Download Chapter 5 Decimals (Basic)

MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
Chapter 5 Decimals (Basic)
Decimals Overview: There are thirteen decimal topics (D1-D13) covering 26 grade level
content expectations. Twenty-six activities have been developed for these topics.
D1
D2
D3
D4
D5
D6
D7
D8
D9
D10
D11
D12
D13
Topics
Meaning
Counting and writing
Size comparison and the numberline
Rounding decimals
Relationship to money (1)
Addition and subtraction (5)
Multiplication of decimals (3)
Division of decimals (2)
Fractions converted to decimals (0)
Decimals converted to fractions (2)
Percent to decimal conversion (2)
Percent computation (4)
Percent computation with easy fractions (1)
GLCEs Activities
2
2
2
5
2
4
0
1
1
2
5
4
3
5
2
2
0
1
2
0
2
0
4
0
1
0
It should not be surprising when students have difficulty understanding rational numbers written
either as decimals or fractions. After multiple years of mathematics with a number system where
given a number there is a next larger and/or next smaller number. This allows counting as a
solution strategy. In the rational number system, counting is only possible with very restricted
sets of numbers. Between any two rational numbers there are infinitely many other rational
numbers. Additionally, much less time is spent working with mathematical operations with
rational numbers than was spent with whole number operations. We assume that since students
can compute with whole numbers, that computation with rational numbers should be easily
mastered. A simple problem may illustrate some of the difficulties.
Definition: An infinite series is the sum of an infinite set where the terms can be
1
1
1
expressed with variables or a pattern can be easily established e.g.
+
+ +…
2
4
8
1/8
1/2
1/4
Problem 1. Express
1
as an infinite series of fractions.
3
1
as an infinite series of decimals.
3
Although these problems are not difficult, the language adds a level of difficulty. It is very
necessary that students be well founded not only in the operations (and see them as extensions of
whole number work) but also that they be well founded in the rational system of numbers.
It should be noted that with the standard practice of reading decimal numbers is different than
that of whole numbers and that the “houses” representation does not fit. When reading 4687, as
Problem 2. Express
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 1
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
four thousand, 6 hundred, eighty-seven each of the place value names is read (left to right).
However, when reading 0.4687 the place value name is not generally written; four-tenths, sixhundredths, eight-thousandth and seven-ten-thousandths. Instead, the whole number place value
names are said followed by the place value name of the last digit; four thousand, six hundred,
eighty-seven ten-thousandths.
A. DECIMAL GLCES, MEAP DATA, AND ACTIVITIES BY TOPIC
D1.
MEANING
N.MR.04.19 Write tenths and hundredths in decimal and fraction forms, and know the decimal
equivalents for halves and fourths. [Core]
N.ME.05.08 Understand the relative magnitude of ones, tenths, and hundredths and the
relationship of each place value to the place to its right, e.g., 1 is 10 tenths, one tenth is 10
hundredths. [Core]
2007 MEAP Release Item Data
#
GLCE
MEAP a <x%
16 N.MR.04.19
Core A
17 N.MR.04.19
Core C
18 N.MR.04.19
Core D
7 N.ME.05.08
Core A
8 N.ME.05.08
Core A
9 N.ME.05.08
Core C
A
65
10
49
63
51
24
All Students
B
C
23
9
11
54
24
3
20
10
19
13
18
36
D
2
24
24
7
17
22
O/M <x%
0
0
0
0
0
0
Students with Disabilities
A
B
C
D O/M
53
32
10
5
0
20
20
38
21
0
59
24
4
13
0
42
26
15
16
0
33
24
22
20
1
29
24
26
20
1
2008 MEAP Release Item Data
#
GLCE
MEAP a <x%
11 N.MR.04.19
Core B
12 N.MR.04.19
Core A
9 N.ME.05.08
Core C
10 N.ME.05.08
Core B
A
9
61
12
21
All Students
B
C
56
27
6
31
13
69
14
36
D
8
2
5
29
O/M <x%
0
0
0
0
Students with Disabilities
A
B
C
D O/M
11
38
39
11
0
38
9
49
5
0
20
25
49
5
0
19
13
44
23
0
2007 MEAP Grade 5
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 2
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
2007 MEAP Grade 6
2007 MEAP Grade 6
2008 MEAP Grade 5
2008 MEAP Grade 6
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 3
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
1. Meaning
Unit knowledge
• Decimals as Parts of a Whole
• Determining what the whole is
• Subdividing the whole into equal-sized parts – not equal shape, but equal size
• Decimals as Measures or Quantities
• Decimal as a number
• e.g., a decimal can be a measurement that is “in between” two whole measures.
