Angle Mysteries: missing angle puzzles

What it does on screen

The board is a drawing of lines with some angles given in black and one marked with a lilac question mark. The class has to find the question mark. On the right is a panel called How we found it, with one row for every step the answer takes. Before you start, the rows are empty, so the class can see how many steps it will be.

Press Next step and the tool finds one angle. It appears in the colour of the fact it used, for example blue for a straight line or red for opposite angles. The angles it needed get a ring in the same colour, so the class can see exactly where the number came from. The row on the right names the fact and writes the sum, like "180 − 60 − 50 = 70".

Along the top you pick the level and Easier or Harder. In the black bar at the bottom are Back, Next step, Show all, Hide and Reveal for the answer, New puzzle and New trick.

The ten levels

• 1 Straight line. Angles on a straight line add up to 180°. A square in the corner means a right angle, 90°.
• 2 Round a point. Angles all the way round a point add up to 360°.
• 3 Opposite angles. Where two lines cross, the angles facing each other are equal.
• 4 Crossing lines. No new trick. Three lines through one point, so the first three have to be mixed.
• 5 Triangles. Angles in a triangle add up to 180°. Tick marks on two sides mean the two angles at the bottom match.
• 6 Four-sided shapes. Angles in any four-sided shape add up to 360°.
• 7 F angles. A line crossing two parallel lines makes the same angles at each one (corresponding angles).
• 8 Z angles. Inside a Z between parallel lines, the two angles are equal (alternate angles).
• 9 Circles. Angles round the centre make 360°, and two radii make an isosceles triangle.
• 10 Mystery webs. Two pairs of parallel lines and a line crossing them. A few angles are given and the answer takes five or six steps.

The Level button lists all ten, with a star for every puzzle the class has finished at each one. The first time you open a level, a New trick card shows its fact with a small picture. Press New trick to bring it back.

How the steps work

• Next step finds one angle. The right arrow key and a clicker do the same.
• Back takes the last step away again.
• Show all fills in every step up to the answer.
• Hide and Reveal. With the answer Hidden, the last step stays a question mark until you press Reveal. Turn it off and Next step goes all the way.
• Easier and Harder change how many steps the puzzle takes. On the mystery webs, Harder looks for the longest chain it can find.

The tool only uses the facts a level has unlocked. On level 3 it will never use a triangle, so the steps always match what the class has been taught so far.

How to use it in a lesson

1. Start with the New trick card. Read the fact together and point at the picture.
2. Give them the puzzle. Leave the answer hidden and give the class a minute or two on mini whiteboards. Ask them to write which fact they used, not just the number.
3. Step through it. Press Next step and ask "which fact was that?" before anyone reads the panel. The colour gives it away to the ones who are stuck.
4. Reveal. Only once everyone has an answer written down.
5. Do it again. New puzzle, same level. After two or three, press Harder.
6. Use the pen. Write over the board to label an angle a, b or c, or have a child come up and mark the angle they found first.

Ideas by year group

• Year 4. Level 1 on Easier, with right angles. Talk about the square meaning 90° before any adding.
• Year 5. Levels 1 and 2. Angles on a straight line and round a point are both in the Year 5 curriculum.
• Year 6. Levels 3 to 6. Opposite angles, triangles and four-sided shapes, then Harder so they have to chain two or three facts.
• Year 6 greater depth. Levels 7 and 8 for a taste of parallel lines, which comes up properly in Year 7.
• Year 7 and up. Levels 9 and 10. A mystery web on Harder makes a good starter for a whole class.

The misconceptions it helps with

Getting the number but not the reason. Many children can find an angle but cannot say why. Every step here names its fact, and a good habit is to ask for the fact before the number.

Guessing from the picture. An angle that looks like 90° is not 90° unless it has the square. The drawings are accurate, but the class should still work from the facts, not their eyes.

Adding to the wrong total. 180° for a straight line and a triangle, 360° for round a point and a four-sided shape. The colours keep the two families apart.

Seeing an F or a Z that is not there. F and Z angles only work between parallel lines, the ones with the arrows. On the webs there are lines without arrows, and the tool never uses them for an F or a Z.

Getting lost in a long puzzle. The ring around the angles each step used shows that a hard puzzle is just a few easy steps in a row.

Frequently asked questions