Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
Content Standard A: Mathematical facts, concepts, principles, and theories
Numeration: Understand and use numeration
Understanding Numbers
The student demonstrates conceptual understanding
• of whole numbers to 20 by
[K] N-1 demonstrating 1-1 correspondence
142, 144, 397–398, 400, 430–431, 461, 465,
(M1.1.1)
566, 578, 580–586, 588–589, 605, 608, 673
[K] N-2 recognizing and counting whole
1–48, 49–52, 77–110, 121–130, 187–190,
numbers from 0-20 (M1.1.1)
239–246, 259–264, 303–306, 329–334, 349–
353, 357–360, 454, 513–518, 521, 529–534,
542, 572
[K] N-3 writing and ordering whole numbers
35–36, 52, 62–63, 79–80, 89, 94, 99, 143, 153,
from 0-20 (M1.1.1)
157, 161, 164, 167, 171, 177, 179, 187, 191,
193, 195, 201, 207, 211, 213, 215, 219, 220,
223, 227, 231, 267, 421, 439, 454, 453, 461–
462, 567, 590, 671–674
[K] N-4 counting whole numbers backwards
56, 217, 224–226
from 10 to 0 (M1.1.1)
[K] N-5 identifying ordinal position, first to the
336–337, 339, 340, 350
tenth (M1.1.4)
• of simple fractions by
[K] N-6 dividing an even numbered set of
348, 414, 434–435, 504–505, 536, 567, 570,
concrete objects (up to 20) into halves (M1.1.5) 580
[K] N-7 identifying halves (M1.1.5)
See Grade 1.
[K] N-8 identifying full, half full, and empty
See Grade 1.
containers (M1.1.5)
Understanding Meaning of Operations
The student demonstrates conceptual understanding of mathematical operations by
[K] N-9 recognizing (+), (–), and (=) signs
160, 162, 169, 187, 208, 217, 254, 299, 309,
(M1.1.3)
345, 347, 348, 373, 379, 403, 442–443, 453,
465, 549
[K] N-10 using objects or pictures to model
155–160, 191–194, 253–258, 268–269, 271–
addition and subtraction of whole numbers
274, 293–296, 358, 362, 377–382, 396–397,
(M1.1.3)
399, 423–426, 493–496, 530–534, 536, 542–
546, 577–580, 590
[K] N-11 using number lines or objects related
139, 144, 160, 294, 354, 378–379, 396–397,
to real situations (M1.1.3)
400, 424
Number Theory
The student demonstrates conceptual understanding of number theory by
[K] N-12 demonstrating skip counting by 2’s,
243, 246, 249, 255, 267, 271, 283, 289, 303,
5’s, and 10’s with support (M1.1.6)
365, 389, 395, 401, 407, 413, 419, 423, 427,
433, 445, 457, 463, 469, 481, 485, 497, 559–
561, 565, 597, 607, 611, 619, 625, 631, 635,
645, 649, 655, 665, 671
Measurement: Select and use systems, units, and tools of measurement
Measurable Attributes
The student demonstrates understanding of measurable attributes by
Kindergarten
Page 1 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
[K] MEA-1 making comparisons between
144, 278–279, 659–664
objects using concepts of big/little, long/short,
large/small, more/less, same (M2.1.1)
[K] MEA-2 identifying coins by name: penny,
138–140, 208, 241, 619–624
nickel, dime, and quarter (M2.1.5)
Measurement Techniques
The student demonstrates ability to use measurement techniques by
[K] MEA-3 identifying instruments used to
631–634, 649–658
measure length, time, and temperature
(M2.1.3)
[K] MEA-4 naming in sequence the days of the See Grade 2.
week (M2.1.1)
[K] MEA-5 telling time to the hour using analog 631–644
and digital clocks (M2.1.4)
Estimation and Computation: Perform basic arithmetic functions, make reasoned
estimates, and select and use appropriate methods or tools
Estimation
The student determines reasonable answers to real-life situations, paper/pencil
computations, or calculator results by
[K] E&C-1 comparing the number of objects in
40–41, 66, 74, 84, 94, 98, 104, 112–113, 128,
different sets using more, less, same
138, 144, 160, 278–279, 319–320, 338, 343,
344, 397–398, 410, 425–426, 430–431, 464–
465, 580, 588–589, 667
[K] E&C-2 estimating the number of objects in
189, 333, 517, 575, 588–589
a given set as more or less than 10 (M3.1.1)
Computation
The student accurately solves problems (including real-world situations) involving
[K] E&C-3 adding and subtracting whole
196–197, 210, 212, 214, 218, 237–238, 248–
numbers up to ten using manipulatives
250, 252, 255, 257–258, 260–261, 266, 272,
(M3.1.3)
276, 282, 294, 296, 322, 324, 326, 330, 337,
350, 354, 378–379, 382, 405, 413–414, 418,
472–473, 515–516, 531–532, 543–544, 546
Functions and Relationships: Represent, analyze, and use patterns, relations, and
functions
Describing Patterns and Functions
The student demonstrates conceptual understanding of functions, patterns, or sequences
by
[K] F&R-1 recognizing patterns found in
145–154, 202, 206, 208, 289–290, 391, 393,
common objects, sounds, and movements
394, 502, 594
(M4.1.1)
[K] F&R-2 identifying, sorting, and classifying
14, 46–47, 54–55, 61, 114–115, 134–135, 228,
objects by attribute and identifying objects that
230, 288–290, 297, 359, 465, 520, 588–590,
do not belong to a particular group (M4.1.1)
594, 604
[K] F&R-3 recognizing, identifying, and
146–147, 184–185, 188, 202–203, 205–206,
continuing simple patterns of color, shape, or
229, 289–290, 292, 298, 308, 356, 380, 390–
size (M4.1.1)
391, 393, 408–409, 427–432, 499–500, 519–
522, 562, 564, 594
Modeling and Solving Equations and Inequalities
The student demonstrates algebraic thinking by
Kindergarten
Page 2 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Math Expressions
Teacher’s Guide
210, 212, 214, 218, 237–238, 248–250, 252,
255, 257–258, 260–261, 266, 272, 276, 282,
294, 296, 322, 324, 326, 330, 337, 350, 354,
378–379, 382, 405, 418, 516
[K] F&R-5 showing more, less, or equal to
40–41, 66, 74, 84, 94, 98, 104, 112–113, 128,
using objects (M4.1.4)
138, 144, 160, 278–279, 319–320, 338, 343,
344, 397–398, 410, 425–426, 430–431, 464–
465, 580, 588–589
Geometry: Construct, transform, and analyze geometric figures.
Geometric Relationships
The student demonstrates an understanding of geometric relationships by
[K] G-1 sorting and classifying shapes
46–48, 54–55, 60–64, 75–78, 80–82, 88, 90–
according to similar attributes (M5.1.1)
91, 114–115, 174–176, 228–230, 298, 301,
308, 355, 458–459, 564, 594
[K] G-2 describing objects using three
46–47, 78, 88, 288–290, 298, 301, 308, 327–
attributes such as size, color, and shape
328, 594
(M5.1.1)
[K] G-3 identifying triangle, circle, rectangle,
54–55, 60–64, 75–78, 80–82, 88, 90–91, 114–
and square (M5.1.1)
115, 174–176, 185–186, 228–230, 288–290,
308, 327–328, 355, 390, 458–459, 485–488,
564, 594
Similarity, Congruence, Symmetry, and Transformation of Shapes
The student demonstrates conceptual understanding of similarity, congruence, symmetry,
or transformations of shapes by
[K] G-4 comparing geometric shapes (M5.1.3)
20, 32, 46–47, 54–55, 60–64, 100, 114–115,
165–166, 174–176, 185–186, 228–230, 298,
301, 327–328, 355, 458–459, 485–488
Position and Direction
The student demonstrates understanding of position and direction by
[K] G-5 identifying positions of objects that are
27, 43, 67–68, 106, 283
above, below, before, after, next to, in the
middle of, in front of, behind... (M5.1.6)
Construction
The student demonstrates a conceptual understanding of geometric drawings or
constructions by
[K] G-6 drawing, copying, or describing
54–55, 60–64, 75–78, 80–82, 88, 90–91, 114–
triangles, squares, rectangles and circles
115, 166, 168, 174–176, 186–186, 222, 229–
(M5.1.7)
230, 288–292, 327–328, 356, 411, 458–459,
614
Statistics and Probability: Formulate questions, gather and interpret data, and make
predictions
Data Display
The student demonstrates an ability to classify and organize data by
[K] S&P-1 constructing real graphs using
40–42, 44, 51, 112–113, 116, 138, 278–279,
concrete objects or pictographs with support
316–317, 338, 343, 344, 463–467, 478–480,
(M6.1.1)
588–589, 591, 604
[K] S&P-2 collecting and recording data with
44, 108, 112–113, 278–279, 305, 316–317,
support (M6.1.1)
338, 343–344, 467, 478, 588–589, 591, 604
Alaska
Grade Level Expectation
[K] F&R-4 adding or subtracting whole
numbers to 10 using manipulatives to solve
story problems (M4.1.4)
Kindergarten
Page 3 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
Analysis and Central Tendency
The student demonstrates an ability to analyze data (comparing, explaining, interpreting,
evaluating; or drawing or justifying conclusions) by
[K] S&P-3 describing information from real
40–42, 44, 51, 112–113, 116, 138, 305, 316–
graphs or pictographs (M6.1.2)
317, 338, 343, 344, 588–589, 591, 604
Probability
The student demonstrates a conceptual understanding of probability and counting
techniques by
[K] S&P-4 making simple predictions using
86, 113, 328, 588–589
events or repeated observations (M6.1.4)
Content Standards B, C, D, and E: Process skills and abilities Applying conceptual
knowledge and skills as designated in all strands of Content Standard A by problem
solving, communicating, reasoning, and making connections
Problem Solving: Understand and be able to select and use a variety of problem-solving
strategies
The student demonstrates an ability to problem solve by
[K] PS-1 solving simple problems using
This Grade Level Expectation is met
concrete objects (M7.1.2)
throughout the program. These are some of the
many examples.
