Vending Machine IV — Scratch L3 Lesson 4

Learnt28 min · round, floor, ceiling, abs
Basic24 min · discount, change and a till
Challenge 1–327 min · half price, out by, the report
Extrabonus · round the customer’s way

WHAT IT SHOULD LOOK LIKE

The last lesson of the arc. A discount lands on half a cent, the machine has to choose a whole one — and at closing time the till has to add up.

10% off a 45c muffin

closing time

panels run left to right

Review — where we got to 5 min

([floor v] of ()) and (() mod ()) break change into coins.
(pick random (1) to (6)) makes a machine different every morning.
Roll once into a variable, then use the variable everywhere.

Quick-fire

Your machine takes 10% off a 45c muffin. What should the customer pay — and what is awkward about the answer?

Reveal the answer

40.5c, and there is no half-cent coin. Today is about what a machine does when the maths lands between two coins.

Today’s Topic 3 min

A percentage off, and the number it leaves behind
(round ()) — to the nearest whole number
([floor v] of ()) and ([ceiling v] of ()) — always down, always up
([abs v] of ()) — how far out, without the minus sign

Learning outcome

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

Work out a percentage of a price.
Choose between round, floor and ceiling, and say why.
Use abs to measure a difference in either direction.

Learnt — tidying a number up 28 min

1 · Ten per cent off

Per cent means out of a hundred. Taking 10% off means the customer pays 90 out of every 100 — so multiply by 90 and divide by 100:


set [exact v] to (((price) * (90)) / (100))

Two operators, nested — exactly the shape you built in Lesson 3-1.

For a 45c muffin that is 40.5. Correct, and impossible: no machine can take half a cent.

WHAT IT SHOULD LOOK LIKE

Ten per cent off means paying ninety per cent. Ninety per cent of 45 is 40.5 — a price no machine can charge.

the exact answer

the price it can charge

panels run left to right

2 · Round goes to the nearest


set [to pay v] to (round (exact))

40.5 rounds to 41. 40.2 would round to 40. Round picks whichever whole number is closer.

Runs here in the page. Nothing to install.

How to use this: Click the green flag and read the three boxes as it talks through the sum.

45c, 10% off, 40.5c exactly — and 41c to pay. Watch the exact box and the to-pay box disagree.

3 · Floor, ceiling and round, side by side

You met floor last lesson. It has two neighbours in the same dropdown, and the three of them do different jobs:

Block	What it does	40.5 becomes
`(round ())`	Nearest whole number	41
`([floor v] of ())`	Always down — the customer wins	40
`([ceiling v] of ())`	Always up — the shop wins	41

WHAT IT SHOULD LOOK LIKE

The same number, three ways. Round goes to the nearest; floor always goes down; ceiling always goes up.

55.5 through all three

Runs here in the page. Nothing to install.

How to use this: Click the green flag and watch five random numbers go through all three blocks. Read the four boxes together.

Five decimals, four boxes. Round and ceiling agree above .5, round and floor agree below it.

4 · The rest of the dropdown

Open that dropdown again and look down the list. Floor, ceiling and abs are three of about a dozen, and the others are there whenever you need them:


([sqrt v] of (81))

9 — the square root. The number that times itself makes 81.


([sin v] of (90))

1 — for angles. You will want this when a sprite has to move along a curve.

There is also cos, tan, ln, log, e ^ and 10 ^. You do not need them today. What you need is to know that one block holds all of them, so when a project needs a square root you go looking in a dropdown rather than for a block that does not exist.

Try it now. Drag the block out, choose sqrt, type 81 and click it. Then 100, then 2. The last one gives 1.4142135623730951 — which is a good moment to remember (round ()).

5 · The till, and abs

At the end of the day a shop counts the money in the till and compares it with what the sums say should be there. The difference matters; which way it went does not, not at first:


set [out by v] to ((takings) - (expected))

243 − 240 = 3. But 237 − 240 = −3.


set [out by v] to ([abs v] of ((takings) - (expected)))

Both come out as 3. Abs throws the minus sign away.

Abs is short for absolute value: how big a number is, ignoring whether it is above or below zero.

WHAT IT SHOULD LOOK LIKE

The till is out by 3c whether there is too much in it or too little. `abs` throws the minus sign away, so one number answers “how wrong?”.

3c too much

3c too little

panels run left to right

Runs here in the page. Nothing to install.

How to use this: Click the green flag and watch three tills checked in turn: too much, too little, and exactly right.

243 and 237 are both “out by 3”. 240 balances, and the box reads 0.

Basic — discount, change and a till 24 min

Open your machine. Three things to add, and then it is finished.