• Decimals as Indicated Division
• E.g., 3 pizzas shared by 10 people
• Decimals as Fractions
• Special fractions with denominators of 10, 100, …
• A natural extension of the place-value system for representing quantities less than
one
• Decimals as Percents
• Fractions represented as hundredths
2. Models for Decimals
Circular, Rectangular, Money, and Number Line
Activity 1:
Show and discuss the Decimal 1.234 PowerPoint
Activity 2: Circle
Fill in one of the sectors (pie pieces) on the Circle
Decimal Building Mat.
Write the number. (0.01)
Fill in one more of the adjacent sectors.
Write the number (0.02)
Continue through seven more sectors
Write the number. (0.09)
Fill in one more of the sectors.
Write the number. (0.10)
Fill in four more of the sectors.
Write the number. (0.14)
June 2009
Allan, Huellmantel, Scott
Materials needed:
Decimal 1.234 power point
Materials Needed:
Circle Decimal Building Mat
Dry erase pens
Chapter 5 Page 4
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
D2.
COUNTING AND WRITING
N.ME.04.15 Read and interpret decimals up to two decimal places; relate to money and place
value decomposition. [Core]
N.ME.04.18 Read, write, interpret, and compare decimals up to two decimal places. [Not
assessed at state level]
2007 MEAP Release Item Data
#
GLCE
MEAP
a <x%
19 N.ME.04.15
Core
B
20 N.ME.04.15
Core
A
21 N.ME.04.15
Core
B
All Students
A
B
C
D
10
65
7
18
54
13
28
5
32
56
9
3
Students with Disabilities
O/M <x% A
B
C
D O/M
0
53
32
10
5
0
0
20
20
38
21
0
0
59
24
4
13
0
2008 MEAP Release Item Data
#
GLCE
MEAP
a <x%
41 N.ME.04.15
Core
B
42 N.ME.04.15
Core
C
All Students
A
B
C
D
16
61
10
13
20
39
33
8
Students with Disabilities
O/M <x% A
B
C
D O/M
0
25
40
12
22
0
0
30
41
21
8
0
2007 MEAP Grade 5
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 5
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
2008 MEAP Grade 5 #42
Activity 1: Base Ten Model
Place three ones on the Decimal Building Mat.
Record the number on the mat.
Place seven-tenths on the mat.
Record the number on the mat.
How much is on the mat? (3.7)
Place six hundredths on the mat.
How much is on the mat? (3.76)
Write the number in expanded notation. (3 + .7 + .06)
Materials Needed:
Decimal Building Mat
Copies of decimal grids, scissors,
Base Ten Blocks, and
Dry erase pens
Activity 2: Renaming with the Base Ten Model
Materials Needed:
Use the Decimal Building Mat with two decimal grids on it.
Decimal Building Mat with two grids
On the top number grid, fill in 783 thousandths.
Dry erase pens
On the second grid we will make exchanges.
Can any of the thousandths be exchanged for ones? (no)
Can any of the thousandths be exchanged for tenths? (yes)
How many tenths? (7)
Draw them on the second grid and write the number of tenths.
Cross the seven-tenths off the top grid.
Can any of the remaining thousandths be exchanged for hundredths? (yes)
How many hundredths? (8)
Draw them on the second grid and write the number of hundredths.
Cross the eight-hundredths off the top grid.
How many thousandths are left? (3)
Draw them on the second grid and write the number of thousandths.
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 6
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
Write the number in expanded notation and read it aloud. (0 + .7 + .08 + .003)
Activity 3:
Counting across transition points presents a problem for many children. Unfortunately, they
are apt to count “… point 8, point 9, point 10, point eleven, …
Activity 4:
Show the PowerPoint, Counting with Decimals
Materials needed:
Counting with Decimals power point
Activity 5: Circle Conversions
Place the one half circle fraction overhead piece on the Circle
Materials Needed:
Decimal Mat.
Decimal Building Mat with two
Write the fraction and its decimal equivalent. (0.50)
grids
Overhead fraction pieces
Place the one-fourth-circle fraction overhead piece on the
Circle Decimal Mat.
