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

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.

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

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

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

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

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

Using the Base-Ten Blocks Model for Addition

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.

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

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

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 baseten blocks to model a subtraction problem.

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.

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

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.

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.

 Expanded algorithm:  Standard algorithm:

The End
Section 3.3
Linda Roper