20, 32, 86, 128, 130, 136, 210, 212, 214, 218,
237–238, 248–250, 257–258, 260–326, 330,
350, 354, 378–379, 382, 405, 418, 588–590
Communication: Form and use appropriate methods to define and explain mathematical
relationships
The student communicates his or her mathematical thinking by
[K] PS-2 telling how objects were used to solve 22, 32, 40–41, 44, 132, 254–255, 257–258,
simple problems (M8.1.2)
279, 588–590, 621, 626
Reasoning: Use logic and reason to solve mathematical problems
The student demonstrates an ability to use logic and reason by
[K] PS-3 explaining what makes sense
11, 16, 24, 37, 41, 44, 75, 85, 105, 109, 112–
(M9.1.3)
113, 116, 133, 136, 150, 170, 180–181, 217,
241, 249, 257, 269, 272, 279, 301, 305, 339,
354, 381, 384, 393, 396, 399, 416, 460, 467,
470, 521, 536, 563, 566, 575, 622, 637, 661
[K] PS-4 drawing pictures that support simple
This Grade Level Expectation is met
mathematical statements (M9.1.2)
throughout the program. These are some of the
many examples.
21–22, 24–26, 31, 38, 46, 90, 98, 108, 116,
129, 178, 182, 194, 269, 273, 296, 316–317,
396–397, 400, 426, 416, 418, 424, 426, 548,
598
Connections: Apply mathematical concepts and processes to situations within and
outside of school.
The student understands and applies mathematical skills and processes across the
content strands by
Kindergarten
Page 4 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Alaska
Grade Level Expectation
[K] PS-5 using real world context (i.e., self,
friends, and family) (M10.1.2)
Kindergarten
Houghton Mifflin
Math Expressions
Teacher’s Guide
This Grade Level Expectation is met
throughout the program. These are some of the
many examples.
2–3, 12–13, 21, 24–25, 32, 38, 52, 57, 98,
108–109, 112–113, 116, 132–133, 139, 174–
175, 178, 191–194, 212, 271–274, 362, 396,
424
Page 5 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
Content Standard A: Mathematical facts, concepts, principles, and theories
Numeration: Understand and use numeration
Understanding Numbers
The student demonstrates conceptual understanding
• of whole numbers to one hundred by
[1] N-1 reading, writing, ordering/counting and
1–26, 45–50, 99–108, 136–137, 140, 293–304,
modeling correspondence of whole numbers
325–336, 373–375, 417–422, 424–426
[1] N-2 comparing whole numbers using the
122, 126, 154, 157, 164, 256, 479–485, 503,
words greater than, less than or equal to
512, 527, 533, 545
[1] N-3 identifying ordinal position, first to the
42, 637–642
twentieth (M1.1.4)
[1] N-4 dividing an even numbered set of
94, 585–590, 606–608, 613, 631, 643
concrete objects (up to 50) into halves (M1.1.5)
• of simple fractions by
[1] N-5 dividing geometric shapes into equal
592–598, 600–601, 604, 608–610, 614, 616
halves, fourths, and thirds (M1.1.5)
Understanding Meaning of Operations
The student demonstrates conceptual understanding of mathematical operations by
[1] N-6 using objects, pictures, and problem
39–44, 51–86, 109–132, 171–194, 209–216,
situations to model addition and subtraction of
223–240, 247–272, 279–292, 311–320, 346,
whole numbers (M1.1.3)
353–364, 380–382, 425, 448–453 456–457,
461, 521–529, 531, 573–583, 677–684, 707–
724, 745, 751–752, 754–755, 772, 784–785,
788–789, 794, 800, 804
[1] N-7 identifying groups of objects as
94, 577, 583, 586, 682
repeated addition or equal shares (M1.1.3)
Number Theory
The student demonstrates conceptual understanding of number theory by
[1] N-8 skip counting by 2’s to 20 and 5’s and
9, 297, 299, 305, 308, 311, 317, 325, 422, 426,
10’s to 100 (M1.1.6)
599, 631, 659, 665, 671, 682, 685, 697, 703,
707, 713, 725, 731
[1] N-9 identifying odd and even numbers up to 95–96, 98, 103
20 (M1.1.6)
[1] N-10 identifying fact families (M1.1.3)
281, 743–745
Measurement: Select and use systems, units, and tools of measurement
Measurable Attributes
The student demonstrates understanding of measurable attributes by
[1] MEA-1 measuring and/or comparing objects 533–544, 813–856
using standard and nonstandard units (M2.1.2)
[1] MEA-2 identifying money by its value (e.g.,
146–152, 387–416, 659–663
penny, nickel, dime, quarter, dollar) (M2.1.5)
Measurement Techniques
The student demonstrates ability to use measurement techniques by
[1] MEA-3 drawing a line segment to the
535
nearest inch (M2.1.3)
[1] MEA-4 telling time to the nearest half hour
643–648
using analog and digital clocks (M2.1.4)
Grade 1
Page 6 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
[1] MEA-5 comparing concepts such as:
373–375, 534, 537, 540, 542–544, 638
before/after, shorter/longer (M2.1.1)
[1] MEA-6 reading a calendar (distinguishing
Calendar Routine page xxi: Use with units 7–
yesterday, today, and tomorrow) (M2.1.1)
10
[1] MEA-7 recognizing money symbols ($, ¢)
390–398, 412–416, 661–676
(M2.1.5)
[1] MEA-8 identifying equal values of a coin up 393–398, 400–401, 412–413, 406–407, 409,
to a dollar (5 pennies = 1 nickel, 5 nickels = 1
665–674
quarter) (M2.1.5)
Estimation and Computation: Perform basic arithmetic functions, make reasoned
estimates, and select and use appropriate methods or tools
Estimation
The student determines reasonable answers to real-life situations, paper/pencil
computations, or calculator results by
[1] E&C-1 estimating “how many” and “how
824, 826–827, 830, 839, 858–862
much” in a given set up to 20
[1] E&C-2 identifying whether estimation or
243, 861–862
counting is appropriate with support (M3.1.1)
Computation
The student accurately solves problems (including real-world situations) involving
[1] E&C-3 recalling addition and subtraction
28–32, 40–41, 52, 55–56, 58–59, 61–62, 64–
facts 0-10 (M3.1.2)
86, 110–140, 160–164, 169–170, 172–204,
210–211, 214–216, 224–228, 230–234, 236–
246, 263–264, 268, 271–272, 281, 284–286,
288, 320, 322–324, 336, 448–450, 452–454,
458, 460, 462, 464–465, 467, 576–577, 743–
745, 753, 759, 765, 789
[1] E&C-4 recalling doubles to 20 (M3.1.2)
94, 573–584
Functions and Relationships: Represent, analyze, and use patterns, relations, and
functions
Describing Patterns and Functions
The student demonstrates conceptual understanding of functions, patterns, or sequences
by
[1] F&R-1 identifying, naming (e.g., aabb,
8–12, 15–17, 22–23, 52–53, 58–59, 72–73, 77,
abab), and continuing a variety of patterns
98, 100, 156, 293, 418–422, 424–425, 530,
(M4.1.1)
547–549, 552–553, 558–560, 576, 578
[1] F&R-2 creating patterns involving number,
11–12, 17, 53, 55, 79, 100, 418–422, 530, 558,
shape, size, rhythm, or color (M4.1.1)
560
Modeling and Solving Equations and Inequalities
The student demonstrates algebraic thinking by
[1] F&R-3 adding and subtracting whole
43, 55, 56, 61, 67, 70–71, 76–79, 82, 85, 113,
numbers to 20 using manipulatives to solve
117–121, 125, 155, 166, 169, 181, 187, 199,
story problems (M4.1.4)
227, 230, 257, 263, 267, 270–271, 522–523
[1] F&R-4 creating and solving problems using 39–44, 51–86, 109–132, 171–194, 209–216,
words, symbols, and drawings (M4.1.4)
223–240, 247–272, 279–292, 311–320, 346,
353–364, 380–382, 425, 448–453 456–457,
461, 521–529, 531, 573–583, 677–684, 707–
724, 745, 751–752, 754–755, 772, 784–785,
788–789, 794, 800, 804
Grade 1
Page 7 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
[1] F&R-5 using the terms equal to, more than, 122, 126, 154, 157, 164, 256, 479–485, 503,
and less than for numbers up to 20 (M4.1.4)
512, 527, 533, 545
Geometry: Construct, transform, and analyze geometric figures.
Geometric Relationships
The student demonstrates an understanding of geometric relationships by
[1] G-1 identifying the attributes of 214–16, 20, 22–25, 34–37, 552–556, 562–568,
dimensional shapes (e.g., a triangle has three
592–593, 830–834
sides) (M5.1.1)
[1] G-2 identifying and classifying 2
14–18, 20, 22–26, 32, 34–37, 552–556, 562–
dimensional shapes through visual
568, 592–593, 830–834
observations and properties (e.g., which of
these shapes is a triangle) (M5.1.1)
[1] G-3 relating real-world examples (e.g., a
15–16, 23, 554, 556, 565–566, 833
door is shaped like a rectangle) to the ideas
and concepts of geometry (M5.1.2)
Similarity, Congruence, Symmetry, and Transformation of Shapes
The student demonstrates conceptual understanding of similarity, congruence, symmetry,
or transformations of shapes by
[1] G-4 comparing shapes in the real world
554, 556, 565–566, 833
(M5.1.3)
Position and Direction
The student demonstrates understanding of position and direction by
[1] G-5 modeling directional and positional
130, 167, 261, 373–375, 438, 518, 638–639
concepts: before, after, between, next to,
around, above, below, in the middle of...