Write the fraction and its decimal equivalent. (0.25)
Place the one-fifth-circle fraction overhead piece on the Circle Decimal Mat.
Write the fraction and its decimal equivalent. (0.20)
Place the one-tenth-circle fraction overhead piece on the Circle Decimal Mat.
Write the fraction and its decimal equivalent. (0.10)
D3.
SIZE COMPARISON AND THE NUMBER LINE
N.ME.04.17 Locate tenths and hundredths on a number line. [Extended Core]
N.ME.06.05 Order rational numbers and place them on the number line. [Core]
2007 MEAP Release Item Data
#
GLCE
MEAP
a <x%
71 N.ME.04.17
E Core
B
66 N.ME.06.05
E Core
A
A
12
31
All Students
B
C
D
71
7
10
11
19
39
O/M <x%
0
0
Students with Disabilities
A
B
C
D O/M
16
58
10
15
1
19
18
28
34
1
2008 MEAP Release Item Data
#
GLCE
MEAP
a <x%
35 N.ME.04.17
E Core
D
47 N.ME.06.05
E Core
C
A
8
14
All Students
B
C
D
6
18
67
4
73
8
O/M <x%
1
0
Students with Disabilities
A
B
C
D O/M
14
10
22
53
1
22
10
54
13
0
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 7
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
2008 MEAP Grade 5
Activity 1: Number Line
Locate seven on one of the Blank Number Lines.
Label the number line.
Locate seven and six-tenths on one of the Blank Number Lines.
Label the number line.
Locate seven and sixty-five-hundredths on one of the Blank Number Lines.
Label the number line.
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 8
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
Draw a picture to show the placement of 7.65 on the first number line.
Activity 2:
Show and discuss Locate 6.248 power point
Activity 3:
Show and discuss Squares power point
Materials needed:
Locate 6.248 power point
Squares power point
Activity 4:
Prior to this activity, it is necessary for participant to
have gone through the Pythagorean Theorem Activity in
the Geometry Chapter and to have experiences with the
relationship of square root to the dimensions and area of
a square.
Hand out the worksheet, decimeter ruler activity.
Cut the ruler out at the top of the page.
Measure and label the length of the sides of the smaller
triangle. (both are 1 decimeter)
Discuss the length of the hypotenuse. ( 2 decimeters)
Measure the length of the hypotenuse to find a two decimal place approximation for  2.
Repeat the activity for the larger triangle to find an approximation for  5.
D4.
ROUNDING DECIMALS
 To the nearest whole number
 To the nearest tenth
 To the nearest hundredth
 To the nearest thousandth
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 9
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
Activity 1:
Use the Rounding Worksheet.
Round 56.36 to the nearest tenth.
Materials Needed
Rounding Worksheet
To round to the nearest tenth label the nearest smaller tenth on the left end of the worksheet
and label the number line the next tenth on the right end of the number line.
Locate the number on the number line.
Which endpoint is closest to it.
Activity 2:
Use the Rounding Worksheet.
Round 56.367 to the nearest hundredth.
Materials Needed
Rounding Worksheet
To round to the nearest hundredth label the nearest smaller hundredth on the left end of the
worksheet and label the number line the next hundredth on the right end of the number line.
Locate the number on the number line.
Which endpoint is closest to it.
D5.
RELATIONSHIP TO MONEY
N.ME.03.21 Understand the meaning of 0.50 and 0.25 related to money e.g., $1.00 shared by
two people means $1.00 ÷ 2 = ½ dollar = $0.50. [Core]
2007 MEAP Release Item Data
#
GLCE
MEAP
a <x%
43 N.ME.03.21
Core
A
44 N.ME.03.21
Core
C
45 N.ME.03.21
Core
C
All Students
A
B
C
D
80
5
9
5
3
28
55
13
4
3
86
6
2008 MEAP Release Item Data
#
GLCE
MEAP
a <x%
34 N.ME.03.21
Core
D
35 N.ME.03.21
Core
C
A
17
10
All Students
B
C
D
13
24
45
10
68
11
Students with Disabilities
O/M <x% A
B
C
D O/M
0
67
9
14
11
0
0
5
28
49
18
0
0
8
5
74
12
1
O/M <x%
0
0
Students with Disabilities
A
B
C
D O/M
24
20
20
34
0
15
12
56
16
0
2008 MEAP Grade 4 #34
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 10
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
Activity 1: Money
Show $4.50 using bills and coins.
