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Lesson 2.4 Place Value with a Calculator

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Objectives
To provide practice with place-value skills using a
calculator routine; and to review reading and writing large
numbers.
1
materials
Teaching the Lesson
Key Activities
Students enter a number in their calculators and then change one or more digits in the display
by adding or subtracting one or more numbers.
Key Concepts and Skills
• Read and write large numbers. [Number and Numeration Goal 1]
• Identify places in whole numbers and the values of the digits in those places.
[Number and Numeration Goal 1]
• Add and subtract multidigit whole numbers. [Operations and Computation Goal 2]
• Solve open sentences. [Patterns, Functions, and Algebra Goal 2]
Щ— Math Journal 1, p. 36
Щ— Study Link 2 3
б­њ
Щ— Teaching Aid Master (Math Masters,
p. 388 or 389; optional)
Щ— Transparency (Math Masters, p. 47;
optional)
Щ— calculator
Щ— slate
Ongoing Assessment: Recognizing Student Achievement Use a Math Log or Exit Slip.
[Number and Numeration Goal 1]
2
Ongoing Learning & Practice
Students play Fishing for Digits to practice identifying digits in whole numbers and expressing
their value.
Students practice and maintain skills through Math Boxes and Study Link activities.
materials
Щ— Math Journal 1, p. 37
Щ— Student Reference Book, p. 242
Щ— Study Link Master (Math Masters,
p. 48)
Щ— Game Master (Math Masters,
p. 472; optional)
Щ— calculator
Щ— overhead calculator (optional)
3
materials
Differentiation Options
READINESS
Students use a place-value tool to practice
finding numbers that are 10 more or less,
100 more or less, or 1,000 more or less than
a given number.
ENRICHMENT
Students decipher a place-value code.
Щ— Teaching Masters (Math Masters,
pp. 49 and 50)
Щ— Teaching Aid Masters (Math
Masters, pp. 399–402)
Щ— scissors; stapler
See Advance Preparation
Additional Information
Advance Preparation For the optional Readiness activity in Part 3, decide whether you will
prepare Compact Place-Value Flip Books (Math Masters, pp.399–402) ahead of time or have
students make them.
100
Unit 2 Using Numbers and Organizing Data
Technology
Assessment Management System
Math Log or Exit Slip
See the iTLG.
Getting Started
Mental Math and
Reflexes
Students display a number on
their calculators for their partners to
read. They also take turns dictating
numbers for their partners to display
on their calculators.
Math Message
(Write 56,385 and
7,490,613 on the board.)
Be prepared to read the numbers aloud.
Study Link 2 3
Follow-Up
б­њ
Have partners compare
answers. Ask students to draw a
star next to any problems they wish to
discuss with the whole class.
1 Teaching the Lesson
б­¤ Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
Have pairs of students read the numbers to each other. Then ask
someone to read the number 56,385 aloud. Students indicate
thumbs-up if they agree with the reading.
Ask students to respond to the following questions on their slates
and refer to a place-value chart if necessary.
в—Џ
Which digit is in the tens place? 8 How much is that digit
worth? 80
в—Џ
Which digit is in the hundreds place? 3 How much is that digit
worth? 300
в—Џ
Which digit is in the ones place? 5 How much is that digit
worth? 5
Ask someone to read 7,490,613 to the class and pose questions
similar to the ones above.
в—Џ
Which digit is in the ten-thousandths place? 9 How much is
that digit worth? 90,000
в—Џ
Which digit is in the millions place? 7 How much is that digit
worth? 7,000,000
в—Џ
Which digit is worth 200 times as much as the 3 in the ones
place? The 6 in the hundreds place is worth 600.
Tell students that in this lesson they will solve calculator
problems that require them to focus on the digits and values of
digits in numbers.
Lesson 2 4
б­њ
101
б­¤ Practicing Place-Value Skills
WHOLE-CLASS
ACTIVITY
with a Calculator
(Math Journal 1, p. 36; Math Masters, p. 47)
Make a chart on the board or use a transparency of Math Masters,
page 47. (See below.) For each problem, provide the “Change to”
digit and the “Operation” sign for students to record on journal
page 36 as you guide the class through the examples.
Students solve each problem on their calculators. Only the given
digit may be changed. All of the other digits in the starting
number must remain the same. Discuss students’ solutions.
ELL
Adjusting
the Activity
Have students build the starting number with
base-10 blocks and take away or add the
necessary blocks to show the new number.
Ask students to take note of how many
blocks they added or subtracted and
translate that into what they would do on
the calculator.
