Geometry Art II — Scratch L4 Lesson 6

Learnt28 min · round twice, the star rule, a star block
Basic24 min · three stars from one block
Challenge 1–327 min · a sky, six points, the jump rule
Extrabonus · click to add stars

WHAT IT SHOULD LOOK LIKE

Turn a little further at every corner and a shape turns into a star. One rule gives every one of these.

5, 7 and 9 points

Review — Lesson 5 5 min

The arrow draws the way it points.
Going all the way round a shape is a turn of 360 degrees.
So each corner turns 360 ÷ sides, and polygon (sides) (size) :: custom draws any regular shape.

Quick-fire

How far does the arrow turn at each corner of an octagon — a shape with 8 sides?

Reveal the answer

45 degrees. 360 ÷ 8 = 45.

Today’s Topic 3 min

A star is a shape where the arrow turns further at each corner
The star rule — turn 180 − (180 ÷ points)
A star (points) (size) :: custom block that changes colour as it draws

Learning outcome

By the end of this lesson you will be able to:

Say why turning 144 instead of 72 turns a pentagon into a star.
Work out the turn for a star with any odd number of points.
Make a star block and use it three times.

Learnt — from shapes to stars 28 min

1 · Same moves, bigger turn

Here are two scripts. The only difference is the turn.


repeat (5)
  move (100) steps
  turn cw (72) degrees
end

A pentagon.


repeat (5)
  move (160) steps
  turn cw (144) degrees
end

A star.

WHAT IT SHOULD LOOK LIKE

Same five moves. Turn 72 and the arrow goes round once — a pentagon. Turn 144 and it goes round twice — a star.

turn 72

turn 144

panels run left to right

Runs here in the page. Nothing to install.

How to use this: Click the green flag. The pentagon is drawn first, then the star. Watch the turn box.

72 goes round once. 144 goes round twice and crosses over itself.

2 · The spikiest star

A turn of 180 is a U-turn — the arrow goes straight back the way it came. A turn of nearly 180 sends it back at a sharp angle, and that makes a sharp spike. So the spikiest star turns:

turn cw ((180) - ((180) / (points))) degrees

180, take away 180 ÷ points.

Points	Sum	Turn
5	180 − 36	144
7	180 − 25.7	about 154
9	180 − 20	160

Runs here in the page. Nothing to install.

How to use this: Click the green flag. Three stars are drawn: 5, 7 and 9 points.

Every star here uses the same rule. Only the number of points changes.

3 · A star block

Make it a block, just like the polygon. This one changes colour on every line.


define star (points) (size)
repeat (points)
  move (size) steps
  turn cw ((180) - ((180) / (points))) degrees
  change pen (color v) by (8)
  wait (0.08) seconds
end

Six blocks. The colour change inside the loop gives every spike its own colour.

Basic — three stars from one block 24 min

Open your project from Lesson 5. Keep the board and the arrow.

Step 1 — the star block

Make a Block called star with two inputs, points and size.
Build the six-block definition from the Learnt.

Step 2 — the big star

Under when flag clicked: erase all, set pen size to (3), and a pen colour.
pen up, go to x: (-75) y: (75), point in direction (90), pen down.
star (9) (150) :: custom.

Step 3 — two small stars

Travel to x: -215, y: -60 and draw star (5) (70) :: custom.
Travel to x: 145, y: -60 and draw another one.
Give each star its own starting colour.


when flag clicked
erase all
set pen size to (3)
set pen color to [#ff4fa3]
pen up
go to x: (-75) y: (75)
point in direction (90)
pen down
star (9) (150) :: custom
set pen color to [#ffd23f]
pen up
go to x: (-215) y: (-60)
point in direction (90)
pen down
star (5) (70) :: custom
set pen color to [#4fd1ff]
pen up
go to x: (145) y: (-60)
point in direction (90)
pen down
star (5) (70) :: custom

“Travel, then draw” — three times.

Runs here in the page. Nothing to install.

How to use this: Click the green flag. One big 9-point star, then two small 5-point stars.

What you are aiming at: three calls of one star block.

My star does not close — it keeps going round.

Check the brackets. It must be 180 take away (180 ÷ points) — put the divide block inside the subtract block, not the other way round.

My star is a single colour.

change pen (color v) by (8) must be inside the repeat, in the define hat.

A line joins two of my stars.

Use pen up before go to x: (0) y: (0), and pen down after it.

