Alaska State Standards for Mathematics: Grade 4

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

[4] N-1. Reading, writing, ordering, or [counting L] (M1.2.1)

[4] N-2. Modeling (base ten blocks) or identifying place value positions to ten thousands (M1.2.2)

[4] N-3. Converting between whole numbers expressed in expanded notation and standard form (M1.2.4)

[4] N-4. Identifying, describing with explanations, or illustrating equal parts of a whole, a region, or a set (using models) (M1.2.4)

[4] N-5. Identifying, describing with explanations, or illustrating equivalent fractions or mixed numbers (M1.2.4. & M3.2.5)

[4] N-6. [Using models, explanations, number lines, or real-life situations L] describing or illustrating the processes of multiplication (M1.2.3)

[4] N-7. [Using models, explanations, number lines, or real-life situations L] describing or illustrating the relationship between multiplication and addition (M1.2.3)

[4] N-8. [Using models, explanations, number lines, or real-life situations L] describing or illustrating the relationship between multiplication and division (M1.2.3)

[4] N-9. [Using models, explanations, number lines, or real-life situations L] describing or illustrating the process of adding or subtracting fractions with like denominators (2 to 12) (M1.2.5)

[4] N-10. [Describing or illustrating identity property of multiplication L] (M1.2.7)

[4] N-11. [Modeling (with manipulatives) and explaining commutative property of multiplication L] (M1.2.7)

[4] N-12. Identifying or listing factors and multiples of a number (M1.2.6)

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

[4] MEA-1. [Estimating length to the nearest half-inch or centimeter L] (M2.2.1)

[4] MEA-2. [Estimating temperature (degree Celsius or Fahrenheit) or weight (pounds or kilograms) to the nearest unit L] (M2.2.1)

[4] MEA-3. Identifying or using equivalent measures for length (inch, foot, yard: 12 inches = 1 foot, 3 feet = 1 yard, 36 inches = 1 yard; centimeter, meter: 100 centimeters = 1 meter) (M2.2.2)

[4] MEA-4. Selecting an appropriate unit of metric measurement to estimate length, weight or temperature (M2.2.1)

[4] MEA-5. Measuring length to the nearest half-inch or [centimeter L] (M2.2.1, M2.2.3, & M2.2.4)

[4] MEA-6. Telling time in 5 minute increments using analog clocks (M2.2.5)

[4] MEA-7. Counting back change from $5.00 (L) (M2.2.6)

[4] MEA-8. Determining possible combinations of coins and bills to given amounts (M2.2.6)

[4] MEA-9. Simulating multiple purchases and calculating the amount of change from a given bill(s) up to $50.00 (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.

[4] E&C-1. Identifying or using [a variety of L] strategies (e.g., rounding to appropriate place value, multiplying by powers of ten, using front-end estimation) to estimate the results of whole number addition or subtraction computations to 10,000, or simple multiplication or division (M3.2.1)

[4] E&C-2. [Recalling basic multiplication facts, products to 100, and corresponding division facts efficiently (L) (M3.2.2)

[4] E&C-3. Adding or subtracting three-digit whole numbers (M3.2.3)

[4] E&C-4. Multiplying two-digit numbers by single-digit numbers (M3.2.4)

[4] E&C-5. Adding fractions with like denominators to 12 (M3.2.3)

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

[4] F&R-1. Extending patterns that use addition, subtraction, multiplication, or symbols, up to 10 terms, represented by models (function machines), tables, sequences, or in problem situations (M4.2.1)

[4] F&R-2. Using rules to express the generalization of a pattern using words, lists, or tables (L) (M4.2.4)

[4] F&R-3. Using manipulatives, including a calculator, as tools when describing, extending, or representing a number sequence (L) (M4.2.1. & M4.2.3.

[4] F&R-4. Using an open number sentence (addition, subtraction or multiplication) to solve for an unknown represented by a box or circle (__ x 8 = 56, 3 x 6 =__) (M4.2.5)

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

[4] G-1. Using the attributes and properties of angles to identify and compare triangles (acute, right, or obtuse) and regular polygons (M5.2.1)

[4] G-2. Using the attributes and properties of solid figures (edges, vertices, or the number or shape of faces) to [model L], identify, compare, or describe solid figures (cubes, cylinders, rectangular prisms, or spheres) (e.g., cans, dice, boxes, balls) (M5.2.2)

[4] G-3. Identifying or drawing all lines of symmetry to identify figures that are symmetrical (M5.2.3)

[4] G-4. Identifying shapes that are congruent (M5.2.3)

[4] G-5. Illustrating or identifying the results of transformations (turns) of polygons by continuing a given pattern (M5.2.5)

[4] G-6. Estimating or determining area or perimeter of rectangles, squares and irregular shapes on grids with a key or ruler (M5.2.4)

[4] G-7. Describing the relative location of places or objects on a map using compass directions of north, south, east or west (L) (M5.2.6)

[4] G-8. Identifying or drawing parallel or intersecting line segments (L) (M5.2.7)

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

[4] S&P-1. [Designing an investigation and collecting L], organizing or displaying, using appropriate scale, data in real-world problems (e.g., social studies, friends, or school), using bar graphs, tables, charts, or diagrams with whole numbers up to 25 (M6.2.1. & M6.2.2)

[4] S&P-2. Using information from a variety of displays (tables, bar graphs, or Venn diagrams) (M6.2.2)

[4] S&P-3. Using mode or range with up to 5 pieces of data with a value of 10 or less each (M6.2.3)

[4] S&P-4. Predicting or explaining the probability of all possible outcomes in a simple experiment (e.g., spinners, dice, coins) (M6.2.4)

[4] S&P-5. Determining possible combinations in a given situation involving up to 3 items (e.g., how many ways can you choose two fruits out of a basket containing oranges and bananas?)(M6.2.5)

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.