AUDITORY
б­њ
KINESTHETIC
б­њ
TACTILE
б­њ
VISUAL
Start with
Place of Digit
Change to
Operation
New Number
a.
570
Tens
0
ШЉ
500
b.
409
Hundreds
8
Ш‰
809
c.
54,463
Thousands
9
Ш‰
59,463
d.
760,837
Tens
0
ШЉ
760,807
e.
52,036,458
Ones
9
Ш‰
52,036,459
f.
Ten Thousands
5
Ш‰
52,056,459
g.
Millions
1
ШЉ
51,056,459
Say:
Problem 1
в—Џ
Enter 570 in your calculator.
в—Џ
Underline the digit in the tens place on your chart. 7
в—Џ
Change the digit in the tens place to 0. Use the
key.
Write “0” in the “Change to” column and “Ϫ” in the
“Operation” column.
в—Џ
(Give students time to carry out the operation on
the calculator.) How did you do that? Press
в—Џ
70
.
What is the new number? 500 (Students record the new
number on their chart.)
Problem 2
Links to the Future
Solving these problems requires students
to informally identify solutions to open
sentences and explain the strategies they
used. The solutions, for example, to
Problems 1 and 3 can be more formally
expressed as 570 ПЄ x П­ 500; x П­ 70 and
54,463 П© x П­ 59,463; x П­ 5,000. Lesson
3-11, Open Sentences, will provide students
with further instruction regarding Patterns,
Functions, and Algebra Goal 2.
102
Unit 2 Using Numbers and Organizing Data
в—Џ
Enter 409.
в—Џ
Use the
в—Џ
How did you do that? Press
в—Џ
What is the new number? 809
key to change the digit in the hundreds place to 8.
400
.
Problem 3
в—Џ
Enter 54,463.
в—Џ
Use the
to 9.
в—Џ
How did you do that? Press
в—Џ
What is the new number? 59,463
key to change the digit in the thousands place
5,000
.
Adjusting the Activity
Problem 4
в—Џ
Pose similar problems, but do not
Enter 760,837.
indicate which operation key (
в—Џ
Use the
should be used. Remind students that only
в—Џ
How did you do that? Press
в—Џ
What is the new number? 760,807
key to change the digit in the tens place to 0.
30
or
)
the given digit may change.
.
AUDITORY
б­њ
KINESTHETIC
б­њ
TACTILE
б­њ
VISUAL
Problem 5
в—Џ
Enter 52,036,458.
в—Џ
Use the
Press
в—Џ
Use the
to 5. Press
в—Џ
Use the
Press
в—Џ
key to change the digit in the ones place to 9.
1
.
key to change the digit in the ten-thousands place
20,000
.
key to change the digit in the millions place to 1.
1,000,000
.
What is the new number? 51,056,459
б­¤ Solving Change Problems
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 36)
Students solve the calculator “change” problems in Problem 2 on
journal page 36.
Ongoing Assessment:
Recognizing Student Achievement
Math Log or
Exit Slip
Use a Math Log or an Exit Slip (Math Masters, page 388 or 389) to
assess students’ ability to identify places in whole numbers and the
values of the digits in those places. Have students explain how they solved
Problem 2f on journal page 36. Students are making adequate progress if their
responses include that the digit in the ten-millions place in 873,562,003 is 7. The
value of the 7 is 70,000,000. To change the digit in the ten-millions place to a 1,
subtract 60,000,000. Some students may respond that another way to solve the
problem is to add –60,000,000.
Student Page
Date
Time
LESSON
2 4
б­њ
Calculator “Change” Problems
1. Follow your teacher’s directions to complete the “change” problems below.
Use your calculator.
4
Place of
[Number and Numeration Goal 1]
Start with
Digit
a.
570
Tens
b.
409
Hundreds
c.
54,463
d.
760,837
Tens
e.
52,036,458
Ones
New
Change to
Operation
0
8
9
0
9
5
1
ПЄ
П©
П©
ПЄ
П©
П©
ПЄ
Thousands
f.
Ten Thousands
g.
Millions
Number
500
809
59,463
760,807
52,036,459
52,056,459
51,056,459
2. Complete these calculator “change” problems on your own.
Start with
ଙ
a.
893
b.
5,489
c.
94,732
d.
218,149
e.
