Responding to errors in classifying shapes

See my entry for 19 July, where I provided an example of a Learning and Teaching task from the new Student Workbook (Haylock with Manning) for Mathematics Explained for Primary Teachers, 4th edition. Here are the responses to the children's errors in classifying shapes that we provide in the workbook.

(a) A 6-year-old insists that a square drawn with its sides at an angle of 45 degrees to the edges of the page is a diamond and not a square.

Turn the paper round and talk about what happens. Get the child to cut out the shape and put it on the desk. Compare it with plastic squares from the shape box. Put the plastic square on a piece of paper and rotate it slowly. Is it still a square? Get the child to draw round it. Ask the child what they notice.

(b) A 7-year-old calls a sphere a circle and a cube a square.

Draw a circle on the sphere (largest possible). Draw round the edges of one of the faces of the cube to make a square. Copy the circle and square onto a piece of paper. Have a discussion about the difference between solid shapes (like spheres and cubes) and flat shapes drawn on a piece of paper (like circles and squares). Use various other examples of 2-D and 3-D shapes and ask children whether they are solid shapes or flat shapes. Get the children to identify all the flat shapes making up a solid shape, like a triangular prism.

(c) A 9-year-old says that the diagonals of a parallelogram are lines of symmetry.

Ask the child to cut out several parallelograms and fold them along their diagonals. Do the two halves fold exactly one on top of the other? No! So, is it a line of symmetry? Also, draw round a plastic or card parallelogram, then turn it over and see if it will now fit in its box. Or place a mirror along the diagonal; look in the mirror. Is the shape you can see the original parallelogram?

Haylock with Manning Student Workbook arrived!

A parcel containing copies of the new Student Workbook to accompany the fourth edition of Mathematics Explained for Primary Teachers was delivered to me last week! It's very exciting to see it in print. Those who ordered copies pre-release should be getting them any day now. I'm expecting the new fourth edition of Mathematics Explained within a few days and I'm looking forward to seeing the phrase 'This title has not yet been released' disappear from the book-selling websites.

My colleague and good friend at UEA, Ralph Manning, helped me with the student workbook and set up the student trials of our first draft. For each of Chapters 6–29 of Mathematics Explained we have included in the workbook tasks that check understanding, tasks that require using and applying the mathematical content, and tasks about learning and teaching.

Below is an example of a learning and teaching task, for the chapter on Classifying Shapes.

"Here are some common errors made by primary school children about shapes. How would you respond to these?

(a) A 6-year-old insists that a square drawn with its sides at an angle of 45 degrees to the edges of the paper is a diamond and not a square.

(b) A 7-year-old calls a sphere a circle and a cube a square.

(c) A 9-year-old says that the diagonals of a parallelogram are lines of symmetry."

I'll post our answers on my blog some time next week. Or you could buy the book, of course ...!