Transcript Lesson 1.3- Estimation- - WW

LESSON 1.3
ESTIMATION
Homework Check & REVIEW
Class work and Homework
1. Exercise 1.2.3 & Exercise 1.2.4
2. Pages 20-21 Q# 1, 2, 5acegik, 7
Due: Tuesday, September 24
ESTIMATION
 As you walk around and live your life wouldn't it be good if you
could easily estimate:
 how much a bill would be,
 which product was the best value for money
 and make other estimates such as lengths and angles?
 Also, wouldn't it be good if you could quickly guess how many
people were in a room, how many cars in the street, how many
boxes on the shelf, or even how many seagulls on the beach?
 We are not talking exact answers here, but answers that are
good enough for your life.
LEARNING GOALS
By the end of this lesson, you will be able to:
 Describe the importance and utility of estimation
 Estimate measurements
 Use rounding to estimate a sum
 Calculate then round to solve word problems
 Estimate a tip amount
Why Estimate?
• People tip to reward good service. In
restaurants, they usually tip 10% to 15% of
the bill. People do not always carry a
calculator with them. Neither do they want to
perform long multiplication by hand in order
to calculate the tip. Good estimation skills
help solve this type of problem.
CALCULATION & ROUNDING
Rounding is used to approximate or estimate.
Numbers are usually rounded to the nearest
10, 100, 1000, 10 000, 100 000 or even a 1,
000 000.
Decimals can also be rounded, usually to the
nearest tenth, hundredth, thousandth…
ROUNDING WHOLE
NUMBERS
Whole numbers (also called integers) are counting
numbers e.g. 1, 2, 3, 4…
Negative numbers are also whole numbers e.g. -1, -2, 3…
Decimals are NOT whole numbers e.g. 0.4, 7.4, 2.36,
7.32…
Fractions are NOT whole numbers e.g. ½ 2 ¾, 25 ¼ …
ROUNDING TO NEAREST
10TH
STEPS FOR SUCCESS!
When rounding to the nearest 10 there are three main
things to remember;
1. Identify the units digit.
2. If the units digit is a 1, 2, 3 or 4 we round down.
3. If the units digit is a 5, 6, 7, 8, or 9 we round up.
EXAMPLE:
1. Identify the units digit.
2. If the units digit is a 1, 2, 3 or 4 we round down.
3. If the units digit is a 5, 6, 7, 8, or 9 we round up.
22
57
728.9
58.1
Estimating Measurements
A. Estimate the width of the top of your desk. Write
down how much you think the desk is in centimetres.
B. Measure a 10-cm long part of your hand. Use your
10 cm hand to find the approximate width of your desk.
C. Use a ruler to measure the width of your desk.
D. By how much was your estimate in part A off? Was
your estimate in part B closer to the actual width?
Using Rounding to Estimate a Sum
Sarah is buying five items, prices at:
$8.50
$19.78
$12.34
$10.67
$35.25
• Approximately how much is her bill, before
taxes?
Round prices to the nearest dollar and add!
35 + 9 + 20 + 12 + 11 = 87
Calculating Then Rounding
Brandon runs 8 km every day to train for a crosscountry meet. He measured his stride to be 1.3 m long.
Approximately how many strides (to the nearest 100)
does he need to run 8 km?
Solution: Rounding his stride to the nearest metre
would result in a very inaccurate answer. In a situation
such as this, divide for accuracy. Then, round the
result…
8 km = 8000 m
8000/1.3 = 6153.846
Brandon needs approximately 6200 strides to run 8 km.
Estimating a Tip
• People usually tip 10% to 15% of the bill when paying a
restaurant bill. Determine the approximate 15% tip for a
$14.35 restaurant bill
SOLUTION:
1. Take 10% of the total
2. Round to the nearest half dollar for small amounts;
3. Round to the nearest dollar for large amounts;
4. Add half of the 10% amount.
For this restaurant bill, the approximate tip
is $2.25
KEY CONCEPTS
• When only approximate answers are needed, round first,
then calculate using mental math.
• When more accuracy is needed, use accurate calculations,
then round the answer to an approximate number of
places.
• To consider how reasonable an answer is, use mental
arithmetic with rounded numbers to check.
What the practice of
Mental Math can do!
ROUNDING TO NEAREST ____
STEPS FOR SUCCESS!
When rounding to the nearest ______ there are three
main things to remember;
1. Identify the units digit.
2. If the units digit is a 1, 2, 3 or 4 we round down.
3. If the units digit is a 5, 6, 7, 8, or 9 we round up.
Reasonableness of Answers
 Round to the greatest place value to estimate products
 Rounding is one way to estimate products. Now that we have
determined that rounding can be used to estimate results we can
also justify the reasonableness of rounding products as well.
 For instance, let's take a look at the cost of a six pack of soda.
We know that a six pack of soda cost about $2.99.
 So, if we round $2.99 to the nearest dollar, it would be $3.00.
 Saying a six pack of soda costs $3.00 would be reasonable.
 Saying a six pack of soda costs $10.00 would not be
reasonable.
Hundreds
Nearest ten
SO: Round to the greatest
place value to estimate
products. Use the rounded
number to justify the
reasonableness of
estimating.
SUCCESS CRITERIA
 I am able to describe the importance and utility of
estimation
 I am able to estimate measurements
 I am able to round for estimating a sum & product
 To nearest _________
 I am able to calculate then round to solve word
problems
 I am able to estimate a tip amount
Unit #1: Number Sense and Algebra
Lesson #
Lesson
1.1
Integers
1.2
Order of Operations
(square roots &
exponents)
1.3
Estimation
1.4
Evaluating Expressions
1.5
Fractions
1.6
Percents and Decimals
1.7
Discounts, Markups and
Taxes
1.8
Ratios, Equivalent
Ratios
1.9
Rates
1.10
Proportions
1.11
Exponents (powers,
exponent rules, zero and
negative, scientific
notation)
1.12
Polynomials (intro,
adding/subtracting,
multiplying,
• Adding and Subtracting
• Multiplying and Dividing