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## Arizona Math Standards - 2nd Grade

MathScore aligns to the Arizona Math Standards for 2nd Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.

View the Arizona Math Standards at other levels.

## Number Sense and Operations

C1 Number Sense
1. Make a model to represent a given whole number 0 through 999.
2. Identify a whole number represented by a model with a word name and symbol 0 through 999. (Counting Squares )
3. Count aloud, forward or backward, in consecutive order (0 through 999).
4. Identify whole numbers through 999 in or out of order.
5. Write whole numbers through 999 in or out of order. (Counting Squares )
6. State equivalent forms of whole numbers using multiples of 10 through 1,000 (430 + 200 = 600 + 30).
7. State verbally whole numbers, through 999, using correct place value (e.g., A student will read 528 as five hundreds, two tens, and eight ones.).
8. Construct models to represent place value concepts for the one's, ten's, and hundred's places.
9. Apply expanded notation to model place value through 999 (e.g., 378 = 3 hundreds + 7 tens + 8 ones). (Place Value to 1000 )
10. Identify odd and even (including 0) whole numbers through 999. (Odd or Even )
11. Compare two whole numbers through 999. (Number Comparison )
12. Use ordinal numbers.
13. Order three or more whole numbers through 999 (least to greatest or greatest to least). (Order Numbers to 1000 )
14. Make models that represent given fractions (halves and fourths).
15. Identify in symbols and words a model that is divided into equal fractional parts (halves and fourths).
16. Count money through \$5.00 using manipulatives and pictures of bills and coins. (Making Change 2 , Counting Money )
17. Identify the value of a collection of money using the symbols ¢ and \$ through \$5.00. (Counting Money )
18. Use decimals through hundredths in contextual situations with money. (Counting Money )
19. Compare two decimals using money, through hundredths, using models, illustrations, or symbols. (Compare Decimals )
20. Distinguish the equivalency among decimals, fractions and percents (e.g., half-dollar = 50¢ = 50%).
C2 Numerical Operations
1. Demonstrate the process of addition through two three-digit whole numbers, using manipulatives. (Requires outside materials )
2. Demonstrate the process of subtraction using manipulatives with two-digit whole numbers. (Requires outside materials )
4. Add one- and two-digit whole numbers with regrouping. (Addition Grouping , Long Addition to 1000 , Mental Addition and Subtraction to 100 , Mental Addition and Subtraction )
5. Subtract one- and two-digit whole numbers with regrouping. (Long Subtraction , Mental Addition and Subtraction to 100 , Mental Addition and Subtraction , Long Subtraction to 1000 )
7. Select the grade-level appropriate operation to solve word problems. (Basic Word Problems , Arithmetic Word Problems , Basic Word Problems 2 )
8. Solve word problems using addition and subtraction of two 2-digit numbers, with regrouping AND two 3-digit numbers without regrouping.
9. Count by multiples of three. (Skip Counting )
10. State multiplication facts: 2s, 5s and 10s. (Beginner Multiplication )
11. Demonstrate the associative property of addition [e.g., (3 + 5) + 4 = 3 + (5 + 4)]. (Associative Property 1 )
12. Apply grade-level appropriate properties to assist in computation.
13. Apply the symbols: +, -, ×, ÷, =, ≠, <, >, %.
14. Use grade-level appropriate mathematical terminology.
15. Demonstrate addition of fractions with like denominators (halves and fourths) using models.
16. Demonstrate subtraction of fractions with like denominators (halves and fourths) using models.
17. Add and subtract money without regrouping using manipulatives and paper and pencil, through \$5.00. (Making Change )
C3 Estimation
1. Solve problems using a variety of mental computations and reasonable estimation.
2. Estimate the measurement of an object using U.S. customary standard and non-standard units of measurement.
3. Compare an estimate to the actual measure.
4. Evaluate the reasonableness of an estimate.

