Section 3.3

Algorithms for Addition and Subtraction

Mathematics for Elementary School Teachers - 4th EditionO’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

278 + 146 = ?278 + 146 = 424

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 base-ten blocks to model a subtraction problem.

Developing Algorithms for Subtraction: Using Models as a FoundationOne 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 = ?245 – 18 = 227

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.

Example: 635 – 248 Expanded algorithm: Standard algorithm:

The EndSection 3.3

Linda Roper