65,307,000
Place of
Digit
Change to
Tens
3
ПЄ
Hundreds
7
П©
Thousands
6
П©
Ten Thousands
0
ПЄ
Millions
9
f. 873,562,003
Ten Millions
1
g. 103,070,651
Hundred Millions
8
New
Number
Operation
П©
ПЄ
П©
833
5,789
96,732
208,149
69,307,000
813,562,003
803,070,651
36
Math Journal 1, p. 36
Lesson 2 4
б­њ
103
Game Master
Name
Date
Time
1 2
4 3
Fishing for Digits Record Sheet
Beginning Number
1
2 Ongoing Learning & Practice
X
New Number
New Number
2
б­¤ Playing Fishing for Digits
New Number
New Number
3
New Number
(Student Reference Book, p. 242; Math Masters, p. 472; optional)
New Number
4
PARTNER
ACTIVITY
New Number
New Number
5
Fishing for Digits combines place-value and calculator skills. The
steps in the game are similar to the calculator practice done in
this lesson. Go over the game directions on page 242 in the
Student Reference Book. Play a sample round as a class using an
overhead calculator, if available. If you want students to use the
Fishing for Digits Record Sheet (Math Masters, page 472), model
its use first.
New Number
Final Number
Name
Date
Time
1 2
4 3
Fishing for Digits Record Sheet
Beginning Number
1
X
New Number
New Number
2
New Number
New Number
3
New Number
б­¤ Math Boxes 2 4
New Number
4
5
INDEPENDENT
ACTIVITY
б­њ
New Number
New Number
New Number
(Math Journal 1, p. 37)
Final Number
Math Masters, p. 472
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 2-2. The skill in Problem 6
previews Unit 3 content.
б­¤ Study Link 2 4
INDEPENDENT
ACTIVITY
б­њ
(Math Masters, p. 48)
Home Connection Students practice place-value skills
and reading, writing, and ordering numbers up to one
billion.
Student Page
Date
Study Link Master
Time
LESSON
2 4
б­њ
Name
б­њ
with the digits 3, 0, 3, 8, and 0? Fill in the
circle next to the best answer.
algorithm.
a.
83,003
B
83,030
C
83,300
D
80,033
b.
145
П© 34
3.
About
5
centimeters
3
b.
c.
24
21
128
a. 16 П¬ 2 П­
in. П­ 2 ft
b. 20 П¬ 10 П­
ft П­ 7 yd
c.
48 in.
137 yd 2
8
ft
e.
9
8
2
6.
П­ 40 П¬ 5
d. 60 П¬ 10 П­
a.
80,007,941
c.
8,714,366
80,000,000
8,000,000
835,099,714
d.
860,490
800,000,000
800,000
487,000,063
15,000,297
a.
four hundred eighty-seven million, sixty-three
b.
fifteen million, two hundred ninety-seven
I am an 8-digit number.
• The digit in the thousands place is the result of dividing 64 by 8.
• The digit in the millions place is the result of dividing 63 by 9.
• The digit in the ten-millions place is the result of dividing 54 by 6.
• The digit in the tens place is the result of dividing 40 by 5.
• The digit in the hundred-thousands place is the result of dividing 33 by 11.
• All the other digits are the result of subtracting any number from itself.
6
П­ 45 П¬ 5
9 7, 3 0 8, 0 8 0
20
37
Math Journal 1, p. 37
104
b.
Write each number using digits.
What number am I?
129
97,654,320
Try This
6. Divide mentally.
in.
d. 1 yd 1 ft П­
e. 413 ft П­
5.
centimeters
97
2
5 8 1, 9 7 0, 0 0 0
Write the value of the digit 8 in each numeral below.
b.
ft
the hundred-millions place,
the ten-thousands place,
the millions place,
the hundred-thousands place,
the ten-millions place, and
all other places.
Write the largest number you can. Use each digit just once.
3 5 0 7 9 2 6 4
4.
a.
About
1
4
in
in
in
in
in
in
10 11
nearest centimeter.
a. 14 in. П­
Write the number that has
5
7
1
9
8
0
15,964
1,400,960
1,509,460
15,094,600
150,094,400
4. Measure these line segments to the
5. Complete.
2.
15,964 1,509,460 150,094,400
1,400,960 15,094,600
297
П© 136
4
Sample answer:
Write the numbers in order from
smallest to largest.
433
179
3. Draw a concave pentagon.
1.
2. Add mentally or with a paper-and-pencil
Time
Place Values in Whole Numbers
24
1. What is the largest number you can make
A
Date
STUDY LINK
Math Boxes
Unit 2 Using Numbers and Organizing Data
Math Masters, p. 48
Teaching Master
Name
3 Differentiation Options
Date
LESSON
б­њ
Display each number below in your place-value flip book. Then display, read,
and record the numbers that are 10 more, 100 more, and 1,000 more.