## Data Analysis, Probability, and Discrete Mathematics

C1 Data Analysis (Statistics)
1. Formulate questions to collect data in contextual situations.
2. Make a simple pictograph or tally chart with appropriate labels from organized data.
3. Interpret pictographs using terms such as most, least, equal, more than, less than, and greatest. (Tally and Pictographs )
4. Answer questions about a pictograph using terms such as most, least, equal, more than, less than, and greatest. (Tally and Pictographs )
5. Formulate questions based on graphs, charts, and tables.
6. Solve problems using graphs, charts, and tables. (Tally and Pictographs )
C2 Probability
1. Name the possible outcomes for a probability experiment.
2. Predict the most likely or least likely outcome in probability experiments (e.g., Predict the chance of spinning one of the 2 colors on a 2-colored spinner.).
3. Predict the outcome of a grade-level appropriate probability experiment.
4. Record the data from performing a grade-level appropriate probability experiment.
5. Compare the outcome of an experiment to predictions made prior to performing the experiment.
6. Compare the results of two repetitions of the same grade-level appropriate probability experiment.
C3 Discrete Mathematics - Systematic Listing and Counting
1. Make arrangements that represent the number of combinations that can be formed by pairing items taken from 2 sets, using manipulatives (e.g., How many types of sandwiches can one make with 3 different types of fillings and 2 types of bread if only one type of bread and 1 kind of filling is used for each sandwich?).
C4 Vertex-Edge Graphs
1. Color pictures with the least number of colors so that no common edges share the same color (increased complexity throughout grade levels).

## Patterns, Algebra, and Functions

C1 Patterns
1. Communicate a grade-level appropriate pattern, using symbols or numbers
2. Extend a grade-level appropriate repetitive pattern (e.g., 12, 22, 32, ___, ___, ___). (Patterns: Numbers , Patterns: Shapes )
C2 Functions and Relationships
1. Describe the rule used in a simple grade-level appropriate function (e.g., T-chart, input/output model, and frames and arrows). (Function Tables , Function Tables 2 )
C3 Algebraic Representations
1. Use variables in contextual situations.
2. Find the missing element (addend, subtrahend, minuend, sum, and difference) in addition and subtraction number sentences for sums through 18 and minuends through 9 (e.g., 13 - _ = 8). (Missing Term )
C4 Analysis of Change
1. Identify the change in a variable over time (e.g., an object gets taller, colder, heavier). (Line Graphs )
2. Make simple predictions based on a variable (e.g., a child's height from year to year). (Line Graphs )

## Geometry and Measurement

C1 Geometric Properties
1. Compare attributes of 2-dimensional shapes (square, rectangle, triangle, and circle). (Geometric Shapes )
2. Recognize congruent shapes. (Congruent And Similar Triangles )
3. Recognize line(s) of symmetry for a 2-dimensional shape.
C2 Transformation of Shapes
1. Recognize same shape in different positions (flip/reflection).
C3 Coordinate Geometry
C4 Measurement - Units of Measure - Geometric Objects
1. Identify the type of measure (e.g., weight, height, and time) for each attribute of an object.
2. Select the appropriate U.S. customary measure of accuracy:
• length - inches, feet, yards, miles,
• capactiy/volume - pints, quarts, and
• mass/weight - ounces.
3. Tell time to the quarter hour using analog and digital clocks. (Telling Time )
4. Determine the passage of time using units of days and weeks within a month using a calendar.
5. Select the appropriate tool to measure the given characteristic of an object.
6. Measure a given object using the appropriate unit of measure:
• length - inches, miles,
• capacity/volume - pints, quarts, and
• mass/weight - ounces.
7. State equivalent relationships:
• 12 inches = 1 foot,
• 60 minutes = 1 hour,
• 12 months = 1 year, etc.

## Structure and Logic

C1 Algorithms and Algorithmic Thinking
1. Create contextual problems that require addition or subtraction with one- or two-digit numbers.
C2 Logic, Reasoning, Arguments, and Mathematical Proof
1. Identify the concepts some, every, and many within the context of logical reasoning.
2. Identify the concepts all and none within the context of logical reasoning.