process

grade description

KINDERGARTEN By the end of kindergarten, students will understand small numbers, quantities, and

simple shapes in their everyday environment. They will also count, compare, describe and sort objects, and

develop a sense of properties and patterns. Students will begin to understand measurement through the

direct comparison of objects, money by making fair trades with coins and the concept of time by

0

experiencing a daily schedule. Instruction and assessment should include the use of manipulatives and

appropriate technology. Topics should be represented in multiple ways including concrete/pictorial,

verbal/written, numeric/data-based, graphical, and symbolic. Concepts should be introduced and used in

the context of real world phenomena.

GRADE 1 By the end of grade one, students will understand and use the concept of ones and tens in the

place value number system. The students will add and subtract small numbers with ease. They will

represent quantity with numbers, models, diagrams, and number sentences. They will begin to use tools for

1

measuring and observe, create, and decompose geometric shapes and solve simple problems including

those involving spatial relationships. The students will pose questions, record data, and interpret simple

charts and picture graphs.

GRADE 2 By the end of grade two, students will understand place value and number relationships in

addition and subtraction and use simple concepts of multiplication. They will measure length with

2 appropriate units. Students will classify shapes and see relationships among them by recognizing their

geometric attributes. They will know the relationships of time and count back change. The students will

collect, analyze, and interpret data using bar graphs and Venn diagrams.

GRADE 3 By the end of grade three, students will understand place value. They will further develop their

understanding and their skills with addition and subtraction of whole numbers and decimals. They will also

expand their knowledge base of multiplication and division of whole numbers. Students will understand the

3

concepts of length, perimeter, area, and time. Students will broaden their understanding of characteristics

of previously studied geometric figures. They will solve problems by collecting, organizing, displaying, and

interpreting data.

GRADE 4 By the end of grade four, students will add and subtract decimal fractions and common fractions

with common denominators. They will also understand how and when it is appropriate to use rounding.

Students will use common measurement units to determine weight. Students will develop their

4

understanding of measuring angles with appropriate units and tools. Students will understand the

characteristics of geometric plane and solid figures. They will also use tables, graphs, and charts to record

and analyze data.

GRADE 5 By the end of grade five, students will further develop their understanding of multiplication and

division of whole numbers, decimals, and fractions. They will also understand and investigate algebraic

mathematical expressions. Students will also expand their understanding of computing area and volume of

5

simple geometric figures. Students will understand the meaning of congruent geometric shapes and the

relationship of the circumference of a circle to its diameter. They will also use percentages and circle

graphs to interpret statistical data.

GRADE 6 By the end of grade six, students will understand the four arithmetic operations as they relate to

positive rational numbers; convert between and compute with different forms of rational numbers;

understand the concept of ratio and solve problems using proportional reasoning; understand and use line

6

and rotational symmetry; determine the surface area and volume of solid figures; use variables to represent

unknown quantities in formulae, algebraic expressions and equations; utilize data to make predictions; and

determine the probability of a given event.

GRADE 7 By the end of grade seven, students will understand and use rational numbers, including signed

numbers; solve linear equations in one variable; sketch and construct plane figures; demonstrate

understanding of transformations; use and apply properties of similarity; examine properties of geometric

7 shapes in space; describe and sketch solid figures, including their cross-sections; represent and describe

relationships between variables in tables, graphs, and formulas; analyze the characteristics of linear

relationships; and represent and analyze data using graphical displays, measures of central tendency, and

measures of variation.

GRADE 8 By the end of grade eight, students will understand various numerical representations, including

square roots, exponents and scientific notation; use and apply geometric properties of plane figures,

including congruence and the Pythagorean theorem; use symbolic algebra to represent situations and solve

8

problems, especially those that involve linear relationships; solve linear equations, systems of linear

equations and inequalities; use equations, tables and graphs to analyze and interpret linear functions; use

and understand set theory and simple counting techniques; determine the theoretical probability of simple

events; and make inferences from statistical data, particularly data that can be modeled by linear functions.



GRADE 9 (Mathematics 1) Relations, functions: types, algebraic and graphical manipulations, modeling;

9

arithmetic and geometric sequences and series, logic and implications, properties of triangles and

quadrilaterals, counting methods in probability and data analysis, coordinate geometry.



GRADE 10 (Mathematics 2) Relations; functions: evaluation and inverses, linear, quadratic, piecewise, and

10

exponential; modeling with these types of functions, solution of linear & quadratic equations and

inequalities, complex numbers, right triangles and trigonometry; circles and spheres; statistical inference.



GRADE 11 (Mathematics 3) Matrices: computations and applications; polynomial functions; coordinates in

11

space, exponential and logarithmic functions; solving equations involving polynomials, and exponential and

logarithmic functions, conic sections; discrete and continuous distributions in probability.

grade strand description

NUMBER AND OPERATIONS Students will correctly represent the number and order of objects

0 N

using numbers and understand them.

NUMBER AND OPERATIONS Students will understand how to represent numbers, and be able to

1 N

add and subtract small numbers.



NUMBER AND OPERATIONS Students will further develop their understanding of numbers

2 N

(including fractions) and how to represent them. The students will understand and apply addition,

subtraction and multiplication through concrete maniputaion and perform basic calculations.



NUMBER AND OPERATIONS Students will use decimal fractions and common fractions to

3 N

represent parts of a whole. They will also understand the four arithmetic operations for whole

numbers and use them in basic calculations, and apply them in problem solving situations.

NUMBER AND OPERATIONS Students will further develop their understanding of whole numbers

and master the four basic operations with whole numbers by solving problems. They will also

4 N understand rounding and when to use it appropriately. Students will further develop their

understanding of addition and subtraction of decimal fractions and common fractions with like

denominators.



NUMBER AND OPERATIONS Students will further develop their understanding of the concept of

5 N

whole numbers. They will also understand the meanings of multiplication and division of decimals

and use decimals and common fractions in computation, as well as in problem solving situations.

NUMBER AND OPERATIONS Students will understand the meaning of the four arithmetic

6 N operations as related to positive rational numbers and will apply these concepts and associated

skills in real world situations.

NUMBER AND OPERATIONS Students will further develop their understanding of the concept of

7 N

rational numbers and apply them to real world situations.

NUMBER AND OPERATIONS Students will understand the numeric and geometric meaning of

8 N

square root, apply properties of integer exponents and use scientific notation.

10 N NUMBER AND OPERATIONS Students will use the complex number system.

3 A

ALGEBRA Students will understand how to express relationships as mathematical expressions.

ALGEBRA Students will investigate and represent mathematical relationships between quantities

4 A

using mathematical expressions in problem-solving situations.

ALGEBRA Students will represent and investigate mathematical expressions algebraically by using

5 A

variables.

ALGEBRA Students will investigate relationships between two quantities. They will write and solve

6 A

proportions and simple one-step equations that result from problem situations.

ALGEBRA Students will demonstrate an understanding of linear relations and fundamental

7 A

algebraic concepts.

ALGEBRA Students will use linear algebra to represent, analyze and solve problems. They will use

8 A equations, tables, and graphs to investigate linear relations and functions, paying particular

attention to slope as a rate of change.

ALGEBRA Students will explore functions and solve simple equations. Students will simplify and

9 A

operate with radical, polynomial, and rational expressions.



ALGEBRA Students will investigate piecewise, exponential, and quadratic functions, using

10 A

numerical, analytical, and graphical approaches, focusing on the use of these functions in problem-

solving situations. Students will solve equations and inequalities and explore inverses of functions.

ALGEBRA Students will investigate exponential, logarithmic and polynomial functions of degree

11 A

higher than 2. Students will understand matrices and use them to solve problems.

0 G

GEOMETRY Students will recognize and name basic geometric shapes and spatial relationships.

GEOMETRY Students will understand the concepts of basic geometric shapes and spatial

1 G

relationships of concrete objects.

GEOMETRY Students will understand basic and compound geometric shapes together with the

2 G

elements from which they are composed.

GEOMETRY Students will further develop their understanding of characteristics of previously

3 G

studied geometric figures.

GEOMETRY Students will understand and build plane and solid geometric figures. They will also

4 G

graph points on the coordinate plane.

5 G GEOMETRY Students will further develop their understanding of geometric figures.

GEOMETRY Students will further develop their understanding of plane and solid geometric figures,

6 G incorporating the use of appropriate technology and using this knowledge to solve authentic

problems.

GEOMETRY Students will further develop and apply their understanding of plane and solid

geometric figures through the use of constructions and transformations. Students will explore the

7 G properties of similarity and further develop their understanding of 3-dimensional figures. Line and

rotational symmetry, Surface area and volume, Ratio as a representation of quantitative

relationships

GEOMETRY Students will use and apply geometric properties of plane figures, including

8 G

congruence and the Pythagorean theorem.

GEOMETRY Students will explore, understand, and use the formal language of reasoning and

9 G justification. Students will apply properties of polygons and determine distances and points of

concurrence.

GEOMETRY Students will explore right triangles and right-triangle trigonometry. They will

10 G understand and apply properties of circles and spheres, and use them in determining related

measures.

GEOMETRY Students will understand and use the analytic geometry of conic sections and of

11 G

planes and spheres in space.

DATA ANALYSIS AND PROBABILITY Students will pose questions and gather data about

0 D

themselves and their surroundings.

