STAMS™ SERIES
D
STRATEGIES
TO
ACHIEVE
MATHEMATICS
SUCCESS
□ PROVIDES INSTRUCTIONAL ACTIVITIES FOR 12 MATHEMATICS STRATEGIES
□ USES A STEP-BY-STEP APPROACH TO ACHIEVE MATHEMATICS SUCCESS
□ PREPARES STUDENTS FOR ASSESSMENT IN MATHEMATICS COMPREHENSION
TABLE OF CONTENTS
Strategy One
Building Number Sense . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Strategy Two
Using Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Strategy Three
Applying Addition
Strategies One–Three
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Strategy Four
Applying Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Strategy Five
Applying Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Strategy Six
Applying Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Strategies Four–Six
REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Strategy Seven
Converting Time and Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Strategy Eight
Converting Customary and Metric Measures . . . . . . . . . . . . . . . . . . . . . . . . 82
Strategy Nine
Using Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Strategies Seven–Nine
REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Strategy Ten
Using Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Strategy Eleven
Determining Probability and Averages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Strategy Twelve
Interpreting Graphs and Charts
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Strategies Ten–Twelve
REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Strategies One–Twelve
FINAL REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Strategies to Achieve Mathematics Success (STAMS™ Series) Book D—CURRICULUM ASSOCIATES®, Inc.—www.curriculumassociates.com—800-225-0248
Strategy
Two
USING ESTIMATION
PART ONE: Think About Estimation
WHAT DO YOU KNOW ABOUT ESTIMATING NUMBERS?
An estimate is a number that is close to another number.
An estimate may be rounded to the nearest whole number, or the nearest ten, hundred,
thousand, ten thousand, and so forth.
▶
Answer each question on the line provided.
a.
To the nearest 10: Is 38 closer to 30 or 40? _____________________
b. To the nearest 100: Is 115 closer to 100 or 200? _____________________
c.
To the nearest 1,000: Is 2,776 closer to 2,000 or 3,000? _____________________
d. To the nearest whole number: Is 29.7 closer to 29 or 30? _____________________
e.
To the nearest 100: Is 5,162 closer to 5,100 or 5,200? _____________________
f.
To the nearest 10: Is 5,162 closer to 5,160 or 5,170? _____________________
▶
Write five four-digit numbers that, when rounded to the nearest thousand, would
be 4,000. ______, ________, ________, _______, and ________
▶
Round each decimal to the nearest whole number.
Write each answer on the line provided.
a.
513.9 would be rounded to _____________________.
b. 6,598.12 would be rounded to _____________________.
c.
499.87 would be rounded to _____________________.
d. 7,022.31 would be rounded to _____________________.
e.
781.43 would be rounded to _____________________.
You just reviewed estimating and rounding numbers.
14
Using Estimation
Strategies to Achieve Mathematics Success (STAMS™ Series) Book D—CURRICULUM ASSOCIATES®, Inc.—www.curriculumassociates.com—800-225-0248
WHAT DO YOU KNOW ABOUT ROUNDING NUMBERS
THAT CONTAIN THE DIGIT 5?
If the digit one place to the right of the place being rounded to is 5 or greater,
round up.
If the digit one place to the right of the place being rounded to is 4 or less,
round down.
▶
Round 4,945 to the nearest 10, 100, and 1,000.
a.
▶
to the nearest 10:
b. to the nearest 100:
______________
c.
______________
to the nearest 1,000:
Round 68,057 to the estimation indicated.
a.
to the nearest 10:
______________
b. to the nearest 100:
______________
c.
______________
to the nearest 1,000:
d. to the nearest 10,000:
▶
______________
______________
Round 55,555 to the estimation indicated.
a.
to the nearest 10:
______________
b. to the nearest 100:
______________
c.
______________
to the nearest 1,000:
d. to the nearest 10,000:
______________
You just reviewed information about rounding numbers.
Together, write four five-digit numbers. Then, working alone,
round each number to the nearest 10, the nearest 100, the
nearest 1,000, and the nearest 10,000. Take turns sharing and
discussing your results.
Using Estimation
15
Strategies to Achieve Mathematics Success (STAMS™ Series) Book D—CURRICULUM ASSOCIATES®, Inc.—www.curriculumassociates.com—800-225-0248
PART TWO: Learn About Estimation
Estimation is used to find a number that is close to an exact number.
Study the estimation chart that Sagar’s teacher made. As you study,
think about how to find an estimate.
Number
Nearest
10
Nearest
100
Nearest
1,000
Nearest
10,000
7,081
7,080
7,100
7,000
46,776
46,780
46,800
47,000
50,000
138,223
138,220
138,200
138,000
140,000
You use estimation to find the nearest ten, hundred, thousand, or ten thousand, and
so forth, of a number. The estimate for 7,081 to the nearest thousand is 7,000.
You use estimation to check if a sum of numbers makes sense. First, you round the
addends. If you round the addends 1,382 and 2,716 to the nearest hundred, you get
1,400 and 2,700. If you add 1,400 2,700, you get 4,100, which is the estimated sum
of 1,382 2,716. The estimated sum of 4,100 is very close to the actual sum of 4,098.
