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This work is protected by United States copyright laws and is provided solely for the use of teachers and administrators in teaching
courses and assessing student learning in their classes and schools. Dissemination or sale of any part of this work (including on
the World Wide Web) will destroy the integrity of the work and is not permitted.
Copyright © 2012 Pearson Education, Inc., or its affiliate(s). All Rights Reserved. Printed in the United States of America. This publication is protected by
copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or
by any means, electronic, mechanical, photocopying, recording, or likewise. The publisher hereby grants permission to reproduce these pages, in part or in whole,
for classroom use only, the number not to exceed the number of students in each class. Notice of copyright must appear on all copies. For information regarding
permissions, write to Pearson Curriculum Group Rights & Permissions, One Lake Street, Upper Saddle River, New Jersey 07458.
America’s Choice, the America’s Choice A logo, Math Navigator, the Pearson logo, and the Pearson Always Learning logo are trademarks, in the U.S. and/or other
countries, of Pearson Education, Inc. or its affiliate(s).
ISBN:
1 2 3 4 5 6 7 8 9 10 978-0-66364-307-3
16 15 14 13 12
Contents
Lesson 1
Letter to Parents
1
Lessons 3, 19 Hundreds, Tens, and Ones Place-Value Table Workspace
3
Lessons 5, 9
Hundred Chart
4
Blank Hundred Chart
5
Set of nine hundred charts to 1,000
(from the 101–200 Chart through the 901–1,000 Chart)
6
Lesson 5
Lessons 5, 9
Lesson 10
Counting Coins: Half Dollars
15
Lesson 10
Counting Coins: Quarters
16
Lesson 3
Place Value Cards
17
Misconceptions
32
Class Profile
38
A Complete Solution to a Math Story
42
What to Do If You Get Stuck
43
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
iii
Letter to Parents
Introduction to Math Navigator
Dear Parent/Guardian,
_________________________________________ has been selected to participate in Math Navigator!
Math Navigator is one of the ways that our school is working to help all students succeed in
mathematics. The program gives students the additional time and instruction they need to improve
their performance in this important subject.
Your child will be participating in the Place Value and Computational Strategies to 1,000 module. The
main goal of this module is to help students extend their place value understanding and number
sense as they develop strategies for computation with two- and three-digit numbers. Students will
learn to read, write, and interpret numbers using numerals, number names, and expanded form.
They will also compare three-digit numbers based on the meanings of the hundreds, tens, and
ones digits. Students will explore a variety of strategies for adding and subtracting to 100 fluently—
flexibly, efficiently, and accurately—and use models, drawings, and strategies to explore addition
and subtraction to 1,000. Students will also explore the general method of adding or subtracting the
hundreds, the tens, and the ones. Throughout the module, students will record their thinking about
computations in writing, and explain why strategies work.
There are a variety of materials students will use with this module: one of them is a set of Study
Cards. These cards include mathematical ideas for students to master, game cards, and blank cards
that students can customize with concepts that they need to work on. Students are encouraged to
use these cards during the lessons, as well as during free time and at home. Please encourage your
child to share them with you.
The more enthusiastic you can be about Math Navigator, the more it will help your child. Ask
questions each day about what your child learned and how the Math Navigator class was different
from your child’s regular math class. It is important for you to acknowledge what your child has
accomplished both on a day-to-day basis and after completing the Math Navigator module.
We are excited about using Math Navigator with students. Learn more about this special program
and how it works by reading the short description that follows. If you have any questions about the
program, please do not hesitate to contact us here at school.
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
1
Letter to Parents
How Math Navigator Works
Structure of a Module
Each module contains 20 days of 30- or 45-minute lessons, including a pre-test and post-test. During
the 20 days, students have two or three checkpoint lessons that assess their understanding of the
concepts in the module.
Frequent Skills Practice
Most lessons include a Show Me session in which students practice and reinforce skills. It is also a
time for students to learn strategies and techniques that make computation easier.
Emphasis on Understanding
The lessons are carefully designed to uncover mistakes that result from students misunderstanding
something. We call such mistakes misconceptions. Misconceptions need to be corrected because they
can interfere with new learning. Math Navigator modules do not attempt to reteach everything that
students have learned about a topic. Instead, they help students understand the mathematics of the
procedures and concepts that they have already learned so that they can correct the misconceptions
that are getting in the way of their progress.
Learning to Think Mathematically
Lessons are structured to teach students to think like mathematicians. Students will learn how to
ask themselves questions before beginning a problem; to use diagrams, tables, and other methods
of representing problems; and to estimate as a way of determining whether their answers are
reasonable. Most importantly, they will come to see that mistakes are opportunities for learning,
rather than something to hide.
