Using the State Curriculum: Mathematics, Grade 3

There are three relationships that can exist between two quantities: The first is greater than the second, the first is less than the second or the first and the second are the same, or equal. These examples include the symbols used to show these relationships between quantities:

1. 3 > 1 Three is greater than 1
2. 1 < 3 One is less than 3
3. 3 = 3 Three is equal to three.

3 is greater than 1 (3>1) because 3 of something: 3 cats, 3 bananas, 3 toys, etc. is a greater quantity than 1 which represents only a single item, such as a cat, a banana, a toy.

1 is less than 3 (1<3) because 1 represents an individual object while 3 represents multiple objects. 3>1 and 1<3 are two ways of describing the relationship between two numbers and are equivalent statements.

When comparing any pair of numbers, the questions of:

• Which has more?
• Which has less?
• Are they equal?

are used to determine their relationship. If necessary, students can use manipulatives to explore the one-to-one correspondence of the two numbers. This will physically show which has more or less, or if they are equal.

Students can also use the number line to determine one of the three relationships between two numbers. As students represent numbers on a number line, they should discover and be able to model that, as you move to the right on a number line, the value increases. They should also discover and be able to model that, if you move to the left, the value decreases.

The statement of an equation or an inequality is called a number sentence.

An inequality compares expressions using a > (greater than) or < (less than) symbol. The expressions on opposite sides of the relation symbol do not have the same value.

4 < 5 is read "Four is less than five."
10 > 2 is read "Ten is greater than two."
72 + 30 > 45 + 45 is read "Seventy-two plus thirty is greater than forty-five plus forty-five."

An equation shows expressions on both sides of an = sign that have the same numerical value.

Both inequalities and equations are made up of only numbers and symbols. They do not contain words. They have only one relationship sign, >, <, or =.

At this level students are expected to write equations and inequalities using whole numbers through 1000.

Expressions indicate an operation between numbers and represent a single numeric quantity. For example, 5+3 represents the quantity 8. There are many expressions that also represent the quantity 8. Students should be encouraged to explore the many expressions that can represent a numeric quantity. At this level students should increasingly throughout the year be able to write expressions with all four operational symbols that represent whole numbers through 50. Students often confuse expressions with equations and use the symbol = along with the expression.

Expression: 3 + 8
Equation: 3 + 8 = 11
Inequality: 3 + 8 > 9