Objective
To provide practice estimating whether a product is in
the tens, hundreds, thousands, or more.
1
materials
Teaching the Lesson
Key Activities
Students make magnitude estimates for products and mark their estimates on a magnitude
bar that shows tens, hundreds, thousands, and so on.
Key Concepts and Skills
• Solve problems involving products where factors are multiples of 10, 100, 1,000, and so on.
[Operations and Computation Goal 3]
• Estimate whether a product is in the tens, hundreds, thousands, or more.
Math Journal 1, pp. 114 and 115
Study Link 5 3
Teaching Master (Math Masters,
p. 147)
calculator
See Advance Preparation
[Operations and Computation Goal 6]
• Explore meanings of average. [Data and Chance Goal 2]
Key Vocabulary
rough estimate • magnitude estimate
2
materials
Ongoing Learning & Practice
Students play Multiplication Wrestling.
Students practice and maintain skills through Math Boxes and Study Link activities.
Ongoing Assessment: Recognizing Student Achievement Use Math Masters,
page 488. [Patterns, Functions, and Algebra Goal 4]
3
materials
Differentiation Options
READINESS
Students use curved number
lines to practice rounding.
ENRICHMENT
Students use estimation to
find missing numbers and
digits in multiplication
number sentences.
Math Journal 1, p. 116
Student Reference Book, p. 253
Study Link Master (Math Masters,
p. 148)
Game Master (Math Masters,
p. 488)
per partnership: 4 each of number
cards 0–9 (from the Everything
Math Deck, if available) or a
10-sided die
EXTRA PRACTICE
Students estimate products.
Additional Information
Advance Preparation For the Math Message, make one copy of Math Masters, page 147
for every three students. Cut the masters apart and place them near the Math Message. For
Part 1, find out the total number of fourth graders and the total enrollment in your school.
Teaching Masters (Math Masters,
pp. 149 and 150)
5-Minute Math, pp. 19, 95, and 182
Technology
Assessment Management System
Math Masters, page 488
See the iTLG.
Lesson 5 4
331
Getting Started
Mental Math and Reflexes
Math Message
Continue to focus on multiplying by tens. This work will prepare
students for the partial-products algorithm that is introduced in
Lesson 5-5. Suggestions:
Take an answer sheet (Math Masters,
page 147 ), and complete it.
5 40 200
2 60 120
40 20 800
40 60 2,400
70 30 2,100
50 90 4,500
60 700 42,000
70 800 56,000
90 400 36,000
Study Link 5 3
Follow-Up
Partners compare answers. Have students
share their strategies for estimating sums.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
(Math Journal 1, p. 114)
Ask someone to read aloud the first two paragraphs of “What Do
Americans Eat?” on journal page 114. Give students a minute or
two to read the survey results and then discuss them. Suggestions:
Student Page
Date
LESSON
5 4
Time
What Do Americans Eat?
The U.S. Department of Agriculture conducts a survey to find out how much food
Americans eat. A large number of people are asked to keep lists of all the foods
they eat over several days.
181
These lists are then used to estimate how much of each food was eaten during one
year. The average American eats more than 2,000 pounds of food per year. This is
about 5 12 pounds of food per day.
●
Does any of this information surprise you?
●
Do you think any of this information has changed since it was
collected? Probably yes. The eating habits of Americans change
over time. This survey was taken in 2002.
●
What is meant by the “average” American? Does everyone eat
1
more than 2,000 pounds of food per year, or about 52 pounds
1
per day? Some people eat 52 pounds of food per day; some eat
1
1
more than 52 pounds, and some eat less than 52 pounds per
day. If all the food eaten by all Americans were divided into
equal shares, each person’s share would then be more than
1
2,000 pounds of food per year, or about 52 pounds per day. The
average American is one who eats an equal share each day.
Results show that the average American eats or drinks about the following amounts
in one year:
16
pounds of apples
27
pounds of bananas
5
pounds of broccoli
10
pounds of carrots
30
pounds of cheese
255
pounds of fish
28
cups of yogurt
17
22
pounds of ice cream
cups of milk
pounds of candy
Use your answers to the Math Message question to complete these statements.
1. I will eat about
2. I will drink about
3. I will eat about
eggs in one year.
Answers vary.
cups of milk in one year.
cups of yogurt in one year.
4. Based on your answers to Problems 1–3, do you think you eat like an average American?
Explain why or why not.
Answers vary.
