Lesson
9 Estimating Products
Problem Solving:
Designing a Logo
Estimating Products
How do we estimate products?
We learned how to estimate sums and differences. In estimation, we
round the numbers in a problem to numbers that are easier to work
with. We learned how to use quarter rounding and how to round to the
nearest 10; 100; and 1,000.
Look at the following problem. We round the numbers in the problem
to estimate the product.
47
39
47
25
30
35
40
45
50
55
60
65
70
75
55
60
65
70
75
The number 47 rounded to the nearest ten is 50.
39
25
30
35
40
45
50
The number 39 rounded to the nearest ten is 40.
The product is about 2,000.
Remember that rounding can be very useful.
• Rounded numbers give us an answer that is close to the
actual answer.
• Rounded numbers are easier to work with.
• We can solve problems mentally using rounded numbers.
• We do not always need an exact answer to solve a problem.
Let’s practice rounding and estimation in multiplication.
170 Unit 3 • Lesson 9
Lesson 9
Because we know the estimation techniques for addition and subtraction,
it is easy to estimate in multiplication. Let’s look at another example that
shows how to estimate a product.
Example 1
To estimate a product,
round the factors to
create an extended
fact that can be solved
mentally.
49 S rounds to S 50
3
3
Estimate the product of 49 and 3.
49
25
30
35
40
45
50
55
60
65
70
75
450
500
The factor 49 rounded to the nearest ten is 50. This creates the
extended fact 50 × 3 = 150, which we can solve mentally. There
is no need to round both numbers.
A good estimate of 49 × 3 is 150.
Let’s see how a three-digit number being multiplied by a one-digit
number is estimated.
Example 2
386 S rounds to S 400
6
6
2,400
Estimate the product
of 386 and 6.
386
0
50
100
150
200
250
300
350
400
The factor 386 rounded to the nearest hundred is 400. The other factor,
6, does not need to be rounded. These numbers create the extended
fact 400 × 6 = 2,400, which can be solved mentally.
A good estimate of 386 × 6 is 2,400.
Using a calculator, we find that the exact product of 386 × 6 is 2,316.
This is close to our estimated product of 2,400, so the answer is
reasonable.
In both examples above, we only rounded one factor. Because the
bottom number is only one digit, we do not need to round it. Examples
1 and 2 show you that for numbers with more than one digit, we round
each factor to the nearest ten or hundred.
We can check an estimate
if we compute it by hand
or on a calculator. This
helps us determine if the
estimate is reasonable or
if we have made an error.
Unit 3 • Lesson 9 171
Lesson 9
How do we use estimation to solve word
problems that require multiplication?
We can also use estimation to solve multiplication word problems that
do not require an exact answer.
Example 1
Solve the word problem using estimation.
Problem:
The students in Ms. Randall’s physics class are building bridges with
plastic straws. The class is divided into 5 groups, and each group
needs 85 straws. Ms. Randall has a box of 500 straws. Does she have
enough straws for all of the groups?
Begin by asking the following questions:
• What is the problem asking for?
• What is the important information?
Because the problem asks us to compare two values, we do not need
to find the exact number of straws Ms. Randall needs. Instead, we can
estimate the number of straws she needs and compare it to the number
of straws she has.
85 S rounds to S 90
5
5
450
Ms. Randall needs about 450 plastic straws. This number is less than
500, so Ms. Randall has enough straws for all of the groups.
Apply Skills
Turn to Interactive Text,
page 118.
172 Unit 3 • Lesson 9
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Lesson 9
Problem Solving: Designing a Logo
How does a graphic designer use measurement?
A logo is an image that uses words and pictures to represent a
company, brand, or product. Graphic designers are hired to create logos
that are appealing and will catch people’s attention.
When graphic designers create logos, they use measurement just
like when they design advertisements. A sample logo that a graphic
designer might create for a pizza place is shown below.
1 cm
4 cm
7.2 cm
A designer needs to consider:
• size of text
• size of image
• size of logo
We know that designing jobs require creativity, but designers must be
able to use mathematics to measure.
Problem-Solving Activity
Turn to Interactive Text,
page 119.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 3 • Lesson 9 173
Lesson 9
Homework
Activity 1
Multiply to solve the set of basic and extended multiplication facts.
1. 5 × 5
2. 8 × 9
5 × 50
5 × 500
3. 7 × 4
8 × 90
8 × 900
7 × 40
7 × 400
Activity 2
Use traditional multiplication to find the product.
1.
64
2
2.
128
87
5
3.
435
962
4
3,848
4.
729
5
3,645
Activity 3
Estimate the product.
Model
1.
2.
21 2
3.
29
30
3 3
90
67 5
45 7
4.
685 6
5.
495 3
6.
241 6
3.
5,109
+ 2,981
Activity 4 • Distributed Practice
Add or subtract.
1.
505
 29
2.
476
4.
6,000
 1,000
5,000
174 Unit 3 • Lesson 9
9,100
 897
8,203
5.
7,872
+ 387
8,259
8,090
6.
777
+ 432
1,209