(M5.1.6)
Construction
The student demonstrates a conceptual understanding of geometric drawings or
constructions by
[1] G-6 drawing, copying, or describing a
14–17, 20, 25, 34–37, 546–547, 549–550,
variety of shapes (M5.1.7)
552–556, 562–568, 574–575, 592–593, 830–
834, 842, 845
[1] G-7 identifying geometric shapes in real15–16, 23, 554, 556, 565–566, 833
world objects (M5.1.7)
Statistics and Probability: Formulate questions, gather and interpret data, and make
predictions
Data Display
The student demonstrates an ability to classify and organize data by
[1] S&P-1 constructing and using real graphs,
483, 486–490, 492–496, 500–501, 504–507,
pictographs, and bar graphs (M6.1.1)
510, 513–514, 516–519, 626
[1] S&P-2 collecting and recording data
486–490, 492–496, 500–501, 504–507, 510,
(M6.1.1)
513–514, 516–519, 540–544, 618–622, 625–
626
[1] S&P-3 interpreting data with support
480–484, 492–496, 498–502, 504–508, 510–
(M6.1.1)
511, 513–514, 516–520, 540–544, 618–622,
624–630
Analysis and Central Tendency
The student demonstrates an ability to analyze data (comparing, explaining, interpreting,
evaluating; or drawing or justifying conclusions) by
Grade 1
Page 8 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Alaska
Grade Level Expectation
[1] S&P-4 describing information from simple
charts/graphs (M6.1.2)
Houghton Mifflin
Math Expressions
Teacher’s Guide
486–490, 492–496, 498–502, 504–508, 510–
511, 513–514, 516–520, 540–544, 618–622,
624–630
Probability
The student demonstrates a conceptual understanding of probability and counting
techniques by
[1] S&P-5 predicting, interpreting, and
511, 620–621, 627, 629
comparing data using events or repeated
observations (M6.1.4)
Content Standards B, C, D, and E: Process skills and abilities Applying conceptual
knowledge and skills as designated in all strands of Content Standard A by problem
solving, communicating, reasoning, and making connections
Problem Solving: Understand and be able to select and use a variety of problem-solving
strategies
The student demonstrates an ability to problem solve by
[1] PS-1 creating and solving simple problems
This Grade Level Expectation is met
using a variety of strategies (M7.1.1 & M7.1.2)
throughout the program. These are some of the
many examples.
116–120, 122, 125–138, 172–176, 178–182,
184–188, 260, 294–295, 300–301, 313, 315,
319–320, 580–581, 583, 586, 589, 594, 641
Communication: Form and use appropriate methods to define and explain mathematical
relationships
The student communicates his or her mathematical thinking by
[1] PS-2 translating problems from everyday
122–123, 126, 174–175, 186–187, 197–199,
language into math language and symbols (+, - 284, 287, 340–341, 480–483, 533–538, 600–
, =) (M8.1.1)
602, 660, 666, 780, 819–834
[1] PS-3 using everyday language to explain
This Grade Level Expectation is met
thinking about problem solving strategies and
throughout the program. These are some of the
solutions to problems (M8.1.3)
many examples.
134–135, 142–143, 154–155, 242–243, 274–
275, 318–319, 344–345, 360, 464–465, 528–
529, 531, 666–667, 680–681, 686, 694, 762
Reasoning: Use logic and reason to solve mathematical problems
The student demonstrates an ability to use logic and reason by
[1] PS-4 explaining why a prediction or solution 129, 243, 318–319, 344–345
is reasonable (M9.1.3)
[1] PS-5 drawing pictures that support
This Grade Level Expectation is met
mathematical statements (M9.1.2)
throughout the program. These are some of the
many examples.
109–114, 115–120, 171–176, 177–182, 218–
219, 244, 246, 301–303, 306–307, 332, 335–
336, 552–553, 567, 595, 602–603, 680–681,
752, 758
Connections: Apply mathematical concepts and processes to situations within and
outside of school.
The student understands and applies mathematical skills and processes across the
content strands by
Grade 1
Page 9 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Alaska
Grade Level Expectation
[1] PS-6 using real world context (i.e., self,
friends, and family)* (M10.1.2)
Grade 1
Houghton Mifflin
Math Expressions
Teacher’s Guide
This Grade Level Expectation is met
throughout the program. These are some of the
many examples.
40–41, 52, 110–111, 136, 151, 198, 204, 240,
284, 336, 344–345, 376, 446, 560, 607, 613,
640, 667, 714–715, 717, 723, 733, 808, 848
Page 10 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
Content Standard A: Mathematical facts, concepts, principles, and theories
Numeration: Understand and use numeration
Understanding Numbers
The student demonstrates conceptual understanding
• of whole numbers to one thousand by
[2] N-1 reading, writing, ordering/counting and
33–34, 117, 144–148, 297–312, 334, 337–342,
modeling correspondence of whole numbers
399, 467–478, 578–579, 697–732, 744, 892–
(M1.1.1)
893, 898–902, 904–908, 910–914
[2] N-2 modeling and identifying place value
297–320, 369, 705–709, 711, 714–715, 721–
positions: ones, tens, and hundreds (M1.1.2)
722, 727
• of simple fractions by
[2] N-3 identifying fractions as equal parts of a
933–943
whole, a region, or a set (M1.1.5)
[2] N-4 reading and writing numerals for simple 936–943
fractions (M1.1.5)
Understanding Meaning of Operations
The student demonstrates conceptual understanding of mathematical operations by
[2] N-5 describing or illustrating the processes
27–36, 46–47, 50, 71, 73, 96, 112–115, 116,
of addition and subtraction of whole numbers
120, 123–129, 131–136, 138–141, 196–197,
and their relationships (M1.1.3)
199, 215–222, 321–328, 354–357, 362–363,
365, 371–376, 531, 535, 575–582, 585–588,
591–597, 603, 613–624, 638–639, 648, 653–
654, 660–663, 751–756, 773–778, 780–781,
787–789, 791, 795–796, 799, 808–813, 815–
819, 821–822, 824–826, 834, 844
Number Theory
The student demonstrates conceptual understanding of number theory by
[2] N-6 modeling or explaining the commutative 14, 41
and identity properties of addition (M1.1.7)
[2] N-7 identifying or using patterns in the
254, 259, 332–333, 396, 401, 445–448, 713–
number system (skip count by 2’s, 5’s, or 10’s;
715, 744, 892–893, 896, 889, 892–893, 897,
add or subtract by 10; identify even or odd
910–911, 913–914, 916
numbers) (M1.1.6)
[2] N-8 modeling fact families (M1.1.3)
113–115, 126–127, 133–136, 140–141, 192,
194, 199
Measurement: Select and use systems, units, and tools of measurement
Measurable Attributes
The student demonstrates understanding of measurable attributes by
[2] MEA-1 measuring to the nearest inch or
973–975, 977–978, 983–984
foot (M2.1.3)
[2] MEA-2 comparing and ordering objects by
671, 688–689, 691, 852–853, 857–859, 863,
length, weight, area, time, temperature
965–970, 980–981, 984
(M2.1.1)
[2] MEA-3 comparing objects to standard and
966–970, 973, 975, 980–981
nonstandard units to identify objects that are
greater than, less than, and equal to a given
unit (M2.1.2)
Grade 2
Page 11 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
[2] MEA-4 identifying coins, their value, or the
22–23, 387, 390–391, 393, 564–567, 571,
value of a set of coins up to one dollar (M2.1.5) 573–574, 734–738, 740–741, 743
Measurement Techniques
The student demonstrates ability to use measurement techniques by
[2] MEA-5 selecting and using appropriate
966–967, 969, 983
tools of measurement (M2.1.3)
[2] MEA-6 drawing a line segment to the
See Grade 3.
