Ray's New Higher Arithmetic · Arts. 51–52 · Unit 3: Addition

7. Addition: definition and principles

Goal: Your student states what addition is and why only like numbers can be added, and adds a column of numbers carrying correctly.

⏱ About 30 minutes · 6 steps

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You'll need

  • The book
  • A slate, small whiteboard or scrap paper
  • A notebook and pencil

What's in the book

Addition defined, the five principles of addition, and the worked example 639 + 82 + 543, explained order by order.

The lesson, step by step

  1. Warm-up

    Mental: 47 + 38, 125 + 75, 999 + 1.

  2. The idea

    Read:

    Addition is the process of uniting two or more like numbers into one equivalent number.

    Then the principles:

    Only like numbers can be added.

    The sum is the same in whatever succession the numbers are added.

    Ask: Can you add 2 apples and 3 peaches into one number? (Only by calling them both "fruit": that makes them like numbers.)

  3. Work the book's example

    Read the example aloud: What is the sum of 639, 82, and 543? Set the numbers in columns. Add the units: 14 units = 1 ten and 4 units. Write 4, carry 1. Continue with tens and hundreds. The sum is 1264.

  4. Why we carry

    Ask your student to explain carrying using the principle that units of the same order, and only such, can be added directly.

  5. Guided practice

    Add together: 875 + 46 + 3092 + 18. (4031.)

  6. Wrap-up

    Ask: Which principle lets us check a sum by adding the column the other way? (The sum is the same in whatever succession the numbers are added.)

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