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
2
Hundreds, Tens, and Ones Place-Value
Table Workspace
Hundreds
Tens
Ones
Lessons 3, 19
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
3
Lessons 5, 9
Hundred Chart
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71
72 73 74 75 76 77 78 79 80
81
82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
Place Value and Computational Strategies to 1,000
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4
Lesson 5
Place Value and Computational Strategies to 1,000
Blank Hundred Chart
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
5
Lesson 5
101–200 Chart
101 102 103 104 105 106 107 108 109 110
111 112 113 114 115 116 117 118 119 120
121 122 123 124 125 126 127 128 129 130
131 132 133 134 135 136 137 138 139 140
141 142 143 144 145 146 147 148 149 150
151 152 153 154 155 156 157 158 159 160
161 162 163 164 165 166 167 168 169 170
171 172 173 174 175 176 177 178 179 180
181 182 183 184 185 186 187 188 189 190
191 192 193 194 195 196 197 198 199 200
Place Value and Computational Strategies to 1,000
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6
Lesson 5
201–300 Chart
201 202 203 204 205 206 207 208 209 210
211 212 213 214 215 216 217 218 219 220
221 222 223 224 225 226 227 228 229 230
231 232 233 234 235 236 237 238 239 240
241 242 243 244 245 246 247 248 249 250
251 252 253 254 255 256 257 258 259 260
261 262 263 264 265 266 267 268 269 270
271 272 273 274 275 276 277 278 279 280
281 282 283 284 285 286 287 288 289 290
291 292 293 294 295 296 297 298 299 300
Place Value and Computational Strategies to 1,000
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7
Lesson 5
301–400 Chart
301 302 303 304 305 306 307 308 309 310
311 312 313 314 315 316 317 318 319 320
321 322 323 324 325 326 327 328 329 330
331 332 333 334 335 336 337 338 339 340
341 342 343 344 345 346 347 348 349 350
351 352 353 354 355 356 357 358 359 360
361 362 363 364 365 366 367 368 369 370
371 372 373 374 375 376 377 378 379 380
381 382 383 384 385 386 387 388 389 390
391 392 393 394 395 396 397 398 399 400
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
8
Lessons 5, 9
401–500 Chart
401 402 403 404 405 406 407 408 409 410
411 412 413 414 415 416 417 418 419 420
421 422 423 424 425 426 427 428 429 430
431 432 433 434 435 436 437 438 439 440
441 442 443 444 445 446 447 448 449 450
451 452 453 454 455 456 457 458 459 460
461 462 463 464 465 466 467 468 469 470
471 472 473 474 475 476 477 478 479 480
481 482 483 484 485 486 487 488 489 490
491 492 493 494 495 496 497 498 499 500
Place Value and Computational Strategies to 1,000
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9
Lesson 5
501–600 Chart
501 502 503 504 505 506 507 508 509 510
511 512 513 514 515 516 517 518 519 520
521 522 523 524 525 526 527 528 529 530
531 532 533 534 535 536 537 538 539 540
541 542 543 544 545 546 547 548 549 550
551 552 553 554 555 556 557 558 559 560
561 562 563 564 565 566 567 568 569 570
571 572 573 574 575 576 577 578 579 580
581 582 583 584 585 586 587 588 589 590
591 592 593 594 595 596 597 598 599 600
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
10
Lessons 5, 9
601–700 Chart
601 602 603 604 605 606 607 608 609 610
611 612 613 614 615 616 617 618 619 620
621 622 623 624 625 626 627 628 629 630
631 632 633 634 635 636 637 638 639 640
641 642 643 644 645 646 647 648 649 650
651 652 653 654 655 656 657 658 659 660
661 662 663 664 665 666 667 668 669 670
671 672 673 674 675 676 677 678 679 680
681 682 683 684 685 686 687 688 689 690
691 692 693 694 695 696 697 698 699 700
Place Value and Computational Strategies to 1,000
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11
Lesson 5
701–800 Chart
701 702 703 704 705 706 707 708 709 710
711 712 713 714 715 716 717 718 719 720
721 722 723 724 725 726 727 728 729 730
731 732 733 734 735 736 737 738 739 740
741 742 743 744 745 746 747 748 749 750
751 752 753 754 755 756 757 758 759 760
761 762 763 764 765 766 767 768 769 770
771 772 773 774 775 776 777 778 779 780
781 782 783 784 785 786 787 788 789 790
791 792 793 794 795 796 797 798 799 800
Place Value and Computational Strategies to 1,000
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12
Lesson 5
801–900 Chart
801 802 803 804 805 806 807 808 809 810
811 812 813 814 815 816 817 818 819 820
821 822 823 824 825 826 827 828 829 830
831 832 833 834 835 836 837 838 839 840
841 842 843 844 845 846 847 848 849 850
851 852 853 854 855 856 857 858 859 860
861 862 863 864 865 866 867 868 869 870
871 872 873 874 875 876 877 878 879 880
881 882 883 884 885 886 887 888 889 890
891 892 893 894 895 896 897 898 899 900
Place Value and Computational Strategies to 1,000
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13
Lesson 5
901–1,000 Chart
901 902 903 904 905 906 907 908 909 910
911 912 913 914 915 916 917 918 919 920
921 922 923 924 925 926 927 928 929 930
931 932 933 934 935 936 937 938 939 940
