Place Value and Operations
with Whole Numbers
Critical Area Developing understanding and fluency with multi-digit
multiplication, and developing understanding of dividing to find quotients
involving multi-digit dividends
1
Place Value, Addition, and
Subtraction to One Million
Domain Number and Operations in Base Ten
Common Core Standards 4.NBT.1, 4.NBT.2, 4.NBT.3, 4.NBT.4
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. P1
. P2
. P3
. P5
. P7
. P9
P11
P13
P15
. . . . . . . . . . . . . . . P17
© Houghton Mifflin Harcourt Publishing Company
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
School-Home Letter (English) . . . . . . . . . . .
School-Home Letter (Spanish) . . . . . . . . . . .
Model Place Value Relationships . . . . . . . . . .
Read and Write Numbers . . . . . . . . . . . . . .
Compare and Order Numbers . . . . . . . . . . .
Round Numbers . . . . . . . . . . . . . . . . . . . .
Rename Numbers . . . . . . . . . . . . . . . . . . .
Add Whole Numbers . . . . . . . . . . . . . . . . .
Subtract Whole Numbers . . . . . . . . . . . . . .
Problem Solving • Comparison Problems with
Addition and Subtraction . . . . . . . . . . . . . .
iii
2
Multiply by 1-Digit Numbers
Domains Operations and Algebraic Thinking
Number and Operations in Base Ten
Common Core Standards 4.OA.1, 4.OA.2, 4.OA.3, 4.NBT.5
School-Home Letter (English). . . . . . . . . . . . . . . . .
School-Home Letter (Spanish) . . . . . . . . . . . . . . . .
2.1 Algebra • Multiplication Comparisons . . . . . . . . . . .
2.2 Algebra • Comparison Problems . . . . . . . . . . . . . . .
2.3 Multiply Tens, Hundreds, and Thousands . . . . . . . . .
2.4 Estimate Products . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Multiply Using the Distributive Property . . . . . . . . . .
2.6 Multiply Using Expanded Form . . . . . . . . . . . . . . .
2.7 Multiply Using Partial Products . . . . . . . . . . . . . . . .
2.8 Multiply Using Mental Math . . . . . . . . . . . . . . . . .
2.9 Problem Solving • Multistep Multiplication Problems .
2.10 Multiply 2-Digit Numbers with Regrouping . . . . . . . .
2.11 Multiply 3-Digit and 4-Digit Numbers with Regrouping
2.12 Algebra • Solve Multistep Problems Using Equations . .
3
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P19
P20
P21
P23
P25
P27
P29
P31
P33
P35
P37
P39
P41
P43
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P45
P46
P47
P49
P51
P53
P55
P57
P59
Multiply 2-Digit Numbers
Domains Operations and Algebraic Thinking
Number and Operations in Base Ten
3.1
3.2
3.3
3.4
3.5
3.6
3.7
iv
School-Home Letter (English) . . . . . . . . . .
School-Home Letter (Spanish) . . . . . . . . . .
Multiply by Tens . . . . . . . . . . . . . . . . . . .
Estimate Products . . . . . . . . . . . . . . . . . .
Area Models and Partial Products . . . . . . . .
Multiply Using Partial Products . . . . . . . . .
Multiply with Regrouping . . . . . . . . . . . . .
Choose a Multiplication Method . . . . . . . . .
Problem Solving • Multiply 2-Digit Numbers .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
© Houghton Mifflin Harcourt Publishing Company
Common Core Standards 4.OA.3, 4.NBT.5
4
Divide by 1-Digit Numbers
Domains Operations and Algebraic Thinking
Number and Operations in Base Ten
Common Core Standards 4.OA.2, 4.OA.3, 4.NBT.6
School-Home Letter (English) . . . . . . . . . . .
School-Home Letter (Spanish) . . . . . . . . . . .
4.1 Estimate Quotients Using Multiples . . . . . . . .
4.2 Remainders . . . . . . . . . . . . . . . . . . . . . . .
4.3 Interpret the Remainder . . . . . . . . . . . . . . .
4.4 Divide Tens, Hundreds, and Thousands . . . . .
4.5 Estimate Quotients Using Compatible Numbers
4.6 Division and the Distributive Property . . . . . .
4.7 Divide Using Repeated Subtraction . . . . . . . .
4.8 Divide Using Partial Quotients . . . . . . . . . . .
4.9 Model Division with Regrouping . . . . . . . . . .
4.10 Place the First Digit . . . . . . . . . . . . . . . . . .
4.11 Divide by 1-Digit Numbers . . . . . . . . . . . . .
4.12 Problem Solving • Multistep Division Problems
© Houghton Mifflin Harcourt Publishing Company
5
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P61
P62
P63
P65
P67
P69
P71
P73
P75
P77
P79
P81
P83
P85
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P87
P88
P89
P91
P93
P95
P97
P99
Factors, Multiples, and Patterns
Domain Operations and Algebraic Thinking
Common Core Standards 4.OA.4, 4.OA.5
5.1
5.2
5.3
5.4
5.5
5.6
School-Home Letter (English) . . . .
