At 3 in the afternoon, late in September, Mrs Tallow led her class out to the field. She carried a metre stick under one arm and a long tape measure in her hand. Behind her came the whole class with notebooks, pencils, and a great many questions. The low sun had turned the light on the grass a warm, honey-gold colour. Every shadow lay long and sharp, as if someone had drawn it with a ruler. In the far corner stood the big oak, grey-green and wide and very calm. Mrs Tallow told the class that they were going to find the height of that oak.⏎
Then she said the thing that made everybody groan: she would not be giving them the answer. Rafi was 10, and he liked to know how a trick worked before he believed in it. Junie was 11, and she stood beside him with her hands deep in her coat sleeves. She had already guessed that the answer was hiding somewhere in the shadows. Rafi folded his arms and said, "You can't measure a whole tree with a little stick!" Junie said that she was not sure yet, but that she wanted to see the sums first.⏎
Mrs Tallow pushed the metre stick into the soft ground until it stood up straight. The stick was 1 m tall, and its shadow stretched away across the grass, thin and dark. Mrs Tallow handed the tape to Junie and asked her to read the length out loud. Junie knelt down, pulled the tape flat, and called out that the shadow was 1.4 m. Rafi asked, "So what's a little stick got to do with a tree that big?"⏎
Then Mrs Tallow set out three rules, and she held up a finger for each one. There would be no guessing, no peeping at her notebook, and no climbing on anything. Mrs Tallow said, "The tree will tell you its own height, if you ask it politely." Junie knelt on the path and drew two triangles in chalk, one big and one small. The small one held the stick and its shadow; the big one held the oak and its shadow. Both triangles leaned the same way, because the same low sun had made them both.⏎
Rafi looked at Junie's chalk and said that a nice drawing is not a real answer. Measuring the shadow of the oak took the whole class and a fair bit of shouting. The tape was only 30 m long, so they had to lay it flat and keep it straight. Two pupils held one end against the trunk, where the sun-warmed bark met the grass. Rafi and three others walked the tape out step-by-step towards the shadow's far tip. Mrs Tallow called across the field, "Keep the tape flat, or you'll make the oak grow!"⏎
The tip would not hold still, because a shadow has a soft edge that fades away. In the end the class agreed on 23 m, and everybody wrote that number down. Rafi said that the stick was tiny and the oak was huge, so the two could not match. Junie turned round and asked, "Is the sun shining on your stick from some other sun?" A few pupils laughed, and Rafi went pink and then began to laugh as well. Mrs Tallow said that Junie had just given away about half of the secret.⏎
The light comes in at one angle, and it meets everything on the field at that angle. So a tall thing and a short thing must lay their shadows down in the same way. Junie put it plainly: every shadow out here is 1.4 times as long as the thing itself. Rafi's pencil came out, and he began to work the sum out on the back page. He divided 23 by 1.4, crossed it all out, and then checked the whole sum again. The second time he got the same answer, and he stared at it for a long moment.⏎
Junie did the same sum in her head and landed in very nearly the same place. So the oak stands about 16.4 m tall, which is higher than the school's roof. Rafi asked, "Doesn't the trick fall apart when the ground slopes down a bit?" Mrs Tallow said that a slope would bend the answer, but this field was flat. Rafi said that a tidy sum is not proof, and that he wanted a proper test. Mrs Tallow looked delighted; that was exactly what she had been hoping to hear.⏎
At the edge of the field grew a young rowan, short enough to measure by hand. The rowan's shadow ran 5.6 m across the path, so the rule promised 4 m of tree. Two pupils held the tape up the rowan itself, from the soil to the tip-top twig. It came to 4 m, and Junie shouted, "It matched, right down to the last little bit!"⏎
Next came a small pear tree by the gate, with a shadow of 3.5 m. The rule gave 2.5 m, and the tape on the trunk gave 2.5 m as well. Rafi said, "Fine, it works, and I'm not even slightly sorry that I argued." Junie asked, "Would it still work at noon, when there's hardly any shadow at all?" Mrs Tallow said that the rule would hold, but the numbers would be much smaller. A short shadow is harder to read, so a small slip-up grows into a big one. That is why the day's last hour is kind to anyone with a tape measure.⏎
By 3:40 the light had shifted, and every shadow on the field had grown longer. Mrs Tallow asked them, "What's a longer shadow going to do to our tidy rule?" Junie measured the stick again and found a shadow of 1.7 m this time. The oak's shadow had crept out to 28 m, past the left-hand corner of the shed. Rafi divided once more and got about 16.5 m, which is near enough the same tree. He said that the tree had not grown; the sun had simply slid along the sky. Mrs Tallow laughed and said, "You've all been doing maths for half an hour!" Even then Mrs Tallow would not say whether the class had it right or not.⏎
She said that the rowan and the pear had already given them their answer. (She did write the height in her notebook, and she kept that notebook shut.) On the walk back in, Rafi kept his eyes on his own long-legged shadow. He worked out his own height from it, and he was only a little bit wrong. Junie held the gate open and asked him to do the shed and the flagpole next.