How many pennies (hundredths) equal $4.50?
How many dimes (tenths) equal $4.50?
How many dollars (ones) equal $4.50?
Activity 2: Money
Open the Place Value Chart with the decimal portion open.
We are going to make the number three hundred fifty-six and thirtyseven hundredths.
Materials Needed:
Place Value Chart
Paper money
Coins
Materials Needed:
Place Value Chart
Paper money
Coins
Place the hundreds on the mat.
How many hundreds? (3)
Place the tens on the mat.
How many tens in the tens place? (5)
How much is that in tens? (35)
Place the ones on the mat.
How many ones in the ones place? (6)
How much is on the mat in hundreds. (3.56)
How much is on the mat in tens? (35.6)
How much is on the mat in ones? (356)
Place three-tenths on the mat.
How many tenths in the tenths place? (3)
How much on the mat in tenths? (3,563 tenths)
How much on the mat in ones? (356.3 ones)
Place seven hundredths on the mat.
How much is on the mat in hundredths? (35,637 hundredths)
How much on the mat in tenths? (3,563.7 tenths)
How much is on the mat in ones? (356.37 ones)
Write the amount on the mat in expanded notation. (300 + 50 + 6 + .3 + .07)
D6.
ADDITION AND SUBTRACTION
N.MR.04.31 For problems that use addition and subtraction of decimals with up to two-digits,
represent with mathematical statements and solve. [Future Core]
N.FL.04.32 Add and subtract decimals up to two decimal places. [Future Core]
N.FL.04.34 Estimate the answers to calculations involving addition, subtraction, or
multiplication. [Extended Core]
N.FL.05.18 Given an applied situation involving addition and subtraction, write mathematical
statements describing the situation. [Core]
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 11
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
2007 MEAP Release Item Data
#
GLCE
MEAP
a <x%
91 N.MR.04.31
F Core
A
82 N.FL.04.32
F Core
A
66 N.FL.04.34
E Core
C
All Students
A
B
C
D
73
17
6
5
79
9
8
4
2
10
80
8
Students with Disabilities
O/M <x% A
B
C
D O/M
0
55
27
9
8
1
0
72
10
11
7
0
0
4
13
71
12
1
2008 MEAP Release Item Data
#
GLCE
MEAP
a <x%
61 N.MR.04.31
F Core
A
52 N.FL.04.32
F Core
A
N.FL.04.34
E Core
All Students
A
B
C
D
87
4
7
2
56
21
3
19
Students with Disabilities
O/M <x% A
B
C
D O/M
0
76
7
12
5
0
1
46
25
7
21
1
Terminology:
 Ragged decimals
 Horizontal form
5.603, 2.9, 7, .25, .003
3.2 – 8.44
Activity 1: Addition
Place the double mat above the single mat. The addends will be
placed on the double mat and the sum moved to the single
mat.
On the top, make 3.467
Place 3 ones, cut from the Decimal Grids on the top of the
top mat. Write 3 in the space provided.
Place 4 tenths on the top row. How many more would it
take to make another unit? (6) Record.
Place 6 hundredths on the top row. This is how much of a
tenth? (6 tenths) Record.
Place 7 thousandths on the top row. This is how much of a
hundredth? (7 tenths) Record.
On the second row make 1.538 using pieces cut from the
decimal grids.
Record one and five-tenths and three-hundredths and
eight-thousandths.
Materials Needed:
Decimal Building Mat both
sheets
A supply of Decimal Grids to
cut
Collect all of the thousandths on the mat and place them in the appropriate place on the third
row. How many are there? (15)
Is it necessary to exchange? (yes) Make the exchange and record. (Decide where to record
the exchange. As with whole numbers, it may, be best for some students to record the
exchange at the bottom so they can recognize it as fifteen-thousandths.
Combine all of the hundredths and place them in the appropriate place on the last row.
How many are there? (10)
Is it necessary to exchange? (yes)
Make the exchange and record.
Combine all of the tenths and place them in the appropriate place on the last row.
How many are there? (10)
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 12
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
Is it necessary to exchange? (yes)
Make the exchange and record.
Combine all of the ones and place them in the appropriate place on the last row.
How many are there? (5)
Is it necessary to exchange? (no)
Record. What is the sum? (5.005)
Activity 2: Take Away Subtraction
Place the Decimal Building Mats as in the previous activity.