DATA ANALYSIS AND PROBABILITY Students will pose questions, collect, organize and interpret

1 D

data about themselves and their surroundings.

DATA ANALYSIS AND PROBABILITY Students will pose questions, collect, organize, and interpret

2 D

data about themselves and their surroundings.

DATA ANALYSIS AND PROBABILITY Students will gather, organize, and display data and

3 D

interpret graphs.

DATA ANALYSIS AND PROBABILITY Students will gather, organize, and display data. They will

4 D

also compare features of graphs.

DATA ANALYSIS AND PROBABILITY Students will gather, organize, and display data and

5 D

interpret graphs.



DATA ANALYSIS AND PROBABILITY Students will demonstrate understanding of data analysis by

6 D

posing questions to be answered by collecting data. They will represent, investigate, and use data

to answer those questions. Students will understand experimental and theoretical probability.

DATA ANALYSIS AND PROBABILITY Students will demonstrate understanding of data analysis by

posing questions, collecting data, analyzing the data using measures of central tendency and

7 D

variation, and using the data to answer the questions posed. Students will understand the role of

probability in sampling.

DATA ANALYSIS AND PROBABILITY Students will use and understand set theory and simple

8 D counting techniques; determine the theoretical probability of simple events; and make inferences

from data, particularly data that can be modeled by linear functions.

DATA ANALYSIS AND PROBABILITY Students will use counting techniques and determine

probability. Students will demonstrate understanding of data analysis by posing questions to be

9 D

answered by collecting data. Students will organize, represent, investigate, interpret, and make

inferences from data.

DATA ANALYSIS AND PROBABILITY Students will demonstrate understanding of data analysis by

posing questions to be answered by collecting data. Students will organize, represent, investigate,

10 D

interpret, and make inferences from data. They will use regression to analyze data and to make

inferences.

DATA ANALYSIS AND PROBABILITY Students will use a normal distribution to calculate

11 D probabilities. They will organize, represent, investigate, interpret, and make inferences using data

from both observational studies and experiments.



0 M MEASUREMENT Students will explore quantitative situations involving, length, capacity, weight,

and height by direct comparison. Students will explore time through calendars and schedules.

1 M MEASUREMENT Students will measure basic quantitative attributes of concrete objects.

MEASUREMENT Students will understand length, time, and temperature and choose an

2 M

appropriate tool to measure them.

MEASUREMENT Students will understand and measure time and length. They will also model and

3 M

calculate perimeter and area of simple geometric figures.

MEASUREMENT Students will measure weight in appropriate metric and standard units. They will

4 M

also measure angles.

MEASUREMENT Students will compute the area of geometric plane figures. They will also

understand the concept of volume and compute the volume of simple geometric solids and

5 M

measure capacity. Students will convert from one unit to another within one system of

measurement.



MEASUREMENT Students will understand how to determine the volume and surface area of solid

6 M

figures. They will understand and use the customary and metric systems of measurement to

measure quantities efficiently and to represent volume and surface area appropriately.

