Space+and+Measurement

Identify and describe the attribute of mass || ** GDB Lime ** 6 Mass 1-2 || ** Sample Units of Work ** Estimate and measure the mass of an object using equal arm balance and appropriate informal units || ** 1989 Syllabus ** Mass 4-6 || ** Westdale PS Units of Work **
 * ** Key Idea ** ||||||  Resources  ||
 * ** KI 1 **
 * Early Stage 1 **
 * MES1.4 **
 * 1989 Syllabus **
 * Pushing, Pulling and Lifting p.34
 * Free Play with an Equal Arm Balance p.34
 * Mystery Boxes p.34
 * Mystery Bags p.34
 * Sorting p.35 || ** Teaching Measurement ES1 and ST1 **
 * Two Groups p.118
 * Hefting p.118
 * Twin Bags p.119
 * Blindfold p.119
 * Heavy Bag, Light Bag p.119 ||
 * ** KI 4 **
 * Stage 1 **
 * MS1.4 **
 * One –Many Comparisons p.2
 * Observe, Predict, Interpret p.2
 * Balance Investigation p.2
 * Equal Masses p.2
 * Choose the Unit p.2
 * Differences in Mass p.2
 * Guess, Check and Record p.3
 * Match My Mass p.3
 * What’s in your Cupboard p.3
 * Using an Equal-arm Balance (WM) p.3
 * Conservation of Mass p.3 || ** Teaching Measurement ES1 and ST1 **
 * Make Another Bag p.130
 * What Do You Think? p.130
 * Make a Balance p.131
 * A Cup of Rice p.131
 * Does It Balance? P 131
 * Which is Heavier p.134
 * Heaviest Pencil Case p.134
 * Has to be the Same Mass p.135
 * Mystery Boxes p.135
 * No More Gaps p.135
 * Work it Out p.138
 * Heavier or Lighter? p.138
 * Let’s be Accurate! p.139
 * Solve the Mystery p.139 ||

**Area ** || Area 3 || ** Sample Units of Work ** Ordering Leaves Students collect or are given a collection of leaves. Possible questions include: - which leaf is the biggest/smallest? - how can you tell which leaf has the biggest/smallest area? - can you show me a leaf that is smaller/bigger than this one? - can you sort the leaves according to their size? Students are shown an outline of a tree shape and are asked to identify the group of leaves they would use: - if they had to cover the tree shape completely and explain why - if they had to use as many leaves as possible - if they weren’t allowed to use many leaves. Students are then given an outline of a tree shape and are asked to glue leaves onto the shape so it is completely covered.
 * **Week 9 **
 * Resources  ||
 * ** 1989 Syllabus **
 * Ordering Leaves p.28

B ag of Shapes The teacher prepares several bags containing a variety of shapes. The students are organised into small groups. Each group is given a bag of shapes. In turns, each student randomly selects two of the shapes from the bag, estimates which one is bigger, and superimposes the shapes to test their prediction. They share their observations with the group. Students are asked to describe how they worked out which shape was bigger and to record their comparisons. Possible questions include: - can you describe what you have done? - how did you compare these two shapes? * Find a Bigger Area p.29 In pairs, students draw a shape on paper and are asked to find three areas that are bigger, smaller or about the same size. Students discuss how they compared the areas. The teacher models comparing by superimposing one shape over another. Students’ responses are listed in a table. In pairs, each student is given a piece of paper and asked to draw a large shape. They paint or colour the area of the shape and cut it out. Students compare the size of their shape with their partner’s shape by superimposing. Students glue their shape onto paper and write a statement comparing their shape with their partner’s shape eg ‘Hugo’s shape is bigger than Alexandra’s.’ Possible questions include: ❚   what is area? ❚   can you show me the area of this shape? ❚   how do I know which area is bigger? Can you show me?
 * Let’s Compare Shapes p.29

||  || Area 4 || ** Sample Units of Work ** Students select one type of object to cover a given shape or area eg envelopes, lids, leaves, tiles, sheets of newspaper. They estimate, then count, the number of objects used. Possible questions include: ❚   why are some objects better than others for covering? ❚   what can we do about the gaps? ❚   what can we do with the part left over? This activity is repeated using areas of various sizes eg drink coasters, pin boards, desktops, the classroom floor
 * ** 1989 Syllabus **
 * Cover and Count p.70

Students draw a shape and colour the inside, to indicate the area of the shape. They then estimate and measure the area, stating the number and type of informal units used. Students discuss if another unit would be more suitable. Students investigate and record findings using other units. Possible questions include: ❚   which informal unit did you find more appropriate to    estimate and measure the area of your shape? Why? ❚   what would you use to measure the area of your desktop? Why? How would you do it? ❚   can you record your findings? Variation: Students could use Kidpix or other drawing applications to draw their shape and use stamps to fill the area.
 * Estimate and Check p.70

