Draw it · Martinとコード

Marks, a number line and strips: three quick pictures that turn a tangled problem into a clear one.

A picture counts with you

Some problems tangle in your head like earphones in a pocket. People get on, get off, someone has how many more… words trip over each other.

For tangled words there is one reliable trick: draw it. Eyes are the strongest tool you have for maths — what you see, you do not have to remember. A picture holds the situation for you, just as paper holds numbers.

And we knock down one fear right away: you do not have to be able to draw. At all. A maths picture is marks, circles, rectangles and arrows. Ugly, fast, useful. A pretty picture in five minutes is worse than a scribble in thirty seconds, because drawing must not eat counting time.

Today you will learn three pictures that solve most tangled problems: marks, a number line and strips.

Sofie reads a problem about a bus: people get off, get on, at the third stop they ask how many are riding. She tries it in her head and the numbers run away like chicks.

Jonáš hands her a pencil: “Draw a bus.” Sofie draws a rectangle on wheels, writes 13 in it. At the stop an arrow out with the number 5, an arrow in with 7. Suddenly she sees it: 13 − 5 = 8, then 8 + 7 = 15. Done.

“But it is a really ugly bus,” she laughs. “So?” Jonáš shrugs. “It counted it.”

💡

Draw fast and ugly: rectangles, marks, arrows. Thirty seconds of drawing, then count. If you catch yourself colouring the bus windows, the picture has long stopped serving the counting — and the pencil ran away from work.

Three pictures in your pocket

Marks and dots — for small counts. Each thing one mark, the fifth slanted across four, so you can count easily in fives. Great for adding a score, votes, days. You know it from the practice table in lesson five.

Number line — for adding and subtracting as jumping. Draw a horizontal line, mark the number where you stand, and jump: right is adding, left is subtracting. Big jumps in tens, small ones in ones. The line is great because you see the method through ten: first jump to a round number, then the rest.

Strips — for comparing. Draw two amounts as two bars under each other, the longer bar is the bigger number. The difference — that how many more from lesson nine — is visible as the bit that sticks out. In problems like “Ema has 8 fewer” strips show at once whether to add or subtract.

How to choose? You count pieces — marks. You add and subtract — the line. You compare — strips. And when you do not know, just start drawing anything: even a wrong picture usually tells you what the right one should have been.

Example 1: a bus with arrows

“13 people ride on the bus. At the stop 5 get off and 7 get on. How many people ride on?”

Picture: a rectangle with the number 13. An arrow out, 5 by it. An arrow in, 7 by it.

Now you count by the arrows, one after another. Out: 13 − 5 = 8. Method: 13 − 3 = 10, then 10 − 2 = 8. In: 8 + 7 = 15. Method: 8 + 2 = 10, then 10 + 5 = 15.

Answer: 15 people ride on. The picture watched the order of events — exactly what tangled in the head.

Example 2: jumps on a number line

Count 32 + 29 on the line.

Draw a line, mark 32. Jump a big jump +20: you land on 52. Now +9 is left — first jump +8 to the round number 60, then +1: you land on 61.

Written: 32 + 20 = 52, 52 + 8 = 60, 60 + 1 = 61.

On the line you see the whole strategy: tens first, then jump to round, then the rest. When you know the method, the line moves into your head — but when you tangle, you can always pull it out on paper again.

Example 3: strips for comparing

“Jonáš has 15 cards, Filip 9. How many more does Jonáš have?”

Picture: two bars under each other. Jonáš’s longer, 15 by it. Filip’s shorter, 9 by it. Line them up on the left — and the difference is the bit Jonáš’s bar sticks out by.

The question how many more turned in the picture into how long is the sticking-out bit. That is subtraction: 15 − 9. Method: 15 − 5 = 10, then 10 − 4 = 6.

Answer: Jonáš has 6 more cards. The word “more” in the question, and still you subtracted — strips defuse this trap from lesson nine at first sight.

⚠️

A picture is a tool, not art. When drawing takes longer than a minute, simplify it: people are marks, a bus is a rectangle, a dog is a circle with a name. The counting is waiting.

Play it

Before you go to the sheet, feel it with your eyes. This is not a test — it is a game. Tap until you see it.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. スタート with ten. When it goes well, add more.

Draw it on the line. Jumps right and left.

Practise the questions

On paper: three pictures, three problems

For each problem pick one of the three pictures, draw it in half a minute and only then count.

“Tereza has 26 beads, she gives 8 to Ema and gets 5 new ones. How many does she have now?” Pick a picture, draw, count in steps.
Count 45 + 38 by jumping on a number line. Write each jump.
“Adam read 32 pages, Sofie 47. How many more pages did Sofie read?” Strips, then the calculation.
Go back to one word problem from lesson nine and solve it again — this time with a picture. Write in one sentence what the picture made easier.

Now you 💪

I know three pictures: marks for pieces, a line for jumping, strips for comparing.
I draw fast and ugly — in half a minute and I count.
I can say which picture fits which problem.

✅

Done when: You have three problems solved with three different pictures and one old problem solved in a new way.

What to take from this lesson

What you see, you do not have to remember. A picture holds the situation for you.
Marks for counting pieces, the fifth slanted across four.
Number line: right plus, left minus, big jumps in tens.
Strips show the difference as the bit that sticks out.
An ugly fast picture beats a pretty slow one.