position grade strand item subitem

197 3 A

198 3 A 1

199 3 A 1 a

200 3 A 1 b



201 3 A 1 c



262 4 A

263 4 A 1

264 4 A 1 a

265 4 A 1 b

266 4 A 1 c

330 5 A

331 5 A 1

332 5 A 1 a

333 5 A 1 b

334 5 A 1 c



380 6 A

381 6 A 1

382 6 A 2

383 6 A 2 a

384 6 A 2 b

385 6 A 2 c



386 6 A 2 d

387 6 A 2 e



388 6 A 2 f



389 6 A 2 g

390 6 A 3



423 7 A

424 7 A 1

425 7 A 1 a

426 7 A 1 b

427 7 A 1 c

428 7 A 2

429 7 A 2 a

430 7 A 2 b

431 7 A 3

432 7 A 3 a

433 7 A 3 b

434 7 A 3 c

435 7 A 3 d





468 8 A



469 8 A 1

470 8 A 1 a

471 8 A 1 b

472 8 A 1 c

473 8 A 1 d

474 8 A 1 e

475 8 A 2

476 8 A 2 a

477 8 A 2 b

478 8 A 2 c

479 8 A 2 d

480 8 A 3

481 8 A 3 a

482 8 A 3 b

483 8 A 3 c

484 8 A 3 d

485 8 A 3 e

486 8 A 3 f



487 8 A 3 g

488 8 A 3 h

489 8 A 3 i

490 8 A 4

491 8 A 4 a

492 8 A 4 b

493 8 A 4 c

494 8 A 4 d

495 8 A 4 e



496 8 A 4 f

497 8 A 4 g

498 8 A 5

499 8 A 5 a

500 8 A 5 b

501 8 A 5 c

502 8 A 5 d

519 9 A



520 9 A 1

521 9 A 1 a

522 9 A 1 b

523 9 A 1 c



524 9 A 1 d

525 9 A 1 e

526 9 A 1 f

527 9 A 1 g



528 9 A 1 h





529 9 A 1 i



530 9 A 2

531 9 A 2 a

532 9 A 2 b

533 9 A 2 c

534 9 A 2 d

535 9 A 2 e

536 9 A 2 f

537 9 A 2 g

538 9 A 3

539 9 A 3 a

540 9 A 3 b

541 9 A 3 c



542 9 A 3 d





580 10 A





581 10 A 1

582 10 A 1 a



583 10 A 1 b





584 10 A 1 c

585 10 A 2

586 10 A 2 a



587 10 A 2 b



588 10 A 2 c

589 10 A 2 d

590 10 A 2 e

591 10 A 2 f



592 10 A 2 g

593 10 A 3

594 10 A 3 a

595 10 A 3 b

596 10 A 3 c

597 10 A 3 d

598 10 A 3 e

599 10 A 4

600 10 A 4 a

601 10 A 4 b

602 10 A 4 c

603 10 A 4 d

604 10 A 5

605 10 A 5 a



606 10 A 5 b

607 10 A 5 c

608 10 A 5 d

638 11 A

639 11 A 1

640 11 A 1 a

641 11 A 1 b

642 11 A 1 c



643 11 A 1 d



644 11 A 2

645 11 A 2 a

646 11 A 2 b

647 11 A 2 c

648 11 A 2 d

649 11 A 2 e

650 11 A 2 f

651 11 A 2 g

652 11 A 3



653 11 A 3 a





654 11 A 3 b



655 11 A 3 c



656 11 A 3 d

657 11 A 4

658 11 A 4 a



659 11 A 4 b

660 11 A 4 c

661 11 A 5

662 11 A 5 a

663 11 A 5 b

664 11 A 5 c

665 11 A 6

666 11 A 6 a

667 11 A 6 b

668 11 A 7

669 11 A 7 a

670 11 A 7 b





50 1 C









98 2 C







208 4 C





276 5 C





46 0 D



47 0 D 1



92 1 D

93 1 D 1

94 1 D 1 a

95 1 D 1 b



136 2 D

137 2 D 1

138 2 D 1 a

139 2 D 1 b

202 3 D

203 3 D 1

204 3 D 1 a

205 3 D 1 b



267 4 D



268 4 D 1

269 4 D 1 a

270 4 D 1 b

271 4 D 1 c

272 4 D 1 d

273 4 D 1 e

335 5 D

336 5 D 1

337 5 D 1 a

338 5 D 1 b

339 5 D 1 c

340 5 D 2



391 6 D



392 6 D 1

393 6 D 1 a

394 6 D 1 b



395 6 D 1 c





396 6 D 1 d

397 6 D 1 e

398 6 D 2



399 6 D 2 a

400 6 D 2 b

401 6 D 2 c





436 7 D





437 7 D 1

438 7 D 1 a

439 7 D 1 b

440 7 D 1 c

441 7 D 1 d



442 7 D 1 e





443 7 D 1 f





444 7 D 1 g





503 8 D



504 8 D 1

505 8 D 1 a

506 8 D 1 b

507 8 D 1 c

508 8 D 2

509 8 D 2 a

510 8 D 2 b

511 8 D 3

512 8 D 3 a

513 8 D 3 b

514 8 D 4

515 8 D 4 a

516 8 D 4 b





559 9 D





560 9 D 1

561 9 D 1 a

562 9 D 1 b

563 9 D 2

564 9 D 2 a

565 9 D 2 b

566 9 D 2 c

567 9 D 2 d

568 9 D 3

569 9 D 3 a



570 9 D 3 b



571 9 D 3 c



572 9 D 4





625 10 D





626 10 D 1

627 10 D 1 a

628 10 D 1 b

629 10 D 1 c





630 10 D 1 d





631 10 D 2

632 10 D 2 a

633 10 D 2 b



634 10 D 2 c



635 10 D 2 d





686 11 D

687 11 D 1





688 11 D 2



689 11 D 2 a

690 11 D 2 b

691 11 D 2 c

692 11 D 3

32 0 G

33 0 G 1



34 0 G 1 a

35 0 G 1 b

36 0 G 1 c

37 0 G 1 d



38 0 G 1 e

39 0 G 2

40 0 G 2 a

41 0 G 2 b



42 0 G 3

43 0 G 3 a

44 0 G 3 b

45 0 G 3 c

85 1 G



86 1 G 1

87 1 G 1 a

88 1 G 1 b

89 1 G 1 c

90 1 G 2



91 1 G 3



130 2 G





131 2 G 1





132 2 G 2





133 2 G 2 a

134 2 G 2 b

135 2 G 3

191 3 G



192 3 G 1



193 3 G 1 a

194 3 G 1 b

195 3 G 1 c

196 3 G 1 d

248 4 G



249 4 G 1

250 4 G 1 a

251 4 G 1 b

252 4 G 1 c

253 4 G 1 d

254 4 G 2

255 4 G 2 a

256 4 G 2 b

257 4 G 2 c

258 4 G 3

259 4 G 3 a

260 4 G 3 b

261 4 G 3 c

327 5 G

328 5 G 1



329 5 G 2





368 6 G



369 6 G 1

370 6 G 1 a

371 6 G 1 b

372 6 G 1 c

373 6 G 1 d

374 6 G 1 e

375 6 G 2

376 6 G 2 a

377 6 G 2 b

378 6 G 2 c

379 6 G 2 d





409 7 G





410 7 G 1

411 7 G 1 a





412 7 G 1 b

413 7 G 2

414 7 G 2 a



415 7 G 2 b

416 7 G 3

417 7 G 3 a





418 7 G 3 b





419 7 G 3 c

420 7 G 4

421 7 G 4 a

422 7 G 4 b

459 8 G



460 8 G 1



461 8 G 1 a

462 8 G 1 b

463 8 G 1 c

464 8 G 1 d

465 8 G 2

466 8 G 2 a

467 8 G 2 b





543 9 G



544 9 G 1

545 9 G 1 a

546 9 G 1 b

547 9 G 1 c

548 9 G 1 d

549 9 G 1 e

550 9 G 2

551 9 G 2 a



552 9 G 2 b

553 9 G 3

554 9 G 3 a

555 9 G 3 b

556 9 G 3 c

557 9 G 3 d

558 9 G 3 e



609 10 G



610 10 G 1

611 10 G 1 a

612 10 G 1 b

613 10 G 2

614 10 G 2 a

615 10 G 2 b

616 10 G 2 c

617 10 G 3

618 10 G 3 a

619 10 G 3 b

620 10 G 3 c

621 10 G 3 d

622 10 G 4

623 10 G 4 a

624 10 G 4 b

671 11 G

672 11 G 1

673 11 G 1 a

674 11 G 1 b

675 11 G 1 c

676 11 G 1 d

677 11 G 1 e

678 11 G 2

679 11 G 2 a

680 11 G 2 b

681 11 G 2 c

682 11 G 3

683 11 G 3 a

684 11 G 3 b

685 11 G 3 c

18 0 M



19 0 M 1

20 0 M 1 a

21 0 M 1 b

22 0 M 1 c

23 0 M 1 d

24 0 M 2

25 0 M 2 a

26 0 M 2 b

27 0 M 2 c

28 0 M 3

29 0 M 3 a

30 0 M 3 b

31 0 M 3 c

76 1 M

77 1 M 1

78 1 M 1 a

79 1 M 1 b

80 1 M 1 c

81 1 M 2

82 1 M 2 a



83 1 M 2 b

84 1 M 2 c

121 2 M



122 2 M 1



123 2 M 1 a

124 2 M 1 b

125 2 M 1 c

126 2 M 2

127 2 M 3

128 2 M 3 a

129 2 M 3 b

176 3 M



177 3 M 1

178 3 M 2

179 3 M 2 a

180 3 M 2 b

181 3 M 2 c

182 3 M 2 d

183 3 M 3

184 3 M 3 a

185 3 M 3 b

186 3 M 3 c

187 3 M 4

188 3 M 4 a

189 3 M 4 b



190 3 M 4 c



239 4 M

240 4 M 1

241 4 M 1 a

242 4 M 1 b

243 4 M 1 c

244 4 M 2

245 4 M 2 a

246 4 M 2 b

247 4 M 2 c





304 5 M





305 5 M 1

306 5 M 1 a

307 5 M 1 b

308 5 M 1 c

309 5 M 1 d

310 5 M 1 e

311 5 M 1 f

312 5 M 1 g

313 5 M 1 h

314 5 M 2

315 5 M 2 a

316 5 M 2 b

317 5 M 3

318 5 M 3 a

319 5 M 3 b

320 5 M 4

321 5 M 4 a

322 5 M 4 b

323 5 M 4 c

324 5 M 4 d

325 5 M 4 e

326 5 M 4 f



352 6 M





353 6 M 1



354 6 M 2

355 6 M 2 a

356 6 M 2 b

357 6 M 2 c

358 6 M 3

359 6 M 3 a

360 6 M 3 b

361 6 M 3 c

362 6 M 3 d

363 6 M 4

364 6 M 4 a

365 6 M 4 b

366 6 M 4 c

367 6 M 4 d

2 0 N

3 0 N 1

4 0 N 1 a

5 0 N 1 b

6 0 N 1 c

7 0 N 1 d

8 0 N 1 e



9 0 N 1 f

10 0 N 1 g

11 0 N 1 h

12 0 N 1 i

13 0 N 1 j

14 0 N 2

15 0 N 2 a



16 0 N 2 b



17 0 N 2 c



51 1 N

52 1 N 1

53 1 N 1 a

54 1 N 1 b

55 1 N 1 c

56 1 N 1 d





57 1 N 1 e





58 1 N 2



59 1 N 2 a



60 1 N 2 b

61 1 N 2 c

62 1 N 3

63 1 N 3 a

64 1 N 3 b

65 1 N 3 c

66 1 N 3 d



67 1 N 3 e





68 1 N 3 f





69 1 N 3 g

70 1 N 3 h





71 1 N 4

72 1 N 4 a



73 1 N 4 b





74 1 N 4 c

75 1 N 4 d



99 2 N



100 2 N 1

101 2 N 1 a





102 2 N 1 b





103 2 N 1 c

104 2 N 2

105 2 N 2 a

106 2 N 2 b

107 2 N 2 c



108 2 N 2 d



109 2 N 2 e

110 2 N 3

111 2 N 3 a

112 2 N 3 b

113 2 N 3 c

114 2 N 3 d

115 2 N 4

116 2 N 4 a

117 2 N 4 b

118 2 N 5

119 2 N 5 a

120 2 N 5 b





142 3 N





143 3 N 1

144 3 N 1 a

145 3 N 1 b



146 3 N 2

147 3 N 2 a

148 3 N 2 b

149 3 N 2 c

150 3 N 2 d

151 3 N 3



152 3 N 3 a

153 3 N 3 b

154 3 N 3 c

155 3 N 3 d

156 3 N 3 e

157 3 N 3 f

158 3 N 3 g

159 3 N 4



160 3 N 4 a





161 3 N 4 b





162 3 N 4 c

163 3 N 4 d

164 3 N 4 e

165 3 N 4 f

166 3 N 4 g

167 3 N 5

168 3 N 5 a

169 3 N 5 b

170 3 N 5 c



171 3 N 5 d



172 3 N 5 e

173 3 N 5 f

174 3 N 5 g

175 3 N 5 h





209 4 N







210 4 N 1

211 4 N 1 a

212 4 N 1 b

213 4 N 2

214 4 N 2 a

215 4 N 2 b



216 4 N 2 c

217 4 N 2 d

218 4 N 2 e



219 4 N 3

220 4 N 3 a

221 4 N 3 b

222 4 N 3 c

223 4 N 3 d



224 4 N 5

225 4 N 5 a

226 4 N 5 b

227 4 N 5 c

228 4 N 5 d

229 4 N 5 e

230 4 N 6

231 4 N 6 a

232 4 N 6 b

233 4 N 6 c

234 4 N 7

235 4 N 7 a

236 4 N 7 b

237 4 N 7 c

238 4 N 7 d



277 5 N



278 5 N 1

279 5 N 1 a

280 5 N 1 b

281 5 N 1 c

282 5 N 2

283 5 N 2 a

284 5 N 2 b

285 5 N 2 c

286 5 N 3

287 5 N 3 a

288 5 N 3 b

289 5 N 3 c

290 5 N 3 d



291 5 N 4

292 5 N 4 a

293 5 N 4 b

294 5 N 4 c

295 5 N 4 d

296 5 N 4 e

297 5 N 4 f

298 5 N 4 g

299 5 N 4 h

300 5 N 4 i

301 5 N 5

302 5 N 5 a

303 5 N 5 b



343 6 N





344 6 N 1

345 6 N 1 a

346 6 N 1 b

347 6 N 1 c

348 6 N 1 d

349 6 N 1 e

350 6 N 1 f

351 6 N 1 g

403 7 N



404 7 N 1

405 7 N 1 a

406 7 N 1 b

407 7 N 1 c

408 7 N 1 d

446 8 N



447 8 N 1

448 8 N 1 a

449 8 N 1 b

450 8 N 1 c

451 8 N 1 d

452 8 N 1 e

453 8 N 1 f

454 8 N 1 g

455 8 N 1 h

456 8 N 1 i

457 8 N 1 j

458 8 N 1 k

574 10 N

575 10 N 1

576 10 N 1 a

577 10 N 1 b

578 10 N 1 c

579 10 N 1 d









48 0 S









96 1 S







140 2 S







206 3 S









274 4 S







341 5 S









517 8 S









636 10 S

693 11 S









1 0









49 1









97 2









141 3









207 4









275 5









342 6









402 7

445 8









518 9







573 10







637 11

description

ALGEBRA Students will understand how to express relationships as mathematical expressions.

