Lesson 5 Another Addition Algorithm

    • Let’s learn another algorithm to add.

Warm-up Notice and Wonder: Another Curious Table

What do you notice? What do you wonder?

Activity 1 A New Addition Algorithm

Here are two algorithms for adding .

Han’s algorithm

Addition. Three-hundred sixty-seven plus two-hundred thirty-one is eight (step one), plus ninety (step two), plus five-hundred (step 3) equals five-hundred ninety-eight (step 4).

Elena’s algorithm

Addition. Three-hundred sixty-seven plus two-hundred thirty-one. Step one equals 8.
Addition. Step two. Three-hundred sixty-seven plus two-hundred thirty one equals ninety-eight.
Addition. Step three. Three-hundred sixty-seven plus two-hundred thirty-one equals five-hundred ninety-eight.

Discuss with your partner:

  1. How is Elena’s algorithm different from Han’s algorithm?

  2. Why do both algorithms work?

Activity 2 Compose New Units

Here are two algorithms for adding .

Han’s algorithm

Addition. Steps 1-4. Three-hundred sixty-five plus one-hundred eighty-two equals seven plus one-hundred forty plus four-hundred equals five-hundred forty-seven.

Elena’s algorithm

Addition. Three-hundred sixty-five plus one-hundred eighty-two equals 7 (step 1).
Addition. Three-hundred sixty-five plus one-hundred eighty-two. Step 2 equals 47.
Addition. Step 3. Three-hundred sixty-five plus one-hundred eighty-two equals five-hundred forty-seven.

Problem 1

How do the algorithms show the 14 tens differently?

Problem 2

Try Elena’s algorithm to find the value of each sum.

Practice Problem

Problem 1

Here is Elena’s algorithm for finding .

Addition. Step one. Two-hundred seventy-three plus four-hundred eighty-one, equals four.
Addition. Step 2. Two-hundred seventy-three, plus four-hundred eighty-one, equals 54.
Addition. Step 3. Two-hundred seventy-three plus four-hundred eighty-one equals seven-hundred fifty-four.
  1. Where does the 100 that Elena wrote in step 2 come from?

  2. Use Elena’s method to find .