Building with shapes · applications

Applications: Building with Shapes

10 question types · Primary 1 · each worked step by step with a figure that follows the steps

PSLE

01

The Sides and Corners of a Triangle and a Square

strategyMark Each Side as You Count It / Then Add the Two Counts

Mei has 1 triangle and 1 square. (a) How many sides do the two shapes have in all? (b) How many corners do the two shapes have in all?

123trianglesquare
Count the sides of the triangle and mark each one: 1, 2, 3. The triangle has 3 sides.
Count the sides of the triangle. Mark each side as you count it: 1, 2, 3. The triangle has 3 sides.
step 1 of 5

Count the sides of one shape at a time. Put a mark on each side as you count it, so that no side is counted twice. Then do the same for the corners.

  1. Count the sides of the triangle. Mark each side as you count it: 1, 2, 3. The triangle has 3 sides.
  2. Count the sides of the square in the same way: 1, 2, 3, 4. The square has 4 sides.
  3. (a) Add the two counts. 3 + 4 = 7. The two shapes have 7 sides in all.
  4. A corner is a point where two sides meet. Put a dot on each corner. The triangle has 3 corners and the square has 4 corners.
  5. (b) 3 + 4 = 7. The two shapes have 7 corners in all. Each shape has as many corners as it has sides.

answer(a) 7 sides; (b) 7 corners

techniqueCounting Sides and Corners

examsPSLE

Common pitfalls

  • Going round the triangle and counting the first side again at the end. That gives 4 sides for a triangle. Mark each side as you count it, and stop when every side has a mark.
  • Counting only the two corners at the bottom of the triangle. The point at the top is a corner too, because two sides meet there.
02

A House Made from a Square, a Triangle and Two Rectangles

strategyName Each Shape in the Picture / Count Each Shape Once

Dad makes a picture of a house from paper shapes. The wall is 1 big square. The roof is 1 triangle on top of the wall. The door is 1 small rectangle. The window is 1 small rectangle too. (a) How many shapes in the picture have 4 sides? (b) How many shapes are in the picture in all?

1 square, 1 triangle, 2 rectangles
The wall is a square. The roof is a triangle. The door and the window are rectangles.
Name each part of the house. The wall is a square. The roof is a triangle. The door and the window are rectangles.
step 1 of 4

Say the name of each shape in the picture. Then count the shapes one by one, and count each shape only once.

  1. Name each part of the house. The wall is a square. The roof is a triangle. The door and the window are rectangles.
  2. Count the sides of each kind of shape. A square has 4 sides. A rectangle has 4 sides. A triangle has 3 sides.
  3. (a) The square and the 2 rectangles have 4 sides. 1 + 2 = 3. There are 3 shapes with 4 sides.
  4. (b) Count every shape once: 1 square, 1 triangle and 2 rectangles. 1 + 1 + 2 = 4. There are 4 shapes in all.

answer(a) 3 shapes; (b) 4 shapes

techniqueMaking Shapes from Smaller Shapes · Counting Sides and Corners

examsPSLE

Common pitfalls

  • Writing 2 for part (a) because only the rectangles are counted. A square has 4 sides too, so the wall is counted with the door and the window.
  • Counting the house as one more shape and writing 5 for part (b). The house is the whole picture. It is made of the 4 shapes, so it is not counted again.
03

Triangles That Make Squares and Small Squares That Make Big Squares

strategyCut One Shape into Its Pieces / Count the Pieces for Every Shape

Ben has paper triangles that are all the same. He puts 2 triangles together to make 1 square. (a) How many triangles does Ben need to make 3 squares? (b) Mei puts 4 small squares together to make 1 big square. How many small squares does Mei need to make 2 big squares?

1 square = 2 triangles
A line from one corner to the corner across from it cuts the square into 2 triangles.
Draw 1 square. Draw a line from one corner to the corner across from it. The line cuts the square into 2 triangles.
step 1 of 5

Draw one shape and cut it into its pieces. Every shape of that kind needs the same number of pieces, so draw all the shapes and count the pieces.