The teacher shows the students a collection of 4 or 5 small rugs. The teacher then poses the problem: ‘I want to use one of these rugs for my pet dog/cat. Which one will give my pet the largest area to lie on?’ Students estimate which rug has the largest area. In small groups, students select materials to cover the rugs to measure which one has the largest area. In small groups, students select an informal unit and calculate the area of the top of the desk. Students are provided with a variety of materials to use as informal units eg paper plates, sheets of paper/cardboard, tiles. The teacher takes digital photographs of student methods, particularly where students are overlapping units, leaving gaps, or not starting or finishing at the edge of the desk. Photographs are displayed for discussion. Possible questions include: ❚   what interesting things do you notice about the way groups measured the top of the desk? ❚   did each group measure the whole area? ❚   if two groups used the same item to cover the desk, why might they have different answers?
 * Rugs p.70
 * Table Tops p.70

* What can it be? p.70 The teacher poses the problem: ‘I measured an item from our room and found that it had an area of 10 tiles. What could it be?’ Students brainstorm items that it might be and then, in pairs, use tiles to measure the area of the items. A class list of items with an area of 10 tiles is compiled. Students discuss how they chose which items to measure. Possible questions include: ❚   can you compare how you measured the area of the book and the desk? ❚   which was easier? Why? ❚ which unit have you found to be more accurate? Why?

Students select a shape or tile to use as a unit to compare the area of different shapes. They estimate the number of units required to completely cover a shape, check and record their results in a table. Students work in groups of three or four to trace the outline of each other’s shadow on the playground using chalk. The teacher provides students with different-sized lids. Each group selects a lid to trace around. Students are asked to cover each shadow with outlines of their lid to find the area. eg ‘The area of my shadow is about 14 ice cream lids.’ Students compare the area of their shadow with those of others and discuss whose shadow has the biggest/smallest area. Possible questions include: ❚   did your lid-shape leave gaps? ❚ is there a shape that would have been better to use? Why?
 * Estimation p.70
 * Shadows p.71

Using a computer drawing package, students are asked to draw a large shape (A). They then select a smaller shape or picture to use as a ‘stamp’. Students ‘stamp’ the smaller shape inside the larger one, without gaps or overlaps. Possible questions include: ❚   how many of the smaller shapes did you fit in your larger shape? ❚   can you work this out without counting each shape oneby- one? Students repeat this activity by creating a second large shape (B). They then compare the shapes A and B and determine which is larger. They discuss their method of comparison. Some students may have compared the number of ‘stamps’ on each shape, but if they used different ‘stamps’ they need to reflect on the importance of using the same ‘stamp’ to compare.
 * Stamping p.71

* Roll the Die Twice p.71 Student A rolls a die to find out how many square tiles to put along the top row of an array. Student B rolls the die to find how many rows to make. The teacher encourages students to predict how many tiles will be needed to complete the array after the second row. Students make the array and draw the pattern on grid paper. Students repeat the game at least twice more. Students cut out arrays drawn on grid paper and order them.

Students are given 12 square tiles. They create a rectangle with an area of 12 tiles. Students draw their rectangles on grid paper then rearrange the tiles to create as many different shapes as they can, with the area remaining unchanged. They record them on grid paper. Students discuss strategies used to create their shapes. Extension: Students create further shapes, selecting different units to measure area, and record them on grid paper eg  Δ =   1 unit, ■    = 1 unit. Students are asked about the number of  units needed to cover their shapes.
 * Rectangles p.72

* Patchwork Quilts p.72


 * Class Notice Board p.72

Students estimate how many student paintings (of the same

size) would fit on a notice board/display area in the

classroom. The teacher selects students to hang their paintings

without gaps or overlaps. Students count paintings displayed.

Possible questions include:

❚

how many paintings could we fit on the notice

board/display area?

❚

are there any paintings that hang over? If so, how can we

count them?

