Mini Minds Hub · Free printable
Angle Arcade: Boss Level: Free Printable Worksheet for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Angle Arcade: Boss Level is a free printable angles worksheet for Year 7 (ages 11 to 12), in Key Stage 3. Pupils work through arcade style puzzles, find x in each one, then add the fact letter. Page 2 gives the grown up notes, help ideas, a stretch task and the answers.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to the pupil and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Pupils work through angle puzzles set out as arcade levels, ending with the Boss Level. In each puzzle they use an angle fact to build a simple equation and find x. They then record the answer and the fact letter in the table. Along the way they name the angle fact they used, so the reason matters as much as the number.
- Puzzle
- Answer + fact
A different puzzle, worked two ways
Two angles on a straight line are 4x and (2x + 18) degrees. Find x.
This is a different puzzle from the sheet, chosen to show the method. Pupils can use either approach.
Method 1: write and solve an equation- Angles on a straight line add up to 180 degrees.
- Write the equation: 4x + 2x + 18 = 180.
- Collect the x terms: 6x + 18 = 180.
- Subtract 18 from both sides: 6x = 162.
- Divide both sides by 6: x = 27.
- Try x = 20. The angles are 80 and 58, which total 138. That is too small.
- Try x = 30. The angles are 120 and 78, which total 198. That is too big.
- Try x = 27. The angles are 108 and 72, which total 180. It works.
Why practise angle facts with puzzles?
At Key Stage 3, pupils move from measuring angles to reasoning about them. A few key facts do a lot of work. Angles on a straight line total 180 degrees. Angles around a point total 360 degrees. Where two straight lines cross, the angles opposite each other are equal. Pupils who know these facts can find missing angles without a protractor.
This sheet adds algebra to those facts. When an angle is written with x in it, pupils must choose the right total, form an equation and solve it. The arcade levels give the practice a clear path from easier puzzles to harder ones. Naming the fact each time helps pupils build the habit of giving a reason, which they will need for proof in later geometry.
Skills and curriculum link
- Finding missing angles
- Naming angle facts
- Forming simple equations
- Solving for x
- Giving reasons
- Checking answers
Angle facts that help
- Angles on a straight lineThey share a straight edge and add up to a fixed total. Sketch the line and mark every angle before writing anything.
- Angles around a pointThey fill a full turn. Use the total for a full turn, not the total for a straight line.
- Crossing linesWhen two straight lines cross, angles that sit opposite each other are equal. Neighbouring angles sit on a straight line.
- Forming an equationAdd every angle in the puzzle, set the sum equal to the right total, then solve step by step. Always check by putting x back in.
Key words
- AngleThe amount of turn between two lines that meet at a point.
- DegreeThe unit we use to measure angles. A full turn is 360 degrees.
- Straight lineA line with no bend. Angles that sit on it add up to a half turn.
- Vertically opposite anglesThe angles facing each other when two straight lines cross. They are equal.
- EquationA statement that two things are equal, such as 3x + 10 = 100.
- UnknownA letter such as x that stands for a number we need to find.
How to use it
- Print both pages. Page 1 is for the pupil. Keep page 2, which has the notes and answers.
- Read the first puzzle together. Ask the pupil to sketch it and decide whether the angles sit on a straight line, around a point or in crossing lines.
- Write the total first, then build an equation in x and solve it.
- Fill in the table with the answer and the fact letter. Name the angle fact used in each puzzle.
- Check against page 2. Ask, "Which fact did you use, and how do you know?" Come back another day to redo the tricky ones.
Help, stretch and game ideas
If it feels too hard
Sketch each puzzle and write the total first, either 180 or 360. Mark every angle on the sketch. Then write the equation in words before using symbols. Start with Level 1 only, and return to the later levels another day.
To stretch confident children
Write your own boss puzzle with an equation in x. Draw the diagram, choose the angle fact, then swap with a partner and solve each other's. Check that your puzzle gives a sensible angle with no negative sizes.
Make it a game
Race a partner through the levels. Whoever reaches the higher score after Level 3 gets a head start on the Boss Level. Each player must name the angle fact aloud before the answer counts.
Mistakes to watch for
Watch forUsing 180 for angles around a point, or 360 for a straight line.
Try thisSketch the puzzle first. Ask whether it is a half turn or a full turn, then write the total at the top before any algebra.
Watch forSlipping when solving, for example turning 3x + 20 = 180 into 3x = 200.
Try thisWrite each step on its own line. Subtract the same number from both sides, then divide both sides.
Watch forFinding x but never checking it.
Try thisPut x back into every angle and add them up. If the total is wrong, the answer or the equation needs another look.
Talk about it
- Which angle fact did you use first, and why?
- How can you tell if angles are on a straight line or around a point?
- Why do we write the total before we start the algebra?
- How could you check your value of x without looking at the answers?
- What makes the Boss Level harder than the first level?
- Can you make up a puzzle where two angles are equal?
Take it off the page
Paper strip angles
Cut two strips of card and join them with a paper fastener. Open them to make different angles and talk about which are acute, right or obtuse.
Angle hunt
Look around the room for angles in door frames, book corners and clock hands. Sketch three and estimate each one in degrees.
Draw a puzzle
Draw two crossing lines with a ruler. Label one angle with x and another with a number, then ask someone to find x and name the fact.
Who it is for
Parents
Sit beside your child for the first puzzle, then let them lead. Ask them to sketch and say the angle fact aloud. You do not need to be confident at algebra, as page 2 has the answers.
Teachers
Use it as a no prep starter before teaching parallel lines, or as a plenary, early finisher task or homework. Pupils can mark their own work using page 2. Ask for the named fact as well as x.
Home educators
Print it as part of a wider maths plan. It pairs well with a protractor and ruler for drawing and checking angles. Use it again later for revision, or for brothers and sisters working at this level.
Where this fits in maths
Before this sheet, pupils have met types of angle, measured and drawn angles with a protractor, and used letters to stand for unknown numbers. They have also solved simple one step and two step equations.
After this sheet, pupils usually move on to angles in parallel lines, then angles in triangles and other polygons. The habit of naming the fact and building an equation carries straight into those topics, and into formal geometric reasoning later on.
Questions parents and teachers ask
- What age is Angle Arcade: Boss Level for?
It is written for Year 7 (ages 11 to 12), in Key Stage 3. It also works as revision for older pupils who need to secure their angle facts before moving on to parallel lines.
- What will pupils practise?
They practise finding missing angles on a straight line, around a point and in crossing lines. They also form simple equations in x and name the angle fact they used for each puzzle.
- How do I use it?
Print both pages and give page 1 to the pupil. Ask them to sketch each puzzle, write the total, solve for x and name the fact. Mark with page 2 and talk through any errors.
- What if it feels too hard?
Let pupils sketch each puzzle and write the total, either 180 or 360, before anything else. Start with Level 1 only, then return to the later levels on another day.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for revision, for brothers and sisters, or for a different class.
- Can teachers use it in class?
Yes. It works as a starter before parallel lines, a plenary, an early finisher task, homework or a table activity. It needs no preparation beyond printing, and pupils can self mark with page 2.
- Is it screen free, and do I need colour?
Yes, it is screen free and needs only paper and a pencil. No colour is needed. It prints well in black and white on plain A4 paper, which keeps printing costs low.
Preview the full PDF
Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.