Ghada World
Study with Ghada› Math Fifth Grade, Primary› Unit 1

Lesson ⁦1-7⁩: Problem-Solving Strategy: Guess and Check

Math · Fifth Grade, Primary · Unit 1: Place Value · First Semester

A 10-question quiz; after every question you'll see the right answer with an explanation.
Earn 5 points for every new star.

Log in and start 🚀

No account? Create one for free

What will you learn in this lesson?

Students practice the guess-and-check strategy: they suggest a reasonable answer, test it, and adjust it until they reach the solution. It's a useful strategy when a direct way to solve isn't clear.

  • Understands the problem and identifies what is given and what is asked
  • Plans the solution using the guess-and-check strategy
  • Solves the problem by adjusting the guess based on the check
  • Checks that the answer meets all the conditions of the problem

💡 Tip: Record your guesses in a table, and notice whether the result was greater or less than needed so your next guess gets closer.

🤖 Ask Ghada about the lesson

Ghada explains the lesson and answers your questions about it. Log in to get started.

Worked examples from the Problem-Solving Strategy: Guess and Check lesson questions

The sum of two numbers is 25, and their difference is 7. What are the two numbers?
  • 16 and 9
  • 15 and 10
  • 18 and 7
  • 17 and 8
✓ 16 and 9
We guess and check: 16 + 9 = 25 and 16 − 9 = 7, so both conditions are met.
Khalid bought a pen and a notebook for 9 riyals, and the notebook costs 3 riyals more than the pen. How much does the notebook cost?
  • 6 riyals
  • 3 riyals
  • 5 riyals
  • 7 riyals
✓ 6 riyals
We guess the notebook is 6 and the pen is 3: the sum is 6 + 3 = 9 and the difference is 6 − 3 = 3, so the guess is correct.
Show more examples (3)
A pen has chickens and rabbits. There are 10 heads and 28 legs. How many rabbits are in the pen?
  • 4
  • 6
  • 5
  • 7
✓ 4
We guess 4 rabbits and 6 chickens: legs 4 × 4 + 6 × 2 = 16 + 12 = 28, and heads 4 + 6 = 10.
What number multiplied by itself gives 144?
  • 12
  • 14
  • 11
  • 72
✓ 12
We check: 11 × 11 = 121 (too small), and 12 × 12 = 144 (correct).
An adult ticket costs 20 riyals, and a child ticket costs 10 riyals. A family paid 90 riyals for 6 tickets. How many adult tickets were there?
  • 3
  • 4
  • 2
  • 5
✓ 3
We guess 3 adults and 3 children: 3 × 20 + 3 × 10 = 60 + 30 = 90 riyals.

FAQ about the Problem-Solving Strategy: Guess and Check lesson

How do I solve: the sum of two numbers is 25 and their difference is 7?

Guess two numbers with a sum of 25 and check the difference: 15 and 10 differ by only 5; then 16 and 9 differ by 7. So the numbers are 16 and 9.

When do I use the guess-and-check strategy?

When a problem has several conditions that are hard to solve directly, such as finding two numbers from their sum and difference, or the number of heads and legs in a barn.

How do I study the lesson Problem-Solving Strategy: Guess and Check and test myself on it?

Start the lesson quiz on Study with Ghada: 10 questions from the Math Fifth Grade, Primary question bank. After each answer you'll see the right answer with an explanation, and any questions you miss move to “Review my mistakes” until you master them.

Are Study with Ghada quizzes free and aligned with the curriculum?

Yes, completely free. They're built on the Math - Grade 5 - Semester 1 lessons in the same order as the book, and every question is reviewed and approved by a teacher before students see it.

Unit 1 lessons: Place Value

⁦1-1⁩ Place Value Through Billions ⁦1-2⁩ Compare Numbers ⁦1-3⁩ Model Decimals ⁦1-4⁩ Place Value Through Thousandths ⁦1-5⁩ Compare Decimals ⁦1-6⁩ Order Numbers and Decimals All Math Fifth Grade, Primary lessons →
← ⁦1-6⁩ Order Numbers and Decimals ⁦2-1⁩ Round Numbers and Decimals →