MA.220.127.116.11 A.1.a: Mathematics
All fractions as part of a whole, as subset of a set, as a location on a number line, and as divisions of whole numbers
MA.18.104.22.168 A.1.b: Mathematics
MA.22.214.171.124 A.2: Mathematics
Recognize the decimal nature of United States currency and compute with money.
MA.126.96.36.199 A.3: Mathematics
Demonstrate a sense of the relative magnitudes of numbers.
MA.188.8.131.52 A.4: Mathematics
Use whole numbers, fractions, and decimals to represent equivalent forms of the same number.
MA.184.108.40.206 A.5.a: Mathematics
Primes, factors, multiples
MA.220.127.116.11 A.6: Mathematics
Compare and order numbers.
MA.18.104.22.168 B.1: Mathematics
Recognize the appropriate use of each arithmetic operation in problem situations.
MA.22.214.171.124 B.2.a: Mathematics
MA.126.96.36.199 B.2.b: Mathematics
MA.188.8.131.52 B.2.c: Mathematics
MA.184.108.40.206 B.3: Mathematics
Use an efficient and accurate pencil-and-paper procedure for division of a 3-digit number by a 2-digit number.
MA.220.127.116.11 B.4: Mathematics
Select pencil-and-paper, mental math, or a calculator as the appropriate computational method in a given situation depending on the context and numbers.
MA.18.104.22.168 B.5: Mathematics
Check the reasonableness of results of computations.
MA.22.214.171.124 B.6: Mathematics
Understand and use the various relationships among operations and properties of operations.
MA.126.96.36.199 C.1: Mathematics
Use a variety of estimation strategies for both number and computation.
MA.188.8.131.52 C.2: Mathematics
Recognize when an estimate is appropriate, and understand the usefulness of an estimate as distinct from an exact answer.
MA.184.108.40.206 C.3: Mathematics
Determine the reasonableness of an answer by estimating the result of operations.
MA.220.127.116.11 C.4: Mathematics
Determine whether a given estimate is an overestimate or an underestimate.
MA.18.104.22.168 A.1.a: Mathematics
Notation for line, ray, angle, line segment
MA.22.214.171.124 A.1.b: Mathematics
Properties of parallel, perpendicular, and intersecting lines
MA.126.96.36.199 A.1.c: Mathematics
Sum of the measures of the interior angles of a triangle is 180°
MA.188.8.131.52 A.2.a: Mathematics
Triangles by angles and sides
MA.184.108.40.206 A.2.b: Mathematics
Quadrilaterals, including squares, rectangles, parallelograms, trapezoids, rhombi
MA.220.127.116.11 A.2.c: Mathematics
Polygons by number of sides.
MA.18.104.22.168 A.2.d: Mathematics
Equilateral, equiangular, regular
MA.22.214.171.124 A.2.e: Mathematics
All points equidistant from a given point form a circle
MA.126.96.36.199 A.3: Mathematics
Identify similar figures.
MA.188.8.131.52 A.4: Mathematics
Understand and apply the concepts of congruence and symmetry (line and rotational).
MA.184.108.40.206 B.1: Mathematics
Use a translation, a reflection, or a rotation to map one figure onto another congruent figure.
MA.220.127.116.11 B.2: Mathematics
Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings.
MA.18.104.22.168 C.1: Mathematics
Create geometric shapes with specified properties in the first quadrant on a coordinate grid.
MA.22.214.171.124 D.1: Mathematics
Select and use appropriate units to measure angles and area.
MA.126.96.36.199 D.2: Mathematics
Convert measurement units within a system (e.g., 3 feet = ___ inches).
MA.188.8.131.52 D.3: Mathematics
Know approximate equivalents between the standard and metric systems (e.g., one kilometer is approximately 6/10 of a mile).
MA.184.108.40.206 D.4: Mathematics
Use measurements and estimates to describe and compare phenomena.
MA.220.127.116.11 E.1: Mathematics
Use a protractor to measure angles.
MA.18.104.22.168 E.2.a: Mathematics
MA.22.214.171.124 E.2.b: Mathematics
MA.126.96.36.199 E.3: Mathematics
Recognize that rectangles with the same perimeter do not necessarily have the same area and vice versa.
MA.188.8.131.52 E.4: Mathematics
Develop informal ways of approximating the measures of familiar objects (e.g., use a grid to approximate the area of the bottom of one's foot).
MA.184.108.40.206 A.1.a: Mathematics
Descriptions using tables, verbal rules, simple equations, and graphs
MA.220.127.116.11 B.1: Mathematics
Describe arithmetic operations as functions, including combining operations and reversing them.
MA.18.104.22.168 B.2: Mathematics
Graph points satisfying a function from T-charts, from verbal rules, and from simple equations.
