Estimation

Clothing

Groceries

Travel Costs

Construction

Computation Estimation

Computation estimation is: using some computation using easy mental strategies using number sense using a variety of strategies getting close to the exact answer

It is not: just a guess doing hand calculations using a calculator exact

Quickly and easily get a

number that is close

enough to the exact

answer to be useful

Simplifi

ed

mental

calcu

lation

When do we estimate?

When there is no need to have an exact answer and an estimate is good enough: for example "Do I have enough money?"

When there is not enough information to get an exact answer: for example, "About how many times will my heart beat in an hour?"

To check if the answer from a calculation is reasonable.

Estimation Vocabulary

Front-end: take only the first number, cut-off (truncate) the other numbers Adjusting with front-end: compensate for the values

that were truncated Compensation: adjust, amend, improve, revise, modify

your estimate, make it bigger, make it smaller

Rounding: round to the nearest to the desired place value

Compatible numbers: numbers grouped together to make computation easy

Use a variety of strategies

There is not really any such thing as a "wrong" estimate... some estimates are less useful than others... any estimate made using the original problem is a

valid estimate.

The goal is not to find the one correct "estimate" but to have the skill to reason about the numbers being used, to be able to come up with a range that is suitable for using to predict the answer, and to have a quick and easy-to-do method for checking to see what a reasonable answer would be.

Questions You Should Ask

"How did you get that answer?"

"Why do you think it's a reasonable answer?"

Estimation Strategies

Front-End Estimation

8857

  4758

7045

+ 2110

8857

  4758

7045

+ 2110

8000

4000

7000

+ 2000

Draw the line after the first number

In each addend.

Front-End Estimation

A. Between 11,000 and 15,000

B. Between 16,000 and 20,000

C. Between 20,000 and 25,000

D. Between 28,000 and 33,000

8000

  4000

7000

+2000

21,000

62,899

  10,236

75,000

+ 37,596

62899

  10236

75000

+ 37596

60,000

10,000

70,000

+ 30,000

Draw the line after the first number

In each addend.

Front-end Estimation

A. Between 150,000 and 159,000

B. Between 160,000 and 169,000

C. Between 170,000 and 179,000

D. Between 180,000 and 189,000

60,000

  70,000

10,000

+ 30,000170,000

Use Front-end Estimation

Estimate the sum: 357,289 + 238,499 = _________

A.500,000 B.580,000 C.595,000 D.600,000

Is the front-end estimation reasonable? What could you do to improve the front-end

estimate?What is the best estimate and why?

No, it is low.

Estimate with compensation.

600,000 is a closer.

Use compatible numbers since 60,000 + 40,000 would be about 100,000 more.

500,000

What error is acceptable?

The numbers: “59”, “54”, “55” are all “50” using front-end estimation.

1,999,999 + 1,999,999 = 2,000,000 What is a better estimate? Is the error acceptable?

Learn multiple estimation strategies. Always ask the question: Is the answer reasonable?

4,000,000No, 2,000,000 is too low.

Rounding

8857

  4758

7045

+ 2110

8857

  4758

7045

+ 2110

9000

5000

7000

+ 2000

A. Between 11,000 and 15,000

B. Between 16,000 and 20,000

C. Between 20,000 and 25,000

D. Between 28,000 and 33,000

9000

  5000

7000

+ 200023,000

Exact: 22,770

247

6542

489

+ 92

247

6542

489

+ 92

200

6500

500

+ 100

200

6500

500

+ 100

A. A little less than 7,000

B. A little more than 7,000

C. A little less than 8,000

D. A little more than 8,0007300

Exact: 7,370

5028

6732

1285

+ 835

5000

7000

1000

+ 1000

5028

6732

1285

+ 835

14,000Exact: 13,880

5028

6732

1285

+ 835

5000

6700

1300

+ 800

5028

6732

1285

+ 835

13,800Exact: 13,880

Identify the estimation strategy

Front-End Rounding

3,876

5,814

3,176

+ 7,895

4,000

6,000

3,000

+ 8,000

3,000

5,000

3,000

+ 7,000

Closer estimate

20,761 18,00021,000

9,876

8,514

6,092

+ 3,895

9,000

8,000

6,000

+ 3,000

10,000

9,000

6,000

+ 4,000

Closer estimate

28,377 26,000 29,000

Estimate

Front-End Roundingvs.

A.Between 13,000 and 14,000

B.Between 12,000 and 13,000

C.Between 11,000 and 12,000

D.Between 10,000 and 11,000

5000

6700

1200

+ 800Exact:13700

290

6840

481

+ 94

Exact: 7705

A. Between 6,500 and 7,000

B. Between 7,000 and 7,500

C. Between 7,500 and 8,000

D. Between 8,000 and 8,500

Real World Problems

23

Can I buy four for $100?

Yesa)4 x $25 = $100 and $23 is less than $25b)$23 rounds to $20 and 4 x $20 = $80c)$23 rounds to $25 and 4 x $25 = $100 (high estimate)

Explai

n

$37

Can I buy three for $100?

Noa)3 x $33 is $99, so 3 x $37 would be more than $100.b)3 x $40 is $120

Explai

n

The soccer ball would have to cost ______ or less for me to purchase five of them for $60.

Can I buy five for $60?

Noa)5 x $15 = $75 which is more than $60.b)5 x $14 = $70 which is more than $60.c)$60 divided by 5 = $12, and $13.87 is more than $12.00.

$12.00

Explai

n

$4.95

Can I buy three for $20?

Yesa)3 x $5 = $15

Explain

Would you have enough money?

Estimate to find your answer.

If you buy 3 items that cost $4.93 each, will $15.00 be enough to buy all 3 items? Explain.

If you buy 2 items for $6.29 and 1 item for $3.55 will $15.00 be enough? Explain.

If you buy items for $4.32, $6.90, and $7.86, will $18.00 be enough? Explain.

Yes, 3 x $5 = $15 (high estimate)

No, $4 + $7 + $8 = $19

No, 2 x $6 + 1 x $4 = $16

0.1 or 10

0.01

or

100

0.001

or

1000

0.0001

or

10,000

1 digit 2 digits