Estimating DecimalsEQ: How can I use estimation techniques?

MA.6.A.3.5

Estimating DecimalsEstimatin

g Decimals

Clustering

Rounding Compatible

Numbers

ClusteringWhat is clustering?

ClusteringWhat is clustering?

A method used to estimate a sum or product when all the numbers are

close to the same value.When would you use clustering to

estimate the solution to a problem involving decimals?

ClusteringWhat is clustering?

A method used to estimate a sum or product when all the numbers are

close to the same value.When would you use clustering to

estimate the solution to a problem involving decimals?

When all the numbers are close to each other.

ClusteringNancy wants to cycle, ice skate,

and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling – 165.5 calories, ice skating – 177.5 calories, and water skiing – 171.5 calories.)

In this example, what number could represent all of the calories?

ClusteringNancy wants to cycle, ice skate,

and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling – 165.5 calories, ice skating – 177.5 calories, and water skiing – 171.5 calories.)

In this example, what number could represent all of the calories? 170

ClusteringNancy wants to cycle, ice skate,

and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling – 165.5 calories, ice skating – 177.5 calories, and water skiing – 171.5 calories.)

In this example, what number could represent all of the calories? 170

ClusteringNancy wants to cycle, ice skate,

and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling – 165.5 calories, ice skating – 177.5 calories, and water skiing – 171.5 calories.)

What operation could you use rather than adding 170 plus 170 plus 170?

ClusteringNancy wants to cycle, ice skate, and

water ski for 30 minutes each. About how many calories will she burn in all? (Cycling – 165.5 calories, ice skating – 177.5 calories, and water skiing – 171.5 calories.)

What operation could you use rather than adding 170 plus 170 plus 170?

Multiplication

RoundingWhen rounding a decimal, how do you

know which digit to look at?

RoundingWhen rounding a decimal, how do you know

which digit to look at?

0. 375 1000 Place a 1 under the decimal and a 0 under

each value past the decimal. Read the whole number and the “spit”

number

Rounding

Explain the rules for rounding a decimal.

Rounding

Explain the rules for rounding a decimal.

◦ Underline the specified place value.

Rounding

Explain the rules for rounding a decimal.

◦ Underline the specified place value.◦ Look to the right of the underlined value.

Rounding

Explain the rules for rounding a decimal.

◦ Underline the specified place value.◦ Look to the right of the underlined value.◦ 5 or more “raise the score” or 4 or less “let it rest”

Rounding

If you rounded all the numbers “up”, how would your estimated answer compare to the actual answer to the problem?

Rounding

If you rounded all the numbers “up”, how would your estimated answer compare to the actual answer to the problem?

If all the numbers were rounded up, the estimated answer would be an

over-estimate

Compatible NumbersWhat are compatible numbers?

Given the expression 33.83 · 1.98, how does the estimated product compare to the actual product? Explain.

Given the expression 72.77 ÷ 26.14, why would you choose not to round the numbers to 73 and 26?

What would you use?

Compatible NumbersWhat are compatible numbers?

Numbers that are close to the given

numbers that make estimation or mental math easier.

Compatible NumbersGiven the expression 33.83 · 1.98, how

does the estimated product compare to the actual product? Explain.

Compatible NumbersGiven the expression 72.77 ÷ 26.14, why

would you choose not to round the numbers to 73 and 26?

Compatible NumbersGiven the expression 72.77 ÷ 26.14, why

would you choose not to round the numbers to 73 and 26?

What would you use?

Estimating DecimalsMake the following estimations and justify

your choicesEstimating

Decimals

Clustering

31.2 · 28.7 · 30.5

Rounding

7.6 · 9.2

Compatible Numbers

18.89 · 5.11