Divisibility Rule for 7 | Mental Math Fluency

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In this lesson, students learn a simple method to determine if a number is divisible by 7 using mental math. The process involves taking the last digit of the number, doubling it, and subtracting that from the remaining digits to check for divisibility. With practice, students can easily apply this rule to various numbers, enhancing their math fluency.

Divisibility Rule for 7 | Mental Math Fluency

Hello and welcome to a fun math adventure! Today, we’re going to learn a cool trick to find out if a number can be divided by 7 without leaving any leftovers. This is called checking if a number is divisible by 7.

How to Check Divisibility by 7

Let’s start with a number, like 644. To see if 644 is divisible by 7, we can use a special rule. Here’s how it works:

  1. Take the last digit of the number. In 644, the last digit is 4.
  2. Double that last digit. So, 4 becomes 8 (because 4 times 2 is 8).
  3. Subtract the doubled number from the rest of the digits. Take 64 (the first two digits of 644) and subtract 8 from it. That gives us 56.
  4. Check if the result (56) is divisible by 7. Since 56 divided by 7 equals 8 with no leftovers, 56 is divisible by 7.

Because 56 is divisible by 7, we know that 644 is also divisible by 7. Isn’t that neat?

Let’s Try Another Number

Now, let’s see if 387 is divisible by 7 using the same steps:

  1. The last digit is 7. Double it to get 14.
  2. Subtract 14 from 38 (the other digits of 387). This gives us 24.
  3. Check if 24 is divisible by 7. Since 24 divided by 7 doesn’t give a whole number, 24 is not divisible by 7.

So, 387 is not divisible by 7. With a bit of practice, you’ll get the hang of this rule!

Practice Makes Perfect

If you want to get better at this, you can practice with different numbers. Try using this rule on numbers you see every day, like in a book or on a sign. The more you practice, the easier it will become!

Thanks for joining this math adventure. Keep practicing, and you’ll be a math whiz in no time!

  • What was your initial reaction to learning about the divisibility rule for 7? Did it change your perspective on mental math?
  • Can you think of a situation in your daily life where knowing this divisibility rule might be useful? How would you apply it?
  • Reflect on a time when you struggled with a math concept. How does this experience compare to learning the divisibility rule for 7?
  • What strategies do you use to remember mathematical rules or tricks, and how might you apply them to master the divisibility rule for 7?
  • How do you feel about the importance of mental math skills in today’s technology-driven world? Does learning tricks like this change your view?
  • What other mathematical tricks or rules have you found particularly interesting or useful? How do they compare to the divisibility rule for 7?
  • How does practicing mental math, such as using the divisibility rule for 7, impact your confidence in handling numbers?
  • What are some ways you can incorporate practicing this divisibility rule into your daily routine to improve your math fluency?
  1. Divisibility Detective

    Grab a list of random numbers from a book or magazine. Use the divisibility rule for 7 to determine which numbers are divisible by 7. Write down your findings and share them with a classmate to compare results.

  2. Number Relay Race

    Form teams and have a relay race where each team member must solve a divisibility problem using the rule for 7. The first team to correctly determine the divisibility of all their numbers wins!

  3. Divisibility Puzzle

    Create a puzzle by writing a series of numbers on a grid. Use the divisibility rule for 7 to find a path through the grid where each number is divisible by 7. Share your puzzle with a friend to solve.

  4. Math Story Time

    Write a short story or comic strip about a character who uses the divisibility rule for 7 to solve a mystery or overcome a challenge. Share your story with the class and discuss how math can be used in real-life situations.

  5. Divisibility Bingo

    Create bingo cards with numbers on them. As the teacher calls out numbers, use the divisibility rule for 7 to mark off numbers that are divisible by 7. The first student to get five in a row wins!

Sure! Here’s a sanitized version of the YouTube transcript:

Hello and welcome to Tutoring Hour! In this video, we’ll test if certain numbers are divisible by 7.

Let’s check our first number, which is 644. We’ll determine if it is divisible by 7. To do this, we need to double the last digit and subtract it from the number formed by the other digits. If the difference is divisible by 7, then the original number is also divisible by 7.

Doubling the last digit, we have 8. Subtracting 8 from 64 gives us 56, which is divisible by 7. Therefore, we can conclude that 644 is divisible by 7. The rule here is slightly more complex compared to others. Nevertheless, with a little practice, you can master it!

Now let’s check if another number is divisible by 7. Doubling the last digit of 387 gives us 12. Now let’s subtract 12 from 38, which leaves us with 375. We’ll repeat the process: doubling the last digit of 375 gives us 10. Subtracting 10 from 37 results in 27. Since 27 is not divisible by 7, we conclude that 387 is also not divisible by 7.

If you want to practice this further, tutoringhour.com is the place to be! If you enjoyed the video, please give us a thumbs up! And if you haven’t subscribed to our channel yet, do that right now!

Thanks for watching Tutoring Hour!

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DivisibilityThe ability of one number to be divided by another number without leaving a remainder. – Example sentence: To check the divisibility of 24 by 6, we see if 24 divided by 6 leaves no remainder.

NumberA mathematical object used to count, measure, and label. – Example sentence: The number 7 is an odd number because it cannot be divided evenly by 2.

LastThe final position in a sequence or series. – Example sentence: In the number 345, the last digit is 5.

DigitA single symbol used to make numerals, ranging from 0 to 9. – Example sentence: The number 123 has three digits: 1, 2, and 3.

DoubleTo multiply a number by two. – Example sentence: If you double the number 4, you get 8.

SubtractTo take one number away from another. – Example sentence: When you subtract 3 from 10, the result is 7.

ResultThe answer obtained after performing a mathematical operation. – Example sentence: The result of adding 5 and 3 is 8.

PracticeRepeated exercise in or performance of an activity to acquire proficiency. – Example sentence: To get better at solving equations, you need to practice regularly.

WholeA number without fractions; an integer. – Example sentence: The number 6 is a whole number because it has no fractional part.

MathThe study of numbers, quantities, and shapes. – Example sentence: In math class, we learned how to solve algebraic equations.

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