School-Home Letter (Spanish) . . . .
Model Factors . . . . . . . . . . . . . .
Factors and Divisibility . . . . . . . . .
Problem Solving • Common Factors
Factors and Multiples . . . . . . . . . .
Prime and Composite Numbers . . .
Algebra • Number Patterns . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
v
Fractions and Decimals
Critical Area Developing an understanding of fraction equivalence,
addition and subtraction of fractions with like denominators, and
multiplication of fractions by whole numbers
Fraction Equivalence and Comparison
Domain Number and Operations—Fractions
Common Core Standards 4.NF.1, 4.NF.2
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P101
P102
P103
P105
P107
P109
P111
P113
P115
P117
School-Home Letter (English) . . . . . . . . . . .
School-Home Letter (Spanish) . . . . . . . . . . .
7.1 Add and Subtract Parts of a Whole . . . . . . . . .
7.2 Write Fractions as Sums . . . . . . . . . . . . . . .
7.3 Add Fractions Using Models . . . . . . . . . . . . .
7.4 Subtract Fractions Using Models . . . . . . . . . .
7.5 Add and Subtract Fractions . . . . . . . . . . . . .
7.6 Rename Fractions and Mixed Numbers. . . . . .
7.7 Add and Subtract Mixed Numbers . . . . . . . . .
7.8 Subtraction with Renaming . . . . . . . . . . . . .
7.9 Algebra • Fractions and Properties of Addition .
7.10 Problem Solving • Multistep Fraction Problems
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P119
P120
P121
P123
P125
P127
P129
P131
P133
P135
P137
P139
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
7
vi
School-Home Letter (English) . . . . . . . . . .
School-Home Letter (Spanish) . . . . . . . . . .
Equivalent Fractions . . . . . . . . . . . . . . . .
Generate Equivalent Fractions . . . . . . . . . .
Simplest Form . . . . . . . . . . . . . . . . . . . .
Common Denominators . . . . . . . . . . . . . .
Problem Solving • Find Equivalent Fractions .
Compare Fractions Using Benchmarks . . . . .
Compare Fractions . . . . . . . . . . . . . . . . .
Compare and Order Fractions. . . . . . . . . . .
Add and Subtract Fractions
Domain Number and Operations—Fractions
Common Core Standards 4.NF.3a, 4.NF.3b, 4.NF.3c, 4.NF.3d
© Houghton Mifflin Harcourt Publishing Company
6
8
Multiply Fractions by Whole Numbers
Domain Number and Operations—Fractions
Common Core Standards 4.NF.4a, 4.NF.4b, 4.NF.4c
8.1
8.2
8.3
8.4
8.5
9
School-Home Letter (English) . . . . . . . .
School-Home Letter (Spanish) . . . . . . . .
Multiples of Unit Fractions . . . . . . . . . .
Multiples of Fractions . . . . . . . . . . . . .
Multiply a Fraction by a Whole Number
Using Models . . . . . . . . . . . . . . . . . . .
Multiply a Fraction or Mixed Number by
a Whole Number . . . . . . . . . . . . . . . . .
Problem Solving • Comparison Problems
with Fractions . . . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P141
P142
P143
P145
. . . . . . . . . . . . . . . . . P147
. . . . . . . . . . . . . . . . . P149
. . . . . . . . . . . . . . . . . P151
Relate Fractions and Decimals
Domains Number and Operations—Fractions
Measurement and Data
© Houghton Mifflin Harcourt Publishing Company
Common Core Standards 4.NF.5, 4.NF.6, 4.NF.7, 4.MD.2
9.1
9.2
9.3
9.4
9.5
9.6
9.7
School-Home Letter (English) . . . . . .
School-Home Letter (Spanish) . . . . . .
Relate Tenths and Decimals . . . . . . . .
Relate Hundredths and Decimals . . . .
Equivalent Fractions and Decimals . . .
Relate Fractions, Decimals, and Money .
Problem Solving • Money . . . . . . . . .
Add Fractional Parts of 10 and 100 . . . .
Compare Decimals . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P153
P154
P155
P157
P159
P161
P163
P165
P167
vii
Geometry, Measurement,
and Data
Critical Area Understanding that geometric figures can be analyzed
and classified based on their properties, such as having parallel sides,
perpendicular sides, particular angle measures, and symmetry
10
Two-Dimensional Figures
Domains Operations and Algebraic Thinking
Geometry
Common Core Standards 4.OA.5, 4.G.1, 4.G.2, 4.G.3
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P169
P170
P171
P173
P175
P177
P179
P181
P183
P185
School-Home Letter (English) . . . . . . . . . .