941 942 943 944 945 946 947 948 949 950
951 952 953 954 955 956 957 958 959 960
961 962 963 964 965 966 967 968 969 970
971 972 973 974 975 976 977 978 979 980
981 982 983 984 985 986 987 988 989 990
991 992 993 994 995 996 997 998 999 1,000
Place Value and Computational Strategies to 1,000
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14
Lesson 10
Place Value and Computational Strategies to 1,000
Counting Coins: Half Dollars
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15
Lesson 10
Place Value and Computational Strategies to 1,000
Counting Coins: Quarters
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
16
Lesson 3
Place Value Cards
Preparing and Using the Place Value Cards
In this lesson you will introduce the Place-Value Cards: a set of ones, tens, and hundreds cards. When folded into a
tent, each card shows a numeral on one side, and a base-ten drawing of the number on the other side. The drawings
use dots to represent ones, sticks to represent tens, and squares to represent hundreds.
To prepare the cards, print the sheets onto stiff paper, cut out the cards, and fold them into tents.
print
cut
fold
flip
The cards can now be used to show three-digit numbers. Below, the 6 card is placed on top of the 10 card to show
16. And this pair of cards is placed on top of the 200 card. The layered cards now show 216.
stack
stack
When you turn the tents around to see the drawings, the cards must be rearranged so the drawings show the
hundreds, then tens, then ones. You can rearrange the cards as shown below.
flip
slide
The place-value cards help students develop the connections between three-digit numbers shown:
• With base-10 blocks
• With drawings (squares, sticks, and ones)
• In expanded form (as the sum of their base ten units)
• As base-ten numerals
Layering the place-value cards help students see that for all three-digit numbers, the hundreds
digit refers to groups of hundreds, the tens digit refers to groups of tens, and the ones digit
refers to some ones. Lifting the ones card reveals the 0 from the 10 “hiding behind” the ones
number (6). Lifting the tens and ones cards reveals the 00 from the 200 hiding behind the tens
and ones numbers (the 16).
Place Value and Computational Strategies to 1,000
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17
1 00 1
Place Value and Computational Strategies to 1,000
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18
2002
Place Value and Computational Strategies to 1,000
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19
3003
Place Value and Computational Strategies to 1,000
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20
4004
Place Value and Computational Strategies to 1,000
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21
5005
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
22
6006
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
23
7007
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
24
8008
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
25
9009
Place Value and Computational Strategies to 1,000
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26
8090
Place Value and Computational Strategies to 1,000
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27
6070
Place Value and Computational Strategies to 1,000
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28
4050
Place Value and Computational Strategies to 1,000
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29
2030
Place Value and Computational Strategies to 1,000
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30
010
Place Value and Computational Strategies to 1,000
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31
Misconceptions
Misconceptions and Errors
AT1
Does not recognize a pattern, including a number pattern
F21
Does not understand the concept of equivalence
O16
Does not recognize or misapplies the associative property
O22
Fails to link addition and subtraction as inverse operations
O23
Is unable to transfer between different representations of the same operation
O33
Subtracts the smaller number from the larger one, digit by digit
PV1
Does not understand or misinterprets the role of zero as a placeholder
PV2
Does not represent a number correctly in different forms: expanded, place value, and
numerical
PV3
Ignores place value and treats each number as a separate number
PV5
Confuses place value in whole numbers
PV6
Does not understand that the value of any digit in a number is a combination of the face
value of the digit and the place
PV7
Orders numbers based on the value of the digits, instead of place value
PV10
Places the symbols for greater than and less than incorrectly when recording the results of
comparisons
PV11
Thinks about any multidigit number only as the number reached after counting by 1s
PV12
Does not understand the relative sizes of digits in place-value notation
example
AT1Does not recognize a pattern, including a number pattern
What is the missing number?