Materials Needed:
Problem:
5.253
Decimal Building Mat both sheets
Dry erase markers
- 2.167
On the top row of the mat record the number and shade the
corresponding parts.
On the second row write the number to be subtracted.
Seven-thousandths is to be circled and drawn to the second row. Is it necessary to exchange
one hundredth for ten thousandths? (yes) Show this being done and record.
Show seven-thousandths being moved to the second row.
How many thousandths remain in the top row? (6) Record it in the bottom row.
Six-hundredths is to be circled and drawn to the second row. Is it necessary to exchange one,
tenth for ten, hundredths? (yes) Show this being done and record.
Show six hundredths being moved to the second row.
How many hundredths remain on the top row? (8) Record it in the bottom row.
One tenth is to be circled in the top row and drawn to the second row. Is it necessary to
exchange? (no)
Show one-tenth being moved from the top row to the second row. Record the tenths
remaining in the top row in the bottom row.
Show two of the ones being moved to the second row. Record the number remaining in the
bottom row.
Activity 3: Comparison Subtraction
Place the Decimal Building Mats as in the previous activity.
Problem:
Materials Needed:
Decimal Building Mat both sheets
Dry erase markers
1.536
- 0.135
On the top row of the mat record the number and shade the corresponding parts.
On the second row of the mat record the number and shade the corresponding parts.
Circle five-thousandths in the second row and join it with the corresponding number of
thousandths in the first row.
In the third row shade and record the number of thousandths remaining in the first row. (1)
Circle the three-hundredths in the second row and match it with an equal number of
hundredths in the first row.
In the third row shade and record the number of hundredths remaining in the first row. (0)
Circle the one-tenth in the second row and match it with an equal number of tenths in the first
row.
In the third row shade and record the number of tenths remaining in the first row. (4)
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 13
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
Subtract the whole portion of the problem.
What is the difference?
Activity 4: Addition and Subtraction Activities with various representations:
Consider both concepts. Teams of 2 using mats: one doing, one drawing, show the sums and
differences of the following numbers
Representation
3 and 0.4
Activity
0.6 and 0.8
0.32 and 0.7
1.4 and 2.03
Circular
Rectangular
Money
Number Line
D7.
MULTIPLICATION
N.FL.04.33 Multiply and divide decimals up to two decimal places by a one-digit whole number
where the result is a terminating decimal, e.g.,
0.42 ÷ 3 = 0.14, but not 5 ÷ 3 = 1. 6 [Future Core]
N.MR.05.15 Multiply a whole number by powers of 10: 0.01, 0.1, 1, 10, 100, 1000 and identify
patterns. [Core]
N.MR.05.17 Multiply one- and two-digit whole numbers by decimals up to two decimal places.
[Core]
2007 MEAP Release Item Data
#
GLCE
MEAP
a <x%
83 N.FL.04.33
F Core
D
64 N.MR.05.15
E Core
B
65 N.MR.05.17
E Core
B
All Students
A
B
C
D
5
6
7
81
14
49
16
20
14
71
8
7
Students with Disabilities
O/M <x% A
B
C
D O/M
0
9
8
9
73
0
0
15
31
22
31
0
0
24
53
13
10
0
2008 MEAP Release Item Data
#
GLCE
MEAP
a
53 N.FL.04.33
F Core
B
18 N.MR.05.15
E Core
C
19 N.MR.05.17
E Core
B
All Students
A
B
C
D
6
82
10
2
7
18
51
23
21
51
15
13
Students with Disabilities
O/M <x% A
B
C
D O/M
0
12
70
14
4
0
0
11
23
40
26
0
0
24
39
20
17
0
June 2009
<x%
Allan, Huellmantel, Scott
Chapter 5 Page 14
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
2008 MEAP Grade 6
2008 MEAP Grade 6
Key ideas:
 Multiplying and getting something smaller
 Distributive multiplication
o Whole x decimal
6 x 1.5 = (6 x 1) + (6 x .5)
o Decimal x decimal < 1
1.5 x .5 =
o Decimal x decimal > 1
1.5 x 1.5 =
Activity 1: Multiplication
One problem is inherent in all area model multiplication; the unit
Materials Needed:
Decimal Multiplication Mat
of the product is a two dimensional area (e.g. 36 cm2) while the
Dry erase markers
unit of the factors is linear (e.g. 6 cm). Although, this is quite
transparent with whole number grids, it is much less transparent when using a decimal grid.
