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Numeration

Numeration. Addition, Subtraction, Multiplication and Division. Vocabulary Activity Sort the following words into table with these headings: Addition, Subtraction, Multiplication and Division. Plus Remain Decrease Double Group Difference Multiple Combine Take away Factor Quotient

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Numeration

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  1. Numeration Addition, Subtraction, Multiplication and Division

  2. Vocabulary ActivitySort the following words into table with these headings: Addition, Subtraction, Multiplication and Division • Plus • Remain • Decrease • Double • Group • Difference • Multiple • Combine • Take away • Factor • Quotient • Split • Left over • Fewer • Add • Sum • Less than • By • Goes into • Shared • Total • Area • Divide • Times • In all • More than • Exceed • Half • Equal • Divisible • Product • Divided by • Minus • How many more • Increase • Equally • Subtract • Altogether • Cut up

  3. Correct PlacementOperations

  4. Estimating Sums and Differences • Before beginning to calculate, estimate what the answer might look like. • 525 + 6 I would know that 525 + 5 is 530, so the answer needs to be a wee bit higher then that. • 62 – 7 I would know that 60 take away 7 is 53, so the answer needs to be close to that.

  5. Getting to 10, 100, 1000, tenths and hundredths first This strategy involves changing one number in a sum to a nearby ten, hundred, thousand, or decimal tenth or hundredth, carrying out the addition using that changed number, and then adjusting the answer to compensate for the original change. The reason a number is changed is to make it more compatible and easier to work with. Remember to adjust your answer to account for the change that was made.

  6. Examples of Getting to 10, 100, 1000, tenths and hundredth first For 52 + 39, think,“ 52 plus 40 is 92, but I added 1 too many to take me to the next 10, so I subtract one from my answer to get 91.” For 345 + 198, think, “345 + 200 is 545, but I added 2 too many; so I subtract 2 from 545 to get 543.” For 4500 plus 1900, think, “4500 + 2000 is 6500 but I added 100 too many; so, I subtract 100 from 6500 to get 6400.” For 0.54 plus 0.29, think, “0.54 + 0.3 is 0.84 but I added 0.01 too many; so, I subtract 0.01 from 0.84 to compensate, to get 0.83.”

  7. Practice Numbers in the 10s and 100s 56 + 8 = 14 + 58 = 72 + 9 = 371 + 18 = 354 + 597 = 304 + 399 = 826+99= 526+799= Numbers in the 1000s 1300 + 800 = 3450 + 4800 = 5400 + 2900 = 2330 + 5900 = 2111 + 4900 = 6421 + 1900 = 15 200 + 2900 = Numbers in the 10ths and 100ths 0.71 + 0.09 = 0.44 + 0.29 = 4.52 + 0.98 = 0.56 + 0.08 = 0.17 + 0.59 = 1.17 + 0.39 = 0.32 + 0.19 = 25.34 + 0.58 =

  8. Make 10 When you are given one or two-digit numbers to add, try using the rule of 10’s. For 58 + 6, think, “58 plus 2 (from the 6) is 60, and 60 plus 4 (the other part of 6) is 64.” For 350 + 59, think, “350 plus 50 is 400, and 400 plus 9 is 409.” For 7400 + 790, think, “7400 plus 600 is 8000, and 8000 plus 190 is 8190.”

  9. Make 10 Practice Practice Items 58+6= 38+5= 170+40 = 630+73 = 780+67 = 1700 + 870 2200 + 910= 5+49= 680+78= 570+41= 560+89= 2800 + 460 = 29+3= 490+18= 450+62= 870+57= 5900 + 660 = 3500 + 590 = 4700 + 470 =

  10. Front-End Addition • 37 + 26, think 30 and 20 is 50, and 7 and 6 is 13, so 50 + 13 is 63 • For 450 + 380, think 400 and 300 is 700, and 50 and 80 is 130, so 700 and 130 is 830 • You try: • For 3300 + 2800, think…

  11. Some more Front-End Addition 45 + 38 = 15 + 66 = 340 + 220 = 3500 + 2300 = 2900 + 6000 = 8800 + 1100 = 34+18= 74+19= 470+360= 5400 + 3400 = 3700 + 3200 = 2700 + 7200 = 53+29= 190+430= 607+304= 6800 + 2100 = 7500 + 2400 = 6300 + 4400 = Numbers in the 10ths and 100ths 4.6 + 3.2 = 3.3 + 2.4 = 1.5 + 1.5 = 5.4 + 3.7 = 6.6 + 2.5 = 0.75 + 0.05 = 1.85 + 2.25 =

  12. Break Up and Bridge • This strategy is similar to front-end addition except that you begin with all of the first number and then add on parts of the second number beginning with the largest place value. • For 45 + 36, think, “45 and 30 (from the 36) is 75, and 75 plus 6 (the rest of the 36) is 81.” • For 537 + 208, think, “537 and 200 is 737, and 737 plus 8 is 745.” • For 5300 plus 2400, think, “5300 and 2000 (from the 2400) is 7300 and 7300 plus 400 (from the rest of 2400) is 7700.” • For 3.6 plus 5.3, think, “3.6 and 5 (from the 5.3) is 8.6 and 8.6 plus 0.3 (the rest of 5.3) is 8.9.”

