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Front End
          &

Rounding
    Gwendolyn Best
 Suffolk Public Schools
Estimation


The next few slides
will help you
test your
estimation skills.
Can I buy three for $100?




                   45
Can I buy three for $100?




                  $23
Can I buy 5 for $50?




       The basketball would have
       to cost ______ or less for
       me to purchase five of
       them for $50.
Can I buy three for $20?




              $
               4.95
Rounding
  to the highest

Place Value                        g hest
                            its hi
                      ber to ome
                 h num lue. S
           d eac ce va              ten-
     Roun le pla             ed to eds,
           ib          round hundr
     poss rs will be ands,
      numbe ds, thous
      tho usan
       or t ens.
1 + 26 + 1,427 + 216



         375    Hundreds
          26      Tens
        1,427   Thousands
         216    Hundreds
Round to the highest place.
     375    Hundreds          400

      26      Tens             30


    1,427   Thousands    1,000


     216    Hundreds          200
After you round, add the numbers!

               400
                30
              1000
            + 200
              1630
8857      8857
              9000
    4758      5000
              4758
    7045      7000
              7045
+   2110   + + 2110
               2000
9000    •   Between 11,000 and 15,000


5000    •   Between 16,000 and 20,000

7000    •   Between 20,000 and 25,000

+2000
        •   Between 28,000 and 33,000
247       247
             200
    6542    7000
            6542
    489       489
              500
+    92    + + 92
               90
200   •   A little less than 7,000
  7000
         •   A little less than 8,000
   500
+   90   •   A little more than 8,000


         •   A little more than 10,000
5028
         5000
 5028
         6732
         7000
 6732
         1285
         1000
 1285
+ 835   ++ 835
           800
Front End Estimation
FRONT END
The name of this strategy gives you a clue
 about how it is used.

The word FRONT should remind you that
 you are only concerned with the front
 portion of the number.

Many people think this strategy is easier
 than rounding to the highest place value.
Draw a line through your list of numbers so
    that you have at least one digit from each
    addend in front of (before) the line.

                                                     ll
                                                ge a
    4,329                                Chan ers
                            4,32 0             b
                                         num he line
      748                                 a fter t s.
                                                   o
                              74 0         t o zer
    2,398
                            2,39 0          ll num he
                                                     bers
                                          A
+       28                                be
                                                     t
                                               fore the
                        +       20         lin  e s ta
                                                       y
                                                     .
                                             s ame
1 + 26 + 1,427 + 216



         375     37 0
          26      20
        1,427   1,42 0
         216     21 0
8857      8857
              8000
    4758      4000
              4758
    7045      7000
              7045
+   2110   + + 2110
               2000
8857
                                 8000
    8857
                                 4000
                                 4758
    4758
                                 7000
                                 7045
    7045
                              + + 2110
                                  2000
+   2110
    Draw the line after the
         first number
       In each addend.
8000    •   Between 11,000 and 15,000


4000    •   Between 16,000 and 20,000

7000    •   Between 20,000 and 25,000

+2000
        •   Between 28,000 and 33,000
247       247
             240
    6542    6540
            6542
    489       489
              480
+    92    + + 92
               90
Estimate to find the best answer.

   240       •   A little more than 7,000
  6540
             •   A little more than 8,000
   480
+   90       •   A little less than 9,000

  7350
             •   A little less than 10,000
5028
         5000
 5028
         6732
         6700
 6732
         1285
         1200
 1285
+ 835   ++ 835
           800
Estimate and choose the most
      reasonable answer.


          Between 11,000 and 15,000
 5000
 6700     Between 16,000 and 20,000

 1200     Between 20,000 and 25,000

+ 800
          Between 28,000 and 33,000
13700
3,876     4,000     3,000
  5,814     6,000     5,000
  3,176     3,000     3,000
+ 7,895   + 8,000   + 7,000
9,876      9,000    10,000
  8,514     8,000     9,000
  6,092     6,000     6,000
+ 3,895   + 3,000   + 4,000

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Math 206 frontend rounding

  • 1. Front End & Rounding Gwendolyn Best Suffolk Public Schools
  • 2. Estimation The next few slides will help you test your estimation skills.
  • 3. Can I buy three for $100? 45
  • 4. Can I buy three for $100? $23
  • 5. Can I buy 5 for $50? The basketball would have to cost ______ or less for me to purchase five of them for $50.
  • 6. Can I buy three for $20? $ 4.95
  • 7. Rounding to the highest Place Value g hest its hi ber to ome h num lue. S d eac ce va ten- Roun le pla ed to eds, ib round hundr poss rs will be ands, numbe ds, thous tho usan or t ens.
  • 8. 1 + 26 + 1,427 + 216 375 Hundreds 26 Tens 1,427 Thousands 216 Hundreds
  • 9. Round to the highest place. 375 Hundreds 400 26 Tens 30 1,427 Thousands 1,000 216 Hundreds 200
  • 10. After you round, add the numbers! 400 30 1000 + 200 1630
  • 11. 8857 8857 9000 4758 5000 4758 7045 7000 7045 + 2110 + + 2110 2000
  • 12. 9000 • Between 11,000 and 15,000 5000 • Between 16,000 and 20,000 7000 • Between 20,000 and 25,000 +2000 • Between 28,000 and 33,000
  • 13. 247 247 200 6542 7000 6542 489 489 500 + 92 + + 92 90
  • 14. 200 • A little less than 7,000 7000 • A little less than 8,000 500 + 90 • A little more than 8,000 • A little more than 10,000
  • 15. 5028 5000 5028 6732 7000 6732 1285 1000 1285 + 835 ++ 835 800
  • 17. FRONT END The name of this strategy gives you a clue about how it is used. The word FRONT should remind you that you are only concerned with the front portion of the number. Many people think this strategy is easier than rounding to the highest place value.
  • 18. Draw a line through your list of numbers so that you have at least one digit from each addend in front of (before) the line. ll ge a 4,329 Chan ers 4,32 0 b num he line 748 a fter t s. o 74 0 t o zer 2,398 2,39 0 ll num he bers A + 28 be t fore the + 20 lin e s ta y . s ame
  • 19. 1 + 26 + 1,427 + 216 375 37 0 26 20 1,427 1,42 0 216 21 0
  • 20. 8857 8857 8000 4758 4000 4758 7045 7000 7045 + 2110 + + 2110 2000
  • 21. 8857 8000 8857 4000 4758 4758 7000 7045 7045 + + 2110 2000 + 2110 Draw the line after the first number In each addend.
  • 22. 8000 • Between 11,000 and 15,000 4000 • Between 16,000 and 20,000 7000 • Between 20,000 and 25,000 +2000 • Between 28,000 and 33,000
  • 23. 247 247 240 6542 6540 6542 489 489 480 + 92 + + 92 90
  • 24. Estimate to find the best answer. 240 • A little more than 7,000 6540 • A little more than 8,000 480 + 90 • A little less than 9,000 7350 • A little less than 10,000
  • 25. 5028 5000 5028 6732 6700 6732 1285 1200 1285 + 835 ++ 835 800
  • 26. Estimate and choose the most reasonable answer. Between 11,000 and 15,000 5000 6700 Between 16,000 and 20,000 1200 Between 20,000 and 25,000 + 800 Between 28,000 and 33,000 13700
  • 27. 3,876 4,000 3,000 5,814 6,000 5,000 3,176 3,000 3,000 + 7,895 + 8,000 + 7,000
  • 28. 9,876 9,000 10,000 8,514 8,000 9,000 6,092 6,000 6,000 + 3,895 + 3,000 + 4,000