| 1. Demonstrate
understanding of the different ways numbers are represented and used in
the real world. |
| MA.A.1.4.1 |
|
associate verbal names, written word names,
and standard numerals with integers, rational numbers, irrational
numbers, real numbers. |
|
1-1,
2-1, 3-1,
8-1, 8-5,
8-6, 14-1
|
| MA.A.1.4.2 |
|
understand the relative size of integers,
rational numbers, irrational numbers, and real numbers. |
|
3-1,
8-5, 8-6,
14-1 |
| MA.A.1.4.3 |
|
understand concrete and symbolic representations
of real and complex numbers in real world situations. |
|
1-1,
3-1, 8-1,
14-1 |
| MA.A.1.4.4 |
|
understand that numbers can be represented
in a variety of equivalent forms, including integers, fractions, decimals,
percents, scientific notation, exponents, radicals, absolute value. |
|
1-1,
2-1, 3-1,
5-5, 8-1,
8-2, 8-3,
8-4, 8-5,
8-6, 14-1
|
| 2. Demonstrate
understanding of number systems. |
| MA.A.2.4.1 |
|
understand the basic concepts of limits
and infinity. |
|
13-2,
13-3 |
| MA.A.2.4.2 |
|
understand and use the real number system. |
|
2-1,
3-1, 14-1
|
| 3. Demonstrate
understanding of the effects of operations on numbers and the relationships
among these operations, select appropriate operations, and compute for problem
solving. |
| MA.A.3.4.1 |
|
understand and explain the effects of addition,
subtraction, multiplication, and division on real numbers, including
square roots, exponents, and appropriate inverse relationships. |
|
1-2,
2-3, 2-4,
2-5, 2-6,
3-2, 4-1,
4-3, 6-6,
8-2, 8-3,
8-4, 8-5,
8-6 |
| MA.A.3.4.2 |
|
select and justify alternative strategies,
such as using properties of numbers, including inverse, identity,
distributive, associative, and transitive, that allow operational
shortcuts for computational procedures in real world or mathematical
problems. |
|
1-2,
1-3, 1-4,
2-5, 2-6,
4-1, 4-3,
8-1, 8-2
|
| MA.A.3.4.3 |
|
add, subtract, multiply, and divide real
numbers, including square roots and exponents, using appropriate methods
of computing, such as mental mathematics, paper and pencil, and calculator. |
|
1-2,
1-3, 1-4,
2-3, 2-4,
2-5, 2-6,
3-2, 4-1,
4-3, 8-1,
8-2, 8-3,
8-4, 8-5,
9-2, 9-3,
9-4, 9-5,
14-3, 14-4,
15-1, 15-2
|
| 4. Use estimation
in problem solving and computation. |
| MA.A.4.4.1 |
|
use estimation strategies in complex situations
to predict results and to check the reasonableness of results. |
|
1-5,
8-6, 11-3
|
| 5. Demonstrate
understanding and apply theories related to numbers. |
| MA.A.5.4.1 |
|
apply special number relationships such
as sequences to real world problems. |
|
|
| 6. Measure quantities
in the real world and use the measures to solve problems. |
| MA.B.1.4.1 |
|
use concrete and graphic models to derive
formulas for finding perimeter, area, surface area, circumference,
and volume of two and three dimensional shapes, including rectangular
solids, cylinders, cones, and pyramids. |
|
1-5,
8-2 |
| MA.B.1.4.2 |
|
use concrete and graphic models to derive
formulas for finding rate, distance, time, angle measures. |
|
5-1,
5-2, 6-5,
13-5 |
| MA.B.1.4.3 |
|
relate the concepts of measurement to similarity
and proportionality in real world situations. |
|
5-1,
5-2, 5-3,
6-5, 6-6
|
| 7. Compare, contrast,
and convert within systems of measurement (both standard/nonstandard and
metric/customary). |
| MA.B.2.4.1 |
|
select and use direct (measured) and indirect
(not measured) methods of measurement as appropriate |
|
8-7,
12-2 |
| MA.B.2.4.2 |
|
