Mathematics
Grade 5
15 min
Add, subtract, multiply, and divide whole numbers: word problems
Add, subtract, multiply, and divide whole numbers: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Identify keywords and phrases that indicate addition, subtraction, multiplication, and division in word problems.
Translate multi-step word problems into mathematical expressions involving whole numbers and mixed operations.
Correctly apply the Order of Operations (PEMDAS/BODMAS) to solve mathematical expressions derived from word problems.
Solve multi-step word problems involving all four basic operations with whole numbers.
Check the reasonableness of their answers to multi-step word problems.
Explain their step-by-step problem-solving process for mixed operation word problems.
Ever wonder how stores calculate your total bill when you buy multiple items, use a coupon, and pay with cash? 🤔 It's all about using mixed operations!
In this lesson, you...
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Key Concepts & Vocabulary
TermDefinitionExample
Word ProblemA mathematical problem presented in words, describing a real-life situation that requires one or more operations to solve.Sarah had 12 apples. She gave 3 to her friend and bought 5 more. How many apples does Sarah have now?
Operation KeywordsWords or phrases in a word problem that suggest which mathematical operation (addition, subtraction, multiplication, or division) to use.'Total' often means addition, 'difference' means subtraction, 'each' or 'times' means multiplication, and 'share equally' means division.
Mathematical ExpressionA combination of numbers, variables (though not used in this lesson), and operation symbols (+, -, ×, ÷) that represents a mathematical idea.The expression for 'add 5 to...
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Core Formulas
Order of Operations (PEMDAS/BODMAS)
P: Parentheses (or Brackets)
E: Exponents (not covered in this lesson)
M: Multiplication
D: Division
A: Addition
S: Subtraction
This rule tells us the sequence to follow when solving expressions with mixed operations. First, solve anything inside parentheses. Then, perform all multiplication and division from left to right. Finally, perform all addition and subtraction from left to right. Remember, multiplication and division have equal priority, as do addition and subtraction; you simply work from left to right for operations of the same priority.
Translating Word Problems into Expressions
1. Read the problem carefully.
2. Identify the question being asked.
3. Look for keywords to determine the operations.
4. Break the problem into smaller...
5 more steps in this tutorial
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Challenging
Mia was asked to solve: 'A farmer collects 200 eggs. He sells 12 cartons that hold 12 eggs each. Then he uses 5 eggs for breakfast. How many eggs are left?' Mia's answer was 19. She made one mistake. What was it?
A.The student multiplied 20 by 5 instead of dividing.
B.The student added $20 instead of subtracting it.
C.The student subtracted $20 from the total prize money before dividing it.
D.The student divided 500 by 20 instead of by 5.
Challenging
After a field trip, a teacher has a box of leftover snacks. She gives 5 snacks to the bus driver. She then divides the rest of the snacks equally among 10 students, and each student gets 4 snacks. How many snacks were in the box to begin with?
A.45
B.40
C.50
D.35
Challenging
Team A and Team B are in a reading contest. Team A has 5 members who each read 12 books. Team B has 6 members who each read 10 books. What is the difference between the total number of books read by Team A and Team B?
A.They read the same number of books.
B.1 book
C.2 books
D.10 books
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