Eligible Content M3.D.2.2.1 

 
Help Me To:   

Find a missing number that makes a number sentence true (1 digit or 2-digit numbers
up to 18 using +, -, or x through 9 x 5)

Did You Know?

Algebra is a branch of mathematics that shows the relations and properties of quantity by
means of numbers, letters and other symbols. Learning math helps you write expressions
and equations and select operation signs that make number sentences true. Understanding
math helps you find the values of the missing numbers.

Look at the example below.  Match the colored words to the colored numbers and symbols in the number sentences to
identify the parts of an equation.

Number sentences/equations contain numbers, operation symbols and an equal sign or a
greater than or less than symbol followed by an answer.

6  +  2  =   8

The operation symbols are   +    -    x    ÷

Look at the example below.  Match the colored words to the colored numbers and symbols to identify the parts of an expression. 

An expression is the part of a number sentence that combines numbers, operation signs
and symbols or letters, but doesn’t have an equal sign or an inequality sign

3  +  5       8  x  a      c - 4

Check What You Know First

Determine the missing number in the number sentence:

  +   8   =   10

15  -  =   7

4  x  =  36

Key Vocabulary

A plus sign ( + )  is a mathematical symbol which means to add numbers.

A minus sign ( - )  is a mathematical symbol which means to subtract numbers.

A greater than ( > )  is a mathematical symbol used to compare two numbers, with the larger number given first. 
Example:  6 > 4

A lesser than ( < )  is a mathematical symbol used to compare two numbers, with the lesser number given first. 
Example:  3 < 6

An equal sign ( = )  is a mathematical symbol which means is equal to.
Example:  3 < 6

A number sentence is a sentence that includes numbers, operation symbols, and a greater than or less than symbol or an equal sign. 
Examples:  3 + 2 = 5,    5 – 2 = 3,    4 + 1 < 6,    8 – 2 > 5

An expression is the part of a number sentence that combines numbers and operation signs, but doesn’t have an equal sign or an
inequality sign.  Examples:  3 + 2,     5 - 2

An equation is a number sentence which states that two amounts are equal. Examples:  3 + 2 = 5,    5 – 2 = 3

An inequality is a mathematical sentence that compares two unequal expressions with symbols < (less than) or > (greater than).  
Examples:  4 + 1 < 6,    8 – 2 > 5

An inverse operation is an opposite operation, or operations that undo each other, such as addition and subtraction or multiplication
and division.  Examples: 3 + 2 = 5,    5 – 2 = 3,     4 x 3 = 12,     12 ÷ 3 = 4

A variable is a symbol or letter that stands for an unknown number.  Example: a + 2 = 5,   6 + 2 = n

A fact family is a set of related multiplication and division, or addition or subtraction, equations using the same numbers.
Examples:  2 x 4 = 8,     4 X 2 = 8,     8 ÷ 4 = 2,     8 ÷ 2 = 4,     1 + 5 = 6,     5 + 1 = 6,     6 – 5 = 1,     6 – 1 = 5

Learn About It Now

To solve a number sentence, you have to find one missing number.  You can use
addition, subtraction, multiplication or division facts to find the missing number.

The missing numbers may be represented by variables which are letters or
symbols such as: 
                      
You can use your knowledge of basic math facts to find the missing numbers in simple
math problems.  That is why it is a good idea to memorize your basic math facts.

For the following problem, you can ask yourself what number added to 8 will give you 10.

+ 8   =  10      Look here for the answer... The answer is 2 ( 2 + 8 = 10)

For the following problem, you can ask yourself what number subtracted from 15 will give you 7. 

15  - =  7        Look here for the answer... The answer is 8 ( 15 - 7 = 8).

For the following problem, you can ask yourself what number multiplied by 4 will give you 36. 

4  x  = 36      Look here for the answer... The answer is 9 ( 4 x 9 = 36)

You can also solve these problems by using inverse operations. An inverse operation
is an opposite operation, or operations that undo each other, such as addition and subtraction
or multiplication and division. 

In the following problem the inverse operation of addition is subtraction.  You can subtract
10 – 8 to get the missing number 2.

+ 8   =  10

In the following problem the inverse operation of multiplication is division.  The inverse operation
would be 36 ÷ 4 to get the missing number 9.

4  x  = 36

You can also look at fact families for simpler problems.  In the following problem, the fact family
would be:

7 + 8 = 15     8 + 7 = 15     15 – 7 = 8     15 – 8 = 7   

If you know the fact family, you will know that 8 is the answer.

15  - =  7

Below is a chart with rules for solving missing numbers.  The vocabulary of terms used
in the chart can be found under the chart. 

Vocabulary of Terms Used in the Chart