Color by number — learning math through play

The picture is divided into areas, and each area has a number. A key under the picture says which color goes with each number. The child reads the number, finds the right crayon and fills the area. When they finish, a whole picture appears out of what looked like random patches.

It's a mix of puzzle and coloring. Children love the moment they discover what the picture shows, and along the way they practise skills that are useful at school.

Color by number practises several things at once:

• recognising numbers, because the child sees the same number many times in different places;
• matching a symbol to a color, the basis of reading keys, maps and charts;
• attention, because every area has to be checked before it's colored;
• planning, when the child decides which number to start with;
• patience and finishing a task.

The simplest versions, with numbers 1–3 and big areas, work for children who already recognise those numbers, usually around age 4–5. Pictures with numbers up to 10 and medium areas suit ages 5–7. Detailed pictures with many colors and small areas are enjoyed from about age 8, and by adults too.

Before your child starts alone, go through the key together and say each color out loud.

A picture's difficulty depends on three things: the number of colors, the size of the areas and how similar the colors are. An order that works well:

• 3–4 colors, big areas, clearly different shades;
• 5–7 colors, medium areas;
• 8–10 colors, small areas, a few similar shades, for example two greens;
• versions with sums: the area shows "2 + 1", and the child works out the answer first.

If your child gets lost in small areas, go back to the previous level.

Lay the crayons next to the key in the same order and label them with small sticky notes. Color number by number: first all the areas with 1, then with 2. Cross off finished numbers in the key so progress is visible.

With small areas, your child can first put a dot of the right color in the area and fill it afterwards. That reduces mistakes.

Color by number is a good chance for simple maths without a workbook. Ask: "are there more areas with 3 or with 5?", "how many areas are left?", "which color covers the most space?". Your child counts, compares and estimates, and the questions come from what's right in front of them.

The same idea works with letters instead of numbers, which helps when learning the alphabet, or with shapes for the youngest, who don't know numbers yet. For older children the areas can hold sums, and the color depends on the answer.

On PrintyKids you'll find ready-made color-by-number pages, and in the "Special needs" section, color by code on a grid, which also trains attention.

Paint-by-number kits became popular in the United States in the 1950s, and the idea is credited to the artist Dan Robbins. Today the same principle appears in workbooks, apps and coloring books for adults.