Year 5 Angles and shapes: check-up and SATs-style questions

Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.

Method. Compare the size of the angle with 90°, 180° and 360° to find its type.

1. Compare the angle with a right angle. A right angle is 90°.
   135° > 90°
2. Compare the angle with a straight line. A straight line is 180°.
   135° < 180°
3. Name the type of angle. An angle more than 90° and less than 180° is obtuse.
   obtuse
4. Write the answer. So the angle 135° is obtuse.
   obtuse

Check. 135° is between 90° and 180°, so it is obtuse. ✓

Watch out. Look at the number of degrees, not at how long the arms look.

Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.

Method. Compare the size of the angle with 90°, 180° and 360° to find its type.

1. Compare the angle with a straight line. A straight line is 180°.
   250° > 180°
2. Compare the angle with a full turn. A full turn is 360°.
   250° < 360°
3. Name the type of angle. An angle more than 180° and less than 360° is reflex.
   reflex
4. Write the answer. So the angle 250° is reflex.
   reflex

Check. 250° is between 180° and 360°, so it is reflex. ✓

Watch out. Look at the number of degrees, not at how long the arms look.

Key words. A protractor measures angles. Its centre goes on the vertex, and one arm lies along the 0 line.

Method. Put the centre on the vertex, line up the 0 line and read the scale where the other arm crosses it.

1. Put the centre of the protractor on the vertex. The centre must be at the corner of the angle.
   centre on the vertex
2. Line up one arm with the 0 line. Then the scale starts at 0 on that arm.
   start at 0 on the base line
3. Read the number where the other arm crosses the scale. Count the scale in 5s and 10s to find the number.
   the arm crosses the scale at 120
4. Write the answer with the degree sign. The angle is obtuse.
   120°

Check. 120° is obtuse, which matches the picture. ✓

Watch out. Read the scale that starts at 0 on the arm you lined up. Do not read the other scale by mistake.

Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.

Method. Add the known angles on a straight line, then take them away from 180.

1. Add the parts we know. The angles on a straight line that we know are 40.
   40
2. Take this away from 180. The angles on a straight line add up to 180, so the missing one is what is left.
   180 − 40 = 140
3. Write the answer.
   140°

Check. 40 + 140 = 180. ✓

Watch out. Do not add the missing part to the total. Take the known parts away from the total.

Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.

Method. Add the known angles at a point, then take them away from 360.

1. Add the parts we know. The angles at a point that we know are 100 + 90 + 70.
   100 + 90 + 70 = 260
2. Take this away from 360. The angles at a point add up to 360, so the missing one is what is left.
   360 − 260 = 100
3. Write the answer.
   100°

Check. 260 + 100 = 360. ✓

Watch out. Do not add the missing part to the total. Take the known parts away from the total.

Key words. An angle is the amount of turn between two lines (the arms) that meet at a point (the vertex). We measure angles in degrees, written with the symbol °.

Method. Each quarter turn is a right angle, so multiply the number of quarter turns by 90.

1. Count the quarter turns. A whole turn is four quarter turns.
   3 quarter turns
2. Multiply by 90°. Each quarter turn is a right angle, which is 90°.
   3 × 90 = 270
3. Write the answer.
   270°

Check. 270 ÷ 90 = 3. ✓

Watch out. A right angle is 90°, not 9° or 100°.

Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.

Method. Find the number of edges, then multiply by the length of one edge.

1. Write the number of edges. A cube has 12 edges.
   12 edges
2. Multiply by the length of one edge. All the edges of a cube are the same length.
   12 × 5 = 60
3. Write the answer.
   60 cm

Check. 60 ÷ 12 = 5. ✓

Watch out. Count the edges first. A cube has 12 of them.

Key words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.

Method. Half of the perimeter is one length and one width. Find the missing side from that.

1. Halve the perimeter. Half of the perimeter is one long side and one short side added together.
   26 ÷ 2 = 13
2. Take away the side we know. What is left is the other side.
   13 − 8 = 5
3. Write the answer.
   5 cm

Check. 2 × (5 + 8) = 26. ✓

Watch out. Halve the perimeter first. Do not take the known side away from the whole perimeter.

Method. Add the known angles at the corner, then take them away from 90.

1. Add the parts we know. The angles at the corner that we know are 40.
   40
2. Take this away from 90. The angles at the corner add up to 90, so the missing one is what is left.
   90 − 40 = 50
3. Write the answer.
   50°

Check. 40 + 50 = 90. ✓

Watch out. Do not add the missing part to the total. Take the known parts away from the total.

Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.

Method. Check the sides and the angles of a square.

1. Check the sides. A square has 4 equal sides.
   4 equal sides
2. Check the angles. A square has 4 equal right angles.
   4 angles of 90°
3. Decide. Both rules are true, so a square is regular.
   Yes

Check. A regular shape has equal sides and equal angles, and a square does. ✓

Watch out. Both rules must be true.

Key words. An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A reflex angle is more than 180° and less than 360°.

Method. Compare the size of the angle with 90°, 180° and 360° to find its type.

