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 2 PO 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.

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.

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

Strategy 2 - FRONT-END ESTIMATION: 7,412 – 3,166 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 7000 – 3000 = – 200 = is about 4, 200 * When one # has many place values…addition/subtraction ONLY

Strategy 2 - FRONT-END ESTIMATION: $ $ $4.43 Add first digits Round leftovers for each number and add Add the numbers together = = is about * Works when trying to add number quickly

Strategy 3 - CLUSTERING: Clustering is used to estimate several numbers that are close to the same value All values are around 8 So, 8  5 = 40

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 Round to ______ Round to ______ ______  ____ = _____

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

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

EXAMPLES: Estimate using an appropriate strategy. Tell which strategy you used. e f. $ $ $7.15 Rounding = 200 Clustering All values are around $7 3  7 = 21

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.

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.

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

Example 2 Estimate about ½ 7/8 – 1/3 1 – ½

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? ¾ rounds to /10 – 5 ¾ 8 ½ - 6 about 2 ½ miles 6/10 rounds to ½ 1 st : Write an equation… 2 nd : Round the fraction part 3 rd : Create a new equation and solve