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.

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

By the end of this lesson, you will be able to:

• 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.

Why Estimate?Why Estimate?

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…

CALCULATION & ROUNDINGCALCULATION & ROUNDING

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 WHOLE NUMBERSROUNDING WHOLE NUMBERS

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.

ROUNDING TO NEAREST 10THROUNDING TO NEAREST 10TH

EXAMPLE:

2257

728.958.1

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.

1. Identify the units digit.

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?

Estimating MeasurementsEstimating Measurements

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

Using Rounding to Estimate a Sum

Brandon runs 8 km every day to train for a cross-country 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.

Calculating Then RoundingCalculating Then Rounding

• 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

Estimating a TipEstimating a Tip

• 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.

KEY CONCEPTSKEY CONCEPTS

What the practice of What the practice of Mental Math can do!Mental Math can do!

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.

ROUNDING TO NEAREST ____ROUNDING TO NEAREST ____

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.

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 AlgebraLesson # Lesson1.1 Integers • Adding and Subtracting

• Multiplying and Dividing

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, expanding/simplifying)

1.13 Solving Equations (1-step, multi-step)