Students will use mathematical expressions to represent relationships between quantities and interpret

given expressions.

Describe and extend numeric and geometric patterns.

Describe and explain a quantitative relationship represented by a formula (such as the perimeter of a

geometric figure).

Use a symbol, such as __ to represent an unknown and find the value of the unknown in a number

sentence.

ALGEBRA Students will investigate and represent mathematical relationships between quantities using

mathematical expressions in problem-solving situations.

Students will represent and interpret mathematical relationships in quantitative expressions.

Understand and apply patterns and rules to describe relationships and solve problems.

Represent unknowns using symbols, such as __.

Write and evaluate mathematical expressions using symbols and different values.

ALGEBRA Students will represent and investigate mathematical expressions algebraically by using

variables.

Students will represent and interpret the relationships between quantities algebraically.

Use variables, such as n or x, for unknown quantities in algebraic expressions.

Investigate simple algebraic expressions by substituting numbers for the unknown.

Determine that a formula will be reliable regardless of the type of number (whole numbers or decimals)

substituted for the variable.

ALGEBRA Students will investigate relationships between two quantities. They will write and solve

proportions and simple one-step equations that result from problem situations.

Students will understand the concept of ratio and use it to represent quantitative relationships.

Students will consider relationships between varying quantities.

Analyze and describe patterns arising from mathematical rules, tables, and graphs.

Use manipulatives or draw pictures to solve problems involving proportional relationships.



Use proportions (a/b=c/d) to describe relationships and solve problems, including percent problems.



Describe proportional relationships mathematically using y = kx, where k is the constant of proportionality.

Graph proportional relationships in the form y = kx and describe characteristics of the graphs.

In a proportional relationship expressed as y = kx, solve for one quantity given values of the other two.

Given quantities may be whole numbers, decimals, or fractions. Solve problems using the relationship

y=kx.

Use proportional reasoning (a/b=c/d and y = kx) to solve problems.

Students will evaluate algebraic expressions, including those with exponents, and solve simple one-step

equations using each of the four basic operations.

ALGEBRA Students will demonstrate an understanding of linear relations and fundamental algebraic

concepts.

Students will represent and evaluate quantities using algebraic expressions.

Translate verbal phrases to algebraic expressions.

Simplify and evaluate algebraic expressions, using commutative, associative, and distributive properties as

appropriate.

Add and subtract linear expressions.

Students will understand and apply linear equations in one variable.

Given a problem, define a variable, write an equation, solve the equation, and interpret the solution.



Use the addition and multiplication properties of equality to solve one- and two-step linear equations.

Students will understand relationships between two variables.

Plot points on a coordinate plane.

Represent, describe, and analyze relations from tables, graphs, and formulas.

Describe how change in one variable affects the other variable.

Describe patterns in the graphs of proportional relationships, both direct (y = kx) and inverse (y = k/x).

ALGEBRA Students will use linear algebra to represent, analyze and solve problems. They will use

equations, tables, and graphs to investigate linear relations and functions, paying particular attention to

slope as a rate of change.

Students will use algebra to represent, analyze, and solve problems.

Represent a given situation using algebraic expressions or equations in one variable.

Simplify and evaluate algebraic expressions.

Solve algebraic equations in one variable, including equations involving absolute values.

Solve equations involving several variables for one variable in terms of the others.

Interpret solutions in problem contexts.

Students will understand and graph inequalities in one variable.

Represent a given situation using an inequality in one variable.

Use the properties of inequality to solve inequalities.

Graph the solution of an inequality on a number line.

Interpret solutions in problem contexts.

Students will understand relations and linear functions.

Recognize a relation as a correspondence between varying quantities.

Recognize a function as a correspondence between inputs and outputs where the output for each input

must be unique.

Distinguish between relations that are functions and those that are not functions.

Recognize functions in a variety of representations and a variety of contexts.

Use tables to describe sequences recursively and with a formula in closed form.



Understand and recognize arithmetic sequences as linear functions with whole number input values.



Interpret the constant difference in an arithmetic sequence as the slope of the associated linear function.

Identify relations and functions as linear or nonlinear.

Translate among verbal, tabular, graphic, and algebraic representations of functions.

Students will graph and analyze graphs of linear equations and inequalitites.

Interpret slope as a rate of change.

Determine the meaning of the slope and y-intercept in a given situation.

Graph equations of the form y = mx + b.

Graph equations of the form ax + by = c.

Graph the solution set of a linear inequality, identifying whether the solution set is an open or a closed half-

plane.

Determine the equation of a line given a graph, numerical information that defines the line or a context

involving a linear relationship.

Solve problems involving linear relationships.



Students will understand systems of linear equations and inequalities and use them to solve problems.

Given a problem context, write an appropriate system of linear equations or inequalities.

Solve systems of equations graphically and algebraically, using technology as appropriate.

Graph the solution set of a system of linear inequalities in two variables.

Interpret solutions in problem contexts.

ALGEBRA Students will explore functions and solve simple equations. Students will simplify and operate

with radical, polynomial, and rational expressions.

Students will explore and interpret the characteristics of functions, using graphs, tables, and simple

algebraic techniques.

Represent functions using function notation.

Graph the basic functions f(x) = x^n, where n = 1 to 3, f(x) = sqrt(x), f(x) = |x|, and f(x) = 1/x.

Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as

reflections across the x- and y-axes.

Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of

increase and decrease, maximum and minimum values, and end behavior.

Relate to a given context the characteristics of a function, and use graphs and tables to investigate its

behavior.

Recognize sequences as functions with domains that are whole numbers.

Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change.

Compare rates of change of linear, quadratic, square root, and other function families.

Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or

neither.



Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions

of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

Students will simplify and operate with radical expressions, polynomials, and rational expressions.

Simplify algebraic and numeric expressions involving square root.

Perform operations with square roots.

Add, subtract, multiply, and divide polynomials.

Expand binomials using the Binomial Theorem.

Add, subtract, multiply, and divide rational expressions.

Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the

formulas (x + y)**2 and (x+y)**3

Use area and volume models for polynomial arithmetic.

Students will solve simple equations.

Solve quadratic equations in the form ax2 + bx + c = 0, where a = 1, by using factorization and finding

square roots where applicable.

Solve equations involving radicals such as + b = c, using algebraic techniques.

Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from

investigation of x**2 + bx + c = 0.

Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient

of 1.

ALGEBRA Students will investigate piecewise, exponential, and quadratic functions, using numerical,

analytical, and graphical approaches, focusing on the use of these functions in problem-solving situations.

Students will solve equations and inequalities and explore inverses of functions.

Students will investigate step and piecewise functions, including greatest integer and absolute value

functions.

Write absolute value functions as piecewise functions.

Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex,

axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is

constant, intervals of increase and decrease, and rates of change.

Solve absolute value equations and inequalities analytically, graphically, and by using appropriate

technology.

Students will explore exponential functions.

Extend properties of exponents to include all integer exponents.



Investigate and explain characteristics of exponential functions, including domain and range, asymptotes,

zeros, intercepts, intervals of increase and decrease, rates of change and end behavior.

Graph functions as transformations of f(x) = a**x.

Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate

technology.

Understand and use basic exponential functions as models of real phenomena.

Understand and recognize geometric sequences as exponential functions with domains that are whole

numbers.



Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

Students will analyze quadratic functions in the forms f(x) = ax**2 + bx + c and f(x) = a(x-h)**2 + k.

Convert between standard and vertex form.

Graph quadratic functions as transformations of the function f(x) = x**2.

Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of

symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

Explore arithmetic series and various ways of computing their sums.

Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

Students will solve quadratic equations and inequalities in one variable.

Solve equations graphically using appropriate technology.

Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic

formula.

Analyze the nature of roots using technology and using the discriminant.

Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear

inequalities.

Students will explore inverses of functions.



Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including

the use of restricted domains.

Explore the graphs of functions and their inverses.

Use composition to verify that functions are inverses of each other.

ALGEBRA Students will investigate exponential, logarithmic and polynomial functions of degree higher

than 2. Students will understand matrices and use them to solve problems.

Students will analyze graphs of polynomial functions of higher degree.

Graph simple polynomial functions as translations of the function f(x) = ax**n.

Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and

multiplicity of real zeros.

Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.



Investigate and explain characteristics of polynomial functions, including domain and range, intercepts,

zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

Students will explore logarithmic functions as inverses of exponential functions.

Define and understand the properties of nth roots.

Extend properties of exponents to include rational exponents.

Define logarithmic functions as inverses of exponential functions.

Understand and use properties of logarithms by extending laws of exponents.

Investigate and explain characteristics of exponential and logarithmic functions including domain and range,

asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Graph functions as transformations of f(x) = ax, f(x) = logax, f(x) = ex, f(x) = ln x.

Explore real phenomena related to exponential and logarithmic functions including half-life and doubling

time.

Students will solve a variety of equations and inequalities.

Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder

theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical

conjugates.

Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate

technology.

Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate

technology. Represent solution sets of inequalities using interval notation.

Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and

paper, or appropriate technology.

Students will perform basic operations with matrices.

Add, subtract, multiply, and invert matrices, when possible, choosing appropriate methods, including

technology.