  1. Draw 1 square. Draw a line from one corner to the corner across from it. The line cuts the square into 2 triangles.
  2. Each square needs 2 triangles. Draw 3 squares and cut each one in the same way.
  3. (a) Count the triangles. 2 + 2 + 2 = 6. Ben needs 6 triangles.
  4. Draw 1 big square. Cut it into 2 rows with 2 small squares in each row. The big square has 4 small squares.
  5. (b) Draw 2 big squares and count the small squares. 4 + 4 = 8. Mei needs 8 small squares.

answer(a) 6 triangles; (b) 8 small squares

techniqueMaking Shapes from Smaller Shapes

examsPSLE

Common pitfalls

  • Writing 3 for part (a) because there are 3 squares. Each square is made of 2 triangles, so count 2 for every square: 2 + 2 + 2 = 6.
  • Writing 6 for part (b) by adding 4 + 2. The 2 tells how many big squares there are. Each big square needs 4 small squares, so add 4 two times: 4 + 4 = 8.
04

A Row of Shapes That Repeats Every Three Shapes

strategyFind the Part That Repeats / Carry It On Shape by Shape

Lin makes a row of shapes. The row goes circle, square, triangle, circle, square. The shapes keep going in the same way. (a) Which shape comes next? (b) Which shape is number 8 in the row?

12345?67?8
Say the shapes out loud: circle, square, triangle, circle, square.
Say the shapes out loud: circle, square, triangle, circle, square. Look for the place where the row starts again.
step 1 of 5

Say the shapes out loud and listen for the part that comes again. That part repeats over and over, so it tells every shape that follows.

  1. Say the shapes out loud: circle, square, triangle, circle, square. Look for the place where the row starts again.
  2. After the triangle there is a circle again. The part that repeats is circle, square, triangle. It has 3 shapes.
  3. (a) Shape 4 is a circle and shape 5 is a square. A triangle comes after the square, so shape 6 is a triangle. It is the same as shape 3.
  4. Carry on in the same way. Shape 7 is a circle and shape 8 is a square.
  5. (b) Shape number 8 is a square. It is the same as shape 2 and shape 5.

answer(a) a triangle, the same as shape 3; (b) a square, the same as shape 2

techniqueContinuing a Shape Pattern

examsPSLE

Common pitfalls

  • Saying that a circle comes next because the row began with a circle. The row starts again only when the part that repeats is finished, and its triangle has not come yet.
  • Counting 8 more shapes from the end of the row. Shape number 8 is counted from the first circle, so only 3 more shapes are needed after shape 5.
05

A Missing Shape in the Middle of a Repeating Row

strategyFind the Part That Repeats / Match the Gap to Its Place in That Part

Tom makes a row of 10 shapes. The row goes circle, square, triangle, rectangle, circle, square, a gap, rectangle, circle, square. One shape is missing at the gap. (a) Which shape is missing? (b) How many triangles are in the full row?

123456?78910
Read the row from the start: circle, square, triangle, rectangle. Then a circle comes again.
Read the row from the start: circle, square, triangle, rectangle. Then a circle comes again.
step 1 of 5

Find the part that repeats at the start of the row. Then look at the shapes on both sides of the gap and find the same place in the part that repeats.

  1. Read the row from the start: circle, square, triangle, rectangle. Then a circle comes again.
  2. The part that repeats is circle, square, triangle, rectangle. It has 4 shapes.
  3. The gap is shape number 7. It comes after a square and before a rectangle.
  4. (a) In the part that repeats, the triangle is between the square and the rectangle. The missing shape is a triangle.
  5. (b) Count the triangles in the full row. Shape 3 and shape 7 are triangles. There are 2 triangles.

answer(a) a triangle, the same as shape 3; (b) 2 triangles

techniqueContinuing a Shape Pattern

examsPSLE

Common pitfalls

  • Thinking that the part that repeats is circle, square. The third shape is a triangle and not a circle, so the part that repeats is longer. Keep reading until the first shape comes again.
  • Writing 1 for part (b) because only 1 triangle can be seen. The missing shape is a triangle too, so the full row has 2 triangles.
06