114
Math Journal 1, p. 114
332
WHOLE-CLASS
ACTIVITY
to Make Magnitude Estimates
eggs
16
350
Using the Food-Survey Data
Unit 5 Big Numbers, Estimation, and Computation
(Math Journal 1, p. 114; Math Masters, p. 147)
Pose problems like the following. Ask students to make rough
estimates for the answers and describe how they made their
estimates. After each estimate is made, ask someone to find the
exact answer using a calculator.
●
●
About how many pounds of bananas might the students in our
class eat in one year? Will the answer be in the tens, hundreds,
thousands, ten-thousands, or more? Sample answer: The
average American eats 27 pounds of bananas per year. That is
about 30 pounds per year. There are 25 students in our class,
so that is about 750 pounds per year. The answer is in the
hundreds.
About how many glasses of milk might all the fourth-grade
students in our school drink in one year? Will the answer be in
the tens, hundreds, thousands, ten-thousands, or more? (You
will need to give the fourth-grade school population.)
●
About how many cups of yogurt might all the students in
our school eat in 1 year? Will the answer be in the tens,
hundreds, thousands, ten thousands, or more? (You will need to
give the school population.) Answers vary.
●
About how many eggs might an average family of four eat in
1 year? Will the answer be in the tens, hundreds, thousands,
ten thousands, or more? Sample answer: The average person
eats 255 eggs per year. A number model for the exact answer is
255 4 . Round 255 to the nearest hundred to get 300;
300 4 1,200. Or, round 255 down to 250, because it is a
close number and easy to use; 250 4 1,000. Both rough
estimates are in the thousands, but very close to 1,000.
●
The average person’s life expectancy in the United States is
about 77 years. About how many pounds of cheese might an
average person eat in a lifetime? Will the answer be in the tens,
hundreds, thousands, ten thousands, or more? Thousands,
30 80 2,400
Name
LESSON
54
Date
Time
What Do Americans Eat?
Answer the following questions:
Answers vary.
1.
How many eggs did you eat in the last 7 days?
2.
How many cups of milk did you drink in the last 7 days?
3.
How many cups of yogurt did you eat in the last 7 days?
Name
LESSON
54
Date
Time
What Do Americans Eat?
Answer the following questions:
Math Masters, page 147
Finally, have students use their answers in the Math Message to
compare their consumption of certain foods to that of an average
American. Students must convert their weekly results to 1-year
totals. Ask volunteers to describe how they might do this. If no one
mentions it, suggest the following procedure:
1. Multiply the total amount eaten in one week by 100. This
gives the total amount eaten in 100 weeks, which is about
2 years.
2. Divide the result by 2. This gives the total amount eaten in
about 1 year.
Have students record their 1 year totals at the bottom of journal
page 114.
NOTE A rough estimate is an estimate of the magnitude of an answer. Will the
answer be in the tens? In the hundreds? In the thousands? A rough estimate is
also called a magnitude estimate.
Lesson 5 4
333
Student Page
Date
Estimating Averages
Time
LESSON
Estimating Averages
5 4
(Math Journal 1, p. 115)
Estimate whether the answer will be in the tens, hundreds, thousands, or more.
182–184
Write a number model to show how you estimated.
Then circle the box that shows your estimate.
These problems focus on estimating the magnitude of an answer.
Students need to make only rough estimates that tell whether the
answer will be in the tens, hundreds, thousands, or more.
Example: Alice sleeps an average of 9 hours per night. How many hours
does she sleep in 1 year?
Number model:
10s
10 400 4,000
100s
1,000s
10,000s
PARTNER
ACTIVITY
100,000s 1,000,000s
Sample answers:
1. An average of about 23 new species of insects are discovered each day.
About how many new species are discovered in one year?
10s
NOTE This skill is isolated so students will realize the importance of making
20 400 8,000
Number model:
100s
1,000s
10,000s
rough estimates when they solve computation problems with or without a
calculator. There will be many opportunities for making more precise estimates
in the lessons that follow.
100,000s 1,000,000s
2. A housefly beats its wings about 190 times per second. That’s about
how many times per minute?
200 60 12,000
Number model:
10s
100s
1,000s
10,000s
Discuss the example with the class. Students can complete the
rest of the page with their partners using any estimation method
that works for them. Bring the class together to discuss estimation
strategies. Then have students check their estimates by finding
the exact answers using a calculator.
100,000s 1,000,000s
3. A blue whale weighs about as much as 425,000 kittens. About how many
kittens weigh as much as 4 blue whales?