Step 1 — today’s discount

Make two variables: exact and to pay.
After the price is rolled, add set [exact v] to (((price) * (90)) / (100)).
Then set [to pay v] to (round (exact)).
Show both boxes and press the flag a few times.

Step 2 — charge the discounted price

Everywhere your machine used price, use to pay instead.
Check the change ladder still adds up.

Step 3 — the till

Make a variable called takings and set it to 0 under the green flag.
After every sale, add change [takings v] by (to pay).
Show the box, and buy three things. Check the total by hand.

Step 4 — tell the customer

Say the discounted price before they choose.
Say the change after they buy.
Say the till total last.


when flag clicked
set [takings v] to (0)
set [price v] to (45)
set [exact v] to (((price) * (90)) / (100))
set [to pay v] to (round (exact))
say (join [10% off today: ] (join (to pay) [c. Press A.])) for (3) seconds

when [a v] key pressed
set [change v] to ((money) - (to pay))
change [takings v] by (to pay)
glide (0.6) secs to x: (-60) y: (-128)
say (join [Change ] (join (change) [c.])) for (2) seconds
say (join [Till: ] (join (takings) [c.])) for (3) seconds

The finished machine, with the coin questions from Lesson 3-1 above it.

Runs here in the page. Nothing to install.

How to use this: Click the green flag, then click the stage once. Type 3, then 2, then press A.

45c less 10% is 41c to pay, 119c change, and 41c in the till. The whole arc in one run.

The to-pay box shows something like 40.50000000000001.

You have rounded the wrong thing, or not rounded at all. The round goes around the whole sum, not around the price.

The till total is bigger than everything I have sold.

set [takings v] to (0) is missing under the flag, so the total carries over from the last run.

The change is wrong by one cent.

The change is being worked out from price and the money is being taken from to pay, or the other way round. Pick one and use it in both places.

The discount is applied twice.

The set [to pay v] to () is inside the key script as well as under the flag, so it runs again on every sale — 90% of 90% is 81%.

CHALLENGE 1 · L3-04-M1🪙 30 Adcoins8 min

Half price day

Change the offer from 10% off to half price, and see how often it lands badly.

The price is rolled, then halved.
The exact half and the rounded price are both shown.
Run it five times and count how many needed rounding.

WHAT IT SHOULD LOOK LIKE

Challenge 1 — half price. Half of an odd number of cents always lands on a half.

35c halved

Runs here in the page. Nothing to install.

How to use this: Click the green flag and watch five prices get halved. Read the exact box each time.

35c halves to 17.5. 50c halves to 25 exactly. About half of them need rounding.

Done when: you can say which prices halve cleanly and which do not, and your machine charges a whole number of cents either way.

Teacher note

The pattern is worth drawing out: a price that is a multiple of 10 halves cleanly; one that is a multiple of 5 but not 10 does not. That is ((price) mod (10)) from last lesson, being useful again.

CHALLENGE 2 · L3-04-M2🪙 50 Adcoins9 min

The worst day

Six days of takings, and the machine finds the day it was furthest out.

Each day the till is a little above or a little below what was expected.
A worst variable keeps the biggest gap so far.
It does not matter whether the till was over or under.

WHAT IT SHOULD LOOK LIKE

Challenge 2 — six days of takings, and the worst one found without ever knowing which side it fell.

the worst day

Runs here in the page. Nothing to install.

How to use this: Click the green flag and watch six days go past. Press it again for a different worst day.

Six tills against an expected 200c, and the biggest gap kept — whichever side it fell.

Done when: a day that is 9c under is reported as badly as a day that is 9c over, and the worst box holds the biggest of the six.

Teacher reveal — keeping the biggest so far


set [out by v] to ([abs v] of ((takings) - (expected)))
if <(out by) > (worst)> then
  set [worst v] to (out by)
end

Without abs the worst box would stay stuck on whichever day was most over, and a day 30c short would never beat it. This "keep the biggest so far" shape is the same one Level 2 used for a high score — and it is one step from the bubble sort in Lesson 3-11.

CHALLENGE 3 · L3-04-M3🪙 70 Adcoins10 min

The end-of-day report

Close the machine down properly. One report, everything in it.

How many snacks were sold.
How much is in the till.
Whether the till balances, and by how much if not.

WHAT IT SHOULD LOOK LIKE

Challenge 3 — the end-of-day report. Everything the arc built, said once.

closing up

Runs here in the page. Nothing to install.

How to use this: Click the green flag and watch five sales, then the report at the end.

5 sold, 205c taken, till out by 0c. A day that adds up.

