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10/08/2011
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Ma3 Shape, space and measures

Hidden shapes

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Teacher's notes

  • Predicts that hidden shape on interactive whiteboard is a hexagon.
  • Visualises hexagon by ‘drawing' its outline with a finger; says that a hexagon 'has six sides'.
  • Predicts that a partly-revealed shape comprising an acute-angled corner will be a 'diamond' then a 'star' since a 'star has lots of pointy bits'.
  • Visualises star by 'drawing' some of the 'pointy bits' with her finger.
  • When complete shape is revealed, recognises that it is a triangle.
  • Likens triangle to an ice-cream cone.
  • Says that a triangle 'has to have three corners and three sides'.

Next steps

  • Hide familiar 2-D shapes in bag; give clues so that others can guess the shape.
  • Compare pairs of familiar 2-D shapes, including identical shapes shown in different orientations, and talk about the ways in which they are the same and how they differ.

Shape sort

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Teacher's notes

  • Is starting to sort 2-D shapes using two criteria on a Carroll diagram.
  • Places red square in correct region on interactive whiteboard.
  • Reasons correctly why shape belongs in region, i.e. 'It's red; it isn't a circle'.
  • Is not yet consistent in choosing correct region, e.g. places blue square in 'not red' and 'circle'.

Next steps

  • Sort the same shapes using different criteria.
  • Continue to sort other objects using two criteria.
  • Explain why shapes that are incorrectly positioned are in the wrong region.

3-D shapes

Teacher's handwritten notes on a pupil's progress in learning about 3-D shapes.
C - do they look like party hats - pyramids/cones, Q - How can we separate cones from pyramids. C - not square like pyramids, take away cones because they've got cucies at bottom like cylingers (put them all tog. Q - What can you tell me about one shape. C - They're pointy and squares (pyramids), B - same as above, point and circle (cones), T - They are short not like cubrids (cubes), C - They're longer than square - because their sides are longer (cuboids). All the C points are highlighted pink and the Q points are highlighted yellow.Down the left-hand side of the page, 'C', 'B', 'T' and 'Q' are written next to each question or statement. Each 'C' is highlighted in pink. Each 'Q' is highlighted in yellow. C � do they look like party hats � pyramids/cones Q � How can we separate cones from pyramids. C � not square like pyramids take away cones because they�ve got circles at bottom like cylinders (put them all tog. Q � What can you tell me about one shape. C � They�re pointy & square (pyramids) B � They�re pointy & circle (cones) T � They are short not like cuboids (cubes) C � They�re longer than square � because [crossed out word] their sides are longer (cuboids)

Teacher's notes

  • Is beginning to use names of 3-D shapes in context.
  • Reasons that a cone is 'not square like a pyramid'.
  • Reasons that cones and cylinders are alike 'because they've got circles at the bottom'.
  • Describes 3-D shapes using terms like 'pointy', 'sides are longer' or by referring to shape of faces, e.g. square.

Next steps

  • Start to use terms 'faces', 'edges' and 'vertices' to describe features of 3-D shapes.
  • Describe hidden 3-D shape to partner without naming it; partner has to find matching shape or name the shape.

Shapes in position

Pupil's completed activity in arranging  gummed 2-D shapes in position.
Against a large red sheet, there are three rows of shapes. The central shape is a large brown circle, which contains a red filled-in circle within it. To the left of this shave is a black hexagon with a red filled-in circle within it. To the right of the central shape is a yellow hexagon with a red filled-in circle in it. Above each of the 2 hexagons and central circle is a blue triangle. Below the 2 hexagons and central circle are 4 white filled-in circles positioned in a horizontal row.
Teacher's handwritten notes on a pupil's spoken instructions during a paired activity to position gummed 2-D shapes.
This note is written on green paper, and titled 'Charlotte instructing Toby'. Below this, there are 7 asterisks with a point following each. The first asterisk is: get a big brown circle � put it in the middle, the second asterisk says: get an orange hexagon � put it beside the circle, the third asterisk: get a black hexagon � put it on the other side of the circle, the fourth asterisk: put a small red circle on each shape, the fifth asterisk: put a small blue triangle above each big shape, the sixth asterisk: put a green circle (small) under the black hexagon and the seventh asterisk: put another one beside it.

Teacher's notes

  • Describes to partner where to position gummed 2-D shapes.
  • Describes shapes by name and features, e.g. 'big brown circle'.
  • Uses range of positional vocabulary, e.g. 'in', 'beside', 'on the side', 'above', 'under'.
  • Combines language of size, colour, shape name and position, e.g. 'Put a small red circle on each shape'.

Next steps

  • Make a design with gummed shapes, conceal it and instruct partner on how to copy it.
  • Compare original and partner's copy to check accuracy of instructions.

Weighing

Pupil's handwritten work to calculate how many cubes are needed to balance three parcels.
The page contains five rectangles, three of which are labelled A, B and C. The rectangle labelled A is on the left of the page. To the right of rectange A is a small square with 13 written next to it. Above this is rectangle C with 45 written inside the shape. Below this is rectangle B with 92 written in side the shape. To the right of this rectangle, there is a small square.Next to an 'A' is a tall rectangle. Next to a 'c' is a rectangle containing a handwritten 45; below this, a handwritten 13 next to a small rectangle. Below a 'B', a rectangle containing a handwritten 92, next a smaller rectangle.Next to an 'A' is a tall rectangle. Next to a 'c' is a rectangle containing a handwritten 45; below this, a handwritten 13 next to a small rectangle. Below a 'B', a rectangle containing a handwritten 92, next a smaller rectangle.

