California State Standards for Mathematics: Grade 4

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CA.NS. Number Sense

1.0. Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers.

1.1. Read and write whole numbers in the millions.

1.2. Order and compare whole numbers and decimals to two decimal places.

1.3. Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand.

1.4. Decide when a rounded solution is called for and explain why such a solution may be appropriate.

1.5. Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalence of fractions (see Standard 4.0).

1.6. Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or 0.50; 7/4 = 1 3/4 = 1.7.5).

1.7. Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.

1.8. Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in ''owing'').

1.9. Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.

2.0. Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals.

2.1. Estimate and compute the sum or difference of whole numbers and positive decimals to two places.

2.2. Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer.

3.0. Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.

3.1. Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.

3.2. Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results.

3.3. Solve problems involving multiplication of multidigit numbers by two-digit numbers.

3.4. Solve problems involving division of multidigit numbers by one-digit numbers.

4.0. Students know how to factor small whole numbers.

4.1. Understand that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3).

4.2. Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.

CA.AF. Algebra and Functions

CA.MG. Measurement and Geometry

2.3. Understand that the length of a vertical line segment equals the difference of the y-coordinates.

3.5. Know the definitions of a right angle, an acute angle, and an obtuse angle. Understand that 90 degrees, 180 degrees, 270 degrees, and 360 degrees are associated, respectively, with 1/4, 1/2, 3/4, and full turns.

3.6. Visualize, describe, and make models of geometric solids (e.g., prisms, pyramids) in terms of the number and shape of faces, edges, and vertices; interpret two-dimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid.

3.7. Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes.

3.8. Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).

CA.SDAP. Statistics, Data Analysis, and Probability

CA.MR. 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.

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