Done when: the report names all three numbers, and the “out by” is 0 on a day where nothing went wrong.

Teacher reveal


set [expected v] to ((sold) * (to pay))
set [out by v] to ([abs v] of ((takings) - (expected)))
say (join (sold) (join [ sold, ] (join (takings) [c taken.]))) for (2.5) seconds
say (join [Till out by ] (join (out by) [c. Closing up.])) for (3) seconds

Ask the class to break it on purpose: add 5c to the takings by hand and watch the report catch it. A report that cannot ever say anything is wrong is not a report.

EXTRA MISSION · L3-04-MX🪙 100 Adcoinsbonus

Round the customer’s way

Build a machine that never short-changes anybody — and that knows exactly what that kindness costs.

The price is floored, so the customer never pays the extra half cent.
The change is ceilinged, so they never get a half cent less back.
A given away variable adds up everything the shop handed over.

WHAT IT SHOULD LOOK LIKE

Extra — a machine that always rounds the customer’s way, and knows exactly what that cost it.

after five sales

Runs here in the page. Nothing to install.

How to use this: Click the green flag and watch five sales. The last bubble says what the generosity cost.

Pay floored, change ceilinged, five times over — and a few cents gone by closing.

Teacher reveal


set [fair pay v] to ([floor v] of (exact))
set [fair change v] to ([ceiling v] of (exact change))
change [given away v] by (((exact) - (fair pay)) + ((fair change) - (exact change)))

⚠️ The total will show something like 5.400000000000001. That is not a bug in the pupil’s code — it is how computers store fractions, and it is worth two minutes of the lesson. The fix is the same trick as rounding money anywhere: ((round ((given away) * (10))) / (10)).

Summary 5 min

A percentage is a multiply and a divide: 10% off is × 90 ÷ 100.
(round ()) goes to the nearest whole number.
([floor v] of ()) always goes down; ([ceiling v] of ()) always goes up.
([abs v] of ()) is how far from zero, with no minus sign.
Which way you round is a decision, not a rule — and somebody pays for it.
One dropdown holds floor, ceiling, abs, sqrt, sinand the rest. Go looking in it before deciding a block does not exist.

Per cent: Out of a hundred. 10% of 45 is 4.5.
Round: Move to the nearest whole number.
Ceiling: The whole number above. Ceiling of 2.1 is 3.
Absolute value: How big a number is, ignoring its sign. Abs of −3 is 3.

Hand in

Share your finished machine and send the link to your teacher. It should take coins, price a snack, hand back real change and close its till at the end of the day.

Next lesson starts a new arc, and a new kind of box: one variable that can hold a whole shelf of prices at once.

Learnt28 min · round, floor, ceiling, abs
Basic24 min · discount, change and a till
Challenge 1–327 min · half price, out by, the report
Extrabonus · round the customer’s way

WHAT IT SHOULD LOOK LIKE

The last lesson of the arc. A discount lands on half a cent, the machine has to choose a whole one — and at closing time the till has to add up.

10% off a 45c muffin

closing time

panels run left to right

Review — where we got to 5 min

([floor v] of ()) and (() mod ()) break change into coins.
(pick random (1) to (6)) makes a machine different every morning.
Roll once into a variable, then use the variable everywhere.

Quick-fire

Your machine takes 10% off a 45c muffin. What should the customer pay — and what is awkward about the answer?

Reveal the answer

40.5c, and there is no half-cent coin. Today is about what a machine does when the maths lands between two coins.

Today’s Topic 3 min

A percentage off, and the number it leaves behind
(round ()) — to the nearest whole number
([floor v] of ()) and ([ceiling v] of ()) — always down, always up
([abs v] of ()) — how far out, without the minus sign

Learning outcome

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

Work out a percentage of a price.
Choose between round, floor and ceiling, and say why.
Use abs to measure a difference in either direction.

Learnt — tidying a number up 28 min

1 · Ten per cent off

Per cent means out of a hundred. Taking 10% off means the customer pays 90 out of every 100 — so multiply by 90 and divide by 100:


set [exact v] to (((price) * (90)) / (100))

Two operators, nested — exactly the shape you built in Lesson 3-1.

For a 45c muffin that is 40.5. Correct, and impossible: no machine can take half a cent.

WHAT IT SHOULD LOOK LIKE

Ten per cent off means paying ninety per cent. Ninety per cent of 45 is 40.5 — a price no machine can charge.

the exact answer

the price it can charge

panels run left to right

2 · Round goes to the nearest


set [to pay v] to (round (exact))

40.5 rounds to 41. 40.2 would round to 40. Round picks whichever whole number is closer.

