**Basic Math II **

**(two-semester course)**

Basic Math II is the second course offered in Classic Math School’s Enrichment Program, intended for students from 1st grade to 3rd grade. This course’s prerequisites include: expertise with numbers compatible to 10, fluency in skip counting (forward and backward), skillfulness with mental math within 100, and 3 digit-numbers column addition and subtraction with regrouping.The scope and depth of the course may vary significantly depending on the students’ level and duration of the course.

Interactive Basic Math II course is designed to be taught in a small group setting using a variety of instructional methods and materials. Hands-on activities, math games and puzzles form an integral part of each class session to enhance students’ understanding and retention.

The topics and problems that are studied in Basic Math II course may include:

- Developing fluency in recognizing the numbers compatible to a 100.
- Counting, reading, and writing whole numbers up to 1,000,000. Identifying the place value of each digit. Reading and writing numbers in standard and expanded notation. Converting numbers from one notation to the other.
- Extending mental math skills using number bonds and decomposition of the greater numbers.
- Rounding larger numbers to the nearest 10,100,1000,10000,100000.
- Mastering vertical addition and subtraction of multidigit numbers, while developing a habit of mental estimation by rounding and/or using the inverse relationship between addition and subtraction. Finding missing digits in addition/subtraction problems.
- Solving and making up 2-3 step word problems involving addition and subtraction of whole numbers within 1,000,000.
- Recognizing and extending linear number patterns that illustrate multiplication.
- Introduction to multiplication as repetitive addition; introduction to division as a repetitive subtraction. Acting them out with manipulatives.
- Recognizing division as an inverse operation to multiplication, using the analogy that subtraction is the inverse of addition. Introducing Family Facts for multiplication/division, and exploring the similarities and differences between them and addition/subtraction Family Facts.
- Investigating the special roles of 0 and 1 in multiplication/division.
- Exploring the multiplication table, looking for different patterns and using it fluently for multiplication and division. Memorizing the multiplication table through extensive visual exposure and regular use.
- Introduction to the order of operations and parenthesis. Introduction of arithmetic expressions, involving all four operations on whole numbers. Evaluating arithmetic expressions step by step, using the chain of equal signs properly.
- Discovering the commutative and associative properties of multiplication, and their absence for division. Introducing the distributive property of multiplication and division over addition/subtraction. Demonstrating how those properties can help perform mental calculations, while sometimes overriding the order of operations.
- Column (vertical) multiplication by one-digit multiplier with carrying versus horizontal multiplication using expanded notation and distributive property. The proper way of performing multiplication by 10 and 100. Estimation of products and quotients as an essential part of computation.
- Solving and making up word problems leading to multiplication and division.
- Revisiting the concept of fractions. Relating the concept of fractions to the concept of division. Re-examining the fraction bar as it relates to division.
- Continuing with pictorial models of fractions, extending them from unit fractions all the way to fractions equal to one whole. Discovering simple equivalent fractions through hands-on activities, and by plotting them on the number line. Making a conjecture about generating a chain of equivalent fractions using multiplication/division.
- Comparing fractions having the same denominators, and fractions that have the same numerators. Recognizing that comparisons are only valid when both fractions refer to the same whole. Exploring the relationship between the value of the fraction itself and the value of its numerator and denominator.
- Introduction to addition and subtraction of simple fractions with the same denominators through pictorial models and hands on activities.
- Introduction to basic probability.
- Identifying, describing, and comparing triangles, rectangles, squares, circles, including the faces of three-dimensional objects.
- Introduction to the concept of area. Recognizing perimeter and area as attributes of plane figures, and distinguishing between linear and square units of measurement. Considering different rectangles having the same area, but different dimensions; relating this to multiplication and division facts. Calculating areas of rectangles, squares, right triangles, and some complex shapes by decomposing them into simpler ones.
- Building on money and time concepts with multiplication/division. Telling and writing time to the accuracy of 5 minutes using the analog clock, and relating it to fractions of an hour/clockface.
- Describing and extending simple patterns of numbers, abstract symbols, and geometric figures. Continued practice with coordinate system.
- Introduction to the basics of Set Theory, and Venn Diagram modeling for two sets. Solving different types of logic problems.