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Understanding Numerical Expressions Facts & Worksheets

In this lesson, we will try to write and interpret numerical expressions, through the use of parentheses, brackets, or braces.

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In this lesson, we will try to write and interpret numerical expressions, through the use of parentheses, brackets, or braces. We will also write simple expressions that record calculations with numbers, and interpret such expressions without evaluating them.

See the fact file below for more information on the Understanding Numerical Expressions or alternatively, you can download our 29-page Understanding Numerical Expressions worksheet pack to utilise within the classroom or home environment.

Key Facts & Information

VOCABULARY

  • Braces
    • Symbols used to group certain parts of a mathematical expression, { }.
  • Brackets
    • Symbols used to group certain parts of a mathematical expression, [ ].
  • Parentheses
    • Symbols used to group certain parts of a mathematical expression, ( ).
  • Numerical Expression
    • A mathematical combination of numbers, operations, and grouping symbols. It is a mathematical phrase that represents a single value. These operations include addition, subtraction, multiplication, and division.
  • Always remember that there should be NO equal sign “=” in a numerical expression. Otherwise, it would be an equation.
  • An equation is a number sentence that describes a relationship between two expressions.
  • Which among the following is a numerical expression?
    • x + y + 3
    • 1 + 3 = 2 + 2
    • (4y + 5) / 3
    • 24 x (8 – 1)

WRITING NUMERICAL EXPRESSIONS

  • In working with numerical expressions from verbal statements, you need to familiarize yourself with key terms representing the four operations: addition, subtraction, multiplication, division.
  • Use parentheses ( ) or brackets to help group calculations to be sure that some calculations are done in a special order.
  • When you use parentheses, you are implying to students “do this first.”
  • Write a numerical expression given the verbal phrase below:
    • The sum of eight and four multiplied by five
  • Looking at the example, you have to understand that you need to obtain the sum of eight and four, and then multiply whatever the answer is to five.
  • This should be done first – the sum of eight and four
  • Then, whatever the answer is – multiply it by five
  • The operation that must be done first must be enclosed in parentheses.
    • So, the numerical expression we can get is: (8 + 4) x 5
  • Write a numerical expression given the verbal phrase below:
    • The sum of eight and the product of four and five
  • Comparing it to the first example, both involve the same numbers and the same operations. Moreover, both of the examples involve numbers eight, four, and five, and the addition and multiplication operations. But do they really mean the same thing? No.
  • In example 2, the operation that must be done first is to multiply four and five, then add eight to whatever product you get.
  • This should be done first – the product of four and five
  • Then, whatever the answer is – add to eight
    • So, the numerical expression we can get is: 8 + (4 x 5)
  • Let’s compare the two verbal phrases.
    • The sum of eight and four multiplied by five: (8 + 4) x 5
    • The sum of eight and the product of four and five: 8 + (4 x 5)
  • We can say that both verbal statements may have exactly the same numbers and may involve the same operations; however, they mean different things. They will yield different answers when evaluated.
  • Pay attention to the given phrase and group the numbers with operations that must be done first.

ORDER OF OPERATIONS

  • In an expression with more than one operation, use the rules called Order of Operations.
  • Some expressions look difficult because they include parentheses and brackets. You can think of brackets as “outside” parentheses. You evaluate inside parentheses first.
  • ORDER OF OPERATIONS
    • Perform all operations within the parentheses first.
    • Do all multiplication and division in order from left to right.
    • Do all addition and multiplication in order from left to right.
  • Besides parentheses ( ), brackets [ ] and braces { } are other kinds of grouping symbols used in expressions. To evaluate an expression with different grouping symbols, perform the operation in the innermost set of grouping symbols first, then evaluate the expression from inside out.
    • 2 x [(9 x 4) – (17 – 6)]
  • Do the operations in the parentheses ( ) first. Multiply, subtract, and rewrite. Do operations in the brackets [ ]. Subtract and rewrite. Multiply 2 and 25 to get 50.
    • 2 x {5 + {(10 – 2)] + (4 – 1)]}
  • Do the operations in the parentheses first. Subtract then rewrite. Next, do the operations in brackets [ ]. Add and rewrite. Then solve operations in braces { }, add and rewrite. Multiply 2 and 6 to get 32.

Understanding Numerical Expressions Worksheets

This is a fantastic bundle which includes everything you need to know about the understanding numerical expressions across 29 in-depth pages. These are ready-to-use Understanding Numerical Expressions worksheets that are perfect for teaching students about the numerical expressions through the use of parentheses, brackets, or braces. We will also write simple expressions that record calculations with numbers, and interpret such expressions without evaluating them.

Complete List Of Included Worksheets

  • Lesson Plan
  • Understanding Numerical Expressions
  • Put in the Jar
  • Speak Numerical Expression
  • Put Into Words
  • Matching Time
  • Which Comes First?
  • Order of Operations
  • Own Expressions
  • Create Your Own Problem
  • Error Analysis
  • Math Maze

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Use With Any Curriculum

These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.

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