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California Math Standards - 3rd Grade

MathScore aligns to the California Math Standards for 3rd 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.

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View the California Math Standards at other levels.

Number Sense

1.0 Students understand the place value of whole numbers:
   1.1 Count, read, and write whole numbers to 10,000. (Place Value )
   1.2 Compare and order whole numbers to 10,000. (Order Numbers )
   1.3 Identify the place value for each digit in numbers to 10,000. (Place Value )
   1.4 Round off numbers to 10,000 to the nearest ten, hundred, and thousand. (Rounding Numbers )
   1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6). (Place Value )
2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:
   2.1 Find the sum or difference of two whole numbers between 0 and 10,000. (Long Addition , Long Subtraction )
   2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10. (Fast Multiplication , Fast Multiplication Reverse , Multiplication Facts Strategies , Fast Division )
   2.3 Use the inverse relationship of multiplication and division to compute and check results. (Inverse Equations 2 )
   2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 x 3 = __). (Multiplication By One Digit )
   2.5 Solve division problems in which a multidigit number is evenly divided by a one-digit number (135 ÷5 = __). (Long Division By One Digit )
   2.6 Understand the special properties of 0 and 1 in multiplication and division. (Fast Multiplication , Fast Multiplication Reverse , Multiplication Facts Strategies , Fast Division )
   2.7 Determine the unit cost when given the total cost and number of units. (Unit Cost )
   2.8 Solve problems that require two or more of the skills mentioned above. (Arithmetic Word Problems , Basic Word Problems 2 , Word Problems With Remainders )
3.0 Students understand the relationship between whole numbers, simple fractions, and decimals:
   3.1 Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g., 1/2 of a pizza is the same amount as 2/4 of another pizza that is the same size; show that 3/8 is larger than 1/4). (Basic Fraction Comparison , Fraction Comparison , Basic Fraction Simplification , Fraction Simplification )
   3.2 Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2). (Basic Fraction Addition , Basic Fraction Subtraction )
   3.3 Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole-number multipliers and divisors. (Money Addition , Money Subtraction , Money Multiplication , Money Division )
   3.4 Know and understand that fractions and decimals are two different representations of the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a dollar). (Fractions to Decimals , Decimals To Fractions , Compare Mixed Values , Positive Number Line )

Algebra and Functions

1.0 Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships:
   1.1 Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities. (Missing Factor , Missing Term )
   1.2 Solve problems involving numeric equations or inequalities. (Compare Expressions , Arithmetic Word Problems , Basic Word Problems 2 )
   1.3 Select appropriate operational and relational symbols to make an expression true (e.g., if 4 __ 3 = 12, what operational symbol goes in the blank?). (Missing Operator )
   1.4 Express simple unit conversions in symbolic form (e.g., __ inches = __ feet x 12).
   1.5 Recognize and use the commutative and associative properties of multiplication (e.g., if 5 x 7 = 35, then what is 7 x 5? and if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?). (Associative Property 2 , Commutative Property 2 )
2.0 Students represent simple functional relationships:
   2.1 Solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit). (Unit Cost )
   2.2 Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s or by multiplying the number of horses by 4). (Patterns: Numbers )

Measurement and Geometry

1.0 Students choose and use appropriate units and measurement tools to quantify the properties of objects:
   1.1 Choose the appropriate tools and units (metric and U.S.) and estimate and measure the length, liquid volume, and weight/mass of given objects.
   1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them. (Requires outside materials )
   1.3 Find the perimeter of a polygon with integer sides. (Perimeter )
   1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes). (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion )
2.0 Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems:
   2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons). (Polygon Names )
   2.2 Identify attributes of triangles (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle). (Triangle Types )
   2.3 Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square). (Quadrilateral Types )
   2.4 Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle.
   2.5 Identify, describe, and classify common three-dimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).
   2.6 Identify common solid objects that are the components needed to make a more complex solid object.

Statistics, Data Analysis, and Probability

1.0 Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions:
   1.1 Identify whether common events are certain, likely, unlikely, or improbable.
   1.2 Record the possible outcomes for a simple event (e.g., tossing a coin) and systematically keep track of the outcomes when the event is repeated many times.
   1.3 Summarize and display the results of probability experiments in a clear and organized way (e.g., use a bar graph or a line plot).
   1.4 Use the results of probability experiments to predict future events (e.g., use a line plot to predict the temperature forecast for the next day). (Line Graphs )

Mathematical Reasoning

1.0 Students make decisions about how to approach problems:
   1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. (Function Tables , Function Tables 2 )
   1.2 Determine when and how to break a problem into simpler parts.
2.0 Students use strategies, skills, and concepts in finding solutions:
   2.1 Use estimation to verify the reasonableness of calculated results. (Money Addition , Money Subtraction )
   2.2 Apply strategies and results from simpler problems to more complex problems. (Many topics align to this standard)
   2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
   2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
   2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
   2.6 Make precise calculations and check the validity of the results from the context of the problem.
3.0 Students move beyond a particular problem by generalizing to other situations:
   3.1 Evaluate the reasonableness of the solution in the context of the original situation.
   3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
   3.3 Develop generalizations of the results obtained and apply them in other circumstances.

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