Teaching Models

Add and Subtract Whole Numbers

Addition and Subtraction of Whole Numbers
The use of a base-ten positional number system for writing numbers led to the development of powerful algorithms for arithmetic operations. An algorithm is an organized procedure for performing a given type of calculation. In the addition and subtraction algorithms, digits are aligned according to place value, and the computation is completed from right to left.

Example: Add 3,378 + 2,983

3,378 + 2,983

Add the ones.
11 ones =
1 ten + 1 one
3,378 + 2,983

Add the tens.
16 tens =
1 hundred + 6 tens
3,378 + 2,983

Add the hundreds.
hundreds = 1
thousand + 3 hundreds
3,378 + 2,983

Add the thousands.

Example: Subtract 3,150 − 1,732

3,150 minus 1,732

Rename.
5 tens 0 ones =
4 tens 10 ones
Subtract the ones.
3,150 minus 1,732

Subtract the tens.
3,150 minus 1,732

Rename.
3 thousands 1 hundred =
2 thousands 11 hundreds
Subtract the hundreds.
3,150 minus 1,732

Subtract the thousands.

Expressions and Equations
An arithmetic expression consists of numbers and operations using parentheses, exponents, multiplication, division, addition, and subtraction. An algebraic expression is like an arithmetic expression, but contains at least one variable. A variable is a letter that represents a number.

When evaluating the expressions in this chapter, students should evaluate first within the parentheses; second, exponents; third, multiplication and division from left to right; and fourth, addition and subtraction from left to right. The equality of two expressions gives an equation. To solve an equation means to find the value of the variable that will make the equation true. These equations are simple enough to be solved by inspection or by using a guess-and-check strategy. Explain that not all equations are as simple as the equations in this chapter, so it is necessary to learn to use inverse operations to solve simple equations before learning to solve more difficult equations.

Examples:

p + 4 = 11
p = 11 − 4
p = 7
 
← Use inverse operations. →
 
x − 3 = 9
x = 9 + 3
x = 12

In future chapters, students will learn more about evaluating expressions and solving equations.


Teaching Model 2.1: Expressions and Addition Properties


Houghton Mifflin Math Grade 5