nearest half inch (M2.1.3)
[2] MEA-7 telling time to the nearest 1⁄4 hour
424–426, 428–434
using analog and digital clocks (M2.1.4)
[2] MEA-8 ordering the months of the year
220, 446, 450
(M2.1.1)
[2] MEA-9 writing the date using words and
444–446, 449–450
numbers (day, month, year) (M2.1.1)
[2] MEA-10 counting change (coins) up to a
387, 390–391, 393, 564–567, 571, 573
dollar (M2.1.5)
[2] MEA-11 recognizing money symbols
384–387, 390–391, 566, 740–741
including a decimal point ($,¢, .) (M2.1.5)
[2] MEA-12 identifying equal values of coins up 22–23, 387, 390–391, 393, 564–565, 574,
to a dollar (M2.1.5)
734–738, 743
Estimation and Computation: Perform basic arithmetic functions, make reasoned
estimates, and select and use appropriate methods or tools
Estimation
The student determines reasonable answers to real-life situations, paper/pencil
computations, or calculator results by
[2] E&C-1 estimating “how many” and “how
340, 344–346, 720, 723
much” in a given set up to 30
[2] E&C-2 estimating the results of simple
364, 406, 602, 634, 652, 842, 844
addition and subtraction problems up to 100
(M3.1.1)
[2] E&C-3 identifying whether estimation or
364, 406, 602, 634, 656
counting is appropriate (M3.1.1)
Computation
The student accurately solves problems (including real-world situations) involving
[2] E&C-4 recalling addition and subtraction
14–18, 38–43, 46–49, 51–57, 84–87, 90–93,
facts to 20 (M3.1.2)
96–98, 102–103, 112–115, 126–129, 132–142,
152, 372, 473, 495, 519, 584, 590, 758
[2] E&C-5 solving two-digit addition and
321–328, 347–382, 575–604
subtraction problems using a variety of models
and algorithms (M3.1.3)
[2] E&C-6 using repeated addition with objects 565, 890–895, 903, 912, 916
to model multiplication (M3.1.4)
[2] E&C-7 using equal shares with objects to
53, 549, 918, 924–926
model division (M3.1.4)
Functions and Relationships: Represent, analyze, and use patterns, relations, and
functions
Describing Patterns and Functions
The student demonstrates conceptual understanding of functions, patterns, or sequences
by
Grade 2
Page 12 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Alaska
Grade Level Expectation
[2] F&R-1 identifying and continuing patterns,
including numbers (M4.1.1)
Houghton Mifflin
Math Expressions
Teacher’s Guide
19, 87, 164–165, 254, 259, 396–400, 445–449,
577, 678–679, 681, 684–686, 714–715, 717–
718, 731, 755, 892–893, 896–897, 910–911,
913–914, 916
14–15, 64, 87, 165, 396–397, 447, 449, 577,
717, 731, 767, 807
[2] F&R-2 describing a rule or relation that
determines and continues a sequence or
pattern (M4.1.1)
Modeling and Solving Equations and Inequalities
The student demonstrates algebraic thinking by
[2] F&R-3 solving a problem with an unknown
16–17, 43, 68–70, 73, 96, 114, 135, 141, 361,
(e.g., 7 + ? = 10) (M4.1.4)
367, 371, 475, 576–578, 590, 654–655, 657,
660–661, 663, 767, 777, 779, 780–781, 783,
785, 821, 825, 828, 831, 833
[2] F&R-4 using the terms equal to, greater
144–145, 147–148, 467–470, 472, 755
than, and less than for numbers up to 100
(M4.1.4)
Geometry: Construct, transform, and analyze geometric figures.
Geometric Relationships
The student demonstrates an understanding of geometric relationships by
[2] G-1 describing attributes of a triangle, circle, 168–172, 276–279, 281–291, 542–545, 551,
square, and rectangle (M5.1.1)
554–555, 557, 670–682, 685, 688–692, 872–
874, 877
[2] G-2 identifying and classifying 3872–878, 880–883
dimensional shapes (e.g., cone, sphere and
cylinder) (M5.1.1)
[2] G-3 relating real-world examples to the
172, 292, 552, 557–558, 872, 930–931
ideas and concepts of geometry* (M5.1.2)
[2] G-4 constructing, comparing, classifying,
168–172, 542–545, 551, 554–555, 557, 670–
and describing the relationship among
682, 685, 873, 881–882, 928–929, 934–935
geometric figures (M5.1.2)
Similarity, Congruence, Symmetry, and Transformation of Shapes
The student demonstrates conceptual understanding of similarity, congruence, symmetry,
or transformations of shapes by
[2] G-5 creating simple shapes using concrete
168–172, 277–279, 281–285, 291, 545, 551,
materials/manipulatives (M5.1.3)
557, 676–678, 873, 874, 877
[2] G-6 identifying or drawing lines of symmetry 928–932
for simple shapes (M5.1.3)
Perimeter, Area, Volume, and Surface Area:
The student solves problems using perimeter or area by
[2] G-7 explaining the difference between
See Grade 3.
perimeter and area (M5.1.4)
[2] G-8 determining perimeter and area of
174–178, 276, 280, 688–692
rectangular shapes using grid paper and/or
manipulatives (M5.1.4)
Position and Direction
The student demonstrates understanding of position and direction by
[2] G-9 describing relative locations of objects
522
using directional terms (inside, outside, right,
left) (M5.1.6)
Grade 2
Page 13 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
[2] G-10 creating a simple map to show
636
location of objects (M5.1.6)
Construction
The student demonstrates a conceptual understanding of geometric drawings or
constructions by
[2] G-11 drawing, copying, or describing a
168–172, 276–285, 288–291, 543–545, 551,
variety of shapes* (M5.1.7)
554–555, 557, 670–682, 685, 688–692, 872–
874, 877, 934–935
Statistics and Probability: Formulate questions, gather and interpret data, and make
predictions
Data Display
The student demonstrates an ability to classify and organize data by
[2] S&P-1 constructing a variety of graphs from 474–476, 456–459, 460, 462–463, 465–466,
realistic situations (M6.1.1)
468–469, 486–500, 505, 509, 511, 514, 516–
517, 523, 526, 529, 535
[2] S&P-2 collecting, recording, interpreting,
455–530, 852–853, 950–959, 980–982
and representing data in a variety of ways
(M6.1.1)
Analysis and Central Tendency
The student demonstrates an ability to analyze data (comparing, explaining, interpreting,
evaluating; or drawing or justifying conclusions) by
[2] S&P-3 describing data from a variety of
465, 511, 518
graphs (e.g., newspapers, magazines, texts,
computers, and other sources) (M6.1.2)
Probability
The student demonstrates a conceptual understanding of probability and counting
techniques by
[2] S&P-4 predicting, interpreting, and
952–960
comparing data using events or repeated
observations* (M6.1.4)
[2] S&P-5 recognizing the difference between
950–954
chance and certainty (M6.1.4)
Content Standards B, C, D, and E: Process skills and abilities Applying conceptual
knowledge and skills as designated in all strands of Content Standard A by problem
solving, communicating, reasoning, and making connections
Problem Solving: Understand and be able to select and use a variety of problem-solving
strategies
The student demonstrates an ability to problem solve by
[2] PS-1 creating and solving a variety of
This Grade Level Expectation is met
problems using appropriate strategies (M7.1.1
throughout the program. These are some of the
& M7.1.2)
many examples.
5, 10–11, 22–23, 28, 31–32, 106–109, 205,
223, 249, 386, 591–593, 602–603, 605–608,
610, 614–616, 803–804, 890–891, 894–895,
901
[2] PS-2 choosing appropriate operations to
16–17, 96–97, 218, 220, 229, 232, 237–240,
solve a given problem (M7.1.2)
242–243, 252, 257, 266, 478, 582, 622, 631–
636, 655, 658, 660–661, 664, 836, 890–891
Grade 2
Page 14 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
Communication: Form and use appropriate methods to define and explain mathematical
relationships
The student communicates his or her mathematical thinking by
[2] PS-3 translating problems from everyday
144–145, 147, 282–283, 288–289, 314–319,
language into math language and symbols (+, - 810, 933–948
, =, <, >) (M8.1.1)
[2] PS-4 using everyday language to explain
This Grade Level Expectation is met
thinking about problem solving strategies and
throughout the program. These are some of the
solutions to problems * (M8.1.3)
many examples.
3–4, 9–10, 16–17, 55, 86, 190–192, 216–218,
222–223, 362–365, 593, 596, 621–622, 660,
728, 759, 763–764, 801, 834–836, 900, 924
[2] PS-5 using manipulatives, models, pictures, This Grade Level Expectation is met
and language to represent and communicate
throughout the program. These are some of the
mathematical ideas (M8.1.2)
many examples.
27–36, 46–47, 112–115, 116, 138–141, 196–
197, 215–222, 276–285, 354–357, 543–545,
554–555, 670–682, 872–874, 934–935
Reasoning: Use logic and reason to solve mathematical problems
The student demonstrates an ability to use logic and reason by
[2] PS-6 explaining why a prediction,
250, 602, 645, 656–657, 723, 842
estimation, or solution is reasonable (M9.1.3)
[2] PS-7 drawing pictures that support or refute 199, 323, 332–333, 339, 587, 606, 609, 614–
mathematical statements (M9.1.2)
615, 617, 621, 623, 748, 761, 765, 770, 774–
775, 777, 803, 840, 890, 894
Connections: Apply mathematical concepts and processes to situations within and
outside of school.
The student understands and applies mathematical skills and processes across the
content strands by
[2] PS-8 using real world context (e.g., self,
This Grade Level Expectation is met
friends, and family)* (M10.1.2)
throughout the program. These are some of the
many examples.
