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Estimation Strategies

Estimation Strategies. Strand 1: Concept 3 PO 1. Solve grade level appropriate problems using estimation. Strand 1: Concept 3 PO 2. Use estimation to verify the reasonableness of a calculation. Strand 1: Concept 3 PO 3. Express answers to the appropriate place or degree of precision

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Estimation Strategies

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  1. Estimation Strategies Strand 1: Concept 3 PO 1. Solve grade level appropriate problems using estimation. Strand 1: Concept 3 PO 2. Use estimation to verify the reasonableness of a calculation. Strand 1: Concept 3 PO 3. Express answers to the appropriate place or degree of precision Strand 1: Concept 3 PO 4. Verify the reasonableness of estimates made from calculator results within a contextual situation. Strand 5: Concept 2PO 1. Solve a logic problem given the necessary information. Strand 5: Concept 2 PO 2. Identify simple valid arguments using if…then statements Strand 5: Concept 2 PO 3. Model a contextual situation using a flow chart.

  2. 6.1 Why Estimate? • Depending on the situation, an estimate is often good enough and an exact answer is not needed. For example, a quick estimate can also help you check whether a total on a calculator or cash register is reasonable.

  3. Round to $ Round to $ Strategy 1- ROUNDING: • USE WHEN #S SHARE A COMMON PLACE VALUE (ALL OPERATIONS) • Round each number to the same place value. $88.71 - $17.43 $___ - $___ = $___

  4. Strategy 2 - FRONT-END ESTIMATION: • Use the first digit of each number and fill in zeros for the rest. • Subtract. • Round leftovers for each number and subtract • Add the numbers together 7,412 – 3,166 7000 – 3000 = 4000 400 – 200 = 200 4000 + 200 is about 4, 200 * When one # has many place values…addition/subtraction ONLY

  5. Strategy 2 - FRONT-END ESTIMATION: • Add first digits • Round leftovers for each number and add • Add the numbers together $6.04 + $3.45 + $4.43 6 + 3 + 4 = 13.00 0.05 + 0.50 + 0.50 = 1.05 13.00 + 1.05 is about 14.05 * Works when trying to add number quickly

  6. Strategy 3 - CLUSTERING: • Clustering is used to estimate several numbers that are close to the same value 7.9 + 8.2 + 8.3 + 7.8 + 7.7 All values are around 8 So, 85 = 40

  7. Round to ______ Round to ______ Strategy 4 - COMPATIBLE NUMBERS: • Used when you are dividing. Round each first number and then round the second number so that it is easily divisible. 7,235  78 ______ ____ = _____

  8. EXAMPLES:Estimate using an appropriate strategy. Tell which strategy you used. a. 576 – 395 b. 5,247 – 3,238 Front-end Rounding 5000 – 3000 = 2000 600 – 400 = 200 250 – 240 = 10 2000 + 10 = 2010

  9. EXAMPLES:Estimate using an appropriate strategy. Tell which strategy you used. c. 3,500  62 d. 527 + 515 + 467 Clustering Compatible Numbers All values are around 500 3500 = 1500 3600  60 = 60

  10. EXAMPLES:Estimate using an appropriate strategy. Tell which strategy you used.  e.82.45 + 79.28 + 37.41 f. $6.99 + $6.94 + $7.15 Clustering Rounding All values are around $7 37 = 21 82 + 80 + 38 = 200

  11. Closure: • Short Answer 1: Write two reasons for using estimation. •  Short Answer 2: Tell what to do if you have several numbers to add and clustering does not work. • Short Answer 3: Show how front-end estimation is different from rounding.

  12. NOTES on Estimating with Fractions • One way to estimate with fractions less than 1 is to round them to 0, ½, or 1. • Round 1/6 to 0. The numerator is much less than the denominator. • Round 3/8 to ½. The numerator is about half the denominator. • Round ¾ to 1 . The numerator is about the same as the denominator.

  13. Example 1 Estimate 1/6 + 3/8 + ¾ • round each fraction • add the estimates 0 + ½ + 1 about 1½

  14. Example 2 Estimate 7/8 – 1/3 • about ½ – ½ 1

  15. Example 3 • Barry jogs 8 6/10 miles daily. Kerry jogs 5 ¾ miles daily. What is a reasonable estimate for how many more miles Barry jogs than Kerry? 1st: Write an equation… 3rd: Create a new equation and solve 8 6/10 – 5 ¾ 2nd: Round the fraction part 8 ½ - 6 6/10 rounds to ½ ¾ rounds to 1. about 2 ½ miles

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