Prekindergarten: Unit PK.MD.B.3-4, Sort objects into given categories and compare quantities

Progressions from Common Core Standards in Mathematics

For an in-depth discussion of the overacting, "big picture" perspective on stuent learning of content related to this unit, seed.

1. The Progressions for K, Counting and Cardinality; K–5, Operations and Algebraic Thinking at: http://commoncoretools .files.wordpress.com/ 2012/07/ccss_progression _gm_k5_2012_07_21.pdf to see the development of the understanding of measurement and data as stated by the Common Core Standards Writing Team, which is also the guiding information for the PARCC Assessment development.

Vertical Alignment: Vertical curriculum alignment provides two pieces of information: (1) a description of prior learning that should support the learning of the concepts in this unit, and (2) a description of how the concepts studied in this unit will support the learning of additional mathematics.

1. Key Advances from Previous Grades:
   Prior to Prekindergarten, students:
   1. Sort toys and play games which incorporate sorting by color, size, or other attributes.
   2. Count as they go up and down the stairs.
2. Additional Mathematics
   In Kindergarten, students:
   1. Describe and compare measureable attributes.
   2. Classify objects and count the number of objects in each category.

In Grades 1 through 5, students:

1. Represent and interpret data.

In Grade 6, students:

1. Develop understanding of statistical variability.
2. Summarize and describe distributions.

In Grade 7, students:

1. Use random sampling to draw inferences about a population.
2. Draw informal comparative inferences about two populations.
3. Investigate chance processes and develop, use, and evaluate probability models.

In Grade 8m students:

1. Investigate patterns of association in bivariate data.

Possible Organization of Unit Standards: This table identifies additional grade-level standards within a given cluster that support the over-arching unit standards from within the same cluster. The table also provides instructional connections to grade-level standards from outside the cluster.

Over-Arch'ng Standards	Support'ng Standards with'n the Cluster	Instructional Connect'ons outside the Cluster
PK.MD.B.3 Sort objects into self-selected and given categories.		PK.CC.B.5 Representing a number (0-5, then to 10) by producing a set of objects with concrete materials, pictures, and/or numerals (with 0 representing a count of no objects), PK.CC.B.6 Recognize the number of objects in a set without counting (Subitizing). (Use 1-5 objects.)
PK.MD.B.4 Compare categories using words such as more or same.		PK.CC.C.7 Explore relationships by comparing groups of objects up to 5 and then 10. 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 group with up to 5 objects).

Connections to the standards for Mathematical Practice: This section provides examples of learning experiences for this unit that support the development of the proficiencies described in the Standards for Mathematical Practice. These proficiencies correspond to those developed through the Literacy Standards. The statements provided offer a few examples of connections between the Standards for Mathematical Pratice and the Content Standards of this unit. The list is not exhaustive and will hopefully prompt further reflection and discussion.

In this unit, educators should consider implementing learning experiences which provide opportunities for students to:

1. Make sense of problems and persevere in solving them.
   1. Determine what the problem is asking for: how many in a set, the number that represents the set, the next number if I add one to the set.
   2. Determine whether concrete manipulatives, pictures or numbers are the best tools for solving the problem.
   3. Check the solution with the problem to verify that it does answer the question asked.
2. Reason abstractly and quantitatively
   1. Compare the objects in each category to determine which has more or less, or if they have the same amount.
   2. Use one-to-one correspondence to compare the objects in two categories.
3. Construct Viable Arguments and critique the reasoning of others.
   1. Compare the sets used by others with yours.
   2. Examine the steps taken that produce an incorrect response and provide a viable argument as to why the process produced an incorrect response.
   3. Use concrete manipulatives to verify the correct quantity of the set, when appropriate and support your answer.
4. Model with Mathematics
   1. a. Construct visual models using concrete or virtual manipulatives, pictures, or equations to justify thinking and display the solution
5. Use appropriate tools strategically
   1. Use counters or other manipulatives, as appropriate.
   2. Use large grid paper if needed to organize the objects.
6. Attend to precision
   1. Use mathematics vocabulary such as more, less, same, equal, etc. properly when discussing problems.
   2. Demonstrate understanding of the mathematical processes required to solve a problem by carefully showing all of the steps in the solving process.
7. Look for and make use of structure.
   1. Use the patterns in arranging objects to make sense of them.
   2. Use the relationships demonstrated in the comparison of the objects in two categories.
8. Look for and express regularity in reasoning
   1. Use the patterns illustrated in one-to-one correspondence to determine the comparison.
   2. Use the relationships demonstrated in the between the number of objects in each category to determine which has more or less

Content Standards with Essential Skills and Knowledge Statements and Clarifications: The Content Standards and Essential Skills and Knowledge statements shown in this section come directly from the Maryland State Common Core Curriculum Frameworks. Clarifications were added as needed. Educators should be cautioned against perceiving this as a checklist. All information added is intended to help the reader gain a better understanding of the standards.

Standard: PK.CC.A.1	Essential Skills and Knowledge	Clarification
PK.MD.B.3 Sort objects into given categories.	Essential Skills and Knowledge See the skills and knowledge as stated in the Standard.	Initially, students may simply separate items into categories without lining them up to compare. Example: Sorting pictures of pets into categories: Once a question is asked, “Which type of pet has more?” or “Do any of the types of pets have the same number?” then the students may realize they need to organize them so they can compare the numbers of animals in the different categories.
PK.MD.B.4 Compare categories using words such as more or ,same	Essential Skills and Knowledge Ability to sort objects into categories and then compare the categories (e.g., There are more bus riders than car riders; or there are the same number of large and small bears.) Ability to compare quantities of the categories visually or by aligning of the items one to one, not by the numeric comparison Knowledge of and ability to apply appropriate comparison vocabulary of ‘more’ or ‘same’	Using pictures of pets sorted into categories, students can decide which has more and if any have the same number as another category. In this case, there are more dogs while the birds and fish have the same number of pets in those two categories. We start with ‘more’ and ‘same’ which are easier for students to understand at this level. In life they will often ask for more snacks, milk, etc. They will also notice if they have the same number of treats as another child. Less is a little more difficult and can definitely be introduced when students are very comfortable with ‘more’ and ‘same’.