Problem: 1.2 x 3.47 =
3.47
x 1.2
Place the Decimal Multiplication Mat on the workspace. (It should
be noted that on the vertical axis only one place decimals are
possible, but, on the horizontal axis two place decimals are
possible.)
Mark 1.2 on the vertical axis.
Mark 3.47 (three and four-tenths and seven hundredths) on the
horizontal axis. (There is a convention to say “and” only at the decimal.
This works well if the decimal portion of a number is read using only the
last decimal place value name. If, as in this case, each decimal place
value name is used, it does not work very well.)
Make the multiplication rectangle. It contains ones squares, tenths strips, and
thousandths pieces.
Write the problem.
June 2009
or
Allan, Huellmantel, Scott
3.47
x 1.2
3.
.4
.6
.08
.084
4.164
Chapter 5 Page 15
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
How many ones pieces in the multiplication rectangle? (3) Write it in the problem. Write the
decimal point.
How many tenths pieces to the right in the multiplication rectangle? (4) Write it in the
problem. Write the decimal point.
How many tenths pieces above in the multiplication rectangle? (6) Write it in the problem.
Write the decimal point.
How many hundredths pieces above in the multiplication rectangle? (8) Write it in the
problem. Write the decimal point.
How many thousandths pieces in the multiplication rectangle? (84) Write it in the problem.
Write the decimal point.
What is the product?
Activity 2:
Sketch a multiplication rectangle for 1.3 x 2.35 and use it to find the product.
Activity 3:
Show and discuss the Rectangular Multiplication power point. Materials needed:
Rectangular Multiplication power point
Activity 4:
Use the multiplication array provided below, fill in the factors, draw the rectangle, compute
the partial products, and compute the product for the following problem.
5.12
x 4.73
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 16
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
Activity 5:
Extend the multiplication array to accommodate hundreds.
D8.
DIVISION OF DECIMALS
N.FL.05.16 Divide numbers by 10’s, 100’s, & 1000’s using mental strategies. [Not assessed by
the state].
N.FL.06.10 Add, subtract, multiply and divide positive rational numbers fluently. [Core]
N.FL.06.15 Solve applied problems that use the four operations with appropriate decimal
numbers. [Core]
2007 MEAP Release Item Data
#
GLCE
MEAP
a
4
N.FL.06.10
Core
C
5
N.FL.06.10
Core
D
6
N.FL.06.10
Core
B
40 N.FL.06.15
Core
A
41 N.FL.06.15
Core
C
42 N.FL.06.15
Core
A
2008 MEAP Release Item Data
#
GLCE
MEAP
a
7
N.FL.06.10
Core
C
8
N.FL.06.10
Core
B
37 N.FL.06.15
Core
C
38 N.FL.06.15
Core
B
<x%
A
14
13
11
81
5
82
All Students
B
C
10
65
23
17
30
29
9
6
5
83
6
7
<x%
A
3
16
17
24
All Students
B
C
D
6
80
11
65
4
14
11
67
4
62
11
2
D
11
47
30
4
6
4
Students with Disabilities
O/M <x% A
B
C
D O/M
0
20
17
46
16
0
0
15
24
31
29
0
0
15
19
28
38
0
0
54
18
16
12
1
0
11
12
62
13
1
0
56
15
18
10
0
O/M <x%
0
0
0
0
Students with Disabilities
A
B
C
D O/M
6
11
59
24
0
32
36
11
20
0
21
25
43
10
0
40
40
13
6
0
2007 MEAP Grade 7
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 17
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
2008 MEAP Grade 7
Key ideas:
 By a whole number
o Dividend > 1
o Dividend < 1
 Equivalent division problems
 By a decimal, estimating to find decimal placement
Activity 1: Division
Use the Decimal Multiplication Mat to show 1.4 / 4.9
Activity 2: Multiplication and Division Activities with various representations.
Consider both concepts. Teams of 2 using mats: one doing, one drawing, show the products
and quotients of the following numbers
Representation
3 and 0.4
Activity
0.6 and 0.8
0.32 and 0.7
1.4 and 2.03
Circular
Rectangular
Money
Number Line
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 18
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
D9.
