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By the end of 4th grade, students understand large numbers and addition, subtraction, multiplication, and division of whole numbers. They describe and compare simple fractions and decimals. They understand the properties of, and the relationships between, plane geometric figures. They collect, represent, and analyze data to answer questions.1) 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: Decimal relate to simple fractions.

2) Read and write whole numbers in the millions. Whole numbers in the millions

3) Order and compare whole numbers and decimals to two decimal places. Comparisons of decimal numbers

4) Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. Rounding numbers

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

6) Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions. Equivalent fractions

7) Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (Example: 1/2 = 0.5 or 0.50 ) Notation of decimals

8) 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. Represent fractions on number line

9) Use concepts of negative numbers. Introduction of negative numbers

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

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

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

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

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

15) Understand that many whole numbers break down in different ways (Example: 18= 6 x 3 = 2 x 3 x 3) Factors of small numbers

16) 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. Prime numbers

17) Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences. Introduction to Algebra

18) Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (Example: demonstrate an understanding and the use of the concept of a variable). Variables

19) Interpret and evaluate mathematical expressions that now use parentheses.

20) Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations.

21) Use and interpret formulas

(Example: area = length x width or A = lw) to answer questions about quantities and their relationships.

22) Understand that an equation such as y = 3 x + 5 is a prescription for determining a second number when a first number is given. Simple equations

23) Students learn addition of like terms. Addition and subtraction of like terms.

24) Students understand perimeter and area. Perimeter and Area

25) Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm

26) Area and perimeter of rectangle. Area and perimeter of Rectangle

27) Use of formulas of area and perimeter and solved problems based on it. Problems based on area and perimeter of rectangle

28) Coordinate Geometry.

29) Parallel lines.Parallel lines

30) Understanding the radius and diameter of a circle. Circle

31) Congruent figures.

32) Symmetry. Symmetry

33) Definition of acute, right and obtuse angles. Types of angles

34) Geometric solids.(Prism, pyramid etc.)

35) Know the definitions of different triangles. Types of triangles

36) Know the definition of different quadrilaterals. Types of quadrilateral

37) All types of graphs and charts.(Example : Bar, Histogram etc.)

Bar graph, Histogram etc .

38) Median and Mode. Median and Mode

39) Probability. (tree diagram)

40) Mathematical Reasoning.

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