CHALLENGE 1 · L4-06-M1🪙 30 Adcoins8 min

A starry sky

Six stars, and a different sky every time you press the flag.

Each star goes to a random place and has a random size.
Each star has 5, 7 or 9 points, chosen at random.
Show the points of the last star on the Stage.

Runs here in the page. Nothing to install.

How to use this: Click the green flag, then click it again for a new sky.

Random places, random sizes, random odd points.

Done when: two presses of the flag give two different skies, and every star is closed.

Teacher reveal


repeat (6)
  set [points v] to (((pick random (2) to (4)) * (2)) + (1))
  pen up
  go to x: (pick random (-210) to (120)) y: (pick random (-40) to (150))
  point in direction (90)
  pen down
  star (points) (pick random (40) to (80)) :: custom
  change pen (color v) by (17)
end

The sum makes 5, 7 or 9 and never an even number. Many pupils try pick random (5) to (9) and get broken stars at 6 and 8 — let them see it.

CHALLENGE 2 · L4-06-M2🪙 50 Adcoins9 min

Six points

The star rule fails for 6. Make a six-point star a different way.

Use two triangles, each with sides of 150.
The second triangle is upside down and sits over the first.
The finished star has six equal points.

WHAT IT SHOULD LOOK LIKE

Challenge 2 — six points cannot be drawn in one line. Two triangles can, the second one turned round.

two triangles

Runs here in the page. Nothing to install.

How to use this: Click the green flag. The blue triangle is drawn first, then the pink one.

Two triangles, one upside down, make six points.

Done when: your star has six points that all look the same size.

Teacher reveal


pen up
go to x: (-75) y: (43)
point in direction (90)
pen down
polygon (3) (150) :: custom
pen up
go to x: (75) y: (-44)
point in direction (-90)
pen down
polygon (3) (150) :: custom

The second triangle starts 150 to the right and 87 lower, facing left. Pupils often find the start point by trial and error, nudging x and y. That is fine — praise the ones who notice it is the corner of the first triangle’s mirror image.

CHALLENGE 3 · L4-06-M3🪙 70 Adcoins10 min

The jump rule

Imagine the points are dots round a clock face. A star joins each dot to one a few steps further on. That step is the jump. The turn is:

turn cw (((360) * (jump)) / (points)) degrees

Make a block jump star (points) (jump) (size) :: custom.
Draw a 7-point star with a jump of 3, and an 8-point star with a jump of 3.
Show points and jump on the Stage.

WHAT IT SHOULD LOOK LIKE

Challenge 3 — the jump rule. Seven points jumping 3, and eight points jumping 3.

turn = 360 × jump ÷ points

Runs here in the page. Nothing to install.

How to use this: Click the green flag. A 7-point star, then an 8-point star.

An 8-point star in one line — the jump rule can do what the star rule could not.

Done when: both stars close up, and you can say what a jump of 1 draws.

Teacher reveal


define jump star (points) (jump) (size)
repeat (points)
  move (size) steps
  turn cw (((360) * (jump)) / (points)) degrees
  wait (0.1) seconds
end

A jump of 1 is a polygon. A jump of 2 on 5 points is the classic star. If the jump and the points share a factor (8 and 2, 6 and 2) the line closes early — another nice thing for a fast pupil to discover.

EXTRA MISSION · L4-06-MX🪙 100 Adcoinsbonus

Click to add stars

Mix Sketch Pad and today. The mouse chooses where; your block draws the star.

The green flag clears the board and draws one 7-point star.
Every click on the Stage adds a new star where you clicked.
Every new star has 5, 7 or 9 points, a random size and a new colour.
Old stars stay on the board.

Runs here in the page. Nothing to install.

How to use this: Click the green flag, then click anywhere on the Stage to add a star.

Your mouse picks the spot. The block draws the star.

Teacher reveal


when stage clicked
pen up
go to x: (mouse x) y: (mouse y)
point in direction (90)
pen down
change pen (color v) by (pick random (10) to (40))
star (((pick random (2) to (4)) * (2)) + (1)) (pick random (40) to (90)) :: custom
pen up

Clicking a sprite does not count as clicking the Stage. If a pupil’s clicks “do nothing”, check they are not clicking on the arrow.

Summary 5 min

A star is a shape where the arrow goes round more than once.
The spikiest star turns 180 − (180 ÷ points). It works for odd numbers of points.
An even number of points needs two shapes, or the jump rule.
A colour change inside the loop gives every line its own colour.