MA.22.214.171.124 C.1.a: Mathematics
Using variables to represent unknown quantities
MA.126.96.36.199 C.1.b: Mathematics
Using concrete materials, tables, graphs, verbal rules, algebraic expressions/equations
MA.188.8.131.52 C.2.a: Mathematics
Changes over time
MA.184.108.40.206 C.2.b: Mathematics
Rates of change (e.g., when is plant growing slowly/rapidly, when is temperature dropping most rapidly/slowly)
MA.220.127.116.11 D.1.a: Mathematics
Whole-number coefficients only, answers also whole numbers
MA.18.104.22.168 D.1.b: Mathematics
Variables on one side of equation
MA.22.214.171.124 A.1.a: Mathematics
Data generated from surveys
MA.126.96.36.199 A.2.a: Mathematics
Bar graph, line graph, circle graph, table
MA.188.8.131.52 A.2.b: Mathematics
Range, median, and mean
MA.184.108.40.206 A.3: Mathematics
Respond to questions about data and generate their own questions and hypotheses.
MA.220.127.116.11 B.1.a: Mathematics
Event, probability of an event
MA.18.104.22.168 B.1.b: Mathematics
Probability of certain event is 1 and of impossible event is 0
MA.22.214.171.124 B.2.a: Mathematics
Given numbers of various types of items in a bag, what is the probability that an item of one type will be picked
MA.126.96.36.199 B.2.b: Mathematics
Given data obtained experimentally, what is the likely distribution of items in the bag
MA.188.8.131.52 B.3: Mathematics
Model situations involving probability using simulations (with spinners, dice) and theoretical models.
MA.184.108.40.206 C.1.a: Mathematics
Organized lists, charts, tree diagrams, tables
MA.220.127.116.11 C.2: Mathematics
Explore the multiplication principle of counting in simple situations by representing all possibilities in an organized way (e.g., you can make 3 x 4 = 12 outfits using 3 shirts and 4 skirts).
MA.18.104.22.168 D.1: Mathematics
Devise strategies for winning simple games (e.g., start with two piles of objects, each of two players in turn removes any number of objects from a single pile, and the person to take the last group of objects wins) and express those strategies as sets of directions.
MA.5.4.5 A.1: Mathematics
Learn mathematics through problem solving, inquiry, and discovery.
MA.5.4.5 A.2.a: Mathematics
MA.5.4.5 A.2.b: Mathematics
MA.5.4.5 A.2.c: Mathematics
Problems with multiple solutions
MA.5.4.5 A.2.d: Mathematics
Problems that can be solved in several ways
MA.5.4.5 A.3: Mathematics
Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.
MA.5.4.5 A.4: Mathematics
Pose problems of various types and levels of difficulty.
MA.5.4.5 A.5: Mathematics
Monitor their progress and reflect on the process of their problem solving activity.
MA.5.4.5 A.6: Mathematics
Distinguish relevant from irrelevant information, and identify missing information.
MA.5.4.5 B.1.a: Mathematics
Reading and writing
MA.5.4.5 B.1.b: Mathematics
Discussion, listening, and questioning
MA.5.4.5 B.2: Mathematics
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.
MA.5.4.5 B.3: Mathematics
Analyze and evaluate the mathematical thinking and strategies of others.
MA.5.4.5 B.4: Mathematics
Use the language of mathematics to express mathematical ideas precisely.
MA.5.4.5 C.1: Mathematics
Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and geometry).
MA.5.4.5 C.2: Mathematics
Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).
MA.5.4.5 C.3: Mathematics
Recognize that mathematics is used in a variety of contexts outside of mathematics.
MA.5.4.5 C.4: Mathematics
Apply mathematics in practical situations and in other disciplines.
MA.5.4.5 C.5: Mathematics
Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).
MA.5.4.5 C.6: Mathematics
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
MA.5.4.5 D.1: Mathematics
Recognize that mathematical facts, procedures, and claims must be justified.
MA.5.4.5 D.2: Mathematics
Use reasoning to support their mathematical conclusions and problem solutions.
MA.5.4.5 D.3: Mathematics
Select and use various types of reasoning and methods of proof.
MA.5.4.5 D.4: Mathematics
Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.
MA.5.4.5 D.5.a: Mathematics
Counterexamples as a means of disproving conjectures
MA.5.4.5 D.5.b: Mathematics
Verifying conjectures using informal reasoning or proofs.
MA.5.4.5 D.6: Mathematics
Evaluate examples of mathematical reasoning and determine whether they are valid.
MA.5.4.5 E.1.a: Mathematics
Concrete representations (e.g., base-ten blocks or algebra tiles)
MA.5.4.5 E.1.b: Mathematics
Pictorial representations (e.g., diagrams, charts, or tables)
MA.5.4.5 E.1.c: Mathematics
Symbolic representations (e.g., a formula)
MA.5.4.5 E.1.d: Mathematics
Graphical representations (e.g., a line graph)
MA.5.4.5 E.2: Mathematics
Select, apply, and translate among mathematical representations to solve problems.
MA.5.4.5 E.3: Mathematics
Use representations to model and interpret physical, social, and mathematical phenomena.
MA.5.4.5 F.1: Mathematics
Use technology to gather, analyze, and communicate mathematical information.
MA.5.4.5 F.2: Mathematics
Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information.
MA.5.4.5 F.3: Mathematics
Use graphing calculators and computer software to investigate properties of functions and their graphs.
MA.5.4.5 F.4: Mathematics
Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).
MA.5.4.5 F.5: Mathematics
Use computer software to make and verify conjectures about geometric objects.
MA.5.4.5 F.6: Mathematics
Use computer-based laboratory technology for mathematical applications in the sciences (cf. science standards).