Alaska State Standards for Mathematics: Grade 3

AK.A.N. Mathematical facts, concepts, principles, and theories: Numeration: Understand and use numeration.

[3] N-1. Reading, writing, ordering, or [counting L] (M1.1.1)

[3] N-2. Modeling (base ten blocks) or identifying place value positions to thousands (M1.1.2)

[3] N-3. Using appropriate representations of ordinal or cardinal numbers (M1.1.4)

[3] N-4. Identifying, describing with explanations, or illustrating equal parts of a whole, a region, or a set (using models) (M1.1.5)

[3] N-5. Identifying, describing with explanations, or illustrating equivalent representation of fractions (using models) (M1.1.5)

[3] N-6. [Using models, explanations, number lines, or real-life situations L] describing or illustrating the processes of addition and subtraction of whole numbers and their relationships (M1.1.3)

[3] N-7. Describing or illustrating identity property of addition (L) (M1.1.7)

[3] N-8. Modeling (with manipulative) and explaining commutative property of addition (L) (M1.1.7)

[3] N-9. Identifying or using patterns in the number system (skip count by 2's, 5's, or 10's; add or subtract by 10; even or odd numbers) (M1.1.6)

AK.A.M. Mathematical facts, concepts, principles, and theories: Measurement: Select and use systems, units, and tools of measurement.

[3] MEA-1. Estimating length to the nearest inch or foot (L) (M2.1.3)

[3] MEA-2. Comparing and ordering objects according to measurable attribute (calendar, length, [temperature, weight, area, or volume L]) (M2.1.1)

[3] MEA-3. Identifying or describing objects that are greater than, less than, or equal to a unit of measure (standard or non-standard) (M2.1.2)

[3] MEA-4. Selecting an appropriate unit of English, metric, or non-standard measurement to estimate the length, time, weight, or temperature (M2.1.3)

[3] MEA-5. Identifying coins, their value, or the value of a set of coins (M2.1.5)

[3] MEA-6. Measuring length to the nearest half-inch (M2.1.3)

[3] MEA-7. Telling time to the nearest 1/4 hour using an analog clock or [distinguishing morning, afternoon, or evening L] (M2.1.4)

[3] MEA-8. Determining elapsed time using a calendar (M2.2.5)

[3] MEA-9. [Counting back change from $1.00 L] (M2.2.6)

AK.A.E. Mathematical facts, concepts, principles, and theories: Estimation and Computation: Perform basic arithmetic functions, make reasoned estimates, and select and use appropriate methods or tools.

[3] E&C-1. Finding "how many" or "how much" to 50 (M3.1.1)

[3] E&C-2. Estimating the results of simple addition and subtraction problems up to 1,000 (M3.1.1)

[3] E&C-3. Recalling basic addition and subtraction facts, sums to 20, and corresponding subtraction facts efficiently (L) (M3.1.2)

[3] E&C-4. Adding or subtracting two-digit whole numbers (M3.1.3)

[3] E&C-5. Using repeated addition to model multiplication with whole numbers with products to 25 (M3.1.4)

[3] E&C-6. Using grouping or "sharing equally" to model division with whole numbers to 25 (M3.1.4)

AK.A.F. Mathematical facts, concepts, principles, and theories: Functions and Relationships: Represent, analyze, and use patterns, relations, and functions.

[3] F&R-1. Identifying a missing element in a pattern up to the next three terms (identifying a number using addition or subtraction or objects); or explaining how missing elements could be found (M4.1.1)

[3] F&R-2. Expressing a generalization of a pattern using words (L) (M4.1.1. & M4.1.2)

[3] F&R-3. Using manipulatives, including a calculator, as tools when describing, extending, or representing patterns (L) (M4.1.1. & M4.13)

[3] F&R-4. Using an open number sentence (addition or subtraction) to solve for an unknown represented by a box or circle (e.g., 5+__=16, __-7=4, 5+2=__) (M4.1.4)

[3] F&R-5. Using appropriate vocabulary or symbols for greater than, less than, or equal to (M4.1.4)

AK.A.G. Mathematical facts, concepts, principles, and theories: Geometry: Construct, transform, and analyze geometric figures.

