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Mastering Division: Expanded Notation for 1,315 ÷ 5 and Beyond

In this lesson, you'll discover how to use expanded notation to simplify division problems like 1,315 ÷ 5. We'll break down challenging divisions into manageable parts, leveraging smart estimations and multiplications to enhance understanding. Learn to represent numbers through expanded notation, making both division and estimation easier. We'll also explore practical applications, such as determining how many items each student receives or ensuring accurate packing of supplies. Join us as we master division through expanded notation!

stuart-frost
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Mastering Division: Expanded Notation for 1,315 ÷ 5 and Beyond

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Presentation Transcript

  1. How would you divide 1,315 ÷ 5?

  2. In this lesson you will learn how to divide by using expanded notation.

  3. Challenging problems can be broken into smaller parts Then I can multiply 26 x 10 and get 260 20 x 13 I know that 20 is 2 times 10 20 = 2 x 10 I can multiply 13 x 2 and get 26 13 x 2 = 26 26 x 10 = 260 20 x 13 = 260

  4. Expanded notation 2,615 = 2,000 + 10 + 600 + 5

  5. 1,315 ÷5 1,500 divides easily by 5 Smart rounding ≈ 1,500 ÷ 5 Smart estimate less than 300

  6. 1,315 ÷ 5 10 ÷5 = 2 = 1,000 1,315 + 10 +300 +5 5 ÷5 = 1 This makes sense since our smart estimate was less than 300 ÷5 200 10 ÷ 5= 2 100 ÷ 5= 20 1000 1,000 ÷ 5= 200 ÷5 300 60 ÷5 2 10 30 ÷ 5 = 6 300 ÷ 5 = 60 1 ÷5 5 0 263 x 5 = 1,315 1,315 ÷ 5 = 263

  7. There are 1,520 pencils for 10 students. How many pencils does each student get? Smart rounding ≈ 1,500 ÷ 10 1,500 divides easily by 10 Smart estimate ≈150

  8. 1,520 ÷ 10 20 ÷10 = 2 = 1,000 1,520 + 20 +500 +0 This makes sense since our smart estimate was 150 10 ÷ 10= 1 100 ÷ 10= 10 ÷10 100 1,000 1,000 ÷ 10= 100 ÷10 500 50 ÷10 2 20 50 ÷ 10 = 5 500÷ 10 = 50 0 152 x 10 = 1,520 1,520 ÷ 10 = 152

  9. In this lesson you have learned how to divide by using expanded notation.

  10. What is 1,250 ÷ 5?

  11. Use expanded notation to show the division of 1,845÷ 5. Make a chart to show your work. • Sidney has 2,125 paper plates to put in 25 boxes. She estimated that she would put 100 plates in each box. Using expanded notation and a chart, show whether or not this is a good estimate.

  12. Which of the following shows the division of 3510 ÷ 5 by using expanded notation? A = 3000 3,510 + 10 +500 +5 C B 0

  13. Sandra needs to store 2,125 paper clips seeds. Only 25 fit in each box. Which chart uses expanded notation to show how many boxes she will need? A = 2,000 2,1 2 5 + 20 +100 +5 C B 0

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