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Writing each intermediate result and count the moment you have it, so the desk only works and never has to hold.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will write multi-step mental work as labeled working lines, keep a count as a tally, and check the last line against an estimate.
The desk holds about four pieces, and a piece fades once something else takes the space. Chunking, from the last lesson, makes each piece bigger.
Chunking has a limit, though: it only works on material you already know. A running total of 47.85 is not a known unit. Nor is I have folded 23 so far. Pieces like these are produced by the task itself, one after another, and each new one pushes on the last. This lesson is about where to put them.
| Term | What it means |
|---|---|
| Offloading | Moving a piece of a task out of your head onto paper, a screen or an object. |
| Intermediate result | A number or answer produced partway through a task and needed for a later step. |
| Running total | The sum so far, updated as each new amount is added. |
| Tally | A mark for each thing counted, often grouped in fives. |
| Working line | One written line per step, showing what was done and its result. |
Multi-step mental work makes pieces as it goes. To split a bill you find the subtotal, then the tip, then the total, then each share. Each result is needed for the next step, and each one sits on the desk while you work out the next.
That is where mistakes come from. While you are working out the tip, the subtotal is waiting. While you divide, the total is waiting. The desk is doing two jobs at once: working and holding. Something gives.
The fix is simple: write each result the moment you have it, one line per step, and read the line when the next step needs it. Now the desk only works. It never holds a result for longer than it takes to write it down.
Counting is the same. A count is a result that changes every few seconds. Held in the head, it is lost the moment someone speaks to you. A tally on paper survives any interruption.
Another way: steps
Another way: story
Keisha is working out how much paint she needs for three walls. In her head she gets 12 by 8, then 10 by 8, then loses the first answer while doing the second. On the back of an envelope she writes wall 1: 96, wall 2: 80, wall 3: 96, total: 272 square feet. Same arithmetic; the envelope did the holding.
In 1978 Graham Hitch asked people to add numbers like 325 + 46 in their heads, heard aloud. Everyone broke the problem into small steps: units, then tens, then hundreds. The errors came from the waiting. A partial result that had to be held while other steps were done was often forgotten, and the more steps came between making it and using it, the likelier it was to be lost.
Evan Risko and Sam Gilbert (2016) reviewed studies of cognitive offloading: people using the world to lighten a mental task, from tilting their head to read a rotated page to setting reminders. People offload more when a task is harder and when they doubt their memory, and offloading usually improves how well the task gets done.
Benjamin Storm and Sean Stone (2015) found a further benefit. People who saved one file of words before studying a second file remembered more of the second. Saving let them stop holding the first. The effect vanished when they did not trust the save.
Offloading has a cost, and it is worth knowing. You tend to remember less of what you have handed over. A running total on a receipt is not something you wanted to keep anyway, so the cost is zero. But if you will need a fact later without the note — a new PIN, a colleague's name — then write it down and practice recalling it on its own. Offloading is for pieces you are using now.
A written step helps only if it is useful when you come back to it:
To check your work, read the lines from top to bottom. Each line should follow from the one above it. Then compare the last line with a rough estimate: if a four-way split of about 80 dollars comes out at 45 each, a line went wrong.
A 24-ounce jar of peanut butter costs 4.29 dollars, and a 40-ounce jar costs 6.99 dollars. Which is cheaper per ounce? Held in the head, this is two divisions and a comparison, with the first answer waiting while you do the second.
Written out: small: 4.29 ÷ 24 = about 17.9 cents an ounce. Large: 6.99 ÷ 40 = about 17.5 cents an ounce. Large is cheaper, by about 0.4 cents an ounce. Many US stores print this unit price on the shelf label for you, which is the store doing the offloading. When the label uses different units for two sizes, the phone calculator and a line in your notes do the same job.
Knitters use row counters, swimmers use lap counters, and people at the gym move a bead or tick a card for each set. Each is a tally outside the head. The count changes too often to chunk, and a single interruption — a question, a text, a stray thought — is enough to lose it. With the tally outside, an interruption costs nothing: you look down and carry on from the number you see.