50, 122, 232, 320, 366, 408, 434, 442, 466,
472, 500, 512, 518, 524, 604, 618, 636, 646,
692, 772, 784, 860, 866, 920, 931, 948
Grade 2
Page 15 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
Content Standard A: Mathematical facts, concepts, principles, and theories
Numeration: Understand and use numeration
Understanding Numbers
The student demonstrates conceptual understanding
• of whole numbers to one thousand by
[3] N-1 reading, writing, ordering, or [counting
1–10, 18, 22–24, 30–36, 281–288
L] (M1.1.1)
[3] N-2 modeling (base ten blocks) or
1–16, 19–20, 22–25, 27, 30–36, 283
identifying place value positions to thousands
(M1.1.2)
[3] N-3 using appropriate representations of
1–10, 18, 22–24, 30–36
ordinal or cardinal numbers (M1.1.4)
• of simple fractions with denominators 2, 3,
4, or 10 by
[3] N-4 identifying, describing with
727–748
explanations, or illustrating equal parts of a
whole, a region, or a set (using models)
(M1.1.5)
[3] N-5 identifying, describing with
782–787, 790–792, 797–801, 804–807, 810–
explanations, or illustrating equivalent
813
representation of fractions (using models)
(M1.1.5)
Understanding Meaning of Operations
The student demonstrates conceptual understanding of mathematical operations by
[3] N-6 [using models, explanations, number
25–26, 32–34, 38–42, 48–49, 59–60, 63, 66,
lines, or real-life situations L] describing or
70, 72–78, 82–84, 87–89, 92–94, 100–105,
illustrating the processes of addition and
116, 163–184, 202–203, 206–207, 317–324,
subtraction of whole numbers and their
353–368
relationships (M1.1.3)
Number Theory
The student demonstrates conceptual understanding of number theory by
[3] N-7 [describing or illustrating identity
537
property of addition L] (M1.1.7)
[3] N-8 [modeling (with manipulatives) and
363
explaining commutative property of addition L]
(M1.1.7)
[3] N-9 identifying or using patterns in the
32–34, 37, 45, 53, 69, 119, 215, 410, 420–421,
number system (skip count by 2’s, 5’s, or 10’s;
424, 449–450, 462–463, 467, 471–473, 478–
add or subtract by 10; even or odd numbers)
479, 497–498, 520–521, 589–590, 622–624,
(M1.1.6)
606–608, 652–653
Measurement: Select and use systems, units, and tools of measurement
Measurable Attributes
The student demonstrates understanding of measurable attributes by
[3] MEA-1 [estimating length to the nearest
913, 915–916, 920–922, 980
inch or foot L] (M2.1.3)
Grade 3
Page 16 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
[3] MEA-2 comparing and ordering objects
911, 915, 921, 924–925, 928, 940–942, 945,
according to measurable attribute (calendar,
951–952, 963, 971, 974, 976–978, 980–983
length, [temperature, weight, area, or volume
L]) (M2.1.1)
[3] MEA-3 identifying or describing objects that 910, 920, 922, 929–930, 940, 943, 945, 948–
are greater than, less than, or equal to a unit of 949, 951, 996–967, 969, 974–975
measure (standard or non-standard) (M2.1.2)
[3] MEA-4 selecting an appropriate unit of
911–912, 920, 930, 932, 968, 970, 972, 974–
English, metric, or non-standard measurement
975
to estimate the length, time, weight, or
temperature (M2.1.3)
[3] MEA-5 identifying coins, their value, or the
290–298, 301
value of a set of coins (M2.1.5)
Measurement Techniques
The student demonstrates ability to use measurement techniques by
[3] MEA-6 measuring length to the nearest
913–916, 921
half-inch (M2.1.3)
[3] MEA-7 telling time to the nearest 1⁄4 hour
702–708
using an analog clock or [distinguishing
morning, afternoon, or evening L] (M2.1.4)
[3] MEA-8 determining elapsed time using a
710–711
calendar (M2.2.5)
[3] MEA-9 [counting back change from $1.00
304, 306–308
L] (M2.2.6)
Estimation and Computation: Perform basic arithmetic functions, make reasoned
estimates, and select and use appropriate methods or tools
Estimation
The student determines reasonable answers to real-life situations, paper/pencil
computations, or calculator results by
[3] E&C-1 finding “how many” or “how much” to 983–984
50 (M3.1.1)
[3] E&C-2 estimating the results of simple
266, 270–271, 276–280
addition and subtraction problems up to 1,000
(M3.1.1)
Computation
The student accurately solves problems (including real-world situations) involving
[3] E&C-3 [recalling basic addition and
17, 25–26, 32–33, 48–49, 163–200, 355–356
subtraction facts, sums to 20, and
corresponding subtraction facts efficiently L]
(M3.1.2)
[3] E&C-4 adding or subtracting two-digit whole 32–33, 48–49, 80, 118, 328–329
numbers (M3.1.3)
[3] E&C-5 using repeated addition to model
422–423, 425, 428, 435, 462, 497–498, 521
multiplication with whole numbers with products
to 25 (M3.1.4)
[3] E&C-6 using grouping or “sharing equally”
433, 450–457, 757
to model division with whole numbers to 25
(M3.1.4)
Grade 3
Page 17 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
Functions and Relationships: Represent, analyze, and use patterns, relations, and
functions
Describing Patterns and Functions
The student demonstrates conceptual understanding of functions, patterns, or sequences
by
[3] F&R-1 identifying a missing element in a
69, 215, 322, 402–403, 405, 408–414, 427,
pattern up to the next three terms (identifying a 434, 543, 590, 596, 604, 606–608, 610, 614,
number using addition or subtraction or
622–623, 625, 656, 690
objects); or explaining how missing elements
could be found (M4.1.1)
[3] F&R-2 [expressing a generalization of a
215, 322, 399, 402–405, 408–414, 420–423,
pattern using words L] (M4.1.1 & M4.1.2)
461–463, 529, 536, 538, 606–608, 622–623,
651–653, 655, 692, 796–798
[3] F&R-3 [using manipulatives, including a
396–399, 405, 413, 427, 434, 655
calculator, as tools when describing, extending,
or representing patterns L] (M4.1.1 & M4.13)
Modeling and Solving Equations and Inequalities
The student demonstrates algebraic thinking by
[3] F&R-4 using an open number sentence
163–213, 218–222, 362–364
(addition or subtraction) to solve for an
unknown represented by a box or circle (e.g.,
5+ =16, -7=4, 5+2= ) (M4.1.4)
[3] F&R-5 using appropriate vocabulary or
282–288, 815, 825, 828–829, 834
symbols for greater than, less than, or equal to
(M4.1.4)
Geometry: Construct, transform, and analyze geometric figures.
Geometric Relationships
The student demonstrates an understanding of geometric relationships by
[3] G-1 using the number or length of sides to
136–158, 247–248, 251
identify, describe, [model L], or compare
triangles or rectangles (including squares)
(M5.1.1)
[3] G-2 using the attributes and properties of
130, 136–138, 140–143, 145, 148–151, 154–
plane figures to [model L], identify, compare, or 157, 245–251, 257–258, 566–569, 874–898,
describe plane figures (circles, rectangles,
900–903, 915, 937
squares, and triangles)[and solid figures
(cubes, cylinders, or spheres) L] (M5.1.1 &
M5.1.2)
Similarity, Congruence, Symmetry, and Transformation of Shapes
The student demonstrates conceptual understanding of similarity, congruence, symmetry,
or transformations of shapes by
[3] G-3 identifying, creating, or drawing lines of 231, 236
symmetry for real-world objects (e.g., block
letters, flags, insects) (M5.1.3)
[3] G-4 comparing or describing shapes
233–235, 239, 241, 244–245, 414
(circles, triangles, or rectangles) as “larger
than,” “smaller than,” or “congruent to,” a given
shape (M5.1.3)
[3] G-5 illustrating or identifying the results of
396–399, 416
transformations (slides) of polygons (M5.1.5)
Grade 3
Page 18 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
Perimeter, Area, Volume, and Surface Area:
The student solves problems using perimeter or area by
[3] G-6 estimating or determining area or
508–512, 562–582, 934, 936–938
perimeter of rectangular or square shapes on
grids (M5.1.4)
Position and Direction
The student demonstrates understanding of position and direction by
[3] G-7 [using directional terms (inside, outside, 778, 990–994, 999
right, left, horizontal, vertical) to describe
relative location of objects in a picture L]
(M5.1.6)
Construction
The student demonstrates a conceptual understanding of geometric drawings or
constructions by
[3] G-8 [drawing real-world objects that consist 144, 146, 881–883, 885–886, 896–898, 961
of geometric shapes (squares, rectangles,
triangles, or circles) L] (M5.1.7)
Statistics and Probability: Formulate questions, gather and interpret data, and make
predictions
Data Display
The student demonstrates an ability to classify and organize data by
[3] S&P-1 [designing an investigation and
137, 155, 370–374, 378–383, 386, 389–390,
collecting, recording L], organizing, displaying,
638, 645, 647, 695, 741, 751, 779, 897
or explaining the classification of data in realworld problems (e.g., literature, self, or family),
using bar graphs, and [Venn diagrams L]
(M6.1.1, M6.1.2, & M6.1.5)
Analysis and Central Tendency
The student demonstrates an ability to analyze data (comparing, explaining, interpreting,
evaluating; or drawing or justifying conclusions) by
[3] S&P-2 using information from a variety of
137, 155, 318–322, 370–374, 378–383, 386–
displays (tallies, tables, pictographs, bar
387, 389–390, 467, 475, 517, 638, 645, 647,
graphs, or [Venn diagrams L] (M6.1.2)
695, 741, 751, 776–779, 897
[3] S&P-3 using the terms “maximum” or
These terms can be introduced on these
“minimum” (M6.1.3)
pages.
378–382, 383
Probability
The student demonstrates a conceptual understanding of probability and counting
techniques by
[3] S&P-4 [explaining the differences between
776–780
chance and certainty or recognizing events that
may be certain or chance events L] (M6.1.4)
[3] S&P-5 [Finding and recording L] and
776–780
making predictions about the likelihood of
outcomes of a simple probability experiment
(e.g., spinner, tossing a coin) (M6.1.4)
Content Standards B, C, D, and E: Process skills and abilities Applying conceptual
knowledge and skills as designated in all strands of Content Standard A by problem
solving, communicating, reasoning, and making connections
Grade 3
Page 19 of 32
Correlation of
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to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
Problem Solving: Understand and be able to select and use a variety of problem-solving
strategies
The student demonstrates an ability to problem solve by
[3] PS-1 selecting and applying an appropriate
This Grade Level Expectation is met
strategy (e.g., guess and check; draw a picture; throughout the program. These are some of the
make a model, extend a pattern) to solve a
many examples.
variety of problems (M7.1.2)
35, 62, 142, 145, 199, 207, 214, 301, 306, 330,
362–365, 366, 409, 442, 601–602, 628, 639,
671, 676–677, 685, 694–695, 747, 757, 861
Communication: Form and use appropriate methods to define and explain mathematical
relationships
The student communicates his or her mathematical thinking by
[3] PS-2 representing mathematical problems
This Grade Level Expectation is met
using manipulatives, models, pictures, and/or
throughout the program. These are some of the
everyday language; or using everyday
many examples.
language to explain thinking about the
24–25, 38–39, 85–86, 95–96, 100–103, 186–
problem-solving strategies and solutions to
187, 218–221, 354–358, 455–456, 492, 501,
problems (M8.1.1, M8.1.2, & M8.1.3)
553, 601–602, 683–685, 758, 858–859, 919,
950
Reasoning: Use logic and reason to solve mathematical problems
The student demonstrates an ability to use logic and reason by
[3] PS-3 drawing conclusions about
8, 97, 100–103, 116–117, 175–176, 180, 183,
mathematical problems; or finding examples
212, 214, 218–221, 330, 337, 340–343, 346–
that support or refute mathematical statements 351, 365, 472, 617–619, 639, 665–666, 671,
(M9.1.1 & M9.1.2)
685, 694–695, 731, 801
[3] PS-4 explaining whether or not a prediction, 270, 276–279, 367, 776–779
estimation, or solution is reasonable (M9.1.3)
Connections: Apply mathematical concepts and processes to situations within and
outside of school.