❚

is there a way we could count all of the paintings without

counting each painting one-by-one?

|| ** Teaching Measurement ES1 and ST1 ** Given a rectangle (“floor plan”), students have to work out how many tiles will cover it (given only one 10 cm tile). Students create the tessellation by tracing or marking. Record the tiling and measurement. || Kinder
 * Tiling the Bathroom p.71

Students throw balls of different mass and compare how far they are able to throw them. Students are encouraged to hold, push, pull, and lift objects, especially those that are of clearly different mass. Students are given a selection of obviously light and obviously heavy objects to sort into groups. A variety of everyday objects can be used eg paper clip, rock, tile, drink bottle. The teacher then discusses with students the reasons for putting objects into different groups. In small groups, students are given the opportunity to experiment with an equal arm balance and a variety of materials. Students work with a minimum of direction and record their findings. Students discuss and compare their results and note any findings about balance.Possible questions include:❚what are the words we use to talk about mass?❚by looking at these two objects, which one do you thinkshow me how you know which mass is heavier?
 * 1. Pushing, Pulling and Lifting**
 * 2. Mystery Bags**Students are each given two opaque shopping bags and are asked to place objects in them so that one bag is heavier than the other. These bags are shared with others to lift anddescribe. Possible questions include:❚what words did you use to describe how the bags felt?❚could you work out which bag was heavier by just looking at them?❚what could you use to help you to work out which bag is eavier?
 * 3. Sorting**
 * 4. Free Play with an Equal Arm Balance**

Years 1 & 2

of students choose suitable measuring units to find the mass of a cup of rice. Students record the mass and state why they chose the units. Class discusses the results and compares the units which were chosen. Some units may have a greater or smaller volume than other units. Estimate then find which of two objects is heavier (but the students are not allowed to heft them or to put them on the balance together). The teacher displays a bag with some blocks in it. Students make a bag that has the same mass by filling with blocks and then hefting the two bags. Students find the mass of their bag by choosing appropriate units and measuring on an equal-arm balance. The measuring process and results are recorded, including a comment on the choice of units.
 * 1. A cup of rice Pair**
 * 2. Which is heavier?**
 * 3. Make another bag**

