Explanation:
To teach long division of 357 ÷ 19 for relational understanding, we will follow these steps:
Step 1: Begin by explaining the concept of division and its relationship to multiplication. Emphasize that division is the process of splitting a quantity into equal parts.
Step 2: Write the dividend (357) inside the long division symbol and the divisor (19) outside the symbol.
Step 3: Start with the leftmost digit of the dividend (3) and divide it by the divisor (19). Since 3 is less than 19, we cannot divide it evenly. Write the quotient (0) above the line and bring down the next digit (5) next to it.
Step 4: Now, divide 35 (the new number) by 19. The quotient is 1, as 19 can be subtracted from 35 once. Write the quotient (1) above the line and subtract 19 from 35, which gives us a remainder of 16. Bring down the next digit (7) next to the remainder.
Step 5: Divide 167 (the new number) by 19. The quotient is 8, as 19 can be subtracted from 167 eight times. Write the quotient (8) above the line and subtract 152 (19 multiplied by 8) from 167, which gives us a remainder of 15.
Step 6: Since there are no more digits to bring down, we have our final remainder of 15. Write the remainder (15) above the line.
Step 7: The quotient is the combination of all the quotients we obtained during the division process, which in this case is 018. Therefore, 357 ÷ 19 = 18 with a remainder of 15.
By following these steps, students will develop a relational understanding of long division and be able to apply the process to solve similar problems.