to two squares. This discussion also led to the conclusion that using the tangram as a model can also be useful for discussing fractions, for example, if the total area of all of the shapes added together is understood to be the whole then the large triangle is one-quarter of the whole, which makes the medium triangle (which is one-half of the large triangle) one-eighth of the whole. This in turn makes the smaller triangle (which is one-half of the medium triangle) one-sixteenth of the whole, which also makes the square and the parallelogram (which both equal two small triangles) two-sixteenths or one-eighth of the whole.

Learning sequence of working with tangrams:

1. Placing shapes directly over the top of a diagram (of the same size) of the target shape with lines shown

2. Assembling the shapes by looking at a smaller-scaled example of the target shape with the lines drawn in

3. Assembling shapes by looking at an example of the target shape with some of the lines drawn in, e.g. Which shape can fit in here? How? Show me...

4. Assembling shapes without looking at an example at all (which effectively is the same as looking at an example without the lines drawn in) but with the correct-side-up identified

5. Assembling the shapes without looking at an example witht without the correct-side-up identified.

Week 8 Workshop - 2D Shapes

This week in our workshop we explored 2D shapes. Firstly, we constructed a 3D shape. We were given two pre-drawn nets of two 3D shapes which we cut out, constructed and sticky-taped together. Then we stuck the two 3D shapes together, and formed a triangular based pyramid. Afterwards, we reflected on what children would actually learn from such an activity if it were being done in a classroom. We discussed the fact that without further discussions about the 3D shape and its attributes, the activity would at best be providing children a chance to work on their fine motor skills and at worst be a complete waste of time.

This got me thinking - what is the purpose of constructing nets? It is supposed to help children understand and visualise the attributes of a 3D shape. Constructing 3D shapes using pre-drawn nets reduces the amount of visualisation and mathematical thinking children need to do, and can easily become a waste of time. Perhaps a better idea would be to get the children to construct their own nets. This may take more time, and may require children to persist through difficulties and multiple attempts. However, if the children are provided with appropriate scaffolding, they should come away with a deeper appreciation of the attributes of 3D shapes, than if they simply constructed a shape using a pre-drawn net.

Secondly, we discussed naming of common 2D shapes. This took up the majority of our lesson. We discussed terms such as: quadrilateral, polygon, rhombus, rectangle, square, trapezium, parallelogram...we discussed how some shapes fit into multiple categories, e.g. a square can also be classified as a quadrilateral, polygon, rhombus, parallelogram, a rectangle and a trapezium (according to the Australian definition of the word). We concluded by saying that what matters most about the teaching and learning of shapes in the early childhood years is developing children's abilities to describe and recognise attributes of shapes. This skill is more important than ascribing the right names to the shapes.

Furthermore, one of the research findings of the study summarised in Hannibal (1999) showed that when the research participants were asked to identify which shapes are triangles from a number of stimuli presented, younger children in particular often drew upon "self-determined triangle-defining criteria" (p.355). It was also shown that this occurred more frequently when other shapes which were easily recognised to not be triangles such as a circle and a square were not present in the stimuli. According to Hannibal (1999) "teachers need to move beyond having children just label shapes to having them understand what defines a shape category" (p.356). In other words, it is important to help children identify the integral attributes of a shape and distinguish these from other non-intregral attributes such as size, ratio and orientation, in order to avoid the development misconceptions in regards to what constitutes shapes such as a triangle, a square, a rectangle, a pentagon, and so forth. Other implications for some teachers may include correcting some of their own misconceptions of what are integral and non-integral attributes of these shapes.

It has been suggested that the common usage of proto-typical shapes (in books, posters or worksheets on shapes) has contributed to the development of these misconceptions held by children (and perhaps even teachers). For example, if children are used to seeing equilateral triangles but are unfamiliar with seeing isosceles or scalene triangles, they are more likely to mistaken non-integral attributes (such as "three sides have to be equal") as integral attributes of a triangle. Therefore teachers should use more non-prototypical shapes in the classroom and including different examples of shapes, in order to show that size, orientation and ratio are not integral attributes.

Thirdly, in the workshop, we participated in an activity which focused on identifying and describing attributes of shapes. This involved creating different polygons out of pieces of paper. We were encouraged to form non-prototypical shapes. Each participant created as many shapes as they could in the given time, then we were asked to sort our shapes by one attribute. The photographs below show how my group sorted our shapes by the attributes of "number of sides".


Starting with shapes that have three sides, four sides, five sides, six sides and so forth...

Then we subcategorised each of our categories. For the shapes that have three sides we divided our shapes into triangles that contain a right-angle (right-angle triangles) and those that did not contain a right angle triangle. The pink line was used to show the subdivision.



We also subdivided our four sided shapes (quadrilaterals) into two groups. We created one group of quadrilaterals that have no right angles, a group of quadrilaterals that have four right angles. Then, we further subdivided the second group (of shapes with four right angles) into shapes that have four equal sides and those who do not.





We sub-divided the five-sided shapes (pentagons) into those that contained a reflex angle and those that do not.



With the activity, the main focus was on identifying and describing attributes of shapes, and justifying the reasoning behind how these shapes were sorted. Another research finding outlined in Hannibal (1999) suggested that when the children were more likely to make correct catagorisation decisions when asked to provide explainations of the reasoning for their decisions in the triangle sorting task. Justifying decisions requires one to reflect on one's actions, which also provides opportunities for self-correction.

From participating in this activity, I also see its potential to assist teachers in identifying misconceptions held by their students (for example if they experience difficulties in counting the number of sides of a shape) as well as develop children's conceptual understandings about shape that is foundational for future geometry learning. It is only by being able to identify and describe the attributes that they can develop a comprehensive understanding of why a square is also a rectangle - which is because that its attributes fulfils both the criterion of a rectangle (a quadrilateral with four right angles and therefore have two sets of parallel sides of equal length) and a square (a quadrilateral with four right angles and all four equal sides are of equal lengths).