Hobbies And Interests
Place Values
Introduce the students to the concept of place values at the beginning of the year, as it will apply to the activities throughout the year. Write the number 5 and explain that since this also equals 1 + 1 + 1 + 1 + 1, the place value of 5 is "ones." Write the number 15 and note that "5" is also a ones. But since 15 = 10 + 5, the 1 is really equal to 10 and is thus a "tens." Write the number 315 and note that the 5 is still a "ones" and the 1 a "tens". But because 315 = 300 + 10 + 5, the 3 is really 300 and is thus a "hundreds."
Present place values in subtraction using a simple problem with single digit numbers: 3 - 2. Because they are ones, this also equals 1 + 1 + 1 - 1 + 1, with the final answer being 1.
Two-Digit Subtraction
Ease the students into two-digit subtraction using the subtraction of two multiples of ten, such as 40 - 10. Explain that when the ones are both zeros, they can be ignored during the subtraction. Subtract the tens, 4 - 1 = 3 and add the 0 back on for an answer of 30.
Move on to more complicated two digit numbers, such as 45 - 13. Write the numbers vertically, so that the 45 is above the 13. Subtract the ones: 5 - 3 = 2 and place that answer on the blank line below the ones column. Subtract the tens: 4 - 1 = 3 and write the answer on the blank line, for a final answer of 32.
Three-Digit Subtraction
Write the problem 380 - 225 on the board so that the numbers are lined up vertically. Instruct students to subtract the ones column first: 0 - 5. Remind the students of the process of regrouping, which they should have learned in the second grade when using two digit numbers. To make it possible to subtract the ones, a tens needs to be "borrowed" from the tens column, making the subtraction: 10 - 5 = 5.
Move on to the tens column and note that the 8 needs to lose one value since it loaned one next door: 7 - 2 = 5. Move to the hundreds column: 3 - 2 = 1.
Four-Digit Subtraction
Towards the end of the school year, introduce the students to the concept of a thousands place and emphasize the importance of being careful when working with such large numbers. Write the problem 3521 - 1257 on the board vertically. Subtract the ones: 1 - 7, so it needs to be regrouped as 11 - 7 = 4.
Move to the tens column, removing one from the 2 since it was loaned: 1 - 5, which requires regrouping from the hundreds to become 11 - 5 = 6. Move the the hundreds column, removing one from the 5 since it was loaned: 4 - 2 = 2. Finish with the thousands column: 3 - 1 = 2. Note that because the thousands didn't need to lend any to the hundreds, the subtraction could be performed as usual.