Find the inverses of two-by-two matrices using pencil and paper, and find inverses of larger matrices using

technology.

Examine the properties of matrices, contrasting them with properties of real numbers.

Students will use matrices to formulate and solve problems.

Represent a system of linear equations as a matrix equation.

Solve matrix equations using inverse matrices.

Represent and solve realistic problems using systems of linear equations.

Students will solve linear programming problems in two variables.

Solve systems of inequalities in two variables, showing the solutions graphically.

Represent and solve realistic problems using linear programming.

Students will understand and apply matrix representations of vertex-edge graphs.

Use graphs to represent realistic situations.

Use matrices to represent graphs, and solve problems that can be represented by graphs.



Concepts/Skill to Maintain: Number words Ordinal numbers Equivalence Basic 2-Dimensional and 3-

Dimensional geometric shapes Spatial relationships, positional words, Calendar time, estimating suing 5

and 10 as benchmarks, coinaage, measurement- comparing and ordering by direct comparison.



Concepts/Skills to Maintain: Fluency with single digit addition/subtraction facts to 18; Fair trades with coins

or bills; Duration and sequence of events; Number patterns-skip count, odd/even, Fractions: halves,

fourths; Tally marks, Picture graphs; Estimation: rounding to nearest ten;Telling time; Measurement

,estimating, comparing, and ordering; Basic geometric figures and spatial relationships.

Concepts / Skills to Maintain: Multiplication and Division of whole numbers, Area, Perimeter, Place Value,

Length, Elapsed Time

Concepts / Skills to Maintain: Add and subtract decimals, Whole numbers and decimals computation,

Angle measurement, Length, area, and weight, Number sense, Add and subtract common fractions with

like denominators, Data usage and representation, Characteristics of 2-D and 3-D shapes, Order of

Operations, Properties of addition and multiplication

DATA ANALYSIS AND PROBABILITY Students will pose questions and gather data about themselves and

their surroundings.

Students will pose information questions, collect data, organize, and display results using objects, pictures,

and picture graphs.

DATA ANALYSIS AND PROBABILITY Students will pose questions, collect, organize and interpret data

about themselves and their surroundings.

Students will create simple tables and graphs and interpret them.

Interpret tally marks, picture graphs, and bar graphs.

Pose questions, collect, sort, organize and record data using objects, pictures, tally marks, picture graphs,

and bar graphs.

DATA ANALYSIS AND PROBABILITY Students will pose questions, collect, organize, and interpret data

about themselves and their surroundings.

Students will create simple tables and graphs and interpret their meaning.

Create, organize and display data using pictographs, Venn diagrams, bar graphs, picture graphs, simple

charts, and tables to record results with scales of 1, 2 and 5.

Know how to interpret picture graphs, Venn diagrams, and bar graphs.

DATA ANALYSIS AND PROBABILITY Students will gather, organize, and display data and interpret

graphs.

Students will create and interpret simple tables and graphs.

Solve problems by organizing and displaying data in charts, tables, and graphs.

Construct and interpret line plot graphs, pictographs, Venn diagrams, and bar graphs using scale

increments of 1, 2, 5, and 10.

DATA ANALYSIS AND PROBABILITY Students will gather, organize, and display data. They will also

compare features of graphs.



Students will gather, organize, and display data according to the situation and compare related features.

Construct and interpret line graphs, line plot graphs, pictographs, Venn diagrams, and bar graphs.

Investigate the features and tendencies of graphs.

Compare different graphical representations for a given set of data.

Identify missing information and duplications in data.

Determine and justify the range, mode, and median of a set of data.

DATA ANALYSIS AND PROBABILITY Students will gather, organize, and display data and interpret

graphs.

Students will analyze graphs.

Analyze data presented in a graph.

Compare and contrast multiple graphic representations (circle graphs, line graphs, line plot graphs,

pictographs, Venn diagrams, and bar graphs) for a single set of data and discuss the ad

Determine and justify the mean, range, mode, and median of a set of data.

Students will collect, organize, and display data using the most appropriate graph.

DATA ANALYSIS AND PROBABILITY Students will demonstrate understanding of data analysis by posing

questions to be answered by collecting data. They will represent, investigate, and use data to answer those

questions. Students will understand experimental and theoretical probability.

Students will pose questions, collect data, represent and analyze the data, and interpret results.

Formulate questions that can be answered by data. Students should collect data by using samples from a

larger population (surveys), or by conducting experiments.

Using data, construct frequency distributions, frequency tables, and graphs.



Choose appropriate graphs to be consistent with the nature of the data (categorical or numerical). Graphs

should include pictographs, histograms, bar graphs, line graphs, circle graphs and line plots.

Use tables and graphs to examine variation that occurs within a group and variation that occurs between

groups.

Relate the data analysis to the context of the questions posed.

Students will use experimental and simple theoretical probability and understand the nature of sampling.

They will also make predictions from investigations.

Predict the probability of a given event through trials/simulations (experimental probability), and represent

the probability as a ratio.

Determine, and use a ratio to represent, the theoretical probability of a given event.



Discover that experimental probability approaches theoretical probability when the number of trials is large.



DATA ANALYSIS AND PROBABILITY Students will demonstrate understanding of data analysis by posing

questions, collecting data, analyzing the data using measures of central tendency and variation, and using

the data to answer the questions posed. Students will understand the role of probability in sampling.

Students will pose questions, collect data, represent and analyze the data, and interpret results.

Formulate questions and collect data from a census of at least 30 objects and from samples of varying

sizes.

Construct frequency distributions.

Analyze data using measures of central tendency (mean, median, and mode), including recognition of

outliers.

Analyze data with respect to measures of variation (range, quartiles, interquartile range).



Compare measures of central tendency and variation from samples to those from a census. Observe that

sample statistics are more likely to approximate the population parameters as sample size increases.



Analyze data using appropriate graphs, including pictographs, histograms, bar graphs, line graphs, circle

graphs, and line plots introduced earlier, and using box and- whisker plots and scsatter plots.



Analyze and draw conclusions about data, including describing the relationship between two variables.

DATA ANALYSIS AND PROBABILITY Students will use and understand set theory and simple counting

techniques; determine the theoretical probability of simple events; and make inferences from data,

particularly data that can be modeled by linear functions.

Students will apply basic concepts of set theory.

Demonstrate relationships among sets through use of Venn diagrams.

Determine subsets, complements, intersection, and union of sets.

Use set notation to denote elements of a set.

Students will determine the number of outcomes related to a given event.

Use tree diagrams to find the number of outcomes.

Apply the addition and multiplication principles of counting.

Students will use the basic laws of probability.

Find the probability of simple independent events.

Find the probability of compound independent events.

Students will organize, interpret, and make inferences from statistical data

Gather data that can be modeled with a linear function.

Estimate and determine a line of best fit from a scatter plot.



DATA ANALYSIS AND PROBABILITY Students will use counting techniques and determine probability.

Students will demonstrate understanding of data analysis by posing questions to be answered by collecting

data. Students will organize, represent, investigate, interpret, and make inferences from data.

Students will determine the number of outcomes related to a given event.

Apply the addition and multiplication principles of counting.

Calculate and use simple permutations and combinations.

Students will use the basic laws of probability.

Find the probabilities of mutually exclusive events.

Find the probabilities of dependent events.

Calculate conditional probabilities.

Use expected value to predict outcomes.

Students will relate samples to a population.

Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data

distribution to another sample data distribution in describing center and variabi

Compare the averages of the summary statistics from a large number of samples to the corresponding

population parameters.



Understand that a random sample is used to improve the chance of selecting a representative sample.

Students will explore variability of data by determining the mean absolute deviation (the average of the

absolute values of the deviations).



DATA ANALYSIS AND PROBABILITY Students will demonstrate understanding of data analysis by posing

questions to be answered by collecting data. Students will organize, represent, investigate, interpret, and

make inferences from data. They will use regression to analyze data and to make inferences.

Using sample data, students will make informal inferences about population means and standard

deviations.

Pose a question and collect sample data from at least two different populations.

Understand and calculate the means and standard deviations of sets of data.

Use means and standard deviations to compare data sets.

Compare the means and standard deviations of random samples with the corresponding population

parameters, including those population parameters for normal distributions. Observe that the different

sample means vary from one sample to the next. Observe that the distribution of the sample means has

less variability than the population distribution.



Students will determine an algebraic model to quantify the association between two quantitative variables.

Gather and plot data that can be modeled with linear and quadratic functions.

Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the

median-median line and "eyeballing".

Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate

technology.

Investigate issues that arise when using data to explore the relationship between two variables, including

confusion between correlation and causation.

DATA ANALYSIS AND PROBABILITY Students will use a normal distribution to calculate probabilities.

They will organize, represent, investigate, interpret, and make inferences using data from both

observational studies and experiments.

Students will create probability histograms of discrete random variables, using both experimental and

theoretical probabilities.



Students will solve problems involving probabilities by interpreting a normal distribution as a probability

histogram for a continuous random variable (z-scores are used for a general normal distribution.

Determine intervals about the mean that include a given percent of data.

Determine the probability that a given value falls within a specified interval.

Estimate how many items in a population fall within a specified interval.

Students will understand the differences between experimental and observational studies by posing

questions and collecting, analyzing, and interpreting data.

GEOMETRY Students will recognize and name basic geometric shapes and spatial relationships.

