Mathematics
Grade 4
15 min
Write variable equations to represent word problems
Write variable equations to represent word problems
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the unknown quantity in a one-step word problem.
Choose a letter to use as a variable for an unknown quantity.
Translate keywords for addition and subtraction into mathematical operations.
Translate keywords for multiplication and division into mathematical operations.
Write a complete one-step equation with a variable to represent a word problem.
Explain what each part of their equation represents in the story.
You have 12 pencils, but some roll off your desk! How can we write a math sentence to figure out how many are left? ✏️
In this lesson, you will learn how to be a math detective! We will turn story problems into special math sentences called equations. Using a letter, called a variable, helps us show the mystery number we need to find.
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Key Concepts & Vocabulary
TermDefinitionExample
Word ProblemA math problem that is presented as a short story or a real-life situation.Sarah has 5 apples. Tom gives her 3 more apples. How many apples does Sarah have now?
VariableA letter or symbol that stands for a number we don't know yet. It's a placeholder for the unknown quantity.In the equation 8 + n = 12, the letter 'n' is the variable.
EquationA math sentence that shows two quantities are equal. It must have an equals sign (=).14 - 6 = 8 is an equation. 14 - 6 is not an equation.
Unknown QuantityThe missing piece of information in a word problem that you need to find.In the problem 'There are 20 students in the class. 12 are boys. How many are girls?', the unknown quantity is the number of girls.
OperationThe action you perform...
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Core Formulas
Addition and Subtraction Patterns
Part + Part = Whole OR Whole - Part = Part
Use these patterns when you are joining groups or separating a large group into smaller parts. If you know the parts and need the whole, you add. If you know the whole and one part, you subtract to find the other part.
Multiplication and Division Patterns
Number of Groups × Size of Each Group = Total
Use this pattern for problems involving equal-sized groups. If you know the number of groups and the size of each, you multiply to find the total. If you know the total and one of the other pieces, you can write a multiplication equation with a variable.
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Challenging
David had 8 red apples and 6 green apples. His friend gave him some more apples. Now David has 20 apples in total. Which equation finds the number of apples (a) his friend gave him?
A.8 + a = 20
B.6 + a = 20
C.14 + a = 20
D.8 + 6 = a
Challenging
A rectangular garden is 10 feet long. The total distance around the garden (the perimeter) is 30 feet. If 'w' is the width of the garden, which equation represents this situation? (Remember, a rectangle has two long sides and two short sides).
A.10 + w = 30
B.10 × w = 30
C.10 + 10 + w = 30
D.10 + 10 + w + w = 30
Challenging
A library has 45 books to put on 3 empty shelves. The librarian wants to put an equal number of books (b) on each shelf. Which equation best models the action of dividing the books among the shelves?
A.b + b + b = 45
B.45 ÷ 3 = b
C.45 - b = 3
D.3 + b = 45
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