Section 3.3

1. Section 3.3 Algorithms for Addition and Subtraction Mathematics for Elementary School Teachers - 4th Edition O’DAFFER, CHARLES, COONEY, DOSSEY, SCHIELACK

2. Developing Algorithms for Addition: Using Models as a Foundation • Base-ten blocks can be used to find a sum and provide models that help explain the addition algorithms. • Recall that addition can be defined as the number of elements in the union of two disjoint sets. Think of the base-ten blocks representing numbers to be added as the elements in disjoint sets; the union of these sets is found by joining the two sets of blocks, combining and regrouping as necessary.

3. Using the Base-Ten Blocks Model for Addition 278 146 +

4. Using the Base-Ten Blocks Model for Addition 278 + 146 = ?

5. Using the Base-Ten Blocks Model for Addition 278 + 146 = ?

6. Using the Base-Ten Blocks Model for Addition 278 + 146 = ?

7. Using the Base-Ten Blocks Model for Addition 278 + 146 = ?

8. Using the Base-Ten Blocks Model for Addition 278 + 146 = 424 278 + 146 = ?

9. Developing Algorithms for Addition: Using Paper-and-Pencil • The values of each place are added first and later combined. • The order in which the numbers with a given place value are added doesn’t matter because all partial sums are recorded.

10. Developing Algorithms for Addition: Using Paper-and-Pencil • Start with the ones and proceed to add, with regrouping, from right to left.

11. Example: 562 + 783 • Standard algorithm:Add the ones, then add the tens and regroup. Add the hundreds: 13 hundreds are 1 thousand and 3 hundreds. • Expanded algorithm:Add the ones, then the tens, then the hundreds, writing partial sums. Add the partial sums.

12. Developing Algorithms for Subtraction: Using Models as a Foundation • Using base-ten blocks for modeling subtraction embraces the take-away interpretation of subtraction rather than building directly from the definition of subtraction of whole numbers. • There may be more than one way to use base-ten blocks to model a subtraction problem.

13. Developing Algorithms for Subtraction: Using Models as a Foundation • One way to solve 245 – 18 using models: • Trade 1 ten for 10 ones, then take away 8 ones, leaving 7 ones. • Take away 1 ten, leaving 2 tens.

14. Using the Base-Ten Blocks Model for Addition 245 – 18 = ? 245 – 18 = 227

15. Developing Algorithms for Subtraction: Using Paper-and-Pencil • Expanded algorithm for subtraction:Start with the greatest number and repeatedly take away as much as possible mentally before moving from left to right.

16. Developing Algorithms for Subtraction: Using Paper-and-Pencil • Standard algorithm for subtraction:Start with the ones and proceed to subtract, with regrouping, from right to left.

17. Example: 635 – 248 • Standard algorithm: • Expanded algorithm:

18. The End Section 3.3 Linda Roper