Students will correctly name simple two and three-dimensional figures, and recognize them in the

environment.

Recognize and name the following basic two-dimensional figures: triangles, quadrilaterals (rectangles,

squares) and circles.

Recognize and name the following three-dimensional figures: spheres and cubes.

Observe concrete objects in the environment and represent the objects using basic shapes.

Combine basic figures to form other basic and complex figures into basic figures; decompose basic and

complex figures into basic figures.

Compare geometric shapes and identify similarities and differences of the following two and three-

dimensional shapes: triangles, rectangles, squares, circles, spheres, and cubes.

Students will understand basic spatial relationships.

Identify when an object is beside another object, above another object, or below another object.

Identify when an object is in front of another object, behind another object, inside another object, or outside

it.

Students will identify, create, extend, and transfer patterns from one representation to another using

actions, objects, and geometric shapes.

Identify missing elements within a given pattern.

Extend a given pattern and recognize similarities in different patterns.

Create a pattern in a different context with attributes similar to a given pattern.

GEOMETRY Students will understand the concepts of basic geometric shapes and spatial relationships of

concrete objects.

Students will study and create various two and three-dimensional figures and identify basic figures

(squares, circles, triangles, and rectangles) within them.

Build, draw, name, and describe triangles, rectangles, pentagons, and hexagons.

Build, represent, name, and describe cylinders, cones, and rectangular prisms.

Create pictures and designs using shapes, including overlapping shapes.

Students will compare, contrast, and/or classify geometric shapes by the common attributes of position,

shape, size, number of sides, and number of corners.

Students will arrange and describe objects in space by proximity, position, and direction (near, far, below,

above, up, down, behind, in front of, next to, and left or right of).

GEOMETRY Students will understand basic and compound geometric shapes together with the elements

from which they are composed.

Students will describe and classify plane figures (triangles, square, rectangle, trapezoid, quadrilateral,

pentagon, hexagon, and irregular polygonal shapes) according to the number of sides and vertices and the

sizes of angles (right angle, obtuse, acute).

Students will describe and classify solid geometric figures (prisms, pyramids, cylinders, cones, and

spheres) according to such things as the number of edges and vertices and the number and shape of faces

and angles.



Recognize the (plane) shapes of the faces of a geometric solid and count the number of faces of each type.

Recognize the shape of an angle as a right angle, an obtuse, or acute angle.

Students will describe the change in attributes as two and three-dimensional shapes are cut and

rearranged.

GEOMETRY Students will further develop their understanding of characteristics of previously studied

geometric figures.

Students will further develop their understanding of geometric figures by drawing them. They will also state

and explain their properties.

Draw and classify previously learned fundamental geometric figures and scalene, isosceles, and equilateral

triangles.

Identify and compare the properties of fundamental geometric figures.

Examine and compare angles of fundamental geometric figures.

Identify the center, diameter, and radius of a circle.

GEOMETRY Students will understand and build plane and solid geometric figures. They will also graph

points on the coordinate plane.

Students will define and identify the characteristics of geometric figures through examination and

construction.

Examine and compare angles in order to classify and identify triangles by their angles.

Describe parallel and perpendicular lines in plane geometric figures.

Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi)

by their properties.

Compare and contrast the relationships among quadrilaterals.

Students will understand fundamental solid figures.

Compare and contrast a cube and a rectangular prism in terms of the number and shape of their faces,

edges, and vertices.

Describe parallel and perpendicular lines and planes in connection with the rectangular prism.

Build/collect models for solid geometric figures (cubes, prisms, cylinders, pyramids, spheres, and cones)

using nets and other representations.

Students will use the coordinate system.

Understand and apply ordered pairs in the first quadrant of the coordinate system.

Locate a point in the first quadrant in the coordinate plane and name the ordered pair.

Graph ordered pairs in the first quadrant.

GEOMETRY Students will further develop their understanding of geometric figures.

Students will understand congruence of geometric figures and the correspondence of their vertices, sides,

and angles.



Students will understand the relationship of the circumference of a circle to its diameter is pi (apporx 3.14).



GEOMETRY Students will further develop their understanding of plane and solid geometric figures,

incorporating the use of appropriate technology and using this knowledge to solve authentic problems.

Students will further develop their understanding of plane figures.

Determine and use lines of symmetry.

Investigate rotational symmetry, including degree of rotation.

Use the concepts of ratio, proportion and scale factor to demonstrate the relationships between similar

plane figures.

Interpret and sketch simple scale drawings.

Solve problems involving scale drawings.

Students will further develop their understanding of solid figures.

Compare and contrast right prisms and pyramids.

Compare and contrast cylinders and cones.

Interpret and sketch front, back, top, bottom and side views of solid figures.

Construct nets for prisms, cylinders, pyramids, and cones.



GEOMETRY Students will further develop and apply their understanding of plane and solid geometric

figures through the use of constructions and transformations. Students will explore the properties of

similarity and further develop their understanding of 3-dimensional figures. Line and rotational symmetry,

Surface area and volume, Ratio as a representation of quantitative relationships

Students will construct plane figures that meet given conditions.

Perform basic constructions using both compass and straight edge, and appropriate technology.

Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an

angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and

constructing a line parallel to a given line through a point not on the line.

Recognize that many constructions are based on the creation of congruent triangles.

Students will demonstrate understanding of transformations.

Demonstrate understanding of translations, dilations, rotations, reflections, and relate symmetry to

appropriate transformations.

Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation,

rotation, or reflection.

Students will use the properties of similarity and apply these concepts to geometric figures.

Understand the meaning of similarity, visually compare geometric figures for similarity, and describe

similarities by listing corresponding parts.

Understand the relationships among scale factors, length ratios, and area ratios between similar figures.

Use scale factors, length ratios, and area ratios to determine side lengtts and areas of similar geometric

figures.

Understand congruence of geometric figures as a special case of similarity: The figures have the same size

and shape.

Students will further develop their understanding of three-dimensional figures.



Describe three-dimensional figures formed by translations and rotations of plane figures through space.

Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and prisms.

GEOMETRY Students will use and apply geometric properties of plane figures, including congruence and

the Pythagorean theorem.

Students will understand and apply the properties of parallel and perpendicular lines and understand the

meaning of congruence.



Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically.

Apply properties of angle pairs formed by parallel lines cut by a transversal.

Understand the properties of the ratio of segments of parallel lines cut by one or more transversals.

Understand the meaning of congruence: that all corresponding angles are congruent and all corresponding

sides are congruent.

Students will understand and use the Pythagorean theorem.

Apply properties of right triangles, including the Pythagorean theorem.

Recognize and interpret the Pythagorean theorem as a statement about areas of squares on the sides of a

right triangle.



GEOMETRY Students will explore, understand, and use the formal language of reasoning and justification.

Students will apply properties of polygons and determine distances and points of concurrence.

Students will investigate properties of geometric figures in the coordinate plane.

Determine the distance between two points.

Determine the distance between a point and a line.

Determine the midpoint of a segment.

Understand the distance formula as an application of the Pythagorean theorem.

Use the coordinate plane to investigate properties of and verify conjectures related to triangles and

quadrilaterals.

Students will understand and use the language of mathematical argument and justification.

Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as

appropriate.



Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

Determine the sum of interior and exterior angles in a polygon.



Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram,

rectangle, rhombus, square, trapezoid, and kite.

Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.



GEOMETRY Students will explore right triangles and right-triangle trigonometry. They will understand and

apply properties of circles and spheres, and use them in determining related measures.

Students will identify and use special right triangles.

Determine the lengths of sides of 30-60-90deg triangles.

Determine the lengths of sides of 45-45-90deg triangles.

Students will define and apply sine, cosine, and tangent ratios to right triangles.

Discover the relationship of the trigonometric ratios for similar triangles.

Explain the relationship between the trigonometric ratios of complementary angles.

Solve application problems using the trigonometric ratios.

Students will understand the properties of circles.



Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

Understand and use properties of central, inscribed, and related angles.



Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

Justify measurements and relationships in circles using geometric and algebraic properties.

Students will find and compare the measures of spheres.

Use and apply surface area and volume of a sphere.

Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

GEOMETRY Students will understand and use the analytic geometry of conic sections and of planes and

spheres in space.

Students will investigate the relationships between lines and circles.

Find equations of circles.

Graph a circle given an equation in general form.

Find the equation of a tangent line to a circle at a given point.

Solve a system of equations involving a circle and a line.

Solve a system of equations involving two circles.

Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses,

and hyperbolas).

Convert equations of conics by completing the square.

Graph conic sections, identifying fundamental characteristics.

Write equations of conic sections given appropriate information.

Students will investigate planes and spheres.

Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

Apply the distance formula in 3-space.

Recognize and understand equations of planes and spheres.

MEASUREMENT Students will explore quantitative situations involving, length, capacity, weight, and height

by direct comparison. Students will explore time through calendars and schedules.

Students will group objects according to common properties such as longer/shorter, more/less,

taller/shorter, and heavier/lighter.

Compare and order objects on the basis of length.

Compare and order objects on the basis of capacity.

Compare and order objects on the basis of height.

Compare and order objects on the basis of weight.

Students will understand the measurement of calendar time.

Know the names of the days of the week, as well as understand yesterday, today and tomorrow.

Know the months of the year.

Know the four seasons.