You also use estimation to find the nearest whole number of a decimal.
Number
Nearest Whole Number
3.8
4
57.9
58
6,489.34
6,489
You use estimation to find a number that is close to another number.
▶
To round a number, find its nearest ten, hundred, thousand, ten thousand,
and so forth. To round a decimal, find its nearest whole number.
▶
Estimate to check if a sum or a difference is reasonable. First round the numbers in
the addition or subtraction problem. Then do the required operation to the rounded
numbers to get the estimate.
16
Using Estimation
Strategies to Achieve Mathematics Success (STAMS™ Series) Book D—CURRICULUM ASSOCIATES®, Inc.—www.curriculumassociates.com—800-225-0248
Sagar made a place-value chart for math homework. Study Sagar’s chart.
Think about finding the nearest ten, hundred, thousand, ten thousand,
and hundred thousand of the number. Then do Numbers 1 through 4.
hundred
ten
thousands thousands thousands
(100,000)
(10,000)
(1,000)
3
1
2,
hundreds
(100)
tens
(10)
ones
(1)
tenths
(.1)
hundredths
(.01)
3
7
8
.4
6
1. Sagar estimated the number in the chart
to the nearest thousand. Which of these
numbers is the correct estimate?
훽 313,000
훾 310,000
훿 320,000
 312,000
3. Sagar estimated the number in the chart
to the nearest ten thousand. Which of
these numbers is the correct estimate?
훽 312,000
훾 313,000
훿 312,400
 310,000
2. Sagar wanted to double the number in
the chart. First, he rounded the number
to the nearest hundred, then he doubled
the number. Which of the following
numbers is about twice the value of the
given number?
훽 624,800
훾 640,600
훿 620,000
 604,000
4. Sagar estimated the number in the
chart to the nearest whole number.
Which of these numbers is the nearest
whole number?
훽 312,379
훾 312,380.6
훿 312,378
 312,400
Talk about your answers to questions 1–4.
Tell why you chose the answers you did.
Using Estimation
17
Strategies to Achieve Mathematics Success (STAMS™ Series) Book D—CURRICULUM ASSOCIATES®, Inc.—www.curriculumassociates.com—800-225-0248
PART THREE: Check Your Understanding
Remember: You use estimation to find a number that is close to another number.
▶
To round a number, find its nearest ten, hundred, thousand, ten thousand,
and so forth. To round a decimal, find its nearest whole number.
▶
Estimate to determine if an actual answer is reasonable. First round the numbers in the
problem. Then do the required operation to the rounded numbers to get the estimate.
Solve this problem. As you work,
ask yourself, “What is the rounded
number of each addend?”
5. Sagar estimated the sum of
4.79 615.38 102.07 to the nearest
whole number. What is the correct
estimate?
훽 721
훾 724
훿 722
 700
18
Solve another problem. As you work,
ask yourself, “How do I round this
number to the nearest ten, hundred,
thousand, or ten thousand, and
so forth?”
6. Sagar determined that his heart beats
about 705,600 times per week. What
number is 705,600 rounded to the
nearest thousand?
훽 700,000
훾 704,000
훿 705,000
 706,000
Using Estimation
Strategies to Achieve Mathematics Success (STAMS™ Series) Book D—CURRICULUM ASSOCIATES®, Inc.—www.curriculumassociates.com—800-225-0248
Look at the answer choices for each question.
Read why each answer choice is correct or not correct.
5. Sagar estimated the sum of
4.79 615.38 102.07 to the nearest
whole number. What is the correct
estimate?
훽 721
This answer is not correct because
4.79 615.38 102.07, when
rounded, is 5 615 102, which
has a sum of 722, not 721.
훾 724
This answer is not correct because
4.79 615.38 102.07, when
rounded, is 5 615 102,
which has a sum of 722, not 724.
● 722
This answer is correct because
4.79 615.38 102.07, when
rounded, is 5 615 102,
which has a sum of 722.
 700
6. Sagar determined that his heart beats
about 705,600 times per week. What
number is 705,600 rounded to the
nearest thousand?
훽 700,000
This answer is not correct because
705,600, rounded to the nearest
thousand, is 706,000, not 700,000.
훾 704,000
This answer is not correct because
705,600, rounded to the nearest
thousand, is 706,000, not 704,000.
훿 705,000
This answer is not correct because
705,600, rounded to the nearest
thousand, is 706,000, not 705,000.
● 706,000
This answer is correct because 705,600,
rounded to the nearest thousand,
is 706,000.
This answer is not correct because
4.79 615.38 102.07, when
rounded, is 5 615 102,
which has a sum of 722, not 700.
Using Estimation
19
Strategies to Achieve Mathematics Success (STAMS™ Series) Book D—CURRICULUM ASSOCIATES®, Inc.—www.curriculumassociates.com—800-225-0248
PART FOUR: Learn More About Estimation
You estimate when you round a number. Numbers can be rounded to different
places, such as hundredths, tenths, ones, tens, hundreds, thousands, and so forth.