Star: A shape whose lines cross, so each corner is a point.
U-turn: A turn of 180 degrees. The arrow faces back the way it came.
Jump: How many dots round the circle each line skips to.

Hand in

Save your stars. Next lesson you draw one shape again and again, turning a little each time — and get a flower.

Learnt28 min · round twice, the star rule, a star block
Basic24 min · three stars from one block
Challenge 1–327 min · a sky, six points, the jump rule
Extrabonus · click to add stars

WHAT IT SHOULD LOOK LIKE

Turn a little further at every corner and a shape turns into a star. One rule gives every one of these.

5, 7 and 9 points

Review — Lesson 5 5 min

The arrow draws the way it points.
Going all the way round a shape is a turn of 360 degrees.
So each corner turns 360 ÷ sides, and polygon (sides) (size) :: custom draws any regular shape.

Quick-fire

How far does the arrow turn at each corner of an octagon — a shape with 8 sides?

Reveal the answer

45 degrees. 360 ÷ 8 = 45.

Today’s Topic 3 min

A star is a shape where the arrow turns further at each corner
The star rule — turn 180 − (180 ÷ points)
A star (points) (size) :: custom block that changes colour as it draws

Learning outcome

By the end of this lesson you will be able to:

Say why turning 144 instead of 72 turns a pentagon into a star.
Work out the turn for a star with any odd number of points.
Make a star block and use it three times.

Learnt — from shapes to stars 28 min

1 · Same moves, bigger turn

Here are two scripts. The only difference is the turn.


repeat (5)
  move (100) steps
  turn cw (72) degrees
end

A pentagon.


repeat (5)
  move (160) steps
  turn cw (144) degrees
end

A star.

WHAT IT SHOULD LOOK LIKE

Same five moves. Turn 72 and the arrow goes round once — a pentagon. Turn 144 and it goes round twice — a star.

turn 72

turn 144

panels run left to right

Runs here in the page. Nothing to install.

How to use this: Click the green flag. The pentagon is drawn first, then the star. Watch the turn box.

72 goes round once. 144 goes round twice and crosses over itself.

2 · The spikiest star

A turn of 180 is a U-turn — the arrow goes straight back the way it came. A turn of nearly 180 sends it back at a sharp angle, and that makes a sharp spike. So the spikiest star turns:

turn cw ((180) - ((180) / (points))) degrees

180, take away 180 ÷ points.

Points	Sum	Turn
5	180 − 36	144
7	180 − 25.7	about 154
9	180 − 20	160

Runs here in the page. Nothing to install.

How to use this: Click the green flag. Three stars are drawn: 5, 7 and 9 points.

Every star here uses the same rule. Only the number of points changes.

3 · A star block

Make it a block, just like the polygon. This one changes colour on every line.


define star (points) (size)
repeat (points)
  move (size) steps
  turn cw ((180) - ((180) / (points))) degrees
  change pen (color v) by (8)
  wait (0.08) seconds
end

Six blocks. The colour change inside the loop gives every spike its own colour.

Basic — three stars from one block 24 min

Open your project from Lesson 5. Keep the board and the arrow.

Step 1 — the star block

Make a Block called star with two inputs, points and size.
Build the six-block definition from the Learnt.

Step 2 — the big star

Under when flag clicked: erase all, set pen size to (3), and a pen colour.
pen up, go to x: (-75) y: (75), point in direction (90), pen down.
star (9) (150) :: custom.

Step 3 — two small stars

Travel to x: -215, y: -60 and draw star (5) (70) :: custom.
Travel to x: 145, y: -60 and draw another one.
Give each star its own starting colour.


when flag clicked
erase all
set pen size to (3)
set pen color to [#ff4fa3]
pen up
go to x: (-75) y: (75)
point in direction (90)
pen down
star (9) (150) :: custom
set pen color to [#ffd23f]
pen up
go to x: (-215) y: (-60)
point in direction (90)
pen down
star (5) (70) :: custom
set pen color to [#4fd1ff]
pen up
go to x: (145) y: (-60)
point in direction (90)
pen down
star (5) (70) :: custom

“Travel, then draw” — three times.

Runs here in the page. Nothing to install.

How to use this: Click the green flag. One big 9-point star, then two small 5-point stars.

What you are aiming at: three calls of one star block.

My star does not close — it keeps going round.

Check the brackets. It must be 180 take away (180 ÷ points) — put the divide block inside the subtract block, not the other way round.

My star is a single colour.

change pen (color v) by (8) must be inside the repeat, in the define hat.

