Year 4 Shapes, Angles and Symmetry: check-up and SATs-style questions

Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.

Method. Turn one step at a time. Remember the order of the compass points going clockwise: North, East, South, West. A quarter turn clockwise moves one place along.

1. Remember the order of the compass points going clockwise. A quarter turn clockwise moves one place along: N, E, S, W. Anticlockwise goes the other way.
   North → East → South → West → North
2. Turn a quarter turn clockwise. 1 quarter turn. Clockwise goes N → E → S → W → N. Anticlockwise goes the other way.
   Start facing South.
   South → West
3. Write the answer.
   The person is now facing West.

Check. Going clockwise, North = 0, East = 1, South = 2, West = 3 quarter turns from North. The total of the turns gives the same direction. ✓

Watch out. Clockwise: N → E → S → W. Anticlockwise is the opposite way, so N → W → S → E.

Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.

Method. Compare the angle with a right angle (the corner of a piece of paper). Smaller is acute. The same is a right angle. Bigger, but less than a straight line, is obtuse.

1. Put the paper corner on one arm of the angle. The dashed lines show the corner of the paper.
2. Look at the other arm. Is it inside the corner, on the corner, or past the corner?
   The other arm is outside the paper corner. It is bigger than a right angle, but it is smaller than a straight line.
3. Name the angle.
   It is obtuse.

Check. Acute < right angle < obtuse < straight line. ✓

Watch out. Look at how wide the angle opens, not how long the arms are.

Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.

Method. Sort the angles into acute, right and obtuse using the corner of a piece of paper. Acute angles are the smallest. Then compare the angles that are in the same group.

1. Test each angle with the paper corner. The dashed lines show the paper corner on each angle.
   ABC
2. Sort them into groups. Acute angles are smaller than a right angle. Obtuse angles are bigger than a right angle.
   B: acute (smaller than a right angle)
   A and C: obtuse (bigger than a right angle)
3. Compare the angles in the same group. The wider the opening, the bigger the angle. Ignore how long the arms are.
   B < A < C
4. Write the order. Start with the smallest.
   B, A, C

Check. Look at the first and last angle: B is the smallest and C is the biggest. ✓

Watch out. A long arm does not make an angle bigger. Only the size of the opening matters.

Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.

Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.

1. Look at the three sides of the triangle. Sides that have the same length are equal.
   The sides are 6 cm, 6 cm and 4 cm.
2. Count the equal sides. The number of equal sides tells us the name.
   There are 2 equal sides.
3. Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.
   The triangle has 2 equal sides: isosceles.

Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 2. ✓

Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.

Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.

Method. Describe the shape: sides, then parallel sides, then right angles. Compare with the six quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium and kite.

1. Count the sides. A shape with 4 straight sides is a quadrilateral.
   It has 4 sides.
2. Look at the sides. Tick marks show equal sides.
   The shape has opposite sides equal.
3. Look for parallel sides and right angles. Arrows on two sides mean they are parallel. A small square means a right angle.
   Pairs of parallel sides: 2.
   Right angles: 0.
4. Decide on the name. Two pairs of parallel sides, with no right angles and sides not all equal.
   It is a parallelogram.

Check. The parallelogram has opposite sides equal, 2 pair(s) of parallel sides and 0 right angle(s). ✓

Watch out. Turning a shape round does not change its name.

Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.

Method. A polygon is named by its number of sides. Count the sides (or the corners, which are the same number) and use the name for that number.

1. Count the sides. Number each corner as you count round the shape. The last number is the number of sides.
   The shape has 7 sides.
2. Remember the names of the polygons. The name depends on the number of sides.
   triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10
3. Find the name. Look for 7 in the list.
   7 sides: heptagon
4. Is it regular? Regular means all sides equal and all angles equal.
   Yes, so it is a regular heptagon.

Check. The shape has 7 corners as well as 7 sides. ✓

Watch out. Count carefully. Number each side so you do not count one twice.

Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.

Method. Use the clues one at a time. After each clue, cross out the shapes that cannot be the answer. The shape that is left is the answer.

1. Use the clue: “I have 4 sides.” Cross out every shape that does not fit. Keep the ones that do.
   Keep: square, rectangle, rhombus, parallelogram, trapezium and kite.
   Cross out: equilateral triangle, isosceles triangle, scalene triangle, right-angled triangle, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon and regular decagon.
2. Use the clue: “I have two pairs of equal sides, and the equal sides are next to each other.” Cross out every shape that does not fit. Keep the ones that do.
   Keep: kite.
   Cross out: square, rectangle, rhombus, parallelogram and trapezium.
3. Write the answer. Only one shape fits every clue.
   The shape is the kite.

Check. Look at the kite: every clue is true for it. ✓

Watch out. Read every clue. One clue on its own often fits more than one shape.

Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.

Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.

1. Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.
   The red dashed lines are the lines of symmetry.
2. Look for every line. Try lines through the corners and through the middles of the sides.
   The equilateral triangle has 3 lines of symmetry.
3. Count the lines.
   The number of lines of symmetry is 3.
4. Write the answer.
   3

Check. Fold along each red line: the two halves fit exactly. ✓

Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.

