A Train Picture Made of Circles, Rectangles and a Square
Ben makes a train picture from flat shapes. The 4 wheels are circles. The sun is a circle too. The 2 carriages are rectangles. The window is 1 square. (a) How many circles are in the picture? (b) How many shapes have straight sides?
Say the name of each shape. A circle is round. A rectangle and a square have straight sides.
- Draw the picture. It has 4 wheels, 1 sun, 2 carriages and 1 window.
- A circle is round and has no straight sides. The wheels and the sun are circles.
- (a) Count the circles: 4 + 1 = 5. There are 5 circles in the picture.
- (b) The rectangles and the square have straight sides: 2 + 1 = 3. There are 3 shapes with straight sides.
answer(a) 5 circles; (b) 3 shapes
techniqueCircles, Triangles, Squares and Rectangles
examsPSLE
Common pitfalls
- Counting only the 4 wheels in part (a). The sun is a circle too, so there are 5 circles.
- Leaving out the window in part (b) because it is inside a carriage. The window is a square, and a square has straight sides.
Triangles That Point Up, Point Down and One Tiny Triangle
Mei draws 3 triangles that point up and 2 triangles that point down. She draws 1 tiny triangle that points to the side. She also draws 2 squares. (a) How many triangles does Mei draw in all? (b) How many shapes does Mei draw in all?
A triangle that is turned is still a triangle. A triangle that is made smaller is still a triangle.
- Draw every shape: 3 triangles that point up, 2 that point down, 1 tiny triangle and 2 squares.
- A triangle has 3 straight sides and 3 corners. It is still a triangle when it is turned or made smaller.
- (a) Count the triangles: 3 + 2 + 1 = 6. Mei draws 6 triangles in all.
- (b) Count the 2 squares as well: 6 + 2 = 8. Mei draws 8 shapes in all.
answer(a) 6 triangles; (b) 8 shapes
techniqueShapes Turned and Resized · Circles, Triangles, Squares and Rectangles
examsPSLE
Common pitfalls
- Saying that the triangles that point down are not triangles. A shape with 3 straight sides and 3 corners is a triangle, whichever way it points.
- Leaving out the tiny triangle. A small triangle is still a triangle, so count it.
Half Circles and Quarter Circles Put Together into Whole Circles
2 half circles put together make 1 whole circle. 4 quarter circles put together make 1 whole circle. (a) Ben uses half circles. How many half circles make 3 whole circles? (b) Mei uses quarter circles. How many quarter circles make 2 whole circles?
Draw each whole circle and cut it into its parts. Then count the parts.
- Draw a circle and cut it through the middle. It makes 2 half circles, so 2 half circles make 1 whole circle.
- Draw 3 whole circles. Cut each one into 2 half circles.
- (a) Count the half circles: 2 + 2 + 2 = 6. Ben needs 6 half circles.
- Draw a circle and cut it into 4 equal parts. Each part is a quarter circle, so 4 quarter circles make 1 whole circle.
- (b) Draw 2 whole circles and cut each one into 4 quarter circles. 4 + 4 = 8. Mei needs 8 quarter circles.
answer(a) 6 half circles; (b) 8 quarter circles
techniqueHalf Circles and Quarter Circles
Common pitfalls
- Saying 3 half circles for 3 whole circles. Each whole circle needs 2 half circles, so count 2 for every circle.
- Using 2 quarter circles for each whole circle in part (b). 2 quarter circles make only a half circle. A whole circle needs 4 quarter circles.
Kitchen Things Sorted into Cylinders, Spheres, Cubes and Cones
Dad puts 7 things on the kitchen table: 1 can, 1 ball, 1 orange, 3 dice and 1 party hat. A can is a cylinder. A ball and an orange are spheres. A dice is a cube. A party hat is a cone. (a) How many spheres are on the table? (b) How many things are cylinders or cubes?
Sort the things by their solid shape. Then count the pile you are asked about.
- Draw the 7 things: 1 can, 1 ball, 1 orange, 3 dice and 1 party hat.
- Make a pile for each solid shape. The can is a cylinder. The ball and the orange are spheres. The 3 dice are cubes. The party hat is a cone.
- (a) Count the pile of spheres: 1 + 1 = 2. There are 2 spheres on the table.
- (b) Add the cylinder and the cubes: 1 + 3 = 4. There are 4 things. Check: 1 + 2 + 3 + 1 = 7 things.
answer(a) 2 spheres; (b) 4 things
techniqueCubes, Spheres, Cones and Cylinders
examsPSLE
Common pitfalls
- Counting only the ball as a sphere. An orange is round all over like a ball, so it is a sphere too.
- Calling the can a cone. A cone has a point at the top. A can is flat at the top and flat at the bottom, so it is a cylinder.
Solid Shapes That Can Roll and Solid Shapes That Can Stack
Sam has 6 things: a ball, an orange, a can, a dice, a brick and a party hat. The ball and the orange are spheres. The can is a cylinder. The dice is a cube. The brick is a cuboid. The party hat is a cone. (a) How many of the things can roll? (b) How many of the things can stack, one on top of another?
A solid shape rolls on a curved face. A solid shape stacks when it is flat on the top and flat on the bottom.
- A solid shape can roll when it has a curved face. The sphere, the cylinder and the cone each have a curved face.
- (a) Count the things that roll: the ball, the orange, the can and the party hat. 4 things can roll.
- A solid shape can stack when it is flat on the top and flat on the bottom. The cylinder, the cube and the cuboid are flat on the top and on the bottom.
