008. Rounding and Estimation Strategies

Learning Intentions

• To understand that in some practical situations, an estimate or approximation is accurate enough
• Round numbers to a degree of accuracy (e.g. to the nearest 100)
• estimate numerical answers to arithmetic questions by rounding each number in the question

Pre-requisite Summary

• Understanding place value (ones, tens, hundreds, thousands)
• Knowing how to compare digits to midpoint values (e.g. in tens, in hundreds)
• Understanding that rounding changes a number to a nearby value
• Familiarity with basic arithmetic operations
• Ability to perform addition, subtraction, multiplication and division

Worked Examples

Worked Example 1

Decide if an estimate is sufficient:

a) A school has students. About how many students is this?

b) A truck carries kg. Is kg a reasonable estimate?

Worked Example 2

Round to the nearest value:

a) to the nearest

b) to the nearest

c) to the nearest

Worked Example 3

Round to the nearest :

a)

b)

c)

Worked Example 4

Estimate by rounding each number:

a)

b)

Worked Example 5

Estimate by rounding each number:

a)

b)

Problems

Problem 1

a) A town has people. About how many people is this?

b) Is a reasonable estimate?

Problem 2

Round to the nearest value:

a) to the nearest

b) to the nearest

c) to the nearest

Problem 3

Round to the nearest :

a)

b)

c)

Problem 4

Estimate by rounding each number:

a)

b)

Problem 5

Estimate by rounding each number:

a)

b)

Exercises

Understanding and Fluency

Exercise 1.

Round to the nearest :

a)

b)

c)

Exercise 2.

Round to the nearest :

a)

b)

c)

Exercise 3.

Round to the nearest :

a)

b)

c)

Exercise 4.

Estimate by rounding each number:

a)

b)

c)

Exercise 5.

Estimate by rounding each number:

a)

b)

c)

Exercise 6.

Estimate by rounding each number:

a)

b)

c)

Reasoning

Exercise 7.

Explain why rounds to to the nearest .

Exercise 8.

A student rounds to to the nearest . Explain the error.

Exercise 9.

Which is the better estimate for :

a)

b)

Explain.

Exercise 10.

Why is estimation useful before solving a problem exactly?

Problem-solving

Exercise 11.

A factory made toys. About how many toys is this to the nearest ?

Exercise 12.

A shop sold items on Monday and on Tuesday. Estimate the total.

Exercise 13.

A school budget is dollars. Estimate to the nearest .

Exercise 14.

A bus travels km per trip for trips. Estimate the distance.

Exercise 15.

A warehouse stores boxes across rows. Estimate how many per row.

Potential Misunderstandings

• Students may round Use the wrong place value digit
• Students may always round down instead of considering midpoint values
• Students may treat incorrectly when rounding
• Students may forget to round all numbers before estimating
• Students may think an estimate must be exact
• Students may mix different levels of rounding in the same calculation

Next: 009. Order of Operations in Arithmetic