Key words. A mirror line is the line a shape is reflected in. Each point of the reflection is the same distance from the mirror line as the point it matches, but on the other side.

Method. Reflect each shaded square in the mirror line. Each square and its partner are the same distance from the mirror line, on opposite sides.

1. Find the mirror line. The red dashed line is the mirror line.
   The mirror line is a vertical line (up and down).
2. Find the partner of each shaded square. Count the squares between each shaded square and the mirror line. The partner has the same number of squares between it and the mirror line, on the other side.
   B2 has 2 squares between it and the mirror line, so its partner has 2 squares between it and the mirror line on the other side: G2.
   B3 has 2 squares between it and the mirror line, so its partner has 2 squares between it and the mirror line on the other side: G3.
   C3 has 1 square between it and the mirror line, so its partner has 1 square between it and the mirror line on the other side: F3.
   C4 has 1 square between it and the mirror line, so its partner has 1 square between it and the mirror line on the other side: F4.
   D4 touches the mirror line, so E4 touches it on the other side.
   D5 touches the mirror line, so E5 touches it on the other side.
3. Shade the new squares. Orange squares were given. Green squares are the new ones.
   Shade 6 more squares: E4, E5, F3, F4, G2, G3.

Check. Fold along the mirror line: every green square lands on an orange square. ✓

Watch out. Count the squares from the mirror line, not from the edge of the grid.

Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.

Method. A square has four equal sides and four right angles. A rectangle needs four right angles and opposite sides equal. Check the square against what a rectangle needs.

1. List what a rectangle needs. Four right angles, and opposite sides equal.
   rectangle: 4 right angles; opposite sides equal
2. Check a square. It has four right angles, and all its sides are equal, so opposite sides are equal too.
   A square has everything a rectangle needs.
3. Decide.
   A square is always a rectangle.

Check. Every square is a rectangle (a special one). ✓

Watch out. Not every rectangle is a square.

Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.

Method. An obtuse angle is bigger than a right angle but smaller than a straight line. Test each angle with the corner of a piece of paper.

1. Test each angle. Smaller than the paper corner is acute. The same is a right angle. Bigger is obtuse.
   ABCD
2. Name each angle.
   A: acute
   B: right angle
   C: obtuse
   D: acute
3. Choose.
   The obtuse angle is C.

Check. Angle C is the only one wider than the paper corner. ✓

Watch out. Obtuse means wide, acute means sharp.

Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.

Method. A quadrilateral has exactly 4 sides. Count the sides of each shape.

1. Count the sides of each shape. Number the sides if it helps.
   A: 4 sides
   B: 5 sides
   C: 4 sides
   D: 3 sides
   E: 6 sides
2. Pick the shapes with 4 sides.
   A and C

Check. A square and a kite both have 4 sides. ✓

Watch out. Pentagon 5, hexagon 6, triangle 3.

Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.

Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.

1. Look at the three sides of the triangle. Sides that have the same length are equal.
   The sides are 9 cm, 7 cm and 6 cm.
2. Count the equal sides. The number of equal sides tells us the name.
   No two sides are equal.
3. Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.
   The triangle has no equal sides: scalene.

Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 0. ✓

Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.

Key words. A line of symmetry (mirror line) cuts a shape into two halves that are mirror images of each other. If you fold along the line, the two halves match exactly.

Method. Find the lines you could fold along so that the two halves match exactly. Count them. Turning the shape round does not change how many there are.

1. Imagine folding the shape. A line of symmetry is a fold line where the two halves match exactly. The shape turned round still has the same lines of symmetry.
   The red dashed lines are the lines of symmetry.
2. Look for every line. Try lines through the corners and through the middles of the sides.
   The cross has 4 lines of symmetry.
3. Count the lines.
   The number of lines of symmetry is 4.
4. Write the answer.
   4

Check. Fold along each red line: the two halves fit exactly. ✓

Watch out. Turning a shape does not change how many lines of symmetry it has. The diagonals of a rectangle are not lines of symmetry.

Key words. A mirror line is the line a shape is reflected in. Each point of the reflection is the same distance from the mirror line as the point it matches, but on the other side.

Method. Reflect each shaded square in the mirror line. Each square and its partner are the same distance from the mirror line, on opposite sides.

1. Find the mirror line. The red dashed line is the mirror line.
   The mirror line is a horizontal line (across).
2. Find the partner of each shaded square. Each square goes the same distance from the mirror line, on the other side (up and down).
   A4 touches the mirror line, so A5 touches it on the other side.
   B1 has 3 squares between it and the mirror line, so its partner has 3 squares between it and the mirror line on the other side: B8.
   B2 has 2 squares between it and the mirror line, so its partner has 2 squares between it and the mirror line on the other side: B7.
   C2 has 2 squares between it and the mirror line, so its partner has 2 squares between it and the mirror line on the other side: C7.
   C3 has 1 square between it and the mirror line, so its partner has 1 square between it and the mirror line on the other side: C6.
   D2 has 2 squares between it and the mirror line, so its partner has 2 squares between it and the mirror line on the other side: D7.
   D3 has 1 square between it and the mirror line, so its partner has 1 square between it and the mirror line on the other side: D6.
   E1 has 3 squares between it and the mirror line, so its partner has 3 squares between it and the mirror line on the other side: E8.
   E2 has 2 squares between it and the mirror line, so its partner has 2 squares between it and the mirror line on the other side: E7.
   F4 touches the mirror line, so F5 touches it on the other side.
3. Shade the new squares. Orange squares were given. Green squares are the new ones.
   Shade 10 more squares: A5, B7, B8, C6, C7, D6, D7, E7, E8, F5.