  13. Practice Break up and Bridge a) Numbers in the 10’s and 100’s 37+42= 74+42= 747+150= 72 + 21 = 325 + 220 = 142 + 202 = 88 + 16 = 301 + 435 = b) Numbers in the 1000’s 7700 + 1200 = 7300 + 1400 = 5090 + 2600 = 4100 + 3600 = 2800 6100 = 17 400 + 1300 = 5700 + 2200 = 3300 + 3400 c) Numbers in the 10ths and 100ths 4.2+3.5= 6.1+2.8= 4.15 + 3.22 = 15.45 + 1.25 = 4.2+3.7= 2.08+3.2= 6.03 + 2.45 = 70.32 + 9.12 =

  14. Finding Compatibles • Compatible numbers are sometimes referred to as friendly numbers or nice numbers in other professional resources. This strategy for addition involves looking for pairs of numbers that combine to make a sum that will be easy to work with. Some examples of common compatible numbers include 1 and 9; 40 and 60; 75 and 25 and 300 and 700.

  15. Compatible “Nice” numbers For 3 + 8 + 7 + 6 + 2, think, “3 and 7 is 10, 8 and 2 is 10, so 10 and 10 and 6 is 26.” For 25 + 47 + 75, think, “25 and 75 is 100, so 100 and 47 is 147.” For 400 + 720 + 600, think, “400 and 600 is 1000, so the sum is 1720.” For 3000 + 7000 + 2400, think, “3000 and 7000 is 10 000, so 10 000 and 2400 is 12 400.”

  16. Practice Compatible “Nice” numbers 11 + 59 = 33 + 27 = 75 + 95 + 25 = 80 + 20 + 79 = 90+86+10= 125+25= 625+75= 290+510= 800+740+200= 4400+1600+3000= 3250+3000+1750= 3000+300+700+2000= 60 + 30 + 40 = 40 + 72 + 60 = 475+25= 300+437+700= 900+100+485= 9000 + 3300 + 1000= 2200+2800+600= 3400 + 5600=

  17. Practice Compatible “Nice” numbers Numbers in the 10ths and 100ths are. 0.6 + 0.9 + 0.4 + 0.1 = 0.7 + 0.1 + 0.9 + 0.3 = 0.4 + 0.5 + 0.6 + 0.2 + 0.5 = 0.80 + 0.26 = 0.2 + 0.4 + 0.8 + 0.6 = 0.2 + 0.4 + 0.3 + 0.8 + 0.6 = 0.25 + 0.50 + 0.75 = 0.45 + 0.63 =

  18. Switch Addition and Multiplication expressions that you know better • 3 + 7 is the same as 7 + 3 (Remember the rule to always begin with the larger number) • 7 X 3 is the same as 3 X 7 (Most people know the lower math facts better then the higher math facts)

  19. Adding and subtracting close to hundreds You can add and subtract numbers ending in 97, 98, 99 by thinking of the nearest hundred. Try these in your notebook: Calculate each sum. 88 + 98 68 + 99] 199 + 58 135 + 198 Calculate each difference. 134 – 98 167 – 99 335 – 199 567 - 298 • 56 + 98 =

  20. When you are Subtracting from Hundreds Try These: 1. 300 – 3 2. 400 – 4 3. 500 – 5 4. 600 – 6 5. 700 – 7 6. 800 – 8 7. 900 - 9 100 – 6 Think of numbers between 90 and 100 when subtracting a one-digit number from hundreds. 200 – 2 must be between 190 and 200. 200 – 2 = 198

  21. Break it Down 12 x 7 is the same as (10 X 7) + (2 X 7) 70 + 14 = 84 Try these: 48 X 6 17 X 4 23 X 8

  22. Multiplying Numbers Close to Tens and hundreds Multiply and then subtract Try these: Multiply by thinking of tens and hundreds. A) 6 x 99 = B) 3 x 98 = C) 3 x 49 = D) 2 x 79 = E) 4 x 199 F) 5 x 198 • To multiply 6 X 98, think of six hundreds instead of six ninety-eights. • Calculate 6 X 100 = 600. Then subtract 12. • 600 – 12 = 588, so 6 x 98 = 588 • Use the information you learned on the last slide to calculate 600 – 12. • I know 600 – 12 is between 580 and 590.

  23. Multiply Numbers by Five Think of 10 when you multiply by 5. Try these: A) 5 x 14 = B) 5 x 16 = C) 5 x 22 = D) 5 x 28 = E) 5 x 48 = F) 5 x 64 = • 5 x 12 = one half of 10 x 12 • 10 x 12 = 120 • One half of 120 = 60

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