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Math · Number Sense & Operations · Math · Addition & Subtraction

Math topic explanations on Within 10.

Study notes

  1. Composing and Decomposing Numbers

    Every number from 0 to 10 can be split into smaller parts or combined from two smaller groups. Understanding these number pairs helps build solid mental math skills.

    For example, consider the number 7:

    • 4 and 3 make 7
    • 5 and 2 make 7
    • 6 and 1 make 7
    • 7 and 0 make 7

    These pairs are known as number bonds. Recognizing number bonds, especially pairs that make 10 (such as 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5), allows you to add and subtract quickly and accurately without counting one by one.

    Combining Groups and Counting On

    Addition represents combining two or more quantities to find the total, or sum. The symbol for addition is + (plus), and the result is indicated with = (equals).

    To solve an addition problem such as 4 + 3:

    1. Start with the first number: Keep 4 in mind.
    2. Count on: Count forward 3 more steps: 5, 6, 7.
    3. State the sum: 4 + 3 = 7.

    Key Property: The order of numbers does not change the sum. For example, 3 + 4 = 7 and 4 + 3 = 7. Starting with the greater number usually makes counting on faster.

    Taking Away and Finding the Difference

    Subtraction means taking a quantity away from a total or finding how much greater one quantity is than another. The symbol for subtraction is - (minus), and the result is called the difference.

    To solve a subtraction problem such as 8 - 3:

    1. Identify the whole: Start at 8.
    2. Count back: Move backward 3 steps: 7, 6, 5.
    3. State the difference: 8 - 3 = 5.

    Subtraction can also answer the question: "How many are left?" If you have 8 counters and remove 3, exactly 5 counters remain.

    Connecting Addition and Subtraction

    Addition and subtraction are inverse operations. That means subtraction reverses the effect of addition. A set of three numbers can form four related facts called a fact family.

    Consider the parts 2 and 6, which make the whole 8:

    • 2 + 6 = 8
    • 6 + 2 = 8
    • 8 - 2 = 6
    • 8 - 6 = 2

    If you know that 2 + 6 = 8, you immediately know that 8 - 6 = 2 without needing to recalculate. Using these relationships makes calculating within 10 efficient and dependable.