Check. Fold along the mirror line: every green square lands on an orange square. ✓

Watch out. Count the squares from the mirror line, not from the edge of the grid.

Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.

Method. Test every shape against both labels. Then put it in the box that matches the answers: yes or no for each label.

1. Look at each shape. Ask the two questions about each shape.
   A: no for “all sides equal”, yes for “has parallel sides”
   B: yes for “all sides equal”, yes for “has parallel sides”
   C: no for “all sides equal”, no for “has parallel sides”
   D: yes for “all sides equal”, no for “has parallel sides”
   E: no for “all sides equal”, yes for “has parallel sides”
   F: no for “all sides equal”, no for “has parallel sides”
2. Fill in the Carroll diagram. Each shape goes in exactly one box.

   	has parallel sides	not: has parallel sides
   all sides equal	B	D
   not: all sides equal	A, E	C, F

3. Check. Count the shapes.
   6 shapes are in the diagram. There are 6 shapes. They all fit.

Check. Every shape is in exactly one box. ✓

Watch out. Every shape belongs in a box, even if it does not have either property.

Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.

Method. Use the clues one at a time. After each clue, cross out the shapes that cannot be the answer. The shape that is left is the answer.

1. Use the clue: “I have 4 sides.” Cross out every shape that does not fit. Keep the ones that do.
   Keep: square, rectangle, rhombus, parallelogram, trapezium and kite.
   Cross out: equilateral triangle, isosceles triangle, scalene triangle, right-angled triangle, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon and regular decagon.
2. Use the clue: “I have two pairs of parallel sides.” Cross out every shape that does not fit. Keep the ones that do.
   Keep: square, rectangle, rhombus and parallelogram.
   Cross out: trapezium and kite.
3. Use the clue: “I have four right angles.” Cross out every shape that does not fit. Keep the ones that do.
   Keep: square and rectangle.
   Cross out: rhombus and parallelogram.
4. Use the clue: “My sides are not all the same length.” Cross out every shape that does not fit. Keep the ones that do.
   Keep: rectangle.
   Cross out: square.
5. Write the answer. Only one shape fits every clue.
   The shape is the rectangle.

Check. Look at the rectangle: every clue is true for it. ✓

Watch out. Read every clue. One clue on its own often fits more than one shape.

Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.

Method. A square is a rectangle, but a rectangle is not always a square. Compare the two shapes.

1. Look at what Ben says. He says all rectangles are squares.
   Ben: “All rectangles are squares.”
2. Test with a rectangle that is not a square. A rectangle can have long sides and short sides.
   This rectangle has sides 5 and 3. Its sides are not all equal, so it is not a square.
3. Answer. A square has four equal sides. This rectangle does not.
   Ben is wrong. Every square is a rectangle, but a rectangle with unequal sides is not a square.

Check. A 3 by 3 rectangle is a square, but a 5 by 3 rectangle is not. ✓

Watch out. Give an example to explain.

Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.

Method. Sort the angles into acute, right and obtuse using the corner of a piece of paper. Acute angles are the smallest. Then compare the angles that are in the same group.

1. Test each angle with the paper corner. The dashed lines show the paper corner on each angle.
   ABCD
2. Sort them into groups. Acute angles are smaller than a right angle. Obtuse angles are bigger than a right angle.
   B: acute (smaller than a right angle)
   C: a right angle
   A and D: obtuse (bigger than a right angle)
3. Compare the angles in the same group. The wider the opening, the bigger the angle. Ignore how long the arms are.
   B < C < D < A
4. Write the order. Start with the smallest.
   B, C, D, A

Check. Look at the first and last angle: B is the smallest and A is the biggest. ✓

Watch out. A long arm does not make an angle bigger. Only the size of the opening matters.

Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.

Method. Follow each turn in order to find the direction. For the total turn, add up the right angles of each turn, whichever way the robot turned.

1. Part (a): follow the turns. Start facing East. Half turn clockwise, quarter turn anticlockwise, three-quarter turn clockwise.
   East → West → South → East
2. Write the direction.
   The robot faces East at the end.
3. Part (b): add the right angles. A half turn is 2 right angles. A quarter turn is 1. A three-quarter turn is 3.
   2 + 1 + 3 = 6 right angles

Check. 6 right angles is a whole turn (4) and a half turn (2). ✓

Watch out. The total counts every turn, even the anticlockwise one.