Shape and Space Find below the Learning Outcomes, mathematical concepts and progression continua associated with the strand units of "Spatial awareness and location", "Shape" and "Transformation". This page will be updated with further support materials and video examples of children's learning in the coming weeks and months.
Spatial awareness and location Shape Transformation Spatial awareness and location Stage 1 Junior & Senior Infants Through appropriately playful and engaging learning experiences, children should be able to Stage 2 1st & 2nd Class Through appropriately playful and engaging learning experiences, children should be able to Stage 3 3rd & 4th Class Through appropriately playful and engaging learning experiences, children should be able to Stage 4 Fifth and Sixth class Through appropriately engaging learning experiences, children should be able to develop a sense of spatial awareness in relation to their bodies and the immediate environment. describe the spatial features of objects and theirmrelative position in space. use spatial knowledge for the purposes of orientation and navigation. visualise and model location using symbolic co-ordinates. describe, interpret and record directional instructions and location. compare and classify angles, recognising them as a property of a shape and as a description of a turn. describe location on the full co-ordinate plane. interpret scale maps and create simple scale drawings. Concepts Everyday language can be used to describe the relative position and direction of objects and people (to other objects and people). Position can be viewed from various vantage points. Non-standard units can be useful to give more accurate directions for movement. Simple maps and/ or drawings can be used to track the movement of objects. More formal language can help us describe position and direction more precisely, e.g. the language of the compass points. The location of objects can be portrayed on a map, with/without a grid system. A grid system of horizontal and vertical lines, labelled with letters and numbers, can be laid over a map and used to identify locations. When drawing maps of locations, it is necessary to think about the relative size and position of key features. Directions and locations can be described with increasing precision, using more formal measures of distance and direction (60 km east) and simple grid reference co-ordinates (A6). There are different ways to think about angles, including: • angles as the corners of 2-D shapes • angles as a measure of turn. There are 360 degrees in a full turn. The extent of a turn is measured in degrees. Half of a full turn (180 degrees) and quarter of a full turn (90 degrees) are used to classify angles. Approximate distances can be calculated by considering the distance represented by each cell of the grid. An exact location on a map can be described and found using co-ordinates. Distances on maps and some plans can be determined using a scale. The relationship between angle measures and compass co-ordinates can be used to plot direction accurately. The co-ordinate plane has a horizontal x-axis and a vertical y-axis. Co-ordinates identify the location of a point. They consist of pairs of numbers, which indicates the distance along the x-axis and the y-axis respectively. Progression Continuum Click on the image to access the progression continuum for the strand unit of 'Spatial awareness and location' Shape Stage 1 Junior & Senior Infants Through appropriately playful and engaging learning experiences, children should be able to Stage 2 1st & 2nd Class Through appropriately playful and engaging learning experiences, children should be able to Stage 3 3rd & 4th Class Through appropriately playful and engaging learning experiences, children should be able to Stage 4 Fifth and Sixth class Through appropriately engaging learning experiences, children should be able to explore and recognise properties of 3-D and 2-D shapes. examine, categorise and model 3-D and 2-D shapes. investigate and analyse the properties of 3-D and 2-D shapes and identify classes of shapes based on these properties. represent shapes with drawings and models, and calculate dimensions of shapes. construct 3-D and 2-D models or structures given defined measurements and/or specific conditions. investigate and construct angles in the context of shape; and solve angle-related problems. Concepts 3-D and 2-D shapes can be classified and sorted by their appearance and by simple properties. 2-D shapes are flat. They have two dimensions, length and width. 3-D shapes, or solids, have three dimensions, length, width and depth. Shapes can be combined to make other shapes and/or structures. 3-D and 2-D shapes can be distinguished, identified, and categorised by their properties. Geometric properties can be categorised according to symmetry, number and type of sides or faces. Shape families describe categories of shapes that have common properties. Sometimes shapes from the same family can look quite different, or have a range of shapes within them. A corner of a 2-D shape makes an angle. Shapes and shape families can be sorted and classified according to multiple properties and rules. For 2-D shapes, these properties include symmetry, parallel or perpendicular sides and nature of angles. For 3-D shapes, properties can include number of faces, edges and vertices. A polygon is any 2-D shape with straight sides. The name indicates how many sides the shape has. In a regular polygon, all the sides are equal and all angles are equal. Prisms and pyramids gain their names from their polygon bases. Properties, rules and measurements of a shape can be investigated by construction, deconstruction and dissection. A net is a representation of a 3-D shape, which can be folded or assembled to re-create the 3-D shape. Shapes have minimal defining lists which define their properties. These can be used to deduce and make connections between classes of shapes. 3-D and 2-D shapes can be measured and tested for the constituent properties and rules. The sum of interior angles of a 2-D shape is determined by the number of its sides. Given some information about lines and angles, measurements can be deduced. To construct nets, models or structures using geometric shapes certain rules must be followed. Progression Continuum Click on the image to access the progression continuum for the strand unit of 'Shape' Transformation Stage 1 Junior & Senior Infants Through appropriately playful and engaging learning experiences, children should be able to Stage 2 1st & 2nd Class Through appropriately playful and engaging learning experiences, children should be able to Stage 3 3rd & 4th Class Through appropriately playful and engaging learning experiences, children should be able to Stage 4 Fifth and Sixth class Through appropriately engaging learning experiences, children should be able to explore the effects of shape movements. understand that shapes and line segments can be reflected, rotated and translated. model and explain the effects of transformations on shapes and line segments. perform and devise a range of steps involving transformations. analyse and show how shapes are enlarged on scaled diagrams. Concepts The movement of shapes and objects can be described using simple words such as flip, turn and slide. A shape’s position, orientation or size can be changed without changing the kind of shape it is. Transformations involve actions on shapes. The mathematical terms reflect, rotate and translate can be used to describe the movement of shapes and objects. A shape or line is reflected when it is the same perpendicular distance from the mirror line. A shape or line is rotated when it is turned around a point. A shape or line is translated when it is moved a certain distance from its original position (without turning). Simple units of measurement and/or grids are useful to describe and plot shape movements. A shape or pattern has reflective symmetry if it remains the same when reflected through a mirror line. The mirror line can be part of the shape/object or external to it. A shape or line is rotated when it is turned around a point called the centre of rotation. The direction and amount of turn can be described used mathematical terminology and angle measures. A shape or pattern has rotational symmetry if it looks the same after a rotation of less than one full turn. Tessellation involves covering a surface with no gaps or overlaps, using one or more geometric shapes. Certain shapes and combinations of shapes can tessellate. Regular tessellations are tessellations of regular polygons. There are three types of regular tessellations: triangles, squares and hexagons. Transformations can involve a number of steps. These steps can be identified, ordered, recorded and performed (with or without technology). Co-ordinates are pairs of numbers, the first of which indicates the point on the x-axis and the second on the y-axis. When shapes are transformed on the co-ordinate plane, their co-ordinates can be predicted and deduced. It is possible to enlarge a shape. Enlarged shapes remain similar to the original shape in terms of their corresponding angles and the proportion of their sides. Progression Continuum Click on the image to access the progression continuum for the strand unit of 'Transformation'
