How to learn Kindergarten: Mathematics

Common Core State Standards for Mathematics, Kindergarten

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1. Counting and Cardinality · Know number names and the count sequence.

1. Rote counting to 100: Rote count forwards and backwards from 0 to 100, beginning from 0, 1, or any given number, by ones
2. Counting in 2s: Count in multiples of 2, 5, and 10 (skip counting)
3. Reading and writing numbers to 20: Read and write numerals from 0 to 20

2. Counting and Cardinality · Count to tell the number of objects.

1. One-to-one counting: One-to-one correspondence when counting objects: each object is paired with exactly one number name
2. How Many in Total?: Cardinality principle: the last number said when counting a set tells how many objects are in the set, regardless of arrangement or order counted
3. One More Each Time: Each successive counting number represents a quantity that is one larger than the previous number
4. Counting objects to 20: Count a set of objects to answer 'how many?' for sets up to 20 (arranged in lines, arrays, circles, or scattered)

3. Counting and Cardinality · Compare numbers.

1. Comparing groups: more or fewer: Compare two groups of objects to determine which has more, fewer, or whether they are equal, using matching and counting strategies
2. Two written numerals between 1 and 10: Compare two written numerals between 1 and 10 to determine which is greater or less

4. Geometry · Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

1. 3-D shapes: Recognise and name common 3-D shapes (cubes, cuboids, pyramids, spheres, cylinders, cones)
2. Positional Language: Describe the position of objects using terms such as above, below, beside, in front of, behind, next to
3. 2-D shapes: Recognise and name common 2-D shapes (circles, triangles, rectangles including squares)
4. Flat vs Solid Shapes: Distinguish two-dimensional (flat) shapes from three-dimensional (solid) shapes

5. Geometry · Analyze, compare, create, and compose shapes.

1. 3-D shapes (age 5+): Analyse and compare 2-D and 3-D shapes using informal language to describe sides, vertices, and other attributes
2. Building & Drawing Shapes: Model shapes by building from components (e.g. sticks and clay balls) and by drawing
3. Combining Simple Shapes: Compose simple shapes to form larger shapes (e.g. two triangles make a rectangle)

6. Measurement and Data · Describe and compare measurable attributes.

1. Measurable Attributes of Objects: Describe and identify measurable attributes of objects such as length, height, weight, and capacity; use comparative language (longer, shorter, heavier, lighter, more, less)
2. Comparing Capacity: Compare and describe capacity and volume using language such as full, empty, more than, less than, half full
3. Comparing Lengths & Heights: Compare two objects directly by length or height and describe the difference using language such as long, short, tall, longer, shorter, taller, double, half
4. Measuring mass and weight (age 4+): Compare two objects directly by mass or weight and describe the difference using language such as heavy, light, heavier than, lighter than

7. Measurement and Data · Classify objects and count the number of objects in each category.

1. Sorting into categories: Classify objects into given categories, count the number in each category, and sort the categories by count

8. Number and Operations in Base Ten · Work with numbers 11–19 to gain foundations for place value.

1. The teen numbers: Understand that the teen numbers (11–19) are composed of ten ones and some further ones (early place value)

9. Operations and Algebraic Thinking · Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

1. Addition as combining or putting together two: Understand addition as combining or putting together two groups to find the total
2. Subtraction as taking away or separating: Understand subtraction as taking away or separating from a group to find how many remain
3. Representing Addition and Subtraction: Represent addition and subtraction using objects, drawings, and mental images
4. Reading +, −, and = symbols: Read, write, and interpret the symbols +, −, and = in number sentences
5. Addition and subtraction word problems: Solve addition and subtraction word problems within 10 using objects or drawings
6. Numbers up to 10 into pairs: Decompose numbers up to 10 into pairs in more than one way (part-part-whole)
7. Number bonds to 9: Find the number that makes 10 when added to a given number from 1 to 9 (number bonds to 10)
8. Fluent adding and subtracting within 5: Fluently add and subtract within 5