1. Compare the angle with a right angle. A right angle is 90°.
   98° > 90°
2. Compare the angle with a straight line. A straight line is 180°.
   98° < 180°
3. Name the type of angle. An angle more than 90° and less than 180° is obtuse.
   obtuse
4. Write the answer. So the angle 98° is obtuse.
   obtuse

Check. 98° is between 90° and 180°, so it is obtuse. ✓

Watch out. Look at the number of degrees, not at how long the arms look.

Key words. An angle is the amount of turn between two lines (the arms) that meet at a point (the vertex). We measure angles in degrees, written with the symbol °.

Method. Learn these facts about turns: a right angle is 90, a half turn is 180 and a whole turn is 360.

1. Recall the fact. A half turn is half of a full turn, and a full turn is 360°.
   a half turn = 180°
2. Write the answer.
   180°

Check. 180 is the right number for a half turn. ✓

Watch out. A whole turn is bigger than a half turn, and a half turn is bigger than a right angle.

Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.

Method. Add the known angles on a straight line, then take them away from 180.

1. Add the parts we know. The angles on a straight line that we know are 72.
   72
2. Take this away from 180. The angles on a straight line add up to 180, so the missing one is what is left.
   180 − 72 = 108
3. Write the answer.
   108°

Check. 72 + 108 = 180. ✓

Watch out. Do not add the missing part to the total. Take the known parts away from the total.

Key words. Angles on a straight line add up to 180°, which is a half turn. Angles at a point add up to 360°, which is a whole turn.

Method. Add the known angles at a point, then take them away from 360.

1. Add the parts we know. The angles at a point that we know are 120 + 85.
   120 + 85 = 205
2. Take this away from 360. The angles at a point add up to 360, so the missing one is what is left.
   360 − 205 = 155
3. Write the answer.
   155°

Check. 205 + 155 = 360. ✓

Watch out. Do not add the missing part to the total. Take the known parts away from the total.

Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.

Method. Count the edges of the shape, one at a time.

1. Picture the shape. A cube has 4 edges on the top, 4 on the bottom and 4 going up.
2. Count the edges. Count each one once and do not miss any.
   12 edges

Check. Counting in a different order gives 12 again. ✓

Watch out. Faces, edges and vertices are different things. Read the question carefully.

Key words. A face is a flat side of a 3-D shape. An edge is where two faces meet. A vertex is a corner (more than one is vertices). A net is a flat pattern that folds up into a 3-D shape.

Method. Count the faces of the net and look at their shapes. Then name the 3-D shape that it folds into.

1. Count the rectangles. Each rectangle becomes one face of the solid.
   6 rectangles
2. Look for matching faces. Opposite faces of a cuboid are the same size.
   the band has two pairs of equal faces, and the top and bottom match
3. Name the solid. A 3-D shape with six rectangular faces is a cuboid.
   cuboid

Check. The solid has 6 faces, the same as the net. ✓

Watch out. A cube has square faces. A cuboid has rectangular faces, and a cube is a special cuboid.

Method. Add the known parts of the long side, then take them away from 18.

1. Add the parts we know. The parts of the long side that we know are 7.
   7
2. Take this away from 18. The parts of the long side add up to 18, so the missing one is what is left.
   18 − 7 = 11
3. Write the answer.
   11 cm

Check. 7 + 11 = 18. ✓

Watch out. Do not add the missing part to the total. Take the known parts away from the total.

Method. Add the known angles at the corner, then take them away from 90.

1. Add the parts we know. The angles at the corner that we know are 28.
   28
2. Take this away from 90. The angles at the corner add up to 90, so the missing one is what is left.
   90 − 28 = 62
3. Write the answer.
   62°

Check. 28 + 62 = 90. ✓

Watch out. Do not add the missing part to the total. Take the known parts away from the total.

Key words. A polygon is a flat shape with straight sides. A regular polygon has all its sides equal and all its angles equal. An irregular polygon does not.

Method. A regular shape has equal sides, so multiply the number of sides by the length of one side.

1. Count the sides. A regular shape has the same length of side all the way round.
   6 sides
2. Multiply by the length of one side. Every side is the same length, so multiply.
   6 × 7 = 42
3. Write the answer.
   42 cm

Check. 42 ÷ 6 = 7. ✓

Watch out. Count the sides carefully. A hexagon has 6 sides, not 5.

Key words. A rectangle has four right angles. Its opposite sides are equal in length. The perimeter is the distance all the way round the outside.

Method. Halve the perimeter, then use the rule that the length is 4 m more than the width.

1. Halve the perimeter. Half of the perimeter is one length and one width.
   64 ÷ 2 = 32
2. Take away the extra 4 m. The length is 4 m more than the width, so take 4 away first.
   32 − 4 = 28
3. Find the width. Two widths make 28 m, so one width is half of 28.
   28 ÷ 2 = 14 m
4. Find the length. The length is 4 m more than the width.
   14 + 4 = 18 m
5. Write the answer.
   Length 18 m, width 14 m

Check. 2 × (18 + 14) = 64 m, which is the perimeter. ✓

Watch out. Halve the perimeter first. Do not take 4 m away from the whole perimeter.