A Figure Copied One Row Lower on a Square Grid

strategyCount the Squares Across and Down / Keep the Size and Move the Rows

Mei draws a rectangle on a square grid. The rows of the grid are numbered from the top. The rectangle is 3 squares wide and 2 squares tall. Its top row is row 2. Mei draws a copy next to it, 1 row lower. (a) How many grid squares does the copy cover? (b) Which row is the top row of the copy?

row123453 squares wide, 2 squares tall
The rectangle has 2 rows, and each row has 3 squares. Its top row is row 2.
Draw the rectangle on the grid. It has 2 rows, and each row has 3 squares.
step 1 of 4

A copy has the same size as the figure. Count the squares across and the squares down, and keep both numbers. Only the place on the grid changes.

  1. Draw the rectangle on the grid. It has 2 rows, and each row has 3 squares.
  2. Count the squares it covers: 3 + 3 = 6 squares.
  3. (a) The copy is the same size as the figure. It is also 3 squares wide and 2 squares tall, so the copy covers 6 squares.
  4. (b) The copy is 1 row lower, so its top row moves from row 2 to row 2 + 1 = 3. The top row of the copy is row 3.

answer(a) 6 squares; (b) row 3

techniqueCopying a Figure on a Grid

examsPSLE

Common pitfalls

  • Drawing the copy 3 squares tall because it is lower on the grid. Moving a figure does not change its size. The copy is still 2 squares tall.
  • Writing row 1 for part (b). The rows are numbered from the top, so a lower row has a bigger number. Add 1 to the row number.
07

The Squares Inside a Rectangle and Inside a Square on a Grid

strategyDraw the Shape Row by Row / Add the Rows

Ali draws a rectangle on a square grid. It is 5 squares long and 3 squares wide. (a) How many grid squares are inside the rectangle? (b) Next Ali draws a square. It has 3 grid squares along each side. How many grid squares are inside the square?

3 rows of 5 squares
The rectangle has 3 rows, and each row has 5 squares.
Draw the rectangle. It has 3 rows, and each row has 5 squares.
step 1 of 4

Draw the shape on the grid one row at a time. Every row has the same number of squares, so add that number once for each row.

  1. Draw the rectangle. It has 3 rows, and each row has 5 squares.
  2. (a) Add the rows: 5 + 5 + 5 = 15. There are 15 grid squares inside the rectangle.
  3. A square has the same number of grid squares along each side. Draw 3 rows with 3 squares in each row.
  4. (b) Add the rows: 3 + 3 + 3 = 9. There are 9 grid squares inside the square.

answer(a) 15 squares; (b) 9 squares

techniqueDrawing Rectangles and Squares

Common pitfalls

  • Adding 5 + 3 = 8 for part (a). That adds one long side and one short side. It does not count the squares inside. Count row by row: 5 + 5 + 5 = 15.
  • Counting only the squares round the edge. The squares in the middle are inside the shape too, so every row is counted in full.
08

Telling a Square from a Rectangle by Its Sides

strategyCompare the Length with the Width / Four Equal Sides Make a Square

Three shapes are drawn on a square grid. Each shape has 4 sides and 4 square corners. Shape A is 4 squares long and 2 squares wide. Shape B is 3 squares long and 3 squares wide. Shape C is 5 squares long and 1 square wide. (a) Which shape is a square? (b) How many of the shapes are not squares?

A42B33C51a square has 4 equal sides
A square has 4 equal sides. A shape that is longer than it is wide is not a square.
A square has 4 equal sides. A shape that is longer than it is wide is not a square.
step 1 of 5

A square and a rectangle both have 4 sides and 4 square corners. Only the square has 4 equal sides, so compare the length of each shape with its width.