The student understands and applies mathematical skills and processes across the
content strands by
[3] PS-5 using real-world contexts such as
This Grade Level Expectation is met
literature, self, and family (M10.1.1. & M10.1.2) throughout the program. These are some of the
many examples.
52, 138, 146, 200, 216, 242, 260, 316, 338,
376, 384, 414, 494, 512, 574, 604, 620, 640,
662, 768, 854, 868, 874, 886, 968, 1010
Grade 3
Page 20 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
Content Standard A: Mathematical facts, concepts, principles, and theories
Numeration: Understand and use numeration
Understanding Numbers
The student demonstrates conceptual understanding
• of whole numbers to ten thousands by
[4] N-1 reading, writing, ordering, or [counting
291–294, 298, 302, 304–305, 307, 310–315
L] (M1.2.1)
[4] N-2 modeling (base ten blocks) or
225H, 281–290, 292–294, 298–299, 302–303,
identifying place value positions to ten
309–315, 439G
thousands (M1.2.2)
[4] N-3 converting between whole numbers
283, 294, 298, 315
expressed in expanded notation and standard
form (M1.2.4)
• of fractions with denominators 2 through
12
[4] N-4 identifying, describing with
713H, 713–728, 739–744, 825
explanations, or illustrating equal parts of a
whole, a region, or a set (using models)
(M1.2.4)
[4] N-5 identifying, describing with
713J, 755, 759, 774–777, 781–782, 788–789,
explanations, or illustrating equivalent fractions 794–795
or mixed numbers (M1.2.4 & M3.2.5)
Understanding Meaning of Operations
The student demonstrates conceptual understanding of mathematical operations by
[4] N-6 [using models, explanations, number
1H, 9, 11–20, 25, 29–34, 36–39, 60–61, 65–70,
lines, or real-life situations L] describing or
84–86, 90–91, 97–104, 131, 235, 440–446,
illustrating the processes of multiplication
451, 454–455, 459–460, 554–558
(M1.2.3)
[4] N-7 [using models, explanations, number
1H, 48–49, 66–68
lines, or real-life situations L] describing or
illustrating the relationship between
multiplication and addition (M1.2.3)
[4] N-8 [using models, explanations, number
27–31, 36–38, 43–50, 57–64, 71–75
lines, or real-life situations L] describing or
illustrating the relationship between
multiplication and division (M1.2.3)
[4] N-9 [using models, explanations, number
745–750, 770, 844, 848
lines, or real-life situations L] describing or
illustrating the process of adding or subtracting
fractions with like denominators (2 to 12)
(M1.2.5)
Number Theory
The student demonstrates conceptual understanding of number theory by
[4] N-10 [describing or illustrating identity
43–45, 47–50, 98, 104, 176, 235
property of multiplication L] (M1.2.7)
[4] N-11 [modeling (with manipulatives) and
14–15, 59–60, 63, 93, 98, 104, 439G, 441–
explaining commutative property of
442, 549, 826
multiplication L] (M1.2.7)
Grade 4
Page 21 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
[4] N-12 identifying or listing factors and
2, 9, 16, 41, 60, 62–63, 167–171, 276, 443,
multiples of a number (M1.2.6)
448–449, 451–452, 604, 614, 622, 630
Measurement: Select and use systems, units, and tools of measurement
Measurable Attributes
The student demonstrates understanding of measurable attributes by
[4] MEA-1 [estimating length to the nearest
561, 951, 980
half-inch or centimeter L] (M2.2.1)
[4] MEA-2 [estimating temperature (degree
590–591, 595, 597, 983, 964–965
Celsius or Fahrenheit) or weight (pounds or
kilograms) to the nearest unit L] (M2.2.1)
[4] MEA-3 identifying or using equivalent
564–566, 569, 570, 577, 948, 953
measures for length (inch, foot, yard: 12 inches
= 1 foot, 3 feet = 1 yard, 36 inches = 1 yard;
centimeter, meter: 100 centimeters = 1 meter)
(M2.2.2)
[4] MEA-4 selecting an appropriate unit of
567–569, 596
metric measurement to estimate length, weight
or temperature (M2.2.1)
Measurement Techniques
The student demonstrates ability to use measurement techniques by
[4] MEA-5 measuring length to the nearest
569, 951, 954
half-inch or [centimeter L] (M2.2.1, M2.2.3, &
M2.2.4)
[4] MEA-6 telling time in 5 minute increments
See Grade 2.
using analog clocks (M2.2.5)
[4] MEA-7 [counting back change from $5.00
271
L] (M2.2.6)
[4] MEA-8 determining possible combinations
288, 882
of coins and bills to given amounts (M2.2.6)
[4] MEA-9 [simulating multiple purchases and
271
calculating the amount of change from a given
bill(s) up to $50.00 L] (M2.2.6)
Estimation and Computation: Perform basic arithmetic functions, make reasoned
estimates, and select and use appropriate methods or tools
Estimation
The student determines reasonable answers to real-life situations, paper/pencil
computations, or calculator results by
[4] E&C-1 identifying or using [a variety of L]
333–340, 376, 380–382, 384–384, 461–468,
strategies (e.g., rounding to appropriate place
497–499, 533–538, 634–635, 639–646
value, multiplying by powers of ten, using frontend estimation) to estimate the results of whole
number addition or subtraction computations to
10,000, or simple multiplication or division
(M3.2.1)
Computation
The student accurately solves problems (including real-world situations) involving
[4] E&C-2 [recalling basic multiplication facts,
1–10, 21–56, 71–88, 105–112
products to 100, and corresponding division
facts efficiently L] (M3.2.2)
Grade 4
Page 22 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
[4] E&C-3 adding or subtracting three-digit
318–326, 342–362
whole numbers (M3.2.3)
[4] E&C-4 multiplying two-digit numbers by
453–482
single-digit numbers (M3.2.4)
[4] E&C-5 adding fractions with like
745–750, 770, 844, 848
denominators to 12 (M3.2.3)
Functions and Relationships: Represent, analyze, and use patterns, relations, and
functions
Describing Patterns and Functions
The student demonstrates conceptual understanding of functions, patterns, or sequences
by
[4] F&R-1 extending patterns that use addition, 2–5, 7, 9, 25–26, 28, 30, 33, 36, 38, 41–42, 56,
subtraction, multiplication, or symbols, up to 10 75–78, 80–81, 88, 91–95, 106–107, 118, 131–
terms, represented by models (function
132, 157, 429–434, 505, 509, 515, 537, 545,
machine), tables, sequences, or in problem
551, 557, 700, 889, 921
situations (M4.2.1)
[4] F&R-2 [using rules to express the
2–3, 25–26, 33, 56, 76–78, 88, 91–94, 118,
generalization of a pattern using words, lists, or 131–132, 157, 429–434, 537, 545, 551, 557,
tables L] (M4.2.4)
700, 889, 921
• [4] F&R-3 [using manipulatives, including a
42, 91, 95, 430, 432–433
calculator, as tools when describing, extending,
or representing a number sequence L] (M4.2.1
&M4.2.3)
Modeling and Solving Equations and Inequalities
The student demonstrates algebraic thinking by
[4] F&R-4 using an open number sentence
15, 39–40, 42, 108, 112, 130, 158, 257, 276,
(addition, subtraction or multiplication) to solve
345, 348, 350, 377, 388
for an unknown represented by a box or circle
(e.g., 9 • = 36, • 8=56, 3 • 6= ) (M4.2.5)
Geometry: Construct, transform, and analyze geometric figures.