FRACTIONS CONVERTED TO DECIMALS
Fraction/division equivalence
16
17
4
4
4
4 ) 16
4 14
4 ) 17
Activity 1: Show equivalencies
1. Given a circular, rectangular, number line picture, give the fraction, decimal, and percent
2. Show 1/2, 1/3, 1/4, 1/5, and 1/8 as a decimal
3. Show 1/4, 2/3, 2 5/8 as a decimal and as a percent
4. Show .24, .06, 12.8, and .065 as a fraction and as a percent
5. Show 50%, 1550%, and .008% as a fraction and as a percent
3. Show 6.248 on the following exploded number line.
Materials needed:
Decimal Picture Worksheet
Decimal Rulers
Decimal Circles
Decimal Building Mat
4. Show 103/160 on a number line
D10.
DECIMALS CONVERTED TO FRACTIONS
N.ME.04.16 Know that terminating decimals represent fractions whose denominators are 10, 10
x 10, 10 x 10 x 10, etc., e.g., powers of ten. [Future Core]
N.ME.06.06 Represent rational numbers as fractions or terminating decimals when possible and
translate between these representations. [Not assessed at the state level].
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 19
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
2007 MEAP Release Item Data
#
GLCE
MEAP
a
84 N.ME.04.16
F Core
A
<x%
2008 MEAP Release Item Data
#
GLCE
MEAP
a
54 N.ME.04.16
F Core
A
<x%
All Students
A
B
C
D
53
9
20
18
A
66
All Students
B
C
D
16
5
13
Students with Disabilities
O/M <x% A
B
C
D O/M
0
36
13
24
27
0
O/M <x%
0
Students with Disabilities
A
B
C
D O/M
54
19
8
17
1
2008 Grade 5 #54
Three types of decimals:
 Terminating decimals (4.5)
 Repeating decimals (.333 …)
 Non-repeating and non-terminating decimals (irrational numbers) (0.1010010001 …)
D11.
PERCENT TO DECIMAL CONVERSION
N.ME.05.09 Understand percentages as parts out of 100, use % notation, and express a part of a
whole as a percentage. [Core]
N.MR.05.22 Express fractions and decimals as percentages, and vice versa. [Core]
2007 MEAP Release Item Data
#
GLCE
MEAP
a
34 N.ME.05.09
Core
D
35 N.ME.05.09
Core
D
36 N.ME.05.09
Core
B
43 N.MR.05.22
Core
C
44 N.MR.05.22
Core
D
45 N.MR.05.22
Core
C
2008 MEAP Release Item Data
#
GLCE
MEAP
a
23 N.ME.05.09
Core
C
24 N.ME.05.09
Core
C
27 N.MR.05.22
Core
C
28 N.MR.05.22
Core
D
June 2009
<x%
<x%
D
71
39
4
3
50
23
Students with Disabilities
O/M <x% A
B
C
D O/M
0
12
18
13
58
1
0
62
9
9
20
1
0
55
20
18
5
1
0
18
20
56
6
1
0
17
29
27
27
1
0
12
27
23
38
1
All Students
A
B
C
D
12
2
83
2
6
13
74
6
8
23
56
12
14
29
20
37
Students with Disabilities
O/M <x% A
B
C
D O/M
0
19
6
69
5
0
0
14
23
53
9
0
0
16
27
38
18
1
0
15
33
29
23
0
A
7
45
51
11
11
10
All Students
B
C
14
8
7
8
35
10
11
74
23
15
30
36
Allan, Huellmantel, Scott
Chapter 5 Page 20
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
2007 MEAP Grade 6
2007 MEAP Grade 6, #45
2008 MEAP grade 6 #28
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 21
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
D12.
PERCENT COMPUTATION
N.FL.06.12 Calculate part of a number given the percentage and the number. [Extended Core]
N.FL.06.13 Solve word problems involving percentages in such contexts as sales taxes and tips
and involving positive rational numbers. [Core]
N.MR.08.07 Understand percent increase and percent decrease in both sum and product form,
e.g., 3% increase of a quantity x is x + .03x = 1.03x
N.MR.08.08 Solve problems involving percent increases and decreases.