Teacher's notes

  • Chooses cubes to balance three parcels on scales.
  • Reasons whether to add or remove cubes between each weighing, e.g. leaves 13 cubes in the pan when changing from lightest to heaviest parcel.
  • Counts on from 13 as she adds more cubes to balance with a heavier parcel.
  • Is starting to count larger sets of cubes in tens.
  • Counts that 13, 45 and 92 cubes are needed to balance the parcels.
  • Records results using drawings and numbers.
  • Explains which parcel is heaviest and lightest.

Next steps

  • Group up to 100 objects into as many tens as possible; find total by counting tens.

Events in order

Pupil's attempt at re-ordering four photographs to show the chronology of a school event.
There are four photographs, which the pupil has numbered 1 to 4 from the top-left photograph, moving clockwise. The image numbered 1 shows a man dressed in a shirt and tie speaking in front of a group of approximately 20 pupils, who are all seated on the floor. There is also a man in a blue shirt and suit seated in front of the pupils, facing the speaker. In the image numbered 2, the man sitting down in the previous image is now speaking on front of the pupils. The pupils are now crouched around an L-shaped table. The table contains a model of a town with houses and buildings. The image numbered 3 shows three pupils, two boys and a girl working together in front of the model. The last image numbered 4 shows pupils standing in groups around tables. There are white baskets containing parts which can be placed on the town model. There is also an adult in the room who appears to be supervising the activity.

Teacher's notes

  • Recognises photographs taken at different times during an event at school.
  • Cuts out photographs and reorders them chronologically.
  • Writes numbers 1 to 4 to show order of events.
  • Responds to questions that use ordinal vocabulary, e.g. 'What does the second picture show?'.

Clock faces

A series of eight analogue clocks showing the time from 12 o'clock, increasing in five-minute increments.
The clocks are yellow and set against a yellow background. The first clock reads 12 o'clock, the second 5 past 12, the third 10 past 12, the fourth a quarter past 12, the fifth 20 past 12, the sixth 25 past 12, the seventh half past 12 and the eighth 35 past 12.

Teacher's notes

  • Finds hidden clocks showing times on the hour, one at a time.
  • Estimates where each clock fits on the time line and positions it.
  • Reads the time from each clock aloud.
  • Adjusts the positions of clocks to show all times from 12 o'clock to 11 o'clock in order.
  • Explains that when the long hand points to 12 the time will be ‘something o'clock'.

Next steps

  • Relate familiar events at home and school to times on the hour; sequence events.
  • Start to read times at the half-hour.

What the teacher knows about Charlotte's attainment in Ma3, Shape, space and measures

Charlotte uses some everyday language to describe 2-D and 3-D shapes but is starting to use more mathematical terms to name and describe them. For example, she often uses 'pointy bits' to describe vertices but also tells her teacher that a triangle 'has to have three corners and three sides'. She names some common 2-D shapes such as triangles and hexagons and 3-D shapes such as a cones and cylinders. She recognises some properties of 3-D shapes, e.g. cones and cylinders have 'circles at the bottom'. She has just started to sort 2-D shapes using two-criteria, e.g. red/circles and to explain why a shape belongs in a particular region but does not yet do this consistently. She uses knowledge of 2-D shapes to predict what partly revealed shapes are and gives reasons for her predictions.

Charlotte responds to and uses positional vocabulary. She interprets questions that include ordinal numbers. She also uses terms such as 'in', 'beside', 'on the side', 'above', for example when describing to a partner where to position shapes to make a design. Entering one instruction at a time, she programmes a simple toy to reach target destinations by pressing keys up, down, left or right to make it go forwards, backwards or turn through a right angle to the left or right. She does not yet distinguish between left and right but describes how she programmes it using words and arm movements, e.g. 'I made it go forwards 3 squares and then turned it this way towards the frog.' She also instructs other children on how to programme the toy.

In recent work, Charlotte has started to use uniform non-standard units to measure mass and length. For example, she uses cubes to balance three parcels, counts the cubes and orders the parcels. She compares them by explaining which is heaviest and lightest and why. Charlotte uses rods and toy snakes of uniform length to measure the length of objects around the classroom. She records how many of each unit is needed and orders the objects. She uses different materials to measure and compare capacity. She counts how many spoonfuls of rice are needed to fill pots and how many cupfuls of water are needed to fill jugs. She puts familiar events in order of time and orders clocks that show times on the hour.

Summarising Charlotte's attainment in Ma3, Shape, space and measures

In her recent development, Charlotte partly meets some criteria for level 2 in each assessment focus. Charlotte meets all assessment criteria for level 1. Reading the complete level descriptions, her teacher decides that level 1 is the best fit.

Since she meets all of the criteria for level 1 consistently and in a range of contexts, and taking into account her start on level 2, Charlotte's teacher refines her judgement to high level 1.

To progress into level 2, Charlotte needs to learn the names of other 2-D shapes such as the pentagon and octagon and to describe their properties. She needs to refine the language she uses to describe 3-D shapes to include terms such as faces, edges and vertices. She should then sort 3-D shapes using knowledge of their properties, e.g. use criteria such as has six faces/does not have six faces. To improve her knowledge of turning movements, she should learn to distinguish between left and right and clockwise and anticlockwise. She needs to recognise right angles in turns and distinguish between whole, half and quarter turns, for example using a programmable toy or in PE. She should measure length to the nearest centimetre or metre. She should measure mass in kilogram then half-kilogram units by reading scales to the nearest labelled division.