[4] PS-1. Selecting and applying appropriate strategy (e.g., lists, guess and check; extended patterns) to solve a variety of problems (M7.2.2)

[4] PS-2. Explaining and verifying results of an original problem and applying what was learned to new situations (M7.2.3)

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

[4] PS-3. Representing problems using mathematical language including concrete, pictorial, and/or symbolic representation; or by organizing and communicating mathematical problem-solving strategies and solutions to problems (M8.2.1, M8.2.2, & M8.2.3)

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

[4] PS-4. Drawing conclusions about mathematical problems (given a rule or generalization, determine whether the example fits) or justifying answers and mathematical strategies (M9.2.1, M9.2.2, & M9.2.3)

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

[4] PS-5. Using real-world contexts such as social studies, friends, and school (M10.2.1. & M10.2.2)

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.

M1.2.1. Read, write, model, order, and count with positive whole numbers to 1,000,000 and negative whole numbers.

M1.2.2. Use, model, and identify place value positions from 0.001 to 1,000,000.

M1.2.3. Model and explain the processes of multiplication and division. Describe the relationships among the four basic operations.

M1.2.4. Identify and describe different uses for the same numerical representation.

M1.2.5. Model and explain the process of adding and subtracting fractions with common denominators and decimals that represent money.

M1.2.6. Identify and describe factors and multiples including those factors and multiples common to a pair or set of numbers.

M1.2.7. Demonstrate the commutative and identity properties of multiplication.

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.

M2.2.1. Estimate and measure weights, lengths, and temperatures to the nearest unit using the metric and standard systems.

M2.2.2. Identify and use equivalent measurements (e.g., 60 minutes = 1 hour, 7 days = 1 week).

M2.2.3. Use a variety of measuring tools; describe the attribute(s) they measure.

M2.2.4. Estimate and measure the dimensions of geometric figures.

M2.2.6. Read, write, and use money notation, determining possible combinations of coins and bills to equal given amounts; count back change for any given situation.

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.

M3.2.1. Describe and use a variety of estimation strategies including rounding to the appropriate place value, multiplying by powers of 10, and using front-end estimation to check the reasonableness of solutions.

M3.2.2. Recall and use basic multiplication and division facts orally and with paper and pencil without a calculator.

M3.2.3. Add and subtract whole numbers, fractions with common denominators to 12, and decimals, including money amounts, using models and algorithms.

M3.2.4. Multiply and divide multi-digit whole numbers by 2-digit numbers, limiting the 2-digit divisors to those that end in 0; multiply and divide decimals that represent money by whole numbers.

M3.2.5. Find equivalent fractions. Convert between fractions and mixed numbers.

M3.2.6. Develop and interpret scales and scale models.

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.

M4.2.1. Use patterns and their extensions to make predictions and solve problems; describe patterns found in the number system including those formed by multiples, factors, perfect squares, and powers of 10.

M4.2.2. Generate and solve simple functions by identifying and applying multiplication and division patterns.

M4.2.3. Use a calculator to find a missing item in a number sequence.

M4.2.4. Use words, lists, and tables to represent and analyze patterns.

M4.2.5. Explain the purpose of variables and use them in open sentences to express relationships and describe simple functions.

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.

M5.2.1. Identify and compare various triangles and quadrilaterals according to their sides and/or angles.

M5.2.2. Compare and contrast plane and solid figures (e.g., circle/ sphere, square/cube, triangle/pyramid) using relevant attributes, including the number of vertices, edges, and the number and shape of faces.

M5.2.3. Identify and model geometric figures that are congruent, similar, and/or symmetrical.

M5.2.4. Distinguish between area and perimeter; find both using a variety of methods including rulers, grid paper, and tiles.

M5.2.5. Identify and model transformations of geometric figures, describing the motions as slides, flips, or rotations.

M5.2.6. Locate and describe objects in terms of their position with and without compass directions; identify coordinates for a given point or locate points of given coordinates on a grid.

M5.2.7. Sketch and identify line segments, midpoints, intersections, parallel, and perpendicular lines.

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.

M6.2.1. Collect, organize, and display data creating a variety of visual displays including tables, charts, and line graphs.

M6.2.2. Present the data using a variety of appropriate representations and explain the meaning of the data.

M6.2.3. Describe and interpret a data set using mean, median, mode, and range.

M6.2.4. Estimate whether a game is mathematically fair or unfair; analyze and present probability data using simple fractions.

M6.2.5. Conduct simple probability experiments using concrete materials and represent the results using fractions and probability.

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.

M7.2.1. Read and summarize a problem, using mathematical terms and symbols.

M7.2.2. Select and apply a variety of strategies including making a table, chart or list, drawing pictures, making a model, and comparing with previous experience to solve problems.

M7.2.3. Explain and verify results of the original problem and apply what was learned to new situations.

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.

M8.2.1. Use the mathematical vocabulary appropriate to the problem.

M8.2.2. Represent mathematical and practical situations using concrete, pictorial, and symbolic representation.

M8.2.3. Organize and communicate mathematical 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.

M9.2.1. Draw logical conclusions about mathematical situations.

M9.2.2. Given a rule or generalization, determine whether the example fits.

M9.2.3. Justify answers and mathematical strategies as 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.

M10.2.1. Apply mathematical processes to social studies.

M10.2.2. Apply mathematical skills and processes to situations with friends and school.