Number model:
10s
400,000 4 1,600,000
100s
1,000s
100,000s 1,000,000s
10,000s
4. An average bee can lift about 300 times its own weight. If a 170-pound person
were as strong as a bee, about how many pounds could this person lift?
300 200 60,000
Number model:
10s
100s
1,000s
10,000s
Adjusting the Activity
100,000s 1,000,000s
115
Math Journal 1, p. 115
Use the example at the top of journal page 115 to illustrate two
meanings for “average sleep time.” Ask students how they would determine the
average nightly sleep time for the entire class. Then ask students how Alice’s
average sleep time of 9 hours may have been calculated. Sample answer:
Alice’s nightly sleep times were recorded for at least one week; for example,
M: 9 hr, T: 8 hr, W: 9 hr, Th: 8 hr, F: 7 hr, S: 11 hr, S: 11 hr. The “equal share”
mean of 9 hours is a good representation of the data. The longer sleep times on
the weekend offset some shorter weekday times like Friday.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
2 Ongoing Learning & Practice
Game Master
Name
Date
Round 1
Time
Multiplication Wrestling Record Sheet
Cards:
1 2
4 3
Playing Multiplication Wrestling
PARTNER
ACTIVITY
(Student Reference Book, p. 253; Math Masters, p. 488)
253
Numbers formed:
Teams: (
º
Products:
)º(
º
º
º
º
)
Students play Multiplication Wrestling to practice calculating
partial products and finding the sum of the partial products.
See Lesson 5-2 for additional information.
Total (add 4 products):
Round 2
Cards:
Numbers formed:
Teams: (
º
Products:
)º(
º
º
º
º
)
Cards:
Numbers formed:
Teams: (
º
Products:
)º(
º
º
º
º
)
Total (add 4 products):
Math Masters, p. 488
334
Math Masters
Page 488
Use Math Masters, page 488 to assess students’ ability to use the distributive
property of multiplication over addition in the context of the partial-products
algorithm. Students are making adequate progress if they can write each factor
as the sum of tens and ones and find the four partial products.
Total (add 4 products):
Round 3
Ongoing Assessment:
Recognizing Student Achievement
Unit 5 Big Numbers, Estimation, and Computation
Some students may be able to demonstrate the use of this property with
decimals or mixed numbers. For example, 4.2 3.5 (4 3) (4 0.5) 1
1
1
1
1 1
(0.2 3) (0.2 0.5) or 52 63 (5 6) (5 3) (2 6) (2 3).
[Patterns, Functions, and Algebra Goal 4]
Student Page
Date
Time
LESSON
Math Boxes 5 4
INDEPENDENT
ACTIVITY
5 4
Math Boxes
1. Fill in the missing numbers on each number line.
(Math Journal 1, p. 116)
a.
5.0
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 5-2. The skill in Problem 5
previews Unit 6 content.
5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9
b.
4.73
4.83 4.93 5.03 5.13 5.23 5.33
2. Measure the line segment to the nearest
Writing/Reasoning Have students write a response to
the following: For Problem 5, explain a shortcut you
might use to solve the division problems. Sample answer:
I used basic division facts to solve the problems. For 350 / 7,
I thought 35 / 7 5. I know 350 / 7 is 10 times as much, so
350 / 7 5 10 50. For 5,600 / 800, I thought 56 / 8 7.
800 7 5,600, so 7 is the answer.
5.53 5.63
a. About
b. About
c. About
circle next to the best answer.
B. 0.50 1.43 (0.77 0.19)
53 mm
5 cm 3 mm
5 . 3 cm
C. 14.46 12.09 3.46
D. 15.8 11.5 1.6 2.7
34–37
148
128 129
4. Insert or to make a true number
5. Divide mentally.
sentence.
a. 18,000 / 9 8,999,999
421,936,500 422,985,600
68,004,002 68,004,100
600,523 601,000
a. 9,000,000
INDEPENDENT
ACTIVITY
d.
b. 350 / 7 c. 3,500 / 5 d.
e.
7
700
2,000
50
700
5,600 / 800
42,000 / 60
6
(Math Masters, p. 148)
5.73
A. (7.6 3.8) 5.2 5.9
c.
Study Link 5 4
5.43
3. Which number sentence is true? Fill in the
millimeter. Record the measurement in
millimeters and centimeters.
b.
6.0
21
116
Math Journal 1, p. 116
Home Connection Students make magnitude estimates
for multiplication problems. Remind students to write a
number model for each estimate.