▶
To round a number to a particular place, look at the digit to the right of that place.
For example, to round 5,763 to the nearest hundred, look at the 6.
▶
The digit 5 is the midpoint for rounding. Numbers that fall below that midpoint
are rounded down. Numbers that fall on or above that midpoint are rounded up.
The 6 in 5,763 falls above the midpoint. Therefore, 5,763 to the nearest hundred
is 5,800.
Sagar wrote some problems for a math contest. Do Numbers 7 through 10.
7. There are 1,760 yards in a mile. What
is this number rounded to the nearest
hundred yards?
훽 1,700
훾 1,800
훿 1,750
 2,000
8. What is 125,880 rounded to the nearest
ten thousand?
훽 120,000
훾 125,000
훿 126,000
 130,000
20
9. Shawna worked for 7.28 hours, Marlene
worked for 8.53 hours. To the nearest
whole number, about how many hours
did both girls work?
훽 14 hours
훾 15 hours
훿 16 hours
 17 hours
10. Estimate, to the nearest thousand,
the sum of 21,384 74,607.
훽 95,000
훾 96,400
훿 96,000
 90,000
Using Estimation
Strategies to Achieve Mathematics Success (STAMS™ Series) Book D—CURRICULUM ASSOCIATES®, Inc.—www.curriculumassociates.com—800-225-0248
Read this part of a report that Sagar wrote about populations.
Then do Numbers 11 through 14.
Last year, 31,748 people lived in
Ashton Falls. This year, the population
is 32,336. So, our town population
has grown by 588 people. There
are reasons why the population has
changed. The town had 150 deaths
and 300 births, and 438 people moved
to town from other areas.
Here are the populations of four
other cities.
Dakari:
992,038
Sampson: 734,676
Mouton: 614,289
Bickford: 547,725
11. What is the population of Mouton
rounded to the nearest hundred people?
훽 614,000
훾 616,000
훿 614,300
 614,200
13. Round Dakari’s population to the
nearest thousand people.
훽 990,000
훾 991,000
훿 992,040
 992,000
12. What is the population of Bickford
rounded to the nearest hundred people?
훽 547,700
훾 548,000
훿 548,700
 540,000
14. To the nearest ten thousand people,
what is the population of Sampson?
훽 740,000
훾 735,000
훿 734,700
 730,000
Using Estimation
21
Strategies to Achieve Mathematics Success (STAMS™ Series) Book D—CURRICULUM ASSOCIATES®, Inc.—www.curriculumassociates.com—800-225-0248
PART FIVE: Prepare for a Test
▶
A test question about estimation may ask you to round a number to its nearest ten,
hundred, thousand, ten thousand, and so forth.
▶
A test question about estimation may ask you to round a decimal to its nearest
whole number.
▶
A test question about estimation may ask you to estimate to determine if an actual
answer is reasonable.
Read the article that Sagar read about Alaska.
Then do Numbers 15 and 16.
Large but Small
Alaska is the largest state in the U.S.
It covers a land area of 570,374 square
miles. However, Alaska ranks forty-eighth
among the states in population. The
population of Alaska in 2000 was 626,932.
ALASKA
Anchorage
Nearly half of Alaska’s population live
in Anchorage. Anchorage is the most
populated city in Alaska, with an estimated
population of 260,000.
Using Estimation
Using Estimation
15. To the nearest hundred thousand
square miles, what is the estimate
of Alaska’s land area?
훽 500,000 square miles
훾 600,000 square miles
훿 570,000 square miles
 570,400 square miles
16. Anchorage’s estimated population
is about 260,000. Which of these
numbers could be the actual
population of Anchorage?
훽 245,862
훾 260,283
훿 254,387
 265,004
22
Using Estimation
Strategies to Achieve Mathematics Success (STAMS™ Series) Book D—CURRICULUM ASSOCIATES®, Inc.—www.curriculumassociates.com—800-225-0248
Sagar read an article about Nevada. Read what he learned.
Then do Numbers 17 and 18.
The Silver State
Nevada is called the Silver State, a reference to
its earlier days as a place where silver was mined.
The state of Nevada covers 110,567 square miles,
or 286,368.53 square kilometers. The capital of
Nevada is Carson City.
NEVADA
Las Vegas and Reno are two other cities in
Nevada. In 2003, Las Vegas had a population of
517,017 and Reno had a population of 193,882.
Using Estimation
Using Estimation
17. Sagar correctly determined, to the
nearest hundred people, the combined
population of Las Vegas and Reno.
What was his correct estimate?
훽 710,900
훾 710,000
훿 700,000
 711,100
18. Sagar determined that Nevada has
an area of 286,368.53 square
kilometers. What is the number
286,368.53 rounded to the nearest
whole number?
훽 287,370
훾 286,369
훿 286,368
 286,360
Using Estimation
23
Strategies to Achieve Mathematics Success (STAMS™ Series) Book D—CURRICULUM ASSOCIATES®, Inc.—www.curriculumassociates.com—800-225-0248