Geometric Relationships
The student demonstrates an understanding of geometric relationships by
[4] G-1 using the attributes and properties of
406–412, 418
angles to identify and compare triangles (acute,
right, or obtuse) and regular polygons (M5.2.1)
[4] G-2 using the attributes and properties of
853–864, 866–874
solid figures (edges, vertices, or the number or
shape of faces) to [model L], identify, compare,
or describe solid figures (cubes, cylinders,
rectangular prisms, or spheres) (e.g., cans,
dice, boxes, balls) (M5.2.2)
Similarity, Congruence, Symmetry, and Transformation of Shapes
The student demonstrates conceptual understanding of similarity, congruence, symmetry,
or transformations of shapes by
[4] G-3 identifying or drawing all lines of
180–181, 183–184, 224, 681
symmetry to identify figures that are
symmetrical (M5.2.3)
[4] G-4 identifying shapes that are congruent
178–179, 184, 414–419, 427
(M5.2.3)
Grade 4
Page 23 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
[4] G-5 illustrating or identifying the results of
182, 402, 431, 681
transformations (turns) of polygons by
continuing a given pattern (M5.2.5)
Perimeter, Area, Volume, and Surface Area
The student solves problems using perimeter or area by
[4] G-6 estimating or determining area or
198–203, 214–216, 218–220
perimeter of rectangles, squares and irregular
shapes on grids with a key or ruler (M5.2.4)
Position and Direction
The student demonstrates understanding of position and direction by
[4] G-7 [describing the relative location of
See Grade 5.
places or objects on a map using compass
directions of north, south, east or west L]
(M5.2.6)
Construction
The student demonstrates a conceptual understanding of geometric drawings or
constructions by
[4] G-8 [identifying or drawing parallel or
186–190, 404
intersecting line segments L] (M5.2.7)
Statistics and Probability: Formulate questions, gather and interpret data, and make
predictions
Data Display
The student demonstrates an ability to classify and organize data by
[4] S&P-1 [designing an investigation and
25, 115, 117, 119–120, 122–123, 132, 141,
collecting L], organizing or displaying, using
143, 146–152, 176, 218, 279, 307, 410, 589–
appropriate scale, data in real-world problems
590, 598, 692–693, 704–705, 708, 805, 831–
(e.g., social studies, friends, or school), using
832
bar graphs, tables, charts, or diagrams with
whole numbers up to 25 (M6.2.1 & M6.2.2)
Analysis and Central Tendency
The student demonstrates an ability to analyze data (comparing, explaining, interpreting,
evaluating; or drawing or justifying conclusions) by
[4] S&P-2 using information from a variety of
25, 115, 117, 119–120, 122–123, 132, 141,
displays (tables, bar graphs, or Venn diagrams) 143, 146–152, 176, 218, 279, 307, 410, 589–
(M6.2.2)
590, 598, 692–693, 704–705, 708, 805, 831–
832
[4] S&P-3 using mode or range with up to 5
304, 307, 668
pieces of data with a value of 10 or less each
(M6.2.3)
Probability
The student demonstrates a conceptual understanding of probability and counting
techniques by
[4] S&P-4 predicting or explaining the
803–804, 808–810
probability of all possible outcomes in a simple
experiment (e.g., spinners, dice, coins)
(M6.2.4)
Grade 4
Page 24 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
[4] S&P-5 determining possible combinations
125
in a given situation involving up to 3 items (e.g.,
how many ways can you choose two fruits out
of a basket containing oranges and bananas?
–three ways: two bananas; one orange and
one banana; and two oranges) (M6.2.5)
Content Standards B, C, D, and E: Process skills and abilities Applying conceptual
knowledge and skills as designated in all strands of Content Standard A by problem
solving, communicating, reasoning, and making connections
Problem Solving: Understand and be able to select and use a variety of problem-solving
strategies
The student demonstrates an ability to problem solve by
[4] PS-1 selecting and applying appropriate
This Grade Level Expectation is met
strategy (e.g., lists, guess and check; extended throughout the program. These are some of the
patterns) to solve a variety of problems
many examples.
(M7.2.2)
17–18, 31, 66–67, 69, 125, 136–137, 163–164,
211, 251, 255, 257, 270, 397D, 432, 451, 459,
473, 481, 513, 519, 576, 659, 661, 678, 680–
681, 686, 858–859, 952
[4] PS-2 explaining and verifying results of an
This Grade Level Expectation is met
original problem and applying what was
throughout the program. These are some of the
learned to new situations (M7.2.3)
many examples.
8, 40, 73, 80, 85, 106, 107, 116, 167, 178, 193,
268, 270, 297, 329, 337–338, 351, 409, 429,
466, 543, 617, 697, 854, 866, 892, 901
Communication: Form and use appropriate methods to define and explain mathematical
relationships
The student communicates his or her mathematical thinking by
[4] PS-3 representing problems using
This Grade Level Expectation is met
mathematical language including concrete,
throughout the program. These are some of the
pictorial, and/or symbolic representation; or by
many examples.
organizing and communicating mathematical
17–18, 31, 66–67, 69, 125, 136–137, 163–164,
problem-solving strategies and solutions to
211, 251, 255, 257, 270, 397D, 432, 451, 459,
problems (M8.2.1, M8.2.2, & M8.2.3)
473, 481, 513, 519, 576, 659, 661, 678, 680–
681, 686, 858–859, 952
Reasoning: Use logic and reason to solve mathematical problems
The student demonstrates an ability to use logic and reason by
[4] PS-4 drawing conclusions about
14–15, 41, 45–49, 59–60, 63, 93, 98, 104,
mathematical problems (given a rule or
136, 156, 279, 385, 439G, 441–442, 549,
generalization, determine whether the example 648–655, 826, 832–835, 883
fits) or justifying answers and mathematical
strategies (M9.2.1, M9.2.2, & M9.2.3)
Connections: Apply mathematical concepts and processes to situations within and
outside of school.
The student understands and applies mathematical skills and processes across the
content strands by
Grade 4
Page 25 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Alaska
Grade Level Expectation
[4] PS-5 using real-world contexts such as
social studies, friends, and school (M10.2.1 &
M10.2.2)
Grade 4
Houghton Mifflin
Math Expressions
Teacher’s Guide
This Grade Level Expectation is met
throughout the program. These are some of the
many examples.
34, 42, 50, 138, 158, 258, 308, 316, 340, 379,
428, 452, 482, 502, 508, 546, 552, 558, 592,
656, 694, 702, 750, 822, 836, 898, 942, 972
Page 26 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
Content Standard A: Mathematical facts, concepts, principles, and theories
Numeration: Understand and use numeration
Understanding Numbers
The student demonstrates conceptual understanding
• of whole numbers to millions by
[5] N-1 reading, writing, ordering, or [counting
171, 183–190, 192, 196, 197, 203, 207, 209,
L] (M1.2.1)
290, 296
[5] N-2 identifying place value positions from
164–167, 169–173, 175, 183–191, 296, 632–
tenths to millions (M1.2.2)
633, 749–750
[5] N-3 converting between whole numbers
186–187, 189
written in expanded notation and standard form
(M1.2.4)
• of positive fractions with denominators 1 through 12 and 100 with proper and mixed
numbers and benchmark percents (10%, 25%, 50%, 75%, 100%) by modeling, identifying,
describing with explanations, or illustrating
[5] N-4 equal parts of a whole, a region, or a
11, 346–347, 351, 353, 416–417
set (M1.2.4)
[5] N-5 equivalent fractions or mixed numbers
384–400, 404–405, 407–408, 416–424, 426,
(M1.2.4 & M3.2.5)
429, 431, 433–436, 439–441, 451, 478, 762
Understanding Meaning of Operations
The student demonstrates conceptual understanding of mathematical operations by
[5] N-6 [using models, explanations, number
3, 64–67, 589–598, 599–604, 613–618, 619–
lines, or real-life situations L] describing or
623, 625–630, 756–760, 767–772, 777–788
illustrating the process of division and its
relationship to subtraction or to multiplication
(M1.2.3)
[5] N-7 [using models, explanations, number
347–349, 352–353, 364–367, 370–373, 390–
lines, or real-life situations L] describing or
394, 399, 402, 406, 410–413, 445–446, 459,
illustrating the process of adding and
467
subtracting proper fractions or mixed numbers
(like denominators) (M1.2.5)
[5] N-8 [using models, explanations, number
199, 200, 201, 214–215, 291, 296
lines, or real-life situations L] describing or
illustrating the process of adding or subtracting
decimals that represent money (M1.2.5)
Number Theory
The student demonstrates conceptual understanding of number theory by
[5] N-9 describing or illustrating commutative or 1F, 16, 19–20, 47, 59, 83, 106–109, 111, 116,
identity properties of addition or multiplication
224–227, 392
using models or explanations (M1.2.7)
[5] N-10 identifying or listing factors and
28, 49, 59, 438, 457–458, 457, 461, 469, 502
multiples common to a pair or set of numbers
(M1.2.6)
Measurement: Select and use systems, units, and tools of measurement
Measurable Attributes
The student demonstrates understanding of measurable attributes by
[5] MEA-1 [estimating length to the nearest
180, 191, 197, 203, 209
one-fourth inch or centimeter L] (M2.2.1)
Grade 5
Page 27 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
[5] MEA-2 [estimating temperature (degree
500
Celsius or Fahrenheit, plus or minus 5
degrees) or weight (half-pounds or kilograms)
to the nearest unit L] (M2.2.1)
[5] MEA-3 identifying or using equivalent
152–153, 242–243, 501–504, 538
measures for weight/mass (16 oz. = 1 pound or
1000 grams = 1 kilogram) and length (1000
millimeters = 1 meter) or time (M2.2.2)
Measurement Techniques
The student demonstrates ability to use measurement techniques by
[5] MEA-4 [measuring temperature or weight
500
using appropriate tools L] (M2.2.1 & M2.2.3)
[5] MEA-5 telling time using analog clocks to
See Grade 3.
the nearest minute and using A.M. or P.M.