Students will understand time as it relates to a daily schedule.

Order daily events.

Tell the time when daily events occur, such as morning, afternoon, and evening.

Know the name of the day of the week when weekly events occur in class

MEASUREMENT Students will measure basic quantitative attributes of concrete objects.

Students will compare and/or order the length, height, weight, or capacity of two or more objects by using

direct comparison or a nonstandard unit.

Directly compare and/or order length, height, weight, and capacity of concrete objects.

Estimate and measure using a non-standard unit that is smaller than the object to be measured.

Measure with a tool by creating a ruled stick, tape, or container by marking off ten segments of the

repeated single unit.

Students will develop an understanding of the measurement of time.

Tell time to the nearest hour and half hour and understand the movement of the minute hand and how it

relates to the hour hand.

Begin to understand the relationship of calendar time by knowing the number of days in a week and months

in a year.

Compare and/or order the sequence or duration of events (e.g., shorter/longer and before/after).

MEASUREMENT Students will understand length, time, and temperature and choose an appropriate tool to

measure them.

Students will know the standard units of inch, foot, yard, and metric units of centimeter and meter and

measure length to the nearest inch or centimeter.



Compare the relationship of one unit to another by measuring objects twice using different units each time.

Estimate lengths, and then measure to determine if estimations were reasonable.

Determine an appropriate tool and unit for measuring.

Students will tell time to the nearest five minutes and know relationships of time such as the number of

seconds in a minute, minutes in an hour and hours in a day.

Students will explore temperature.

Determine a reasonable temperature for a given situation.

Read a thermometer.

MEASUREMENT Students will understand and measure time and length. They will also model and

calculate perimeter and area of simple geometric figures.

Students will further develop their understanding of the concept of time by determining elapsed time of a

full, half, and quarter-hour.

Students will measure length choosing appropriate units and tools.

Use the units kilometer (km) and mile (mi.) to discuss the measure of long distances.

Measure to the nearest half inch, quarter inch and millimeter (mm) in addition to the previously learned

inch, foot, yard, centimeter, and meter.

Estimate length and represent it using appropriate units.

Compare one unit to another within a single system of measurement.

Students will understand and measure the perimeter of geometric figures.

Understand the meaning of the linear unit and measurement in perimeter.

Understand the concept of perimeter as being the length of the boundary of a geometric figure.

Determine the perimeter of a geometric figure by measuring and summing the lengths of the sides.



Students will understand and measure the area of simple geometric figures (squares and rectangles).

Understand the meaning of the square unit and measurement in area.



Model (by tiling) the area of a simple geometric figure using square units (square inch, square foot, etc.).



Determine the area of squares and rectangles by counting, addition, and multiplication with models.

MEASUREMENT Students will measure weight in appropriate metric and standard units. They will also

measure angles.

Students will understand the concept of weight and how to measure weight.

Use standard and metric units to measure the weight of objects.

Know units used to measure weight (gram, kilogram, ounces, pounds, and tons).

Compare one unit to another within a single system of measurement.

Students will understand the concept of angles and how to measure them.

Use tools, such as a protractor or angle ruler, and other methods such as paper folding, drawing a diagonal

in a square, to measure angles.

Understand the meaning and measure of a half rotation (180 deg) and a full rotation (360 deg).

Determine that the sum of the three angles of a triangle is always 180 deg.



MEASUREMENT Students will compute the area of geometric plane figures. They will also understand the

concept of volume and compute the volume of simple geometric solids and measure capacity. Students will

convert from one unit to another within one system of measurement.

Students will extend their understanding of area of geometric plane figures.

Estimate the area of geometric plane figures.

Derive the formula for the area of a parallelogram.

Derive the formula for the area of a triangle.

Find the areas of triangles and parallelograms using formulae.

Estimate the area of a circle through partitioning and tiling.

Find the area of a polygon (regular and irregular) by dividing it into squares, rectangles, and/or triangles and

find the sum of the areas of those shapes.

Derive the formula for the area of a circle.

Find the area of a circle using the formula and pi ââ?°Ë? 3.14.

Students will extend their understanding of perimeter to include circumference.

Derive the formula for the circumference of a circle.

Find the circumference of a circle using the formula and pi ââ?°Ë? 3.14.

Students will measure capacity with appropriately chosen units and tools.

Use milliliters, liters, fluid ounces, cups, pints, quarts, and gallons to measure capacity.

Compare one unit to another within a single system of measurement.

Students will understand and compute the volume of a simple geometric solid.

Understand a cubic unit (u3) is represented by a cube in which each edge has the length of 1 unit.

Identify the units used in computing volume as cubic centimeters (cm3), cubic meters (m3), cubic inches

(in3), cubic feet (ft3), and cubic yards (yd3).

Derive the formula for finding the volume of a cube and a rectangular prism using manipulatives.

Compute the volume of a cube and a rectangular prism using formulae.

Estimate the volume of a simple geometric solid.

Understand the similarities and differences between volume and capacity.

MEASUREMENT Students will understand how to determine the volume and surface area of solid figures.

They will understand and use the customary and metric systems of measurement to measure quantities

efficiently and to represent volume and surface area appropriately.

Students will convert from one unit to another within one system of measurement (customary or metric) by

using proportional relationships.

Students will use appropriate units of measure for finding length, perimeter, area and volume and will

express each quantity using the appropriate unit.

Measure length to the nearest half, fourth, eighth and sixteenth of an inch.

Select and use units of appropriate size and type to measure length, perimeter, area and volume.

Compare and contrast units of measure for perimeter, area, and volume.

Students will determine the volume of fundamental solid figures (right rectangular prisms, cylinders,

pyramids and cones).

Determine the formula for finding the volume of fundamental solid figures.

Compute the volumes of fundamental solid figures, using appropriate units of measure.

Estimate the volumes of simple geometric solids.

Solve application problems involving the volume of fundamental solid figures.

Students will determine the surface area of solid figures (right rectangular prisms and cylinders).



Find the surface area of right rectangular prisms and cylinders using manipulatives and constructing nets.

Compute the surface area of right rectangular prisms and cylinders using formulae.

Estimate the surface areas of simple geometric solids.

Solve application problems involving surface area of right rectangular prisms and cylinders.

NUMBER AND OPERATIONS Students will correctly represent the number and order of objects using

numbers and understand them.

Students will connect numerals to the quantities they represent.

Count a number of objects up to 30.

Produce models for number words through ten.

Write numerals through 20 to label sets.

Sequence and identify using ordinal numbers (1st-10th).

Compare two or more sets of objects (1-10) and identify which set is equal to, more than, or less than the

other.

Estimate quantities using five and ten as a benchmark. (e.g. 9 is one five and four more. It is closer to 10,

which can be represented as one ten or two fives, than it is to five.)

Use informal strategies to share objects equally (divide) between two to three people or sets.

Identify coins by name and value (penny, nickel, dime, and quarter).

Count out pennies to buy items that together cost less than 30 cents.

Make fair trades using combinations involving pennies and nickels and pennies and dimes.

Students will use representations to model addition and subtraction.

Use counting strategies to find out how many items are in two sets when they are combined, separated, or

compared.

Build number combinations up to 10 (e.g., 4 and 1, 2 and 3, 3 and 2, 4 and 1 for five) and for doubles to 10

(3 and 3 for six).

Use objects, pictures, numbers, or words to create, solve and explain story problems (combining,

separating, or comparing) for two numbers that are each less than 10.

NUMBER AND OPERATIONS Students will understand how to represent numbers, and be able to add and

subtract small numbers.

Students will estimate, model, compare, order, and represent whole numbers up to 100.

Represent numbers up to 100 using a variety of models, diagrams, and number sentences. Represent

numbers larger than 10 in terms of tens and ones using manipulatives and pictures.

Correctly count and represent the number of objects in set using numerals.

Compare small sets using the terms greater than, less than, and equal to.

Understand the magnitude and order of numbers up to 100 by making ordered sequences and representing

them on a number line.

Exchange equivalent quantities of coins by making fair trades involving combinations of pennies, nickels,

dimes, and quarters up to one dollar; count out a combination of coins needed purchase items up to one

dollar.

Students will understand place value notation for the numbers 1 to 99. (Discussions may allude to 3-digit

numbers to assist in understanding place value.)



Determine to which ten a given number is closest using tools such as a sequential number line or chart.

Represent collections of less than 30 objects with 2-digit numbers and understand the meaning of place

value.

Decompose numbers from 10 to 99 as the appropriate number of tens and ones.

Students will add and subtract numbers less than 100, as well as understand and use the inverse

relationship between addition and subtraction.

Identify one more than, one less than, 10 more than, and 10 less than a given number.

Skip-count by 2s, 5s, and 10s, forward and backwards; to and from numbers up to 100.

Compose/decompose numbers up to 10 (e. g. 3+5=8, 8=5+2+1).

Understand a variety of situations to which subtraction may apply: taking away from a set, comparing two

sets, and determining how many more or how many less.

Understand addition and subtraction number combinations using strategies such as counting on, counting

back, doubles and making tens.

Know the single-digit addition facts to 18 and corresponding subtraction facts with understanding and

fluency. (Use strategies such as relating to facts already known, applying the commutative property, and

grouping facts into families.)

Apply addition and subtraction to 2 digit numbers without regrouping (e.g.15 + 4, 80-60, 56 + 10, 100-30, 52

+ 5).