Study Link Master
Name
Date
STUDY LINK
54
Time
Estimating Products
Estimate whether the answer will be in the tens, hundreds, thousands,
or more. Write a number model to show how you estimated. Then circle
the box that shows your estimate.
184
Sample answers:
1.
A koala sleeps an average of 22 hours each day. About how many hours
does a koala sleep in a year?
20 400 8,000
Number model:
10s
2.
100s
1,000s
10s
100s
1,000s
10,000s
100,000s 1,000,000s
Golfers lose, on average, about 5 golf balls per round of play. About how many golf
balls will an average golfer lose playing one round every day for one year?
5 400 2,000
Number model:
10s
4.
100,000s 1,000,000s
10 20 200
Number model:
3.
10,000s
A prairie vole (a mouselike rodent) has an average of 9 babies per litter.
If it has 17 litters in a season, about how many babies are produced?
100s
1,000s
10,000s
100,000s 1,000,000s
In the next hour, the people in France will save 12,000 trees by recycling
paper. About how many trees will they save in two days?
Number model:
10s
2 20 10,000 400,000
100s
1,000s
10,000s
100,000s 1,000,000s
Try This
5.
How many digits can the product of two 2-digit numbers have?
Give examples to support your answer.
3 or 4 digits; 10 10 100 and 90 90 8,100
Practice
6.
60 7 420
7.
4 80 320
8.
1,800
200 9
Math Masters, p. 148
Lesson 5 4
335
Teaching Master
Name
Date
LESSON
Time
3 Differentiation Options
A Curved Number Line
54
The number lines below are curved like hills. Use them to help you round numbers.
Example 1:
Example 2:
Round 64 to the nearest ten.
Round 175 to the nearest hundred.
Which multiples of 10 are nearest to 64?
Which multiples of 100 are nearest to 175?
60
70
and
What number is halfway
between 60 and 70?
Will 64 “slide” down
the hill to 60 or to 70?
100 and 200
What number is halfway
between 100 and 200?
65
Will 175 “slide” down
the hill to 100 or 200?
60
READINESS
Rounding Whole Numbers
150
200
65
5–15 Min
Using a Number Line
175 rounded to the nearest hundred is 200.
64 rounded to the nearest ten is 60.
INDEPENDENT
ACTIVITY
150
(Math Masters, p. 149)
64
175
60
1.
100
70
Round 37 to the nearest ten.
Label the curved number line. Mark 37.
37 will “slide” down to
40
2.
.
37 rounded to the nearest ten is
200
432 will “slide” down to
40
.
To explore rounding whole numbers, have students plot numbers
on a curved number line to see which way the numbers will
“slide.” Have students describe how they rounded their numbers.
Encourage vocabulary such as top, bottom, endpoint, middle,
closer, and farther.
Round 432 to the nearest hundred.
Label the curved number line. Mark 432.
432 rounded to the
nearest hundred is
35
400 .
400 .
450
432
37
30
40
400
500
ENRICHMENT
Finding Missing Numbers
Math Masters, p. 149
INDEPENDENT
ACTIVITY
5–15 Min
and Digits
(Math Masters, p. 150)
To apply students’ understanding of estimates, have them
use estimation to find the missing numbers and digits in
multiplication number sentences. Ask students to describe
the strategies they used to solve the problems.
EXTRA PRACTICE
5-Minute Math
Date
LESSON
Time
Missing Numbers and Digits
54
1.
Complete the number sentences.
Fill in the circles using the numbers 3, 4, 6, or 7.
Fill in the rectangles using the numbers 47, 62, 74, or 86.
Some numbers will be used more than once.
a.
c.
e.
2.
7
47
329
6
62
372
6
74
444
b.
d.
f.
86
258
4
62
248
4
74
296
For each problem, fill in the squares using the digits 4, 6, and 7.
a.
6 4
7
b.
c.
4 6
7
448
3.
3
268
Use the digits 6, 7, 8, and 9 to make
the largest product possible.
4.
6 7
4
322
Use the digits 6, 7, 8, and 9 to make
the smallest product possible.
8 7 6
9
7,884
7 8 9
6
4,734
Math Masters, p. 150
336
5–15 Min
To offer students more experience with estimating products,
see 5-Minute Math, pages 19, 95, and 182.
Teaching Master
Name
SMALL-GROUP
ACTIVITY
Unit 5 Big Numbers, Estimation, and Computation