Unit 
Topic 
Standards 
I 
Introduction to PreKindergarten Math
(September) 
Calendar time with math connections
Relating literature to math
Interactive math songs
Quick Images
Using manipulatives appropriately
Math Talk Moves


Cooperative Learning
Math Problem Solving (Acting It Out and Drawings)
Building a classroom that encourages the Standards for Mathematical Practice


1 
Attributes, Sorting,Classifying, and Data
(September) 
Group the shapes by attributes
Sort objects into given categories
Match and sort shapes
Sort objects into given categories
Compare categories using words such as greater than/more, less than, and equal to/same


2 
Understanding Number Relationships 05
(October  November) 
Count verbally to 5 by ones
Recognize the concept of just after or just before a given number in the counting sequence up to 5
Recognize written numerals 05
Understand the relationship between numbers and quantities to 5; connect counting to cardinality
When counting objects, say the number names in the standard order, pairing each object with one and only one number name
Recognize that the last number name said tells the number of objects counted
Represent a number (05) by producing a set of objects with concrete materials, pictures, and/or numerals (with 0 representing a count of no objects)
Recognize the number of objects in a set without counting (Subitizing)
Explore relationships by comparing groups of objects up to 5, to determine greater than/more or less than, and equal to/same
Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies


3 
Shapes, Patterns, and Positional Language
(December  January) 
Match like (congruent and similar) shapes
Group the shapes by attributes
Correctly name shapes (regardless of their orientations or overall size)
Match and sort shapes
Describe threedimensional objects using attributes

4 
Measurement
(February) 
Describe measurable attributes of objects, such as length or weight
Directly compare two objects with a measurable attribute in common, using words such as longer/shorter; heavier/lighter; or taller/shorter


5 
Understanding Number Relationships 010
(March  April) 
Count verbally to 10 by ones
Recognize the concept of just after or just before a given number in the counting sequence up to 10.
Recognize written numerals 010
Understand the relationship between numbers and quantities to 10; connect counting to cardinality.
When counting objects, say the number names in the standard order, pairing each object with one and only one number name.
Recognize that the last number name said tells the number of objects counted.
Recognize that each successive number name refers to a quantity that is one larger.
Represent a number (05, then to 10) by producing a set of objects with concrete materials, pictures, and/or numerals (with 0 representing a count of no objects).
Explore relationships by comparing groups of objects up to 10, to determine greater than/more or less than, and equal to/same
Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (includes groups with up to 5 objects).
Investigate the relationship between ten ones and ten.


6 
Addition and Subtraction
(May  June) 
Explore addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, or verbal explanations.
Decompose quantity (less than or equal to 5, then to 10) into pairs in more than one way (e.g., by using objects or drawings).
For any given quantity from (0 to 5, then to 10) find the quantity that must be added to make 5, then to 10, e.g., by using objects or drawings.


In Prekindergarten there are 3 critical areas:
(1) Developing an understanding of whole numbers, including concepts of correspondence, counting, cardinality, and comparison: Children develop an understanding of the meanings of whole numbers and recognize the number of objects in small groups without counting and by counting – the first and most basic mathematical algorithm. They understand that number words refer to quantity. They use onetoone correspondence to solve problems by matching sets and comparing number amounts and in counting objects to 10 and beyond. They understand that the last word that they state in counting tells "how many", they count to determine number amounts and compare quantities (using language such as "more than" and "less than"), and they order sets by the number of objects in them.
(2) Identifying shapes and describing spatial relationships: Children develop spatial reasoning by working from two perspectives on space as they examine the shapes of objects and inspect their relative positions. They find shapes in their environments and describe them in their own words. They build pictures and designs by combining two and three dimensional shapes, and they solve such problems as deciding which piece will fit into a space in a puzzle. They discuss the relative positions of objects with vocabulary such as "above", "below", and "next to".
(3) Identifying measurable attributes and comparing objects by using these attributes: Children identify objects as "the same" or "different", and then "more" or "less", on the basis of attributes that they can measure. They identify measurable attributes such as length and weight and solve problems by making direct comparisons of objects on the basis of those attributes.
Taken from Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (Reston, Va.:NCTM, 2006, p.11).