A line joins two of my stars.

Use pen up before go to x: (0) y: (0), and pen down after it.

CHALLENGE 1 · L4-06-M1🪙 30 Adcoins8 min

A starry sky

Six stars, and a different sky every time you press the flag.

Each star goes to a random place and has a random size.
Each star has 5, 7 or 9 points, chosen at random.
Show the points of the last star on the Stage.

Runs here in the page. Nothing to install.

How to use this: Click the green flag, then click it again for a new sky.

Random places, random sizes, random odd points.

Done when: two presses of the flag give two different skies, and every star is closed.

Teacher reveal


repeat (6)
  set [points v] to (((pick random (2) to (4)) * (2)) + (1))
  pen up
  go to x: (pick random (-210) to (120)) y: (pick random (-40) to (150))
  point in direction (90)
  pen down
  star (points) (pick random (40) to (80)) :: custom
  change pen (color v) by (17)
end

The sum makes 5, 7 or 9 and never an even number. Many pupils try pick random (5) to (9) and get broken stars at 6 and 8 — let them see it.

CHALLENGE 2 · L4-06-M2🪙 50 Adcoins9 min

Six points

The star rule fails for 6. Make a six-point star a different way.

Use two triangles, each with sides of 150.
The second triangle is upside down and sits over the first.
The finished star has six equal points.

WHAT IT SHOULD LOOK LIKE

Challenge 2 — six points cannot be drawn in one line. Two triangles can, the second one turned round.

two triangles

Runs here in the page. Nothing to install.

How to use this: Click the green flag. The blue triangle is drawn first, then the pink one.

Two triangles, one upside down, make six points.

Done when: your star has six points that all look the same size.

Teacher reveal


pen up
go to x: (-75) y: (43)
point in direction (90)
pen down
polygon (3) (150) :: custom
pen up
go to x: (75) y: (-44)
point in direction (-90)
pen down
polygon (3) (150) :: custom

CHALLENGE 3 · L4-06-M3🪙 70 Adcoins10 min

The jump rule

Imagine the points are dots round a clock face. A star joins each dot to one a few steps further on. That step is the jump. The turn is:

turn cw (((360) * (jump)) / (points)) degrees

Make a block jump star (points) (jump) (size) :: custom.
Draw a 7-point star with a jump of 3, and an 8-point star with a jump of 3.
Show points and jump on the Stage.

WHAT IT SHOULD LOOK LIKE

Challenge 3 — the jump rule. Seven points jumping 3, and eight points jumping 3.

turn = 360 × jump ÷ points

Runs here in the page. Nothing to install.

How to use this: Click the green flag. A 7-point star, then an 8-point star.

An 8-point star in one line — the jump rule can do what the star rule could not.

Done when: both stars close up, and you can say what a jump of 1 draws.

Teacher reveal


define jump star (points) (jump) (size)
repeat (points)
  move (size) steps
  turn cw (((360) * (jump)) / (points)) degrees
  wait (0.1) seconds
end

EXTRA MISSION · L4-06-MX🪙 100 Adcoinsbonus

Click to add stars

Mix Sketch Pad and today. The mouse chooses where; your block draws the star.

The green flag clears the board and draws one 7-point star.
Every click on the Stage adds a new star where you clicked.
Every new star has 5, 7 or 9 points, a random size and a new colour.
Old stars stay on the board.

Runs here in the page. Nothing to install.

How to use this: Click the green flag, then click anywhere on the Stage to add a star.

Your mouse picks the spot. The block draws the star.

Teacher reveal


when stage clicked
pen up
go to x: (mouse x) y: (mouse y)
point in direction (90)
pen down
change pen (color v) by (pick random (10) to (40))
star (((pick random (2) to (4)) * (2)) + (1)) (pick random (40) to (90)) :: custom
pen up

Clicking a sprite does not count as clicking the Stage. If a pupil’s clicks “do nothing”, check they are not clicking on the arrow.

Summary 5 min

A star is a shape where the arrow goes round more than once.
The spikiest star turns 180 − (180 ÷ points). It works for odd numbers of points.
An even number of points needs two shapes, or the jump rule.
A colour change inside the loop gives every line its own colour.

Star: A shape whose lines cross, so each corner is a point.
U-turn: A turn of 180 degrees. The arrow faces back the way it came.
Jump: How many dots round the circle each line skips to.

Hand in

Save your stars. Next lesson you draw one shape again and again, turning a little each time — and get a flower.