solve real world problems involving rated
measures (miles per hour, feet per second). |
|
5-1,
5-5, 6-6,
13-5, 14-5,
15-1 |
| 8. Estimate measurements
in real world problem situations. |
| MA.B.3.4.1 |
|
solve real world and mathematical problems
involving estimates of measurements, including length, time, weight/mass,
temperature, money, perimeter, area, and volume and estimate the effects
of measurement errors on calculations. |
|
6-4,
8-1, 8-6
|
| 9. Visualize and
illustrate ways in which shapes can be combined, subdivided, and changed. |
| MA.C.2.4.1 |
|
understand geometric concepts such as perpendicularity,
parallelism, congruency, similarity, reflections, symmetry. |
|
2-5,
7-7, 11-1,
13-1, 13-2
|
| 10. Use coordinate
geometry to locate objects in two dimensions and to describe objects algebraically. |
| MA.C.3.4.1 |
|
represent and apply geometric properties
and relationships to solve real world and mathematical problems including
ratio, proportion. |
|
7-7,
15-3, 15-4
|
| MA.C.3.4.2 |
|
using a rectangular coordinate system (graph),
apply and algebraically verify properties of two dimensional figures,
including distance, midpoint, slope, parallelism, and perpendicularity. |
|
2-2,
7-1, 7-7,
14-2 |
| 11. Describe, analyze,
and generalize a wide variety of patterns, relations, and functions. |
| MA.D.1.4.1 |
|
describe, analyze, and generalize relationships,
patterns, and functions using words, symbols, variables, tables, and
graphs. |
|
1-1,
6-1, 6-2,
6-3, 6-4,
6-5, 6-6,
7-1, 7-2,
7-3, 7-5,
7-6, 11-1,
11-2, 11-7
|
| MA.D.1.4.2 |
|
determine the impact when changing parameters
of given functions. |
|
7-6,
11-2 |
| 12. Use expressions,
equations, inequalities, graphs, and formulas to represent and interpret
situations. |
| MA.D.2.4.1 |
|
represent real world problem situations
using finite graphs, matrices, sequences. |
|
6-1,
6-2, 7-4
|
| MA.D.2.4.2 |
|
use systems of equations and inequalities
to solve real world problems graphically, algebraically. |
|
13-1,
13-2, 13-3,
13-4, 13-5,
13-7 |
| 13. Demonstrate
understanding and use the tools of data analysis for managing information. |
| MA.E.1.4.1 |
|
interpret data that has been collected,
organized, and displayed in charts, tables, and plots. |
|
1-7,
4-2, 7-4
|
| MA.E.1.4.2 |
|
calculate measures of central tendency (mean,
median, and mode) and dispersion (range) for complex sets of data
and determine the most meaningful measure to describe the data. |
|
1-7,
3-3 |
| MA.E.1.4.3 |
|
analyze real world data and make predictions
of larger populations by using the sample population data and using
appropriate technology, including calculators and computers. |
|
1-6,
1-7, 3-3
|
| 14. Identify patterns
and make predictions from an orderly display of data using concepts of probability
and statistics. |
| MA.E.2.4.1 |
|
determine probabilities using counting procedures,
tables, tree diagrams. |
|
4-2,
5-6, 5-7
|
| MA.E.2.4.2 |
|
determine the probability for simple and
compound events as well as independent and dependent events. |
|
5-6,
5-7 |
| 15. Use statistical
methods to make inferences and valid arguments about real world situations. |
| MA.E.3.4.1 |
|
design and perform real world statistical
experiments that involve more than one variable, then analyze results
and report findings. |
|
|
| MA.E.3.4.2 |
|
explain the limitations of using statistical
techniques and data in making inferences and valid arguments. |
|
1-6
|
|
Extra Examples—