7, ___, 27, 37, 47, 57, … Place Value and Computational Strategies to 1,000
26
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
32
Misconceptions
F21Does not understand the concept of equivalence
example
The student does not understand that adding an amount and then subtracting that amount (or vice
versa) gives the same result.
Finish this student’s work.
37 + 45 = ?
37 + 3 + 45 –> 40 + 45 –> 85
O16Does not recognize or misapplies the associative property
example
The student fails to find an easier way to add, because he fails to recognize that the order in which
numbers are added can be changed without affecting the result. The student labors to find the total.
35 + 42 + 15 = ?
35 + 40 –> 75 + 2 –> 77 + 10 –> 87 + 5 –> 92
O22 Fails to link addition and subtraction as inverse operations
example
The student does not use the adding up strategy (“think addition”) to make subtraction problems
easier to solve. She does not view subtraction problems as missing addend problems. She may count
down, making the common error of counting the starting number as the first subtraction.
73 – 48 = ?
I counted down 40 by tens: 73, 63, 53, 43. Then I counted down 8: 43, 42, 41, 40, 39, 38, 37, 36.
The answer is 36.
Place Value and Computational Strategies to 1,000
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33
Misconceptions
O23 Is unable to transfer between different representations of operations
example
The student has problems reading or creating different representations of addition or subtraction.
Use an open number line to show this strategy for 65 – 19:
I gave the problem 1 so I could subtract 20 from 65.
I took away the tens in 20: 65 … 55, 45. Then I
added one back because I took away one too many.
1
10
44 45
10
55
65
example
O33 Subtracts the smaller number from the larger one, digit by digit
74 9
– 67 5
134
example
PV1Does not understand or misinterprets the role of zero as a placeholder
Write the number for the one hundred six.
16
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
34
Misconceptions
PV2Does not represent a number correctly in different forms: expanded,
place value, and numerical
example
The student has limited his understanding of numbers to one or two representations, or applies the
alternate conception “Write the numbers you hear” when writing numbers in standard form.
Write the number I say: “thirty-seven.”
307
Write the missing number.
36 = 3 +6
example
PV3 Ignores place value and treats each number as a separate number
645
+ 3 62
9107
example
PV5Confuses place value in whole numbers
Read 306. Thirty-six
Write the numeral for four hundred eight. Place Value and Computational Strategies to 1,000
4008
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
35
Misconceptions
example
PV6Does not understand that the value of any digit in a number is a
combination of the face value of the digit and the place
What is the value of the digit 2 in 126?
2
example
PV7 Orders numbers based on the value of the digits, instead of place
value
69 > 102, because 6 and 9 are bigger than 1 and 2.
PV10Places the symbols for greater than and less than incorrectly when
recording the results of comparisons
example
The student finds it challenging to place the > < = symbols correctly.
Write the symbol to make the number sentence true.
35 > 53
Place Value and Computational Strategies to 1,000
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36
Misconceptions
PV11 Thinks about any multi-digit number only as the number reached
after counting by 1s
example
For example, the student thinks about 50 not as 5 tens but as the number reached after
49 counts of 1.
How much is 25?
20, 21, 22, 23, 24, 25
PV12Does not understand the relative sizes of digits in place-value
notation
example
The student fails to view two-digit and three-digit numbers using base-ten units flexibly (as 10 times,
100 times). He fails to understand 207 as 20 tens and 7 ones, or to understand 150 as 15 tens.
150 is the same as how many tens?
5 Place Value and Computational Strategies to 1,000
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37
Class Profile
Class Profile Instructions
About the Class Profile
Completing an analysis of student work gives you a clear picture of the strategies an individual student is applying
to a particular problem or topic in mathematics. Such an analysis is even more powerful when it is applied to the
Math Navigator class as a whole.
The Class Profile gives you both. By reading the Class Profile across a row, you can see where each student stands
at any point in time. Reading down the columns allows you to see the strengths and needs of the entire class at
a glance. By reviewing the Class Profile, you will be able to make decisions that target appropriate instruction to
individuals, small groups, and the whole Math Navigator class.
The first pages of the Class Profile provide assessment items related to the content of the module. The last page is
based on the mathematical practices from the Common Core State Standards for Mathematics.1 On this page, record
evidence of students using these practices.
Recording Data on the Class Profile
When you see—either through discussion, analysis of student work, or direct observation—that a student
understands a concept, still has a misconception, or engages in a mathematical practice, make a note on your Class
Profile. As the student’s understanding increases, update the Class Profile.
