Course Outlines. Elementary Mathematics (Grades K-5) Kids and Numbers (Recommended for K-1 students)
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1 Course Outlines Elementary Mathematics (Grades K-5) Kids and Numbers (Recommended for K-1 students) Shapes and Patterns. Grouping objects by similar properties. Identifying simple figures within a complex figure. Bigger, equal or smaller. Comparison. Line segment. Length. Measuring in non-standard units. Number line. Counting from 1 to 10 and back by 1 & 2 Odd & Even numbers. Addends & Sum. Part & Whole. Counting by 2 or 4 using the number line. Difference. Commutative law of Arithmetic. Tens, counting by fives and tens. Numbers from 10 to 20. Fractions 1/2, 1/4. Roman numerals. First introduction to variables. Identifying US coins. Solving simple problems with them. Elementary puzzles. Elementary Mathematics 1 (Recommended for 1-2 grade students) Number line, counting from 1 to 100. Comparisons (symbols >, <, =). Counting by 2, 4, 5 and 10. Identifying numbers up to Basic addition facts. Basic subtraction facts. Odd and even numbers. Elementary fractions (halves, thirds, fourths, tenths). Addition and subtraction of two-digit numbers. Commutative law of Arithmetic. Introduction to algebra. Unknown variable. Algebraic expressions with an unknown. Comparison of algebraic expressions. Length, width, perimeter and area (rectangles). Perimeter of a triangle. Metric and English units. Congruent simple shapes. Weights and volumes in metric and English units. Simple word problems and equations. Logical problems and puzzles First introduction to negative numbers. Identifying the correct time. Telling time to the nearest ½ hour. 1
2 Working with money - identifying and counting coins and bills. Adding money. Elementary Mathematics 2 (Recommended for 2nd grade students) Number line. Hundreds, tens and ones. Comparisons. Identifying numbers through 10,000. Sorting in increasing/decreasing order. Addition and subtraction (with and without regrouping). Using Less than / Greater than symbols. Multiplication table (0-5 mandatory, 6-12 desirable). Sum, Difference, Product. Commutative and Distributive properties of multiplication. Simple division. Order of operations. Number machines. Patterns. Variables. Simple (and not so simple) equations. Word problems requiring knowledge of simple equations. Perimeter and area of a rectangle and square. Perimeter of a triangle. Volume as a number of cubic units that fit in a three-dimensional figure. Weights, units of weight. Identifying right, acute, and obtuse angles. Sum of the angles in a triangle (as a fact). Coordinates on a plane. Simple fractions. Simple charts and plots. Tables. Multiples. Telling time to the nearest minute. Logical Problems and Puzzles. Elementary Mathematics 3 (Recommended for 3rd grade students) Whole numbers. Counting to 100,000 Multiplication of whole numbers. Multiplication table Division. Remainders. Patterns. Order of operations. Simple fractions and operations on them. Introduction to Equivalent fractions. Comparing and ordering fractions (elementary). Introduction to decimal numbers Rounding to the nearest 10, 100, 1000, etc. Variables and equations. 2
3 Word problems. Problems with proportional reasoning. Measuring length metric and English systems. Areas and volumes. Units of area and volume. Finding perimeter, area and volume (simple figures). Weights. Pounds, grams and kilograms. Angles. Angles in a triangle. Perpendicular and Parallel Lines. Recognizing and drawing lines of symmetry. Elementary algorithms. Conditionals, Cycles. Flowcharts. Sets and their elements. Introduction to Venn diagrams. Union, intersection, empty set. Symmetrical figures. Notion of True and False. Time and calendar: second, minute, hour, day, week, month, and year. Time related problems. Money exchange problems (nickels, dimes, quarters). Average. Elementary Mathematics 4 (Recommended for 4th grade students) Multiplication of two- and three-digit numbers. Division tables. Long division by one- and two-digit numbers. Mental arithmetic (each lesson, at least 5 minutes). Simple algebraic equations. Introduction to inequalities. Plotting the solutions on the number line. Introduction to rounding and approximation. Definition of a set and set operations (union, intersection, difference). Symbolic language for union and intersection. Word problems involving set operations. Divisibility by 2, 3, 5, 6, 9, 10, 100. Prime and composite numbers. Introduction to factors and products. Finding GCF and LCM (introduction). Part of a whole. Fractional notation. Numerator and denominator. Recognizing and creating equivalent fractions. Simplest form of a fraction. Simplifying fractions. Comparing two fractions. Ordering fractions (simple). Recognizing proper and improper fractions. Mixed numbers. Writing an improper fraction as a mixed number. Adding and subtracting of two fractions with common denominator. Adding and subtracting of two fractions with different denominators. Multiplying two fractions. ( Simplify before multiplying rule). Negative numbers (introduction and simple problems). Coordinates and distances on the plane. 3
4 Naming of points, lines, segments, rays, angles and vertices. Plane and solid figures. Recognizing vertices, faces and edges of rectangular prisms and pyramids. Notion of volume. Angles. Comparison and measurement of angles. Sum of the angles of a triangle. Finding a third angle when two are given. Word problems (including creation of a simple equation) involving the angles of a triangle. Quadrilaterals parallelogram, rhombus, rectangle, square, trapezoid. Sum of the angles of a quadrilateral. Perimeter and area of a parallelogram, rectangle, and square. Finding a side of a square given its area (or perimeter). Base and height of a triangle. Area of a triangle. Bases and height of a trapezoid. Area of a trapezoid. Introduction to probability. Computing probabilities of simple events. Relationship between distance, speed and time. Word problems. Elementary Mathematics 5 (Recommended for 5th grade students) Powers of 10. Understanding of place value. Decimals (addition, subtraction, multiplication, division). Rounding and approximation. Negative numbers. Operations (addition, subtraction, multiplication, division) involving negative numbers (integers only). Speed, time, and distance. The distance formula. Work. Formula for work. Elementary word problems involving speed and distance, cost, and work. Moving on a number line in opposite and the same directions with different speeds. Word problems. Simplifying fractions. Addition, subtraction, multiplication and division of two (occasionally three or more) fractions. Comparing and ordering fractions (like and unlike denominators). Proper and improper fractions. Mixed numbers. Addition, subtraction, multiplication and division of two mixed numbers. Connection between division and fractions. Finding what part of a given number is another given number. Order of operations (including fractions and decimals). Algebraic equations and inequalities. Problems involving scalene, isosceles and equilateral triangles. Volumes and surface areas of rectangular prisms. Different types of prisms and pyramids (rectangular, triangular, pentagonal). Convex and concave plane figures. Symmetry. Perimeter and area of a triangle, rectangle, square, parallelogram, trapezoid (review). 4
5 Area of regions composed of triangles, rectangles, parallelograms, and trapezoids. Notion of center, chord, radius and diameter of a circle. Circumference and area of a circle. Naming and measuring angles. Flips and rotations. Points on the coordinate plane. Distance between two points. Midpoint between two points. Sets and set operations. Elementary logic. Probability of simple events. Median, mean, mode, maximum, minimum, and range of a set of numbers. Problems requiring working with pie charts, bar graphs, line graphs, tables. Mental calculations (each lesson at least 5 minutes). Note 1: The topics described in the curriculum outline are approximate. The exact topics covered in class depend on the initial evaluation of the level the students begin the year. In some cases the teacher may choose to include topics from the earlier or later course, or reduce the number of topics covered, depending on the progress of the class. 5
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