Alaska State Standards for Mathematics: Grade 1

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

[1] N-1. Reading, writing, ordering/counting and modeling correspondence of whole numbers.

[1] N-2. Comparing whole numbers using the words greater than, less than or equal to.

[1] N-3. Identifying ordinal position, first to the twentieth (M1.1.4)

[1] N-4. Dividing an even numbered set of concrete objects (up to 50) into halves (M1.1.5)

[1] N-5. Dividing geometric shapes into equal halves, fourths, and thirds (M1.1.5)

[1] N-6. Using objects, pictures, and problem situations to model addition and subtraction of whole numbers (M1.1.3)

[1] N-7. Identifying groups of objects as repeated addition or equal shares (M1.1.3)

[1] N-8. Skip counting by 2's to 20 and 5's and 10's to 100 (M1.1.6)

[1] N-9. Identifying odd and even numbers up to 20 (M1.1.6)

[1] N-10. Identifying fact families (M1.1.3)

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

[1] MEA-1. Measuring and/or comparing objects using standard and nonstandard units (M2.1.2)

[1] MEA-2. Identifying money by its value (e.g., penny, nickel, dime, quarter, dollar) (M2.1.5)

[1] MEA-3. Drawing a line segment to the nearest inch (M2.1.3)

[1] MEA-4. Telling time to the nearest half hour using analog and digital clocks (M2.1.4)

[1] MEA-5. Comparing concepts such as: before/after, shorter/longer (M2.1.1)

[1] MEA-6. Reading a calendar (distinguishing yesterday, today, and tomorrow) (M2.1.1)

[1] MEA-7. Recognizing money symbols ($, cents) (M2.1.5)

[1] MEA-8. Identifying equal values of a coin up to a dollar (5 pennies = 1 nickel, 5 nickels = 1 quarter) (M2.1.5)

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.

[1] E&C-1. Estimating '''how many''' and '''how much''' in a given set up to 20

[1] E&C-2. Identifying whether estimation or counting is appropriate with support (M3.1.1)

[1] E&C-3. Recalling addition and subtraction facts 0-10 (M3.1.2)

[1] E&C-4. Recalling doubles to 20 (M3.1.2)

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

[1] F&R-1. Identifying, naming (e.g., aabb, abab), and continuing a variety of patterns (M4.1.1)

[1] F&R-2. Creating patterns involving number, shape, size, rhythm, or color (M4.1.1)

[1] F&R-3. Adding and subtracting whole numbers to 20 using manipulatives to solve story problems (M4.1.4)

[1] F&R-4. Creating and solving problems using words, symbols, and drawings (M4.1.4)

[1] F&R-5. Using the terms equal to, more than, and less than for numbers up to 20 (M4.1.4)

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

[1] G-1. Identifying the attributes of 2-dimensional shapes (e.g., a triangle has three sides) (M5.1.1)

[1] G-2. Identifying and classifying 2 dimensional shapes through visual observations and properties (e.g., which of these shapes is a triangle) (M5.1.1)

[1] G-3. Relating real-world examples (e.g., a door is shaped like a rectangle) to the ideas and concepts of geometry (M5.1.2)

[1] G-4. Comparing shapes in the real world (M5.1.3)

[1] G-5. Modeling directional and positional concepts: before, after, between, next to, around, above, below, in the middle of... (M5.1.6)

[1] G-6. Drawing, copying, or describing a variety of shapes (M5.1.7)

[1] G-7. Identifying geometric shapes in real-world objects (M5.1.7)

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

[1] S&P-1. Constructing and using real graphs, pictographs, and bar graphs (M6.1.1)

[1] S&P-2. Collecting and recording data (M6.1.1)

[1] S&P-3. Interpreting data with support (M6.1.1)

[1] S&P-4. Describing information from simple charts/graphs (M6.1.2)

[1] S&P-5. Predicting, interpreting, and comparing data using events or repeated observations (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.

[1] PS-1. Creating and solving simple problems using a variety of strategies (M7.1.1 & M7.1.2)

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

[1] PS-2. Translating problems from everyday language into math language and symbols (+, -, =) (M8.1.1)

[1] PS-3. Using everyday language to explain thinking about problem solving strategies and solutions to problems (M8.1.3)

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

[1] PS-4. Explaining why a prediction or solution is reasonable (M9.1.3)

[1] PS-5. Drawing pictures that support mathematical statements (M9.1.2)

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

[1] PS-6. Using real world context (i.e., self, friends, and family) (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.