Runs here in the page. Nothing to install.

How to use this: Click the green flag and read the three boxes as it talks through the sum.

45c, 10% off, 40.5c exactly — and 41c to pay. Watch the exact box and the to-pay box disagree.

3 · Floor, ceiling and round, side by side

You met floor last lesson. It has two neighbours in the same dropdown, and the three of them do different jobs:

Block	What it does	40.5 becomes
`(round ())`	Nearest whole number	41
`([floor v] of ())`	Always down — the customer wins	40
`([ceiling v] of ())`	Always up — the shop wins	41

WHAT IT SHOULD LOOK LIKE

The same number, three ways. Round goes to the nearest; floor always goes down; ceiling always goes up.

55.5 through all three

Runs here in the page. Nothing to install.

How to use this: Click the green flag and watch five random numbers go through all three blocks. Read the four boxes together.

Five decimals, four boxes. Round and ceiling agree above .5, round and floor agree below it.

4 · The rest of the dropdown

Open that dropdown again and look down the list. Floor, ceiling and abs are three of about a dozen, and the others are there whenever you need them:


([sqrt v] of (81))

9 — the square root. The number that times itself makes 81.


([sin v] of (90))

1 — for angles. You will want this when a sprite has to move along a curve.

Try it now. Drag the block out, choose sqrt, type 81 and click it. Then 100, then 2. The last one gives 1.4142135623730951 — which is a good moment to remember (round ()).

5 · The till, and abs

At the end of the day a shop counts the money in the till and compares it with what the sums say should be there. The difference matters; which way it went does not, not at first:


set [out by v] to ((takings) - (expected))

243 − 240 = 3. But 237 − 240 = −3.


set [out by v] to ([abs v] of ((takings) - (expected)))

Both come out as 3. Abs throws the minus sign away.

Abs is short for absolute value: how big a number is, ignoring whether it is above or below zero.

WHAT IT SHOULD LOOK LIKE

The till is out by 3c whether there is too much in it or too little. `abs` throws the minus sign away, so one number answers “how wrong?”.

3c too much

3c too little

panels run left to right

Runs here in the page. Nothing to install.

How to use this: Click the green flag and watch three tills checked in turn: too much, too little, and exactly right.

243 and 237 are both “out by 3”. 240 balances, and the box reads 0.

Basic — discount, change and a till 24 min

Open your machine. Three things to add, and then it is finished.

Step 1 — today’s discount

Make two variables: exact and to pay.
After the price is rolled, add set [exact v] to (((price) * (90)) / (100)).
Then set [to pay v] to (round (exact)).
Show both boxes and press the flag a few times.

Step 2 — charge the discounted price

Everywhere your machine used price, use to pay instead.
Check the change ladder still adds up.

Step 3 — the till

Make a variable called takings and set it to 0 under the green flag.
After every sale, add change [takings v] by (to pay).
Show the box, and buy three things. Check the total by hand.

Step 4 — tell the customer

Say the discounted price before they choose.
Say the change after they buy.
Say the till total last.


when flag clicked
set [takings v] to (0)
set [price v] to (45)
set [exact v] to (((price) * (90)) / (100))
set [to pay v] to (round (exact))
say (join [10% off today: ] (join (to pay) [c. Press A.])) for (3) seconds

when [a v] key pressed
set [change v] to ((money) - (to pay))
change [takings v] by (to pay)
glide (0.6) secs to x: (-60) y: (-128)
say (join [Change ] (join (change) [c.])) for (2) seconds
say (join [Till: ] (join (takings) [c.])) for (3) seconds

The finished machine, with the coin questions from Lesson 3-1 above it.

Runs here in the page. Nothing to install.

How to use this: Click the green flag, then click the stage once. Type 3, then 2, then press A.

45c less 10% is 41c to pay, 119c change, and 41c in the till. The whole arc in one run.

The to-pay box shows something like 40.50000000000001.

You have rounded the wrong thing, or not rounded at all. The round goes around the whole sum, not around the price.

The till total is bigger than everything I have sold.

set [takings v] to (0) is missing under the flag, so the total carries over from the last run.

The change is wrong by one cent.

The change is being worked out from price and the money is being taken from to pay, or the other way round. Pick one and use it in both places.

The discount is applied twice.

The set [to pay v] to () is inside the key script as well as under the flag, so it runs again on every sale — 90% of 90% is 81%.

CHALLENGE 1 · L3-04-M1🪙 30 Adcoins8 min

Half price day

Change the offer from 10% off to half price, and see how often it lands badly.

