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Write One Together

Three short lessons on helping a child write a maths problem about something they love, without taking the pencil: start from their numbers, ask instead of correcting, and swap problems at the table.

Spark & Whetstone · sparkwhetstone.org/learn/write-one-together · CC BY-NC-SA 4.0. Answers are at the end, so you can try each question first.

Lesson 1. Start from what they love

A child who loves swimming, horses or a video game already lives among numbers: laps and times, hands and furlongs, levels and hit points. A problem about that world starts with their nouns and their numbers, not yours.

So the first move is a question, not a problem. Ask what numbers come up when they do the thing they love, and write down what they say. You are collecting raw material; nothing is being tested yet.

Question. Your child loves horses. Which is the best way to begin writing a problem together?

  1. Ask how many horses there are in the world
  2. Hand them a horse problem you wrote last night for them to solve
  3. Ask what numbers come up when they ride or watch horses

Say it back. In your own words: why start by asking for their numbers rather than offering a problem?

Lesson 2. Hand back the pencil

First drafts of a problem are often missing something: a number, a unit, a clear question. That is the useful part. Spotting what is missing is the same thinking it takes to solve a problem.

Resist rewriting it. Ask instead: what would you need to know to answer this? Is there one answer, or several? Could someone who has never seen a horse follow it? Let them make the change.

Question. Your child writes: "A horse runs 3 laps. How fast is it?" What is the most helpful next move?

  1. Tell them it cannot be solved and show them a correct version
  2. Ask what else you would need to know to answer it
  3. Rewrite it properly for them so it can be solved

Say it back. In your own words: why is a problem with something missing a good place to start?

Lesson 3. Solve it, then swap

A finished problem gets two tests. Can its author solve it? And can someone else solve it from the words alone? The second test is the stricter one, and it is where the arithmetic gets checked for free.

So write one each, about different things you love, and swap. Solve each other’s problems out loud. If one cannot be solved, the author fixes it; nobody is marked.

Question. Which of these problems has exactly enough information to answer?

  1. A pony walks for 3 hours with a rider on its back. How far does it go?
  2. A pony walks fast. How far does it go?
  3. A pony walks 2 km an hour for 3 hours. How far does it go?

Say it back. In your own words: why is swapping problems a good test of whether a problem works?

At the table: Write one, swap one

Players: Two or more, ages 6 and up with a grown-up. You'll need: Paper, pencils, and one thing each of you loves.

  1. Each person names something they love and lists three numbers that come up in it.
  2. Each writes one problem using those numbers and a clear question.
  3. Swap and solve out loud; if a problem is missing something, its author fixes it.
  4. Keep the best ones on a card for the fridge.

Answers

  1. Ask what numbers come up when they ride or watch horses — Starting from the numbers they already know keeps the problem theirs. A ready-made problem turns it back into homework; a world-sized fact has no way in.
  2. Ask what else you would need to know to answer it — Speed needs a distance and a time. Asking what is missing lets the child find both, and keeps the pencil in their hand.
  3. A pony walks 2 km an hour for 3 hours. How far does it go? — With a speed and a time, distance is speed × time: 2 × 3 = 6 km. The rider adds a story but no speed.