  1. A square has 4 equal sides. A shape that is longer than it is wide is not a square.
  2. Look at Shape A. It is 4 squares long and 2 squares wide. The sides are not equal, so Shape A is not a square.
  3. (a) Look at Shape B. It is 3 squares long and 3 squares wide. All 4 sides are equal, so Shape B is a square.
  4. Look at Shape C. It is 5 squares long and 1 square wide. The sides are not equal, so Shape C is not a square.
  5. (b) Shape A and Shape C are not squares. That is 2 shapes.

answer(a) Shape B; (b) 2 shapes

techniqueDrawing Rectangles and Squares · Counting Sides and Corners

examsPSLE

Common pitfalls

  • Saying that all three shapes are squares because each one has 4 sides and 4 square corners. A rectangle has those too. A square must also have 4 equal sides.
  • Choosing Shape C because it is the longest shape. The longest shape is not what makes a square. Compare the length of a shape with the width of the same shape.
09

Sorting a Box of Shapes by the Number of Corners

strategyCount the Corners of Each Kind / Make a Pile for Each Count

A box has 3 circles, 4 triangles, 2 squares and 3 rectangles. Ben sorts the shapes by the number of corners. (a) How many shapes have no corners? (b) How many shapes have 4 corners?

3 circles, 4 triangles,2 squares, 3 rectangles
A circle has no corners. A triangle has 3 corners. A square has 4 corners and a rectangle has 4 corners.
Count the corners of each kind of shape. A circle has no corners. A triangle has 3 corners. A square has 4 corners and a rectangle has 4 corners.
step 1 of 4

Count the corners of one shape of each kind. Shapes with the same number of corners go in the same pile. Then count each pile.

  1. Count the corners of each kind of shape. A circle has no corners. A triangle has 3 corners. A square has 4 corners and a rectangle has 4 corners.
  2. Make 3 piles: no corners, 3 corners and 4 corners. Put every shape in its pile.
  3. (a) Only the circles have no corners. There are 3 circles, so 3 shapes have no corners.
  4. (b) The squares and the rectangles have 4 corners. 2 + 3 = 5. There are 5 shapes with 4 corners. Check: the piles have 3 + 4 + 5 = 12 shapes, and the box has 3 + 4 + 2 + 3 = 12 shapes.

answer(a) 3 shapes; (b) 5 shapes

techniqueCounting Sides and Corners

examsPSLE

Common pitfalls

  • Writing 2 for part (b) because only the squares are counted. A rectangle has 4 corners too, so the 3 rectangles go in the same pile as the squares.
  • Leaving the circles out of the sorting because they have no corners. No corners is a pile too, and it has 3 shapes in it.
10

Sticks for Two Triangles, Apart and Sharing a Side

strategyBuild the Shapes from Sticks / Count Each Stick Once

Jun builds triangles from sticks. Each side of a triangle is 1 stick. (a) How many sticks does Jun need for 2 triangles that do not touch? (b) Next Jun builds 2 triangles that share 1 side. How many sticks does he need now?

1231 triangle: 3 sticks
Build 1 triangle. It has 3 sides, so it needs 3 sticks.
Build 1 triangle. It has 3 sides, so it needs 3 sticks.
step 1 of 4

Draw every stick and put a number on it as you count it. A side that belongs to two triangles is still only one stick.

  1. Build 1 triangle. It has 3 sides, so it needs 3 sticks.
  2. (a) The 2 triangles do not touch, so each one needs its own 3 sticks. 3 + 3 = 6. Jun needs 6 sticks.
  3. Now draw the 2 triangles side by side. The side in the middle belongs to both triangles. It is only 1 stick.
  4. (b) Count each stick once: 1, 2, 3, 4, 5. Jun needs 5 sticks. That is 6 − 1 = 5, because 1 stick is shared.

answer(a) 6 sticks; (b) 5 sticks

techniqueCounting Sides and Corners · Making Shapes from Smaller Shapes

examsPSLE

Common pitfalls

  • Writing 6 for part (b) by adding 3 + 3. That counts the shared stick two times. It is 1 stick, so it is counted once.
  • Writing 4 for part (b) by taking away 1 stick for each triangle. Only 1 stick is shared, so only 1 is taken away from 6.
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