[3] G-1. Using the number or length of sides to identify, describe, [model L], or compare triangles or rectangles (including squares) (M5.1.1)

[3] G-2. Using the attributes and properties of plane figures to [model L], identify, compare, or describe plane figures (circles, rectangles, squares, and triangles) [and solid figures (cubes, cylinders, or spheres) L] (M5.1.1. & M5.1.2)

[3] G-3. Identifying, creating, or drawing lines of symmetry for real-world objects (e.g., block letters, flags, insects) (M5.1.3)

[3] G-4. Comparing or describing shapes (circles, triangles, or rectangles) as "larger than," "smaller than," or "congruent to," a given shape (M5.1.3)

[3] G-5. Illustrating or identifying the results of transformations (slides) of polygons (M5.1.5)

[3] G-6. Estimating or determining area or perimeter of rectangular or square shapes on grids (M5.1.4)

[3] G-7. Using directional terms (inside, outside, right, left, horizontal, vertical) to describe relative location of objects in a picture (L) (M5.1.6)

[3] G-8. Drawing real-world objects that consist of geometric shapes (squares, rectangles, triangles, or circles) (L) (M5.1.7)

AK.A.S. Mathematical facts, concepts, principles, and theories: Statistics and Probability: Formulate questions, gather and interpret data, and make predictions.

[3] S&P-1. [Designing an investigation and collecting, recording L], organizing, displaying, or explaining the classification of data in real-world problems (e.g., literature, self, or family), using bar graphs, and [Venn diagrams L] (M6.1.1, M6.1.2, & M6.1.5)

[3] S&P-2. Using information from a variety of displays (tallies, tables, pictographs, bar graphs, or [Venn diagrams L] (M6.1.2)

[3] S&P-3. Using the terms "maximum" or "minimum" (M6.1.3)

[3] S&P-4. Explaining the differences between chance and certainty or recognizing events that may be certain or chance events (L) (M6.1.4)

[3] S&P-5. [Finding and recording L] and making predictions about the likelihood of outcomes of a simple probability experiment (e.g., spinner, tossing a coin) (M6.1.4)

AK.B.PS. Process skills and abilities: Problem Solving: Problem Solving: Understand and be able to select and use a variety of problem-solving strategies.

[3] PS-1. Selecting and applying an appropriate strategy (e.g., guess and check; draw a picture; make a model, extend a pattern) to solve a variety of problems (M7.1.2)

AK.C.PS. Process skills and abilities: Communication: Form and use appropriate methods to define and explain mathematical relationships.

[3] PS-2. Representing mathematical problems using manipulatives, models, pictures, and/or everyday language; or using everyday language to explain thinking about the problem-solving strategies and solutions to problems (M8.1.1, M8.1.2, & M8.1.3)

AK.D.PS. Process skills and abilities: Reasoning: Use logic and reason to solve mathematical problems.

[3] PS-3. Drawing conclusions about mathematical problems; or finding examples that support or refute mathematical statements (M9.1.1. & M9.1.2)

[3] PS-4. Explaining whether or not a prediction, estimation, or solution is reasonable (M9.1.3)

AK.E.PS. Process skills and abilities: Connections: Apply mathematical concepts and processes to situations within and outside of school.

[3] PS-5. Using real-world contexts such as literature, self, and family (M10.1.1. & M10.1.2)

AK.M1. Numeration: A student should understand mathematical facts, concepts, principles, and theories. A student who meets the content standard should understand and use numeration, including numbers, number systems, counting numbers, whole numbers, integers, fractions, decimals, and percents; and irrationals and complex numbers.

M1.1.1. Read, write, order, count, and model one-to-one correspondence with whole numbers to 100.

M1.1.2. Use, model, and identify place value positions of 1's, 10's, and 100's.

M1.1.3. Model and explain the processes of addition and subtraction, describing the relationship between the operations.

M1.1.4. Select and use various representations of ordinal and cardinal numbers.

M1.1.5. Identify, model, and label simple fractions, describing and defining them as equal parts of a whole, a region, or a set.

M1.1.6. Identify, describe, and extend patterns inherent in the number system. Skip count by 2's, 5's, and 10's. Add and subtract by 10. Identify even and odd numbers.

M1.1.7. Demonstrate the commutative and identity properties of addition.

AK.M2. Measurement: A student should understand mathematical facts, concepts, principles, and theories. A student who meets the content standard should select and use appropriate systems, units, and tools of measurement, including estimation.

M2.1.1. Compare and order objects by various measurable attributes including calendar, temperature, length, weight, capacity, area, and volume.

M2.1.2. Compare objects to standard and non-standard units to identify objects that are greater than, less than, and equal to a given unit.

M2.1.3. Choose a unit of measure, estimate the length or weight of objects and then measure to check for reasonableness.

M2.1.4. Tell time to the nearest half hour, distinguishing between morning, afternoon, and evening.

M2.1.5. Identify coins, their value, and the value of given sets of coins.

AK.M3. Estimation and Computation: A student should understand mathematical facts, concepts, principles, and theories. A student who meets the content standard should perform basic arithmetic functions, make reasoned estimates, and select and use appropriate methods or tools for computation or estimation including mental arithmetic, paper and pencil, a calculator, and a computer.

M3.1.1. Make reasonable estimates of "how many" and "how much"; estimate the results of simple addition and subtraction problems.

M3.1.2. Recall and use basic addition and subtraction facts orally and with paper and pencil without a calculator.