Circle the digit that changed.
Number
PARTNER
ACTIVITY
READINESS
б­¤ Using a Place-Value Tool
Use a Place-Value Tool
24
1.
146
2,368
15–30 Min
4,571
(Math Masters, pp. 49 and 399–402)
15,682
2.
100 more
156
2 46
6 08
2, 4 68
4, 6 71
15, 7 82
4
1,000 more
1 ,146
1 ,508
3 ,368
5 ,571
16 ,682
Display each number below in your place-value flip book. Then display, read,
and record the numbers that are 10 less, 100 less, and 1,000 less.
Circle the digit that changed.
Number
10 less
100 less
1,000 less
2,345
2,3 3 5
2, 2 45
1 ,345
3,491
3,4 8 1
6,8 2 9
12,3 5 7
45,1 2 0
3, 3 91
6, 7 39
12, 2 67
45, 0 30
2 ,491
5 ,839
1 1 ,367
4 4 ,130
6,839
12,367
45,130
3.
10 more
518
2,3 7 8
4,5 8 1
15,6 9 2
508
To provide experience identifying the place value of digits in large
numbers, have students use a Compact Place-Value Flip Book to
solve problems. The flipping of the digits in the place-value tool
provides a hands-on way for students to see the operation that
occurs when the digit within a number changes. Have students
describe how they would change the original number to make the
new number for each prompt.
Time
Use your place-value flip book to help you answer the following questions.
a.
What number is 50 more than 329?
b.
What number is 300 more than 517?
c.
What number is 60 less than 685?
d.
What number is 400 less than 932?
379
817
625
532
Math Masters, p. 49
The Compact Place-Value Flip Book can be used to display numbers
from 99,999 to 0.0001. When students have completed the activity,
collect and save the books for use in Unit 4—Decimals and Their Uses.
ENRICHMENT
б­¤ Deciphering a Place-Value Code
PARTNER
ACTIVITY
15–30 Min
(Math Masters, p. 50)
To apply students’ understanding of place value, have
them decipher the packing-system code used at a bakery.
Encourage students to use a visual organizer such as the
following to help them solve the problem. Students might begin by
asking “How many boxes of x muffins?” beginning with 27, then 9,
and so on.
Teaching Master
Name
LESSON
24
б­њ
Date
Time
Crack the Muffin Code
Daniel takes orders at the Marvelous Muffin Bakery. The muffins are packed into
boxes that hold 1, 3, 9, or 27 muffins. When a customer asks for muffins, Daniel
fills out an order slip.
4 175
• If a customer orders 5 muffins, Daniel writes CODE 12 on the order slip.
• If a customer orders 19 muffins, Daniel writes CODE 201 on the order slip.
• If a customer orders 34 muffins, Daniel writes CODE 1021 on the order slip.
1.
Total
Muffins
Boxes
of 27
Boxes
of 9
Boxes
of 3
What would Daniel write on the order slip if a customer asked for 47 muffins? Explain.
1202
Sample answer: Daniel needs 1 box of 27 muffins (the “1”
in the code), 2 boxes of 9 muffins (18 muffins; the first “2”
in the code); zero boxes of 3 muffins (the “0” in the code), and
2 boxes of 1 muffin (2 muffins; the last “2” in the code).
Boxes
of 1
CODE
2.
If the Marvelous Muffin Bakery always packs its muffins into the fewest number
of boxes possible, what is a code Daniel would never write on an order slip? Explain.
CODE
Have students describe how the chart they used to solve the
problem is different from and similar to a base-ten place-value
chart. In this problem, you multiply by 3 to get the next column.
In the base-ten place-value chart, you multiply by 10. In both
charts, each time you have enough in one column, that column
becomes 0 and the next column becomes 1.
Sample answer: 300
CODE 300 means that the bakery would be using 3 boxes
of 9 to pack 27 muffins instead of using 1 box of 27 to pack
27 muffins (CODE 1000).
3.
The largest box used by the bakery holds 27 muffins. Daniel thinks the bakery should
have a box one size larger. How many muffins would the new box hold? Explain.
81
muffins
Sample answer:
There is a pattern in the numbers 1, 3, 9, 27. The rule is П«3.
So, the next number in the pattern is 27 П« 3 П­ 81.
Math Masters, p. 50
Lesson 2 4
б­њ
105
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