Basic Math I
Basic Math I course is the first course offered in Classic Math School’s Enrichment Program. This course does not have any prerequisites and is intended for students from K to 2rd grade. The scope and depth of the course may vary significantly depending on the students’ level, and the duration of the course.
This interactive 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 I course may include:
- Understanding the relationship between numbers and quantities, and understanding that each successive number refers to a quantity that is one larger.
- Systematically decomposing numbers less than or equal to 10 into all possible pairs. Introduction of number bonds. Developing fluency in recognizing numbers compatible to 10, as well as adding and subtracting within 10.
- Introducing Family Facts, with emphasis on the relationship between addition and subtraction. Underlying commutative property for addition versus its absence for subtraction.
- Connecting concrete and abstract thinking by acting out sharing; students see that even number of objects are easy to share, while odd numbers of objects are hard to share. Sharing odd numbers of objects segues into fractions (halves). Introducing doubles of whole numbers, as numbers that are naturally always even.
- Understanding the concept of digit and number. Understanding the relationship between digits and numbers using the analogy of letters and words. Recognizing that number 123 versus number 213 in the same way as the word 'cat’ versus the word 'act'. Introduction to positional base-ten number system.
- Reading and writing numbers in standard and expanded notations. Acting out the process of ‘trading’ between digits of 1-, 2-, or 3-digit numbers; for example, 1 ‘ten’ for 10 ‘ones’, or 1 ‘hundred’ for 10 ‘tens’, and the other way around. Using a variety of place-value models to represent numbers up to a 1000 and identify the place value of each digit.
- Comparing and ordering whole numbers using a number line, and <, >, = symbols. Understanding and using ordinal numbers, as well as using the words ‘before,’ ‘after,’ and ‘between,’ to describe position.
- Skip Counting by “2-s”, “3-s”, “4-s” “5-s”, and “10-s” both forward and backward. Relating skip counting to addition and subtraction. Describing, extending, and completing regular number patterns within 1000.
- Extending the concept of even and odd numbers to greater numbers. Exploring the parity of the sums and the differences of even and odd numbers, explaining and discovering patterns.
- Column (vertical) addition/subtraction of whole numbers with and without regrouping (carrying over) versus horizontal addition/subtraction. The inverse relationship between addition and subtraction. Finding the missing addend/minuend/subtrahend using appropriate inverse operation (or Family Fact). Finding the missing digits in multidigit addition/subtraction problems.
- Commutative and associative property of addition. Extending the concept of ‘compatible numbers.’ Mental math techniques and strategies for horizontal addition and subtraction. Using properties and number decomposition (number bonds) for shortcuts in calculations, encouraging mental math as much as possible.
- Rounding numbers up to 1000 to the nearest 10 or 100. Introducing estimation of sums/differences as an essential part of any computation.
- Solving and making up word problems that involve addition and subtraction of whole numbers within 1000.
- Identifying the value of coins and bills, and finding different combinations of coins and bills that equal the same amount. Understanding decimal notation for money; converting it to dollar+cent notation and backwards.
- Understanding the concept of time, using different types of clocks and calendars. Telling and writing time in hours, half-hours, and quarter-hours using analog and digital clocks. Relating time to events (before/after, shorter/longer).
- Introduction of very basic fractions and fractional notations. Exploring equal parts of a whole or a set. Visualizing unit fractions by shading halves, thirds and fourths of pictorial models and using manipulatives.
- Identifying and describing two-dimensional shapes: rectangles, squares, triangles, parallelograms, rhombuses, trapezoids, and circles. Composing and decomposing these shapes in different ways. Introduction to the concept of congruent shapes and symmetry. Identifying lines of symmetry for common shapes.
- Measuring the length of a line segment, in both traditional and metric systems, using rulers. Practicing estimation of lengths. Calculating perimeters of different shapes.
- Introducing the coordinate system (first quadrant only). Plotting points with given coordinates, and finding coordinates of given points.
- Solving logic problems and articulating the reasoning behind the answer. Introduction to the concept of proofs, including indirect proofs and counterexamples.