How to Teach Decomposed & Composed Numbers for First Grade Math


While struggling to learn math, some young students have difficulty seeing numbers as fluidly as they should -- they don't necessarily understand that numbers can be expressed through combinations of other numbers. Teaching "decomposed numbers" early can be helpful in building up this sense. To decompose a number is simply to turn it into an equation of smaller numbers -- turning "256" into "200 + 50 + 6", for instance. With some physical examples to ease kids into the abstract concept, you can easily teach this habit of thinking about numbers and encourage more efficient and creative mathematical thinking.

Things You'll Need

  • Cards (you can make them with a marker and some construction paper)
  • Show the students a collection of cards: some with one dot on them, and some with 10.

  • Put a few cards on the table so that the dots add up to a reasonably small number -- say 13. Ask the students how many dots there are. Write the number on the board.

  • Ask the students how many dots there are on each card, and write those numbers on the board too, arranged in an equation -- "10 + 1 + 1 + 1 = 13".

  • Tell the students that, as they can see, you can find the total number of dots by adding up the number of dots on each card. Explain that, if you had enough cards, you could express any number you could think of with them.

  • Write a much larger number on the board, like 112. Tell them that this number would take a lot of cards to express, so it'd be best to have a card with a lot more dots on it. Produce a card with 100 dots on it, put it next to a 10-card and two 1-cards, and write the equation on the board.

  • Quiz the students. Write a new number on the board and ask what combination of 100s, 10s, and 1s you'd need to make it. Ask this about a few numbers of different sizes.

  • Hand out a small collection of cards to each student and let them assemble numbers of their own with them. If you want, you can play a kind of bingo -- write a number on the board and ask if anyone can make it with their cards.

  • Assign a few problems in which students have to both break apart single numbers into equations, and work out equations to produce single numbers.


  • Photo Credit cards image by Aleksandr Lobanov from
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