School-Home Letter (Spanish) . . . . . . . . . .
Angles and Fractional Parts of a Circle . . . . .
Degrees. . . . . . . . . . . . . . . . . . . . . . . . .
Measure and Draw Angles . . . . . . . . . . . . .
Join and Separate Angles . . . . . . . . . . . . .
Problem Solving • Unknown Angle Measures
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P187
P188
P189
P191
P193
P195
P197
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Angles
Domain Measurement and Data
Common Core Standards 4.MD.5a, 4.MD.5b, 4.MD.6, 4.MD.7
11.1
11.2
11.3
11.4
11.5
viii
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
© Houghton Mifflin Harcourt Publishing Company
11
.
.
.
.
.
.
.
.
.
.
School-Home Letter (English) . . . . .
School-Home Letter (Spanish) . . . . .
Lines, Rays, and Angles . . . . . . . . . .
Classify Triangles by Angles . . . . . . .
Classify Triangles by Sides . . . . . . . .
Parallel Lines and Perpendicular Lines
Classify Quadrilaterals . . . . . . . . . .
Line Symmetry . . . . . . . . . . . . . . .
Find and Draw Lines of Symmetry . . .
Problem Solving • Shape Patterns . .
12
Relative Sizes of Measurement Units
Domain Measurement and Data
Common Core Standards 4.MD.1, 4.MD.2, 4.MD.4
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P199
P200
P201
P203
P205
P207
P209
P211
P213
P215
P217
P219
P221
© Houghton Mifflin Harcourt Publishing Company
School-Home Letter (English) . . . . . . .
School-Home Letter (Spanish) . . . . . . .
12.1 Measurement Benchmarks . . . . . . . . .
12.2 Customary Units of Length . . . . . . . . .
12.3 Customary Units of Weight . . . . . . . . .
12.4 Customary Units of Liquid Volume . . . .
12.5 Line Plots . . . . . . . . . . . . . . . . . . . .
12.6 Metric Units of Length . . . . . . . . . . . .
12.7 Metric Units of Mass and Liquid Volume .
12.8 Units of Time . . . . . . . . . . . . . . . . . .
12.9 Problem Solving • Elapsed Time . . . . .
12.10 Mixed Measures . . . . . . . . . . . . . . . .
12.11 Algebra • Patterns in Measurement Units
ix
13
Algebra: Perimeter and Area
Domain Measurement and Data
Common Core Standard 4.MD.3
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P223
P224
P225
P227
P229
P231
P233
© Houghton Mifflin Harcourt Publishing Company
13.1
13.2
13.3
13.4
13.5
School-Home Letter (English) . .
School-Home Letter (Spanish) . .
Perimeter . . . . . . . . . . . . . . .
Area . . . . . . . . . . . . . . . . . . .
Area of Combined Rectangles . .
Find Unknown Measures. . . . . .
Problem Solving • Find the Area .
x
End–of–Year Resources
Getting Ready for Grade 5
These lessons review important skills and prepare you
for Grade 5.
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Checkpoint
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
© Houghton Mifflin Harcourt Publishing Company
Lesson 11
Checkpoint
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Checkpoint
Lesson 17
Lesson 18
Lesson 19
Lesson 20
Checkpoint
Add Dollars and Cents . . . . .
Subtract Dollars and Cents . .
Algebra • Order of Operations
Divide by Multiples of Ten . . .
Model Division with 2-Digit
Divisors . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
Place Value Through Millions .
Decimals and Place Value . . .
Round Decimals . . . . . . . . .
Place Value to Compare
Decimals . . . . . . . . . . . . .
Decompose Multiples of
10, 100, 1,000 . . . . . . . . . . .
Number Patterns . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
Add Related Fractions . . . . .
Subtract Related Fractions . .
Compare Fraction Products . .
Repeated Subtraction with
Fractions . . . . . . . . . . . . . .
Fractions and Division . . . . .
. . . . . . . . . . . . . . . . . . . .
Locate Points on a Grid . . . .
Area and Tiling . . . . . . . . . .
Multiply Three Factors . . . . .
Find Area of the Base . . . . . .
. . . . . . . . . . . . . . . . . . . .
LESSON
PRACTICE
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
P235
.P237
.P239
.P241
GRP1
GRP2
GRP3
GRP4
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.P243
.P245
.P247
.P249
.P251
GRP5
. . . . . . . . . . .P253
GRP9
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.P255
.P257
.P259
.P261
.P263
.P265
GRP10
GRP11
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.P267
.P269
.P271
.P273
.P275
.P277
.P279
.P281
GRP15
GRP16
GRP6
GRP7
GRP8
GRP12
GRP13
GRP14
GRP17
GRP18
GRP19
GRP20
xi