The price is rolled, then halved.
The exact half and the rounded price are both shown.
Run it five times and count how many needed rounding.

WHAT IT SHOULD LOOK LIKE

Challenge 1 — half price. Half of an odd number of cents always lands on a half.

35c halved

Runs here in the page. Nothing to install.

How to use this: Click the green flag and watch five prices get halved. Read the exact box each time.

35c halves to 17.5. 50c halves to 25 exactly. About half of them need rounding.

Done when: you can say which prices halve cleanly and which do not, and your machine charges a whole number of cents either way.

Teacher note

The pattern is worth drawing out: a price that is a multiple of 10 halves cleanly; one that is a multiple of 5 but not 10 does not. That is ((price) mod (10)) from last lesson, being useful again.

CHALLENGE 2 · L3-04-M2🪙 50 Adcoins9 min

The worst day

Six days of takings, and the machine finds the day it was furthest out.

Each day the till is a little above or a little below what was expected.
A worst variable keeps the biggest gap so far.
It does not matter whether the till was over or under.

WHAT IT SHOULD LOOK LIKE

Challenge 2 — six days of takings, and the worst one found without ever knowing which side it fell.

the worst day

Runs here in the page. Nothing to install.

How to use this: Click the green flag and watch six days go past. Press it again for a different worst day.

Six tills against an expected 200c, and the biggest gap kept — whichever side it fell.

Done when: a day that is 9c under is reported as badly as a day that is 9c over, and the worst box holds the biggest of the six.

Teacher reveal — keeping the biggest so far


set [out by v] to ([abs v] of ((takings) - (expected)))
if <(out by) > (worst)> then
  set [worst v] to (out by)
end

CHALLENGE 3 · L3-04-M3🪙 70 Adcoins10 min

The end-of-day report

Close the machine down properly. One report, everything in it.

How many snacks were sold.
How much is in the till.
Whether the till balances, and by how much if not.

WHAT IT SHOULD LOOK LIKE

Challenge 3 — the end-of-day report. Everything the arc built, said once.

closing up

Runs here in the page. Nothing to install.

How to use this: Click the green flag and watch five sales, then the report at the end.

5 sold, 205c taken, till out by 0c. A day that adds up.

Done when: the report names all three numbers, and the “out by” is 0 on a day where nothing went wrong.

Teacher reveal


set [expected v] to ((sold) * (to pay))
set [out by v] to ([abs v] of ((takings) - (expected)))
say (join (sold) (join [ sold, ] (join (takings) [c taken.]))) for (2.5) seconds
say (join [Till out by ] (join (out by) [c. Closing up.])) for (3) seconds

Ask the class to break it on purpose: add 5c to the takings by hand and watch the report catch it. A report that cannot ever say anything is wrong is not a report.

EXTRA MISSION · L3-04-MX🪙 100 Adcoinsbonus

Round the customer’s way

Build a machine that never short-changes anybody — and that knows exactly what that kindness costs.

The price is floored, so the customer never pays the extra half cent.
The change is ceilinged, so they never get a half cent less back.
A given away variable adds up everything the shop handed over.

WHAT IT SHOULD LOOK LIKE

Extra — a machine that always rounds the customer’s way, and knows exactly what that cost it.

after five sales

Runs here in the page. Nothing to install.

How to use this: Click the green flag and watch five sales. The last bubble says what the generosity cost.

Pay floored, change ceilinged, five times over — and a few cents gone by closing.

Teacher reveal


set [fair pay v] to ([floor v] of (exact))
set [fair change v] to ([ceiling v] of (exact change))
change [given away v] by (((exact) - (fair pay)) + ((fair change) - (exact change)))

Summary 5 min

A percentage is a multiply and a divide: 10% off is × 90 ÷ 100.
(round ()) goes to the nearest whole number.
([floor v] of ()) always goes down; ([ceiling v] of ()) always goes up.
([abs v] of ()) is how far from zero, with no minus sign.
Which way you round is a decision, not a rule — and somebody pays for it.
One dropdown holds floor, ceiling, abs, sqrt, sinand the rest. Go looking in it before deciding a block does not exist.

Per cent: Out of a hundred. 10% of 45 is 4.5.
Round: Move to the nearest whole number.
Ceiling: The whole number above. Ceiling of 2.1 is 3.
Absolute value: How big a number is, ignoring its sign. Abs of −3 is 3.

Hand in

Share your finished machine and send the link to your teacher. It should take coins, price a snack, hand back real change and close its till at the end of the day.

Next lesson starts a new arc, and a new kind of box: one variable that can hold a whole shelf of prices at once.