2007 MEAP Release Item Data
#
GLCE
MEAP
a
65 N.FL.06.12
E Core
C
34 N.FL.06.13
Core
A
35 N.FL.06.13
Core
D
36 N.FL.06.13
Core
D
2008 MEAP Release Item Data
#
GLCE
MEAP
a
25 N.FL.06.12
E Core
B
33 N.FL.06.13
Core
B
34 N.FL.06.13
Core
C
<x%
A
9
60
10
26
All Students
B
C
16 55
12 19
20 13
12 10
<x%
A
10
16
9
All Students
B
C
68 12
58 21
25 60
D
20
8
56
51
Students with Disabilities
O/M <x% A
B
C
D O/M
0
11
17
39 32
0
0
46
19
23 12
0
0
14
28
18 40
1
0
27
18
17 38
1
D
10
5
6
O/M <x%
1
0
0
Students with Disabilities
A
B
C
D O/M
11
50
19 19
1
24
36
30
9
0
14
30
44 11
0
2007 MEAP Grade 7
2007 MEAP Grade 7
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 22
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
2008 MEAP Grade 7 #34
Three cases of percent (Inductively using stacked binary)
 4 out of 5 = x%
 70% of 50 = x
 50% of x = 120
D13.
PERCENT COMPUTATION WITH EASY FRACTIONS
N.FL.05.20 Solve applied problems involving fractions and decimals; include rounding of
answers and checking reasonableness; use examples involving money. [Core]
2007 MEAP Release Item Data
#
GLCE
MEAP
a
40 N.FL.05.20
Core
C
41 N.FL.05.20
Core
B
42 N.FL.05.20
Core
C
2008 MEAP Release Item Data
#
GLCE
MEAP
a
25 N.FL.05.20
Core
B
26 N.FL.05.20
Core
C
June 2009
<x%
A
10
10
12
All Students
B
C
D
5
81
4
76
5
8
27
44
17
O/M <x%
0
0
0
Students with Disabilities
A
B
C
D O/M
23
11
59
6
1
18
52
12
18
1
15
31
32
21
1
<x%
A
3
5
All Students
B
C
D
79
5
13
19
69
7
O/M <x%
0
0
Students with Disabilities
A
B
C
D O/M
7
54
10
29
0
11
23
52
13
0
Allan, Huellmantel, Scott
Chapter 5 Page 23
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
2008 MEAP Grade 6 #26
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 24
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
B. DECIMALS INVENTORY: (BASIC)
1) Concept
a) Equal Partitioning
b) The Role of Zero and the Decimal Point
c) Decimal Place Value and Trading
d) Translate among Representations (models and symbol)
2) Counting
3) Reading and Writing Decimal Words and Numerals
4) Equivalence, Comparison, and Ordering
5) Basic Computation (Tenths and Hundredths - No Regrouping)
#1-11
#12-14
#15-16
#17-22
#23-26
SEQUENTIAL DECIMALS
INVENTORY
Student Name: ____________________________
School: ________________ Grade: ____________
Copyright © 2005
Assessment developed by Charles Allan, Linda Patriarca, and Wayne Scott with partial support provided by a USDE School Improvement Grant, (Michigan
Department of Education, Office of Special Education). All rights reserved.
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 25
MICHIGAN MATHEMATICS PROGRAM IMPROVEMENT PROJECT
C. SUPPLEMENTAL MATERIALS
Chapter 5: Decimals (Basic) (June 2009, 26 pages, PDF, 601 KB)
Worksheets:
1. Decimal Building Mat (11x17, 2 pages, PDF, 43 KB)
2. Decimal Grids (2 pages, PDF, 17 KB)
3. Decimal Square (PDF, 14 KB)
4. Decimal Circle (PDF, 7 KB)
5. Decimal Circles (PDF, 13 KB)
6. Decimeter Ruler (PDF, 233 KB)
7. Decimal Multiplication Mat (11x17, PDF, 17 KB)
8. Rounding Mat (PDF, 9 KB)
9. Number Lines (PDF, KB)
10. Decimal Picture (PDF, 29 KB)
11. Decimal Product (PDF, 27 KB)
12. Decimal Percent (PDF, 613 KB)
Power Point Presentations:
Decimal 1 and 234 (Power Point, 850 KB)
Counting with Decimals (Power Point, 575 KB)
Locate 6 and 248 ((Power Point, 65 KB)
Rectangular Multiplication (Power Point, 1052 KB)
Diagnostic Inventory:
Decimal (Basic) Diagnostic Inventory (PDF, 245 KB)
June 2009
Allan, Huellmantel, Scott
Chapter 5 Page 26