Represent 2D shapes using a variety of material || ** 1989 Syllabus ** 2D1, 2D7 || ** Sample Units of Work ** students walk around the school and describe the various shapes they see eg "these leaves look round". Students use drawings to draw what they found. Tracing Objects p.38 Print It (Two- and Three-dimensional Space) Students select an object from a collection of environmental and commercial materials such as fruit, stones, boxes and pattern blocks. They are asked to investigate the different parts of the object that can be painted and printed onto paper. Students share and discuss the printed shapes and the ways they were able to create particular shapes. Students are given a piece of string and are asked to make a straight line, a curved line or a closed shape. They are asked to describe their line or shape, and draw what they create. Students make a picture using different-sized paper shapes, including circles, squares, triangles and rectangles. As students are working, the teacher asks the students to name the shapes they are using. Students investigate the shapes or figures that can be made by bending and joining pipe cleaners. Students describe their shape and use drawings to record what they have made. Alternatively, the teacher may take photos. Part A Students are shown a set of attribute blocks and, in turn, are asked to select two of the blocks and state how they are alike and how they are different eg ‘These two shapes are both triangles but one is thick and one is thin.’ Part B The teacher then sorts the attribute blocks into two groups and the students determine how the shapes were sorted. Part C In small groups, a student randomly selects one of three cards and displays the card for the others to see. shapes and collects a variety of objects (some with similar features). Part A Students are asked to sort the shapes and objects into groups eg rough or smooth, colour, size, shape. Students are asked to explain their grouping. Students then sort the shapes and objects in a different way. For example, if the students sort them according to their colour the teacher could ask ‘If these shapes and objects were all red, how would you sort them?’ Part B In small groups, students take turns to sort the shapes and objects for others to determine and explain how they have been sorted. Possible questions include: ❚ how many different ways can you sort the shapes? ❚ is this shape a square, a rectangle or a triangle? How do we know? ❚ how are these shapes (two rectangles) the same or different? ❚ can you name each shape? The teacher provides copies of several different drawings of large triangles. Each student selects a triangle and cuts it out. They begin cutting off triangles. As students work, they describe the kind of cuts that have been made eg ‘I snipped off a corner.’ Possible questions include: ❚ do you know the name of this shape? ❚ can you find two triangles that are the same or similar and one very different triangle? ❚ are all of these shapes triangles? How do you know? Drawing and Describing Shapes (Two-dimensional Space) Students are asked to draw a particular shape eg a circle. They are then asked to draw a different shape eg a rectangle. Possible questions include: ❚ how did you draw the circle? ❚ what was different about the way you drew the rectangle? ❚ can you draw another rectangle that looks different? How is it different? ❚ are there other shapes that can be drawn using curved/straight lines? Can you draw some? Shape and Line Hunt (Two-dimensional Space) The teacher prepares a chart on butchers’ paper with columns labelled ‘circles’, ‘squares’, ‘triangles’ and ‘rectangles’. The students are asked to find pictures in magazines that are similar to the shapes, cut them out, and paste them in the correct column. Students then view the class chart and discuss the pictures and shapes that were found and comment on which shapes were more difficult to find ||  || Identify corners as angles ||  || ** Sample Units of Work ** Students are given a collection of regular and irregular shapes with three sides, four sides, five sides and six sides. Students are asked to sort the shapes into groups according to the number of sides. Students select one of the groups and arrange the shapes to form a picture. Students write a description of their picture, commenting on the shapes they have used. Possible questions include: ❚ can you show me how to draw and name each shape? ❚ what can you tell me about each shape? ❚ how are these shapes different/the same? In small groups, students are given a die and straws of two different lengths. In turn, students roll the die and make a shape with the corresponding number of sides. Students are encouraged to make regular and irregular shapes. Students name each shape, and record their shapes in appropriate groups. Students discuss the difficulties encountered in making a shape when they roll a 1 or a 2, and develop a new rule for the game. For example, students may decide that a turn is missed if a 1 or a 2 is rolle Students find shapes that have a line of symmetry by folding the shapes in half. In pairs, they are given a collection of regular and irregular shapes that could include squares, rectangles, triangles, trapeziums, rhombuses, hexagons and circles. Possible questions include: ❚ which shapes can be folded in half? ❚ which shapes can be folded in half in a different way? ❚ which shapes do not have a line of symmetry? Students glue their shapes onto paper and record their findings In small groups, students select a shape (eg square, circle, triangle, hexagon, rhombus, trapezium) to investigate whether it tessellates. Students trace around the shape and slide it to a new position attempting to cover the surface without leaving gaps. Students share their drawings. They group the shapes according to those that tessellate and those that do not. Student A makes a symmetrical design using pattern blocks. They describe it to Student B who attempts to replicate it. This process is repeated with the students swapping roles. Students should be encouraged to use appropriate language, including the names of the shapes and positional language. The teacher provides a number of flags for students to investigate symmetry. In pairs, students choose flags from those displayed, determine which are symmetrical, and give reasons for their choice. In pairs, students design their own symmetrical flags and display these for others to determine the lines of symmetry. In pairs, students cut out and fold capital letters in different ways to investigate their symmetry. They are then asked to glue the symmetrical letters onto one sheet of paper and the non-symmetrical letters onto another sheet. Some letters have more that one line of symmetry. Students compare and discuss their responses. Possible questions include: ❚ does any student in the class have a name with letters that are all symmetrical? eg TOM In pairs, students make a design by placing a pattern block on paper, tracing around it and then flipping, sliding or turning the block to a new position and repeating the process. Possible questions include: ❚ is your pattern different when you flip, slide or turn? ❚ which patterns are symmetrical? Why? ❚ how did you make your pattern? Students combine the movements of flipping, sliding and turning in a variety of ways to create different designs. Students describe the designs they have created and explain how they were made using the language of ‘flip’, ‘slide’ and ‘turn’. || ** Teaching About Angles ST2 ** Sg ||
 * ** Week 7 **  ** 2D Space **  ||
 * ** Key Idea ** ||||||  Resources  ||
 * ** KI 3 **
 * Early Stage 1 **
 * SGES1.2 **
 * Shape Walk p.38
 * Print It p.38
 * Lines p.38
 * Making Shape Pictures p.38
 * Pipe Cleaner Shapes p.39
 * Sorting Attribute Blocks p.39
 * Sorting And Classifying p.39
 * Cutting up Triangles p.39
 * Drawing and Describing Shapes p.39
 * Shape and Line Hunt p.4
 * ** KI 9 **
 * Stage 1 **
 * SGS1.2 **
 * Sorting Shapes p.77
 * Making Shapes p.77
 * Shape Symmetry p.77
 * Tessellation p.77
 * Barrier Symmetry p.78
 * Flags p.78
 * Alphabet Symmetry p.79
 * Flip, Slide and Turn p.79
 * Pattern Blocks p.12
 * Windmill Patterns p.14
 * Square Corners p.16
 * Acute and Obtuse Angles p.18
 * Angles in Geometrical Patterns p.20
 * Equal Angles
 * Measuring Pattern Block Angles p.24
 * Measuring Angles in the Classroom p.26
 * Measuring Body Angles p.28
 * Drawing two-line Angles p.30
 * Measuring the Angles of Opening of Doors p.32
 * Doors That Open in Different Directions p.34
 * Measuring Angles of Slopes p.36
 * Clocks p.38
 * Drawing Two-line and One-line Angles p.40