- (b) Count the things that stack: the can, the dice and the brick. 3 things can stack. The can is in both counts, because a cylinder can roll and stack.
answer(a) 4 things; (b) 3 things
techniqueCubes, Spheres, Cones and Cylinders · The Cuboid
examsPSLE
Common pitfalls
- Leaving the party hat out of the things that roll. A cone has a curved face, so it rolls on its side.
- Counting the party hat as a thing that can stack. A cone has a point on the top, so nothing can rest on it.
The Faces of a Cuboid Box Counted in Pairs
A tissue box is a cuboid. It has a top and a bottom, a front and a back, and 2 sides. Each of these is a flat face. (a) How many faces does the box have? (b) Ben paints the top and the bottom red. How many faces are not red?
Some faces of a box are hidden at the back, at the bottom and on the far side. Count the faces in pairs so that no face is left out.
- Draw the box. The top and the bottom are a pair. That is 2 faces.
- The front and the back are a pair. That is 2 more faces. The 2 sides are a pair. That is 2 more faces.
- (a) Add the pairs: 2 + 2 + 2 = 6. The box has 6 faces.
- (b) The top and the bottom are red. The front, the back and the 2 sides are not red: 2 + 2 = 4. There are 4 faces that are not red.
answer(a) 6 faces; (b) 4 faces
techniqueThe Cuboid
Common pitfalls
- Counting only the 3 faces you can see: the top, the front and one side. Each of them has a partner on the other side of the box, so there are 6 faces.
- Taking away only 1 face in part (b). Ben paints the top and the bottom, and that is 2 faces.
A Cupboard with Two Shelves Read with Above, Below and Beside
A cupboard has a top shelf and a bottom shelf. There are 5 things in it. The ball is on the top shelf. The ball is above the box. The cup is beside the ball. The book is beside the box, and the bear is beside the book. (a) Which thing is below the ball? (b) How many things are on the top shelf?
Draw the two shelves. Read one sentence at a time and put each thing in its place.
- Draw the 2 shelves. Put the ball on the top shelf.
- The ball is above the box. So put the box on the bottom shelf, under the ball.
- (a) The ball is above the box, so the box is below the ball.
- Beside means next to, on the same shelf. Put the cup beside the ball. Put the book beside the box and the bear beside the book.
- (b) Count the things on the top shelf: the ball and the cup. There are 2 things on the top shelf.
answer(a) the box; (b) 2 things
techniqueAbove, Below and Beside
Common pitfalls
- Saying that the cup is below the ball. The cup is beside the ball, so it is on the same shelf as the ball.
- Counting the box on the top shelf. The ball is above the box, so the box is on the shelf under the ball.
Left and Right in a Row of Toys
There are 5 toys in a row. The car is 2nd from the left. The doll is 2nd from the right. (a) How many toys are to the right of the car? (b) How many toys are between the car and the doll?
Draw a box for each toy. Mark which end is left and which end is right before you count.
- Draw 5 boxes in a row for the 5 toys. Mark the left end and the right end.
- Count from the left: 1st, 2nd. The 2nd box is the car.
- (a) Count the toys to the right of the car: 1, 2, 3. There are 3 toys to the right of the car.
- Count from the right: 1st, 2nd. The 2nd box from the right is the doll.
- (b) Look between the car and the doll. There is 1 toy between them.
answer(a) 3 toys; (b) 1 toy
techniqueAbove, Below and Beside · Ordinal Numbers
examsPSLE
Common pitfalls
- Counting the car as one of the toys to its right. Start counting at the toy after the car.
- Counting the doll as 2nd from the left. The doll is 2nd from the right, so count from the right end.
A Tower of Blocks Described from the Bottom Up
Sam builds a tower of 5 blocks. From the bottom up, the blocks are blue, red, green, yellow and pink. (a) Which block is between the red block and the yellow block? (b) How many blocks are above the red block?
Draw the tower block by block, starting at the bottom. Then look at the drawing to answer.
- Draw the tower from the bottom up: blue, then red, then green, then yellow. Pink is on the top.
- Find the red block and the yellow block. There is one block between them.
- (a) The green block is between the red block and the yellow block.
- (b) Count the blocks above the red block: green, yellow, pink. There are 3 blocks above the red block.
answer(a) the green block; (b) 3 blocks
techniqueAbove, Below and Beside
Common pitfalls
- Reading the tower from the top down. The list starts at the bottom, so blue is the bottom block and pink is the top block.
- Counting the red block itself in part (b). Only the blocks that are higher than the red block are above it.
The Odd One Out in a Group of Shapes
There are 5 shapes on a card: a square, a rectangle, a square standing on one corner, a triangle and a tall thin rectangle. All the shapes but one follow the same rule. (a) Which shape is the odd one out? (b) How many shapes follow the rule?
Count the sides of each shape. The rule is what most of the shapes share, and the odd one out breaks it.
- Count the sides of each shape. The square has 4 sides and the rectangle has 4 sides.
- The square standing on one corner is still a square, so it has 4 sides. The tall thin rectangle has 4 sides too.
- (a) The triangle has 3 sides. The rule is that a shape has 4 sides. The triangle is the odd one out.
- (b) Count the shapes with 4 sides: 1, 2, 3, 4. There are 4 shapes that follow the rule.
answer(a) the triangle, which has 3 sides; (b) 4 shapes
techniqueCircles, Triangles, Squares and Rectangles · Shapes Turned and Resized
examsPSLE
Common pitfalls
- Picking the square standing on one corner because it looks different. It is still a square, and it has 4 sides.
- Picking the tall thin rectangle because of its size. The rule is about the number of sides, and it has 4 sides.