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# Number Sense Book Part 1 Dts

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please make correction ending in 5, tens digits odd and even

35 x 85 = 2975 not 2925

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### Number Sense Book Part 1 Dts

1. 1. Number Sense Number Sense is memorization and practice. The secret to getting good at number sense is to learn how to recognize and then do the rules accurately . Then learn how to do them quickly. Every practice should be under a time limit.
2. 2. The First Step <ul><li>The first step in learning number sense should be to memorize </li></ul><ul><li>PERFECT SQUARES from 12 = 1 to 402 = 1600 </li></ul><ul><li>PERFECT CUBES from 13 = 1 to 253 = 15625 </li></ul><ul><li>These squares and cubes should be learned in both directions. ie. 172 = 289 and the </li></ul>
3. 3. 2 x 2 Foil (LIOF) Working Backwards <ul><li>The last number is the units digit of the product of the unit’s digits </li></ul><ul><li>Multiply the outside, multiply the inside </li></ul><ul><li>Add the outside and the inside together plus any carry and write down the units digit </li></ul><ul><li>Multiply the first digits together and add and carry. </li></ul><ul><li>Write down the number </li></ul>
4. 4. Squaring Numbers Ending In 5 <ul><li>First two digits = the ten’s digit times one more than the ten’s digit. </li></ul><ul><li>Last two digits are always 25 </li></ul>
5. 5. Ending In 5 Consecutive Decades <ul><li>First two digits = the small ten’s digit times one more than the large ten’s digit. </li></ul><ul><li>Last two digits are always 75 </li></ul>
6. 6. Ending In 5 Ten’s Digits Both Even <ul><li>First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits. </li></ul><ul><li>Last two digits are always 25 </li></ul>
7. 7. Ten’s Digits Both Odd – Ending In 5 <ul><li>First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits. </li></ul><ul><li>Last two digits are always 25 </li></ul>
8. 8. Ending in 5 Ten’s Digits Odd & Even <ul><li>First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits. Always drop the remainder. </li></ul><ul><li>Last two digits are always 75 </li></ul>
9. 9. Multiplying By 12 ½ (1/8 Rule) <ul><li>Divide the non-12 ½ number by 8. </li></ul><ul><li>Add two zeroes. </li></ul>
10. 10. Multiplying By 16 2/3 (1/6 Rule) <ul><li>Divide the non-16 2/3 number by 6. </li></ul><ul><li>Add two zeroes. </li></ul>
11. 11. Multiplying By 33 1/3 (1/3 Rule) <ul><li>Divide the non-33 1/3 number by 3. </li></ul><ul><li>Add two zeroes. </li></ul>
12. 12. Multiplying By 25 (1/4 Rule) <ul><li>Divide the non-25 number by 4. </li></ul><ul><li>Add two zeroes. </li></ul>
13. 13. Multiplying By 50 (1/2 Rule) <ul><li>Divide the non-50 number by 2. </li></ul><ul><li>Add two zeroes. </li></ul>
14. 14. Multiplying By 75 3/4 Rule <ul><li>Divide the non-75 number by 4. </li></ul><ul><li>Multiply by 3. </li></ul><ul><li>Add two zeroes. </li></ul>
15. 15. Multiplying By 125 1/8 Rule <ul><li>Divide the non-125 number by 8. </li></ul><ul><li>Add three zeroes. </li></ul>
16. 16. Multiplying When Tens Digits Are Equal & The Unit Digits Add To 10 <ul><li>First two digits are the tens digit times one more than the tens digit </li></ul><ul><li>Last two digits are the product of the units digits. </li></ul>
17. 17. Multiplying When Tens Digits Add To 10 & The Units Digits Are Equal <ul><li>First two digits are the product of the tens digit plus the units digit </li></ul><ul><li>Last two digits are the product of the units digits. </li></ul>
18. 18. Multiplying Two Numbers in the 90’s <ul><li>Find out how far each number is from 100 </li></ul><ul><li>The 1 st two numbers equal the sum of the differences subtracted from 100 </li></ul><ul><li>The last two numbers equal the product of the differences </li></ul>
19. 19. Multiplying Two Numbers Near 100 <ul><li>First Number is always 1 </li></ul><ul><li>The middle two numbers = the sum on the units digits </li></ul><ul><li>The last two digits = the product of the units digits </li></ul>
20. 20. Multiplying Two Numbers With First Numbers Equal & A Zero In The Middle <ul><li>The 1 st two numbers = the product of the hundreds digits </li></ul><ul><li>The middle two numbers = the sum of the units x the hundreds digit </li></ul><ul><li>The last two digits = the product of the units digits </li></ul>
21. 21. Multiplying By 3367 (10101 Rule) <ul><li>Divide the non-3367 number by 3 </li></ul><ul><li>Multiply by 10101 </li></ul>
22. 22. Multiplying A 2-Digit Number By 11 (121 Pattern) <ul><li>Last digit is the units digit </li></ul><ul><li>The middle digit is the sum of the tens and the units digits </li></ul><ul><li>The first digit is the tens digit + any carry </li></ul>Work Right to Left Work Right to Left Work Right to Left Work Right to Left Work Right to Left
23. 23. Multiplying A 3-Digit Number By 111 (1221 Pattern) <ul><li>Last digit is the units digit </li></ul><ul><li>The next digit is the sum of the tens and the units digits </li></ul><ul><li>The next digit is the sum of the tens and the hundreds digit + carry </li></ul><ul><li>The first digit is the hundreds digit + any carry </li></ul>Work Right to Left Work Right to Left Work Right to Left Work Right to Left Work Right to Left
24. 24. Multiplying A 3-Digit Number By 111 (12321 Pattern) <ul><li>Always work from Right to Left Last digit is the units digit </li></ul><ul><li>The next digit is the sum of the tens and the units digits </li></ul><ul><li>The next digit is the sum of the units, tens and hundreds digits + carry </li></ul><ul><li>The next digit is the sum of the tens and hundreds digits + carry </li></ul><ul><li>The next digit is the hundreds digit + carry </li></ul>Work Right to Left Work Right to Left Work Right to Left Work Right to Left Work Right to Left
25. 25. Multiplying A 3-Digit Number By 111 (12321 Pattern) Work Right to Left Work Right to Left Work Right to Left Work Right to Left Work Right to Left