Writing it down means you are not really doing it. Architects, nurses and accountants write intermediate results because it is accurate, not because they cannot hold numbers. The thinking is still yours; the paper does the holding.
I will just remember this one number. One number is fine, until the next step produces a second one and someone asks you a question. Most mental arithmetic slips happen on a result that was only held for a moment.
A note anywhere will do. A result on a sticky note in another room is not there when the next step needs it.
Write the question at the top.
Bill 84.00 dollars, 18 percent tip, split 4 ways. Each pays?
The whole task is visible before any step starts.
Work out the tip and write it on its own line.
Tip: 84.00 × 0.18 = 15.12
The tip is a result the next step needs.
Read the lines and write the total.
Total: 84.00 + 15.12 = 99.12
Both numbers are read from the page, not recalled.
Divide and write each share.
Each: 99.12 ÷ 4 = 24.78
The last step reads the line above it.
Check against a rough estimate.
About 100 ÷ 4 = 25, and 24.78 is close
An estimate catches a line that went wrong.
Name what must be counted.
Folding 60 programs for a school concert
A count that changes every few seconds cannot be chunked.
Set up the tally where the work is.
Index card beside the stack, headed Folded
The count lives outside the head, next to the task.
Mark every program as it is folded, in fives.
4 groups of five + 3 marks → 23
Groups of five are easy to count at a glance.
Carry on after an interruption from the card.
Asked where the tape is; card still says 23
The interruption took the desk but not the count.
Check the finished count.
12 groups of five = 60
Counting groups is quicker and safer than counting marks.
Write each price on its own line.
Detergent 11.49 · Paper towels 8.99 · Coffee 7.50
Each amount is on the page before any adding starts.
Write the running total after each item.
11.49 → 20.48 → 27.98
Each new total reads the line above it.
Subtract the coupon and write the result.
You are adding up the costs of a road trip in your head: gas, a motel, food. Halfway through, which written note helps most?
Working lines for a road trip's gas cost are half written. The trip is 360 miles, the car does 30 miles a gallon, and gas is 3.50 dollars a gallon. Fill in the later lines.
| Working line | |
|---|---|
| Question | 360 miles, 30 mpg, 3.50 a gallon: cost? |
| Gallons | 360 ÷ 30 = 12 |
| Cost | |
| Estimate check |
Match each task to the outside aid that holds its intermediate pieces.
| A running total on the shopping list | A lap counter at the end of the lane | A small table of price and start date | Saying the numbers over | |
|---|---|---|---|---|
| Keeping a grocery bill under budget | ||||
| Swimming 30 laps | ||||
| Comparing three plumbers' quotes |
Four items go into a cart. Write the running total after each one, in whole dollars.
| Item and price (dollars) | Running total |
|---|---|
| Bread, 8 | |
| Apples, 6 | |
| Chicken, 10 | |
| Rice, 4 |
Two walls are each 10 feet wide and 9 feet high. Write the working lines: the area of one wall, then the total.
One wall: a square feet. Total: b square feet.
A 12-pack of paper towels costs 18 dollars and an 8-pack costs 14 dollars. Write the cost per roll for each, in dollars, then how much cheaper per roll the 12-pack is.
12-pack: a a roll. 8-pack: b a roll. The 12-pack is c cheaper per roll.
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Three friends split a 60-dollar bill with a 20 percent tip. Write the working lines in dollars: the tip, the total, and each share.
| Line | Result (dollars) |
|---|---|
| Tip | |
| Total | |
| Each share |
Next time you split a bill or add up costs, write one labeled line per step and check the last line with an estimate. Next: what to write in the few seconds before an interruption. A trial in this course is practice. What is kept is what you wrote on this device today; it is not a score, it is not a test of your memory, and it is never compared with anyone. If you notice trouble with memory or thinking that is new or changing, tell your own doctor or clinician; this course is general practice, not an assessment or treatment. Stopping takes nothing more than closing the page: your place is already saved, and the lesson opens where you left it.
13. Your turn: a running total with a coupon, step 3
27.98 − 3.00 = 24.98
The last step uses the last written total.