M3.1.3. Add and subtract whole numbers to 100 using a variety of models and algorithms.

M3.1.4. Model multiplication as repeated addition and grouping objects; model division as "sharing equally" and grouping objects.

AK.M4. Functions and Relationships: A student should understand mathematical facts, concepts, principles, and theories. A student who meets the content standard should represent, analyze, and use mathematical patterns, relations, and functions using methods such as tables, equations, and graphs.

M4.1.1. Recognize, describe, create, and extend repeating and increasing patterns with a variety of materials including symbols, objects, and manipulatives.

M4.1.2. Generate and solve simple functions by identifying and applying addition and subtraction patterns.

M4.1.3. Use a calculator to find and extend patterns in the number system.

M4.1.4. Complete open space sentences with missing numbers; use appropriate vocabulary including greater than, less than, and equal to; and use the correct symbols.

AK.M5. Geometry: A student should understand mathematical facts, concepts, principles, and theories. A student who meets the content standard should construct, draw, measure, transform, compare, visualize, classify, and analyze the relationships among geometric figures.

M5.1.1. Identify, sort, describe, model, and compare circles, triangles, and rectangles including squares regardless of orientation.

M5.1.2. Identify, sort, describe, model, and compare solid figures including cubes, cylinders, and spheres.

M5.1.3. Identify and create examples of line symmetry; compare and describe given circles, triangles, and rectangles as larger, smaller, or congruent.

M5.1.4. Demonstrate conservation of area using drawings or manipulatives.

M5.1.5. Describe and identify geometric transformations including slides, flips, and turns.

M5.1.6. Use comparative directional and positional words: above, below, inside, outside, on, in, right and left, horizontal, vertical, and middle.

M5.1.7. Draw and build familiar shapes.

AK.M6. Statistics/Probability: A student should understand mathematical facts, concepts, principles, and theories. A student who meets the content standard should collect, organize, analyze, interpret, represent, and formulate questions about data and make reasonable and useful predictions about the certainty, uncertainty, or impossibility of an event.

M6.1.1. Collect, record, organize, display, and explain the classification of data.

M6.1.2. Describe data from a variety of visual displays including tallies, tables, pictographs, bar graphs, and Venn diagrams.

M6.1.3. Use the terms "maximum" and "minimum" when working with a data set.

M6.1.4. Find and record the possibilities of simple probability experiments; explain differences between chance and certainty, giving examples.

M6.1.5. Conduct a survey and tally the results.

AK.M7. Problem-Solving: A student should understand and be able to select and use a variety of problem-solving strategies. A student who meets the content standard should use computational methods and appropriate technology as problem-solving tools; use problem solving to investigate and understand mathematical content; formulate mathematical problems that arise from everyday situations; develop and apply strategies to solve a variety of problems; check the results against mathematical rules; use common sense to help interpret results; apply what was learned to new situations; and use mathematics with confidence.

M7.1.1. Formulate problems from practical and mathematical activities.

M7.1.2. Develop and apply strategies including guess and check, modeling and acting out, drawings, and extending patterns to solve a variety of problems.

M7.1.3. Predict an answer before solving a problem and compare results to check for reasonableness.

AK.M8. Communication: A student should understand and be able to form and use appropriate methods to define and explain mathematical relationships. A student who meets the content standard should express and represent mathematical ideas using oral and written presentations, physical materials, pictures, graphs, charts, and algebraic expressions; relate mathematical terms to everyday language; develop, test, and defend mathematical hypotheses; and clarify mathematical ideas through discussion with others.

M8.1.1. Translate problems from everyday language into math language and symbols.

M8.1.2. Use manipulatives, models, pictures, and language to represent and communicate mathematical ideas.

M8.1.3. Use everyday language to explain thinking about problem-solving strategies and solutions to problems.

AK.M9. Reasoning: A student should be able to use logic and reason to solve mathematical problems. A student who meets the content standard should analyze situations; draw logical conclusions; use models, known facts, and relationships to explain the student's reasoning; use deductive reasoning to verify conclusions, judge the validity of arguments, and construct valid arguments; and use inductive reasoning to recognize patterns and form mathematical propositions.

M9.1.1. Draw conclusions about mathematical problems.

M9.1.2. Find examples that support or refute mathematical statements.

M9.1.3. Explain why a prediction, estimation, or solution is reasonable.

AK.M10. Connections: A student should be able to apply mathematical concepts and processes to situations within and outside of school. A student who meets the content standard should explore problems and describe results using graphical, numerical, physical, algebraic, and verbal mathematical models or representations; use mathematics in daily life; and use mathematics in other curriculum areas.

M10.1.1. Apply mathematical skills and processes to literature.

M10.1.2. Apply mathematical skills and processes to situations with self and family.