Mathematics
Grade 8
15 min
Write numerical expressions
Write numerical expressions
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1
Introduction & Learning Objectives
Learning Objectives
Identify keywords and phrases that indicate mathematical operations.
Translate simple verbal phrases into numerical expressions.
Write multi-step numerical expressions, correctly using parentheses for grouping.
Construct numerical expressions involving exponents.
Differentiate between expressions that require specific ordering (e.g., 'less than', 'divided into') and those that do not.
Verify that a written numerical expression accurately represents the given verbal description.
Ever wonder how mathematicians turn everyday language into powerful calculations? 🧐 It's like decoding a secret message, but for numbers!
In this lesson, you'll master the art of translating verbal phrases and real-world scenarios into precise numeri...
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Key Concepts & Vocabulary
TermDefinitionExample
Numerical ExpressionA mathematical phrase that contains only numbers and operation symbols (like +, -, ×, ÷), but no equal sign. It represents a single numerical value.5 + (3 × 2)
Operation KeywordsWords or phrases that indicate which mathematical operation to perform (addition, subtraction, multiplication, division, exponents).'Sum' means addition, 'product' means multiplication.
Order of Operations (PEMDAS/BODMAS)A set of rules that dictates the sequence in which mathematical operations should be performed to ensure a single, consistent result. (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).In 10 - 2 × 3, multiplication is done before subtraction: 10 - 6 =...
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Core Formulas
Translation Rule for Addition and Subtraction
Keywords like 'sum', 'plus', 'increased by', 'more than' indicate addition (+). Keywords like 'difference', 'minus', 'decreased by', 'less than', 'subtracted from' indicate subtraction (-). Be careful with 'less than' and 'subtracted from' as they reverse the order of the numbers.
When translating, identify the numbers and the operation. For 'a less than b' or 'a subtracted from b', the expression is $b - a$.
Translation Rule for Multiplication and Division
Keywords like 'product', 'times', 'multiplied by', 'of' (especially with fractions) indicate multiplication (...
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Challenging
A student writes 50 - 10 ÷ 5 for the phrase '10 divided by 5, subtracted from 50'. Another student writes (50 - 10) ÷ 5 for 'the difference of 50 and 10, divided by 5'. Which student is correct?
A.Only the first student is correct.
B.Both students are correct.
C.Only the second student is correct.
D.Neither student is correct.
Challenging
The phrase 'the product of 6 and 4, plus 2' is potentially ambiguous. Which expression represents 'the product of 6 and the sum of 4 and 2'?
A.6 × (4 + 2)
B.6 × 4 + 2
C.(6 × 4) + 2
D.6 + 4 × 2
Challenging
A recipe calls for 3 cups of flour. You want to make a full batch and a half batch. The half batch requires dividing the original amount by 2. You also need to add an extra 1/4 cup of flour for dusting. Which expression represents the total flour needed?
A.3 + 1/2 + 1/4
B.3 × 1/2 + 1/4
C.3 ÷ 2 + 1/4
D.3 + (3 ÷ 2) + 1/4
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