Solve and create word problems involving addition and subtraction to 100 without regrouping. Use words,

pictures and concrete models to interpret story problems and reflect the combining of sets as addition and

taking away or comparing elements of sets as subtraction.

Students will count collections of up to 100 objects by dividing them into equal parts and represent the

results using words, pictures, or diagrams.

Use informal strategies to share objects equally between two to five people.

Build number patterns, including concepts of even and odd, using various concrete representations.

(Examples of concrete representations include a hundreds chart, ten grid frame, place value chart, number

line, counters, or other objects.)

Identify, label, and relate fractions (halves, fourths) as equal parts of a collection of objects or a whole using

pictures and models.

Understand halves and fourths as representations of equal parts of a whole.

NUMBER AND OPERATIONS Students will further develop their understanding of numbers (including

fractions) and how to represent them. The students will understand and apply addition, subtraction and

multiplication through concrete maniputaion and perform basic calculations.

Students will use multiple representations of numbers to connect symbols to quantities.

Represent numbers using a variety of models, diagrams, and number sentences (e.g., 4703 represented

as 4,000 + 700 + 3, and units, 47 hundreds + 3, or 4,500 + 203).

Understand the relative magnitudes of numbers using 10 as a unit, 100 as a unit, or 1000 as a unit.

Represent 2-digit numbers with drawings of tens and ones and 3-digit numbers with drawings of hundreds,

tens, and ones.

Use money as a medium of exchange. Make change and use decimal notation and the dollar and cent

symbols to represent the collection of coins and currency.

Students will build fluency with multi-digit addition and subtraction.

Correctly add and subtract two whole numbers up to three digits each with regrouping.

Understand and use the inverse relation between addition and subtraction to solve problems and check

solutions.

Use mental math strategies such as benchmark numbers to solve problems.

Use basic properties of addition (commutative, associative, and identity) to simplify problems (e.g. 98 + 17

by taking two from 17 and adding it to the 98 to make 100 and replacing the original problem by the sum

100 + 15).

Estimate to determine if solutions are reasonable for addition and subtraction.

Students will understand multiplication, multiply numbers, and verify results.

Understand multiplication as repeated addition.

Use repeated addition, arrays, and counting by multiples (skip counting) to correctly multiply 1-digit

numbers and construct the multiplication table.

Use the multiplication table (grid) to determine a product of two numbers.

Use repeated subtraction, equal sharing, and forming equal groups to divide large collections of objects and

determine factors for multiplication.

Students will understand and compare fractions.

Model, identify, label, and compare fractions (thirds, sixths, eighths, tenths) as a representation of equal

parts of a whole or of a set.

Know that when all fractional parts are included, such as three thirds, the result is equal to the whole.

Students will represent and interpret quantities and relationships using mathematical expressions including

equality and inequality signs (=, >, , or = to compare decimals and justify the comparison.

Students will further develop their understanding of the meaning of multiplication and division with decimals

and use them.

Model multiplication and division of decimals.

Explain the process of multiplication and division, including situations in which the multiplier and divisor are

both whole numbers and decimals.

Multiply and divide with decimals including decimals less than one and greater than one.

Understand the relationships and rules for multiplication and division of whole numbers also apply to

decimals.

Students will continue to develop their understanding of the meaning of common fractions and compute

with them.

Understand division of whole numbers can be represented as a fraction (a/b= a dividedby b).

Understand the value of a fraction is not changed when both its numerator and denominator are multiplied

or divided by the same number because it is the same as multiplying or dividing by one.

Find equivalent fractions and simplify fractions.

Model the multiplication and division of common fractions.

Explore finding common denominators using concrete, pictorial, and computational models.

Use , or = to compare fractions and justify the comparison.

Add and subtract common fractions and mixed numbers with unlike denominators.

Use fractions (proper and improper) and decimals interchangeably.

Estimate products and quotients.

Students will understand the meaning of percentage.

Explore and model percents using multiple representations.

Apply percents to circle graphs.

NUMBER AND OPERATIONS Students will understand the meaning of the four arithmetic operations as

related to positive rational numbers and will apply these concepts and associated skills in real world

situations.

Students will understand the meaning of the four arithmetic operations as related to positive rational

numbers and will use these concepts to solve problems.

Apply factors and multiples.

Decompose numbers into their prime factorization (Fundamental Theorem of Arithmetic).



Determine the greatest common factor (GCF) and the least common multiple (LCM) for a set of numbers.

Add and subtract fractions and mixed numbers with unlike denominators.

Multiply and divide fractions and mixed numbers.

Use fractions, decimals, and percents interchangeably.

Solve problems involving fractions, decimals, and percents.

NUMBER AND OPERATIONS Students will further develop their understanding of the concept of rational

numbers and apply them to real world situations.

Students will understand the meaning of positive and negative rational numbers and use them in

computation.

Find the absolute value of a number and understand it as the distance from zero on a number line.

Compare and order rational numbers, including repeating decimals.

Add, subtract, multiply, and divide positive and negative rational numbers.

Solve problems using rational numbers.

NUMBER AND OPERATIONS Students will understand the numeric and geometric meaning of square

root, apply properties of integer exponents and use scientific notation.

Students will understand different representations of numbers including square roots, exponents, and

scientific notation.

Find square roots of perfect squares.



Recognize the (positive) square root of a number as a length of a side of a square with a given area.

Recognize square roots as points and as lengths on a number line.

Understand that the square root of 0 is 0 and that every positive number has two square roots that are

opposite in sign.

Recognize and use the radical symbol to denote the positive square root of a positive number.

Estimate square roots of positive numbers.

Simplify, add, subtract, multiply, and divide expressions containing square roots.

Distinguish between rational and irrational numbers.

Simplify expressions containing integer exponents.

Express and use numbers in scientific notation.

Use appropriate technologies to solve problems involving square roots, exponents, and scientific notation.

NUMBER AND OPERATIONS Students will use the complex number system.

Students will represent and operate with complex numbers.

Write square roots of negative numbers in imaginary form.

Write complex numbers in the form a + bi.

Add, subtract, multiply, and divide complex numbers.

Simplify expressions involving complex numbers.

The following terms and symbols are often misunderstood. These concepts are not an inclusive list and

should not be taught in isolation. However, due to evidence of frequent difficulty an and misunderstanding

associated with these concepts, instructors should pay particular attention to them and how their students

are able to explain and apply them. The definitions are for teacher reference only and are not intended to

be memorized by students. Teachers should present these concepts to students with models and real life

examples. Students should understand the concepts involved and be able to recognize and/or demonstrate

them with words, models, pictures, or numbers. TERMS/SYMBOLS: numbers through 30, number words

through ten, set, longer, shorter, heavier, lighter, morning, afternoon, evening, yesterday, today, tomorrow,

days of the week, months of the year, seasons, triangle, quadrilateral, rectangle, square, circle, sphere,

cube, beside, above, below, in front of, behind, inside, outside, more, less, equal, ordinal numbers, picture

graph

TERMS/SYMBOLS: place value:ones, tens; greater than, less than, equal to; fewer than, more than,

equivalent; sum/add, difference/subtract, coins and bills, fair trade, compar/contrast, length, height, weight;

estimate; hexagon, cyliner, cone, rectangular prism, corner, vertex,=,+,-, even,off, tally makrk, bar graph,

skip counting.

TERMS/SYMBOLS: place value: thousands, sum, difference, product, factor, multiple, multiply, regroup,

array, numerator, denominator, inch, foot, yard, centimeter, meter, polygon, right angle, obtuse, acute,

edge, face, vertex/vertices, prism, plane, >, , ,< composition onto algebraic

function notatition inverses domain, range radical

evaluation intercepts

rates of change symmetry

shifts, flips, dilations even, odd

linear line parallel inverses intercepts fixed/variable costs roots

slope-intercept slope mixtures equations

inconsistent

temperature scales inequalities

functions system

simultaneous

quadratic parabola shifts, flips, maxima,minima length,width,area equations

vertex, axis of increasing,

area inequalities

symmetry decreasing

vertex form factoring vertex motion discriminant

changes (Delta)

multiplicity of zero

indirect

graph combined work

variation

piecewise graph absolute value discontinuity cost

tank-filling

end behavior,

power

translation

polynomial graph degree volume root/factor

passing thru given

arithmetic salinity

points

constructing boxes

functions

exponential graph end behavior rules of salary exponent



logarithmic

trigonometric

sequences:

formula block patterns terms

arithmetic &

pattern interest partial sums

recursive depreciation

half-life

population

operations via

identity array addition commutative classification

technology

row notation for entries scalar multiplication associative systems of equations systems of equations

curves passing thru

column multiplication distributive inverse by reduction

specific points

square transpose areas of triangles inverse by formula

product colinearity matrix equation

matrices

grams by food and

elementary row cramer's rule

nutrient

grams by food type and determinants by

inversion

ingredient minors

calories by activity and system of linear

determinant

weight inequalities (graph)

minimizing maximizing linear

manufacturing costs expressions

loops, parallel paths of a given

directed simple planar adjacency matrix edges,vertices electric transmission

arcs length

graph

path trading patterns

inductive/deduc

implications truth table proof by contradiction

tive

statements biconditional converse

postulate contrapositive

theorem inverse