(M2.2.5)
[5] MEA-6 determining possible combinations
201, 215, 244
of coins and bills to given amounts (M2.2.6)
[5] MEA-7 [simulating multiple purchases and
244
calculating the amount of change from given
bills up to $100.00 L] (M2.2.6)
[5] MEA-8 measuring length to the nearest 1⁄4
181
inch or centimeter (M2.2.1)
Estimation and Computation: Perform basic arithmetic functions, make reasoned
estimates, and select and use appropriate methods or tools
Estimation
The student determines reasonable answers to real-life situations, paper/pencil
computations, or calculator results by
[5] E&C-1 identifying or using [a variety of L]
220, 240–241, 243–244, 246–250, 286, 459,
strategies (e.g., rounding to appropriate place
457, 490, 516–518, 545, 575–581, 614–616,
value, multiplying by powers of ten, using front- 620–623
end estimation to estimate the results of
addition or subtraction computations from
tenths to 100,000, including money, or simple
multiplication or division (M3.2.1)
Computation
The student accurately solves problems (including real-world situations) involving
[5] E&C-2 [recalling basic multiplication facts,
2, 3–5, 7–8, 16–19, 21–24, 30, 44–48, 64–66
products to 144, and corresponding division
facts efficiently L] (M3.2.2)
[5] E&C-3 adding or subtracting four-digit
199, 201, 213, 215, 291, 346–349, 352–353,
whole numbers, fractions with like
364–367, 394
denominators to 12, or decimals involving
money (M3.2.3)
[5] E&C-4 multiplying two-digit whole numbers
510, 518, 520–533, 589–595, 597–598
by two-digit numbers or dividing three-digit
whole numbers by single-digit numbers
(M3.2.4)
Functions and Relationships: Represent, analyze, and use patterns, relations, and
functions
Grade 5
Page 28 of 32
Correlation of
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Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
Describing Patterns and Functions
The student demonstrates conceptual understanding of functions, patterns, or sequences
by
[5] F&R-1 extending patterns that use addition, 7, 16, 23, 42, 44–47, 49, 52–56, 73, 116, 165,
subtraction, multiplication, division or symbols,
184–185, 247, 285, 337, 439, 683–686, 684–
up to 10 terms, represented by models
698, 701, 834–840, 836–840, 844, 846, 850,
(function machines), tables, sequences, or in
852, 854, 856–860
problem situations (M4.2.1)
[5] F&R-2 using rules to express the
45–47, 51–56, 116, 285, 337, 680–686, 695,
generalization of a pattern using words, lists, or 701, 834–840, 836–840, 844, 846, 850, 852,
tables (M4.2.4)
854, 856–860
[5] F&R-3 identifying or applying addition or
52, 53–56, 285, 682–683, 686, 701, 836–840,
subtraction patterns to find missing values in a
844, 846, 850, 852, 854, 856–860
function (M4.1.2)
[5] F&R-4 [using manipulatives, including a
49, 694–695
calculator, as tools when describing, extending,
or representing a number sequence L] (M4.2.1
& M4.2.3)
Modeling and Solving Equations and Inequalities
The student demonstrates algebraic thinking by
[5] F&R-5 using an open number sentence
32–33, 267, 418–421
(addition, subtraction, multiplication, or division)
to solve for an unknown represented by a box
or circle (e.g., 256 ÷ =8, ÷8=56, 36÷3= )
(M4.2.5)
Geometry: Construct, transform, and analyze geometric figures.
Geometric Relationships
The student demonstrates an understanding of geometric relationships by
[5] G-1 using the attributes and properties of
311–316
angles and the number, length, and orientation
of sides to identify or compare triangles
(scalene, isosceles, or equilateral) or
quadrilaterals (parallelograms, trapezoids,
rhombi) (M5.2.1)
[5] G-2 using the attributes and properties of
807–809, 816–819, 821, 824–827
solid figures (edges, vertices, number of faces)
to [model L], identify, compare, or describe
(cubes, cylinders, cones, spheres, pyramids, or
rectangular prisms) (e.g., boxes, buildings,
packages) (M5.2.2)
Similarity, Congruence, Symmetry, and Transformation of Shapes
The student demonstrates conceptual understanding of similarity, congruence, symmetry,
or transformations of shapes by
[5] G- 3 illustrating or identifying the results of
320–321, 665–669, 671, 675, 677, 691, 702
transformation (slides, turns, or flips of
polygons) (e.g., pictures of cultural art, fabric
designs, architecture, logos) (M5.2.5)
[5] G-4 identifying, creating, or drawing
312, 315, 324–328, 344, 923–930
geometric figures that are congruent, similar, or
symmetrical (M5.2.3)
Grade 5
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Houghton Mifflin
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Math Expressions
Grade Level Expectation
Teacher’s Guide
[5] G-5 [modeling designs (e.g., tessellations)
669–670, 696–697, 701, 929
that contain a series of slides, flips, and/or
turns L] (M5.2.5)
Perimeter, Area, Volume, and Surface Area
The student solves problems (including real- world situations) using perimeter or area by
[5] G-6 estimating or determining area or
10, 12–14, 39, 70, 118, 121, 124–125, 127–
perimeter of rectangles using a key, ruler, or
128, 132–133, 135, 141, 145, 156, 227, 482
given measures (M5.2.4)
[5] G-7 [estimating or determining the area and 336–339
circumference of a circle using a grid or
manipulatives L] (M5.2.4 & M5.3.4)
Position and Direction
The student demonstrates understanding of position and direction by
[5] G-8 [locating points of given coordinates on 672–678, 685, 690–692, 702
a grid or identifying coordinates for a given
point (e.g., items on a treasure map) L]
(M5.2.6)
Construction
The student demonstrates a conceptual understanding of geometric drawings or
constructions by
[5] G-9 [identifying or drawing perpendicular
297F, 298–299
line segments or midpoints L] (M5.2.7)
Statistics and Probability: Formulate questions, gather and interpret data, and make
predictions
Data Display
The student demonstrates an ability to classify and organize data by
[5] S&P-1 [designing an investigation and
34–36, 74, 234–235, 246–256, 286, 337, 381,
collecting L], organizing, or displaying, using
388, 448, 497, 503
appropriate scale, data in real-world problems
(e.g., social studies, friends, or school), using
bar graphs, tables, charts, diagrams, or line
graphs with whole numbers up to 50 (M6.2.1 &
M6.2.2)
Analysis and Central Tendency
The student demonstrates an ability to analyze data (comparing, explaining, interpreting,
evaluating; or drawing or justifying conclusions) by
[5] S&P-2 using information from a variety of
34–36, 74, 234–235, 246–256, 286, 337, 381,
displays (tables, bar graphs, line graphs, or
388, 448, 497, 503
Venn diagrams) (M6.2.2)
[5] S&P-3 using mode, median, or range with
290, 596, 610
up to 10 pieces of data with a value of 10 or
less each (M6.2.3)
Probability
The student demonstrates a conceptual understanding of probability and counting
techniques by
[5] S&P-4 predicting or explaining the
443–450, 914–917, 922
probability of all possible outcomes in an
experiment using ratios or fractions to describe
the probability (M6.2.4)
Grade 5
Page 30 of 32
Correlation of
Houghton Mifflin Math Expressions © 2006
to the
Alaska Mathematics Grade Level Expectations
Houghton Mifflin
Alaska
Math Expressions
Grade Level Expectation
Teacher’s Guide
[5] S&P-5 solving or identifying solutions to
See Grade 3.
problems involving money combinations (e.g.,
how many ways can you make 25 cents using
nickels, dimes, or quarters?) (M6.2.5)
Content Standards B, C, D, and E: Process skills and abilities Applying conceptual
knowledge and skills as designated in all strands of Content Standard A by problem
solving, communicating, reasoning, and making connections
Problem Solving: Understand and be able to select and use a variety of problem-solving
strategies
The student demonstrates an ability to problem solve by
[5] PS-1 selecting and applying an appropriate
This Grade Level Expectation is met
strategy (e.g., tables, charts, lists, or graphs;
throughout the program. These are some of
guess and check; extended patterns; make a
the many examples.
model) to solve a variety of problems and verify 6, 11, 26, 33, 39–40, 60, 67, 76, 78, 100–101,
the results (M7.2.2)
103, 134, 154, 227, 264–267, 272–276, 381,
393, 413, 497, 503, 530
[5] PS-2 explaining and verifying results of an
This Grade Level Expectation is met
original problem and applying what was
throughout the program. These are some of
learned to new situations (M7.2.3)
the many examples.
16, 19, 22, 53, 76, 82–83, 85–86, 90, 100–101,
108–109, 177, 187, 198, 219, 247, 252–253,
258, 268, 280, 288, 411, 412, 428, 513, 520,
562, 681, 705, 811, 820, 945
Communication: Form and use appropriate methods to define and explain mathematical
relationships
The student communicates his or her mathematical thinking by
[5] PS-3 representing problems using
This Grade Level Expectation is met
mathematical language including concrete,
throughout the program. These are some of
pictorial, and/or symbolic representation; or
the many examples.
organizing and communicating mathematical
6, 11, 26, 33, 39–40, 76, 78, 100–101, 108–
problem-solving strategies and solutions using
109, 167, 264–267, 272–276, 403–403, 407,
mathematical language (M8.2.1, M8.2.2, &
416–419, 421–422, 497, 503, 683, 685, 702
M8.2.3)
Reasoning: Use logic and reason to solve mathematical problems
The student demonstrates an ability to use logic and reason by
[5] PS-4 drawing logical conclusions about
5, 32–33, 35, 60, 83–86, 103, 109, 144–145,
mathematical situations (given a rule or
204–207, 224–226, 253, 255, 268, 281, 284,
generalization, determine whether the example 288–289, 520–523, 526–529, 534–537
fits); or justifying answers and mathematical
strategies as reasonable (M9.2.1, M9.2.2, &
M9.2.3)
Connections: Apply mathematical concepts and processes to situations within and
outside of school.
The student understands and applies mathematical skills and processes across the
content strands by
Grade 5
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Correlation of
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to the
Alaska Mathematics Grade Level Expectations
Alaska
Grade Level Expectation
[5] PS-5 using real-world contexts such as
social studies, friends, and school (M10.2.1 &
M10.2.2)
Grade 5
Houghton Mifflin
Math Expressions
Teacher’s Guide
This Grade Level Expectation is met
throughout the program. These are some of
the many examples.
36, 68, 96, 104, 150, 222, 196, 202, 208, 222,
278, 216, 244, 292, 328, 334, 368, 388, 408,
460, 468, 568, 782, 766, 802, 936
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