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How to Explain Subtraction and Borrowing

When younger students first learn to subtract larger numbers, they may experience some difficulty in understanding how borrowing works, as it requires abstract thinking. Since learning can be easier if more than one sense is engaged, students may be able to learn the concept better with a tactile or visual aid. A good tool for this are Unifix Cubes or some other counting device that can be combined into groups of 10 and broken down into groups of one.

Things You'll Need

  • Classroom set of Unifix Cubes
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Instructions

    • 1

      Prepare the cubes for the students. Stack cubes into groups of 10 that will be used to represent the "tens" column in their calculations. Give each student at least two group of tens stacks and nine individual pieces to represent to represent the "ones" column.

    • 2

      Explain how the cubes work. Hold up single cubes and tell them that they can be used to represent the numbers 1-9. Hold up a stack of 10 and tell them that it can be used to represent the "tens" column. Draw some examples on the board, or hold up different sets of your own tiles. Ask what numbers are represented to ensure that the students understand how the tiles work.

    • 3

      Pass the cubes out to the class. Turn learning into a game by writing a number on the board and challenging students to see who can represent the number fastest with their tiles. Ask them to represent numbers like multiples of 10 followed by the next lowest number, like 10 followed by 9, 20 followed by 19, etc. This will prepare them for borrowing.

    • 4

      Teach students to subtract using the cubes once they can confidently manipulate them to represent numbers. Keep playing the same game as before, but instead of representing numbers, ask them to represent a number, then subtract from that number. Start simply by only subtracting single digit numbers, or subtracting multiples of 10.

    • 5

      Pause the game and illustrate more complex subtraction with your own cubes. Illustrate a simple equation that does not require borrowing at first. If, for example, the equation is 27 minus 16, show them how single cubes are subtracted from the group of singles and how tens tiles are subtracted from the sticks of ten. Play a few more rounds of the game using equations such as this to ensure that the students understand.

    • 6

      Challenge the students to represent an equation that involves borrowing, such as 26 minus 17, and see if any of the students can figure it out on their own.

    • 7

      Pause the game and illustrate borrowing with your own cubes or by drawing the cubes on the board. For the sample equation mentioned above, break one of the tens sticks down into 10 ones cubes, and "borrow" them over into the group of ones cubes, allowing the tiles to be subtracted. Have the students repeat the sample equation with their cubes.

    • 8

      Continue with the game using borrowing equations until all of the students are able to represent an equation that requires borrowing with their own cubes.

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