Using the Class Profile
Review the Class Profile periodically during the lesson to help you decide which topics would be most beneficial
for your students to focus on during the class discussion. Address topics that most of the students in the Math
Navigator group need to learn during the show me, work time, or probing for understanding parts of the lesson.
Address topics that only some students are struggling with during partner work or in conferences. If only one or two
students need help with a topic, address the topic in an individual conference.
Give a copy of the completed Class Profile to each student’s classroom teacher at the end of the module.
Common Core State Standards Initiative. 2010. “Common Core State Standards for Mathematics”: 6–8. Accessed July 1, 2011.
http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf.
1
Place Value and Computational Strategies to 1,000
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38
Class Profile (1 of 3)
1
2
3
4
5
6
7
8
9
10
Concepts
Student Name
Observed
Errors
C1
: U
nd
e
nu rstan
mb
d
an er re s tha
d o
t
p
ne rese the t
s
n
C2
t am hre e
:U
n
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de
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r
of
f
b u s t an
hu a th
nd
n d re e
le o ds th
re d - d
f 10 at 1
s , t i gi t
C3
ten 00 c
en
: U
s,
s — an
nd
be
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c
a
50
l
t
t
l
h
e
a
nd
d a ou
0,
“hu ght
fou 600, s tha
n d of a
7
t
r, fi
00
t
h
re d
sa
ten ve, , 80 e nu
”
s
0
sa
i
m
,
x
9
b
nd , s e
0
e
0 o ven 0 ref rs 1
C4
0
e
ne
: C
s) , eigh r to 0, 20
om
t, o one 0, 3
p
rn
m e are s
ine , two 00, 4
an
hu , thr 00,
ing two
nd
e
s o thre
red e,
C5
f
the e-d
: U
s (a
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nd
hu git
nd
e
nd
n
0
o n r s t an
re d u m b
ea
ds
s
e
,
d
r
ten s b
t
on
d
s, a ase
es s hu hat i
d
nd
com and ndre n add
on on
o
po nes ds a ing
es
se
n
t
di g
C6
ten ; and d hu hree
: U
it s
nd
s
s
n
d
o
d
or
e
hu meti reds igit n
nu rstan
nd
m
u
m
d
red es i , tens mbe
ten bers, s tha
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s
a
r
on t i
s
ne nd t s ,
ces en
ne and t e su n sub
s ar s ,
ces en
b
t
y to
sar s, o tract racti
y to nes s h ng
C7
t
u
h
: Ex
d e an d n d
re re e com o
p la
po nes; ds an digit
pla ins w
se
a
d
ce ten nd s hun
val hy ad
s o om
d re
ue
di t
e
rh
i
an
un time ds,
d t on s t
C8
d re s i
he
r
: Ex
ds t is
pro ategi
p la
e
p
s
er t
w
pla ins w
i es o r k
ce
,
of
val hy su
op using
u
b
er a
ea
tr a
C9
nd
tio
c
: U
ns
nd
the tion
er s
s tr
p
a
nu
r
t
o
t
a
p e e gi
nd
m
rtie es
its ber is s tha
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t
r
r
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y
e
o
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s e n c an
rat ing
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ho
ut the w
cha
ng ay a
in g
Place Value and Computational Strategies to 1,000
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39
Class Profile (2 of 3)
1
2
3
4
5
6
7
8
9
10
Procedures
Student Name
P1
: C
ou
P2
:
Ski
nts
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Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
40
Class Profile (3 of 3)
1
2
3
4
5
6
7
8
9
10
MP3: Construct viable arguments and critique the reasoning of others.
MP2: Reason abstractly and quantitatively.
MP1: Make sense of problems and persevere in solving them.
MP8: Look for and express regularity in repeated reasoning.
MP7: Look for and make use of structure.
MP6: Attend to precision.
MP5: Use appropriate tools strategically.
Observations
MP4: Model with mathematics.
Student Name
41
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
Place Value and Computational Strategies to 1,000
Mathematical Practice
Standards
A Complete Solution
to a Math Story
✓
Show your thinking.
1 + 2 = 3
✓
Math drawing or diagram
Equation
Answer the question.
There are 3 apples.
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
42
What to Do
If You Get Stuck
Look at posted charts.
Use counters or other materials.
Make a math drawing or diagram.
Use easier numbers.
Ask a friend.
Write what you do know.
Think of questions to ask later.
Place Value and Computational Strategies to 1,000
Copyright © 2012 Pearson Education, Inc. or its affiliate(s). All rights reserved.
43