Prekindergarten: PK.MD.1-2, Describe measurable attributes of objects, such as length or weight

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.

Progressions for K-5, Geometric Measurement 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 as stated by the Common Core Standards Writing Team, which is also the guiding information for the PARCC Assessment development.

Vertical Alignment:

• Possible Key Advances from Previous Play Experiences and Prekindergarten Mathematics:

1. Placing a group of toys in the ‘largest’ box.
2. Picking up an object to see how heavy it feels.
3. Comparing a bowl of cherries with their friend’s or sibling’s bowl to see who has ‘more’.
4. Dramatic play, such as reenacting the story “Goldilocks and the Three Bears” and using ‘big’ and ‘little’ voices.
5. Helping set table and using ‘big’ cups and ‘little’ cups.
6. Lining up dolls or toy cars from longest to shortest.
7. Kicking a ball to see which goes farthest.
8. Participating in a scavenger hunt to find something that is shorter than or longer than a particular object.

• Additional Mathematics
Students in Kindergarten describe measurable attributes of objects, such as length or weight, just as students do in Prekindergarten. They also:

1. Describe several measurable attributes of a single object.
2. Classify objects and count the number of objects in each category.

Students in Grades 1:

1. Order three objects by length (they compare the lengths of two objects indirectly by using a third object).
2. Measure lengths indirectly and by iterating length units.

Students in Grades 2:

1. Measure and estimate lengths in standard units.
2. Relate addition and subtraction to length.

Students in Grades 3 through five:

1. Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
2. Solve problems involving measurement and conversion of measurement from a larger unit to a smaller unit.
3. Convert like measurement units within a given measurement system.

Possible Organization of Unit Standards:

Over-Arching Standards	Supporting Standards within the Cluster	Instructional Connections outside the Cluster
PK.MD.A.1 Describe measurable attributes of objects, such as length or weight.		PK.MD.B.3 Sort objects into given categories. PK.G.A.2: Group the shapes by attributes. PK.G.B.3: Correctly name shapes (regardless of their orientations or overall size). PK.G.B.4 : Match and sort shapes. PK.G.B.5 :Describe three-dimensional objects using attributes.
PK.MD.A.2 Directly compare two objects with a measurable attribute in common, using words such as longer/shorter; heavier/lighter; or taller/shorter.		PK.MD.B.4 Compare categories using words such as greater than/more, less than, and equal to/same. PK.CC.C.7 : Explore relationships by comparing groups of objects up to 10, to determine greater than/more or less than, and equal to/same. PK.CC.C8 : 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).

Connections to the standards for Mathematical Practice:

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: which is longer or shorter, heavier or lighter, how many are the same size.
   2. Determine whether concrete or virtual models, pictures, mental mathematics, ore estimation 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 common attribute of objects to justify your thinking.
   2. Use common attributes of objects to compare them.
3. Construct Viable Arguments and critique the reasoning of others.
   1. Compare the measurement or estimates of 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.
4. Model with Mathematics
   1. 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, snap cubes, string, rulers, scales or other measurement tools as appropriate.
   2. Use sorting mats or boxes to organize objects for comparison.
6. Attend to precision
   1. Use mathematics vocabulary such as longer, shorter, taller, heavier, lighter, etc. properly when discussing problems.
   2. Demonstrate understanding of the mathematical processes required to solve a measurement problem by carefully showing all of the steps in the solving process.
   3. Use <, =, and > appropriately to compare expressions.
7. Look for and make use of structure.
   1. Use the unit patterns of measurement to compare objects.
   2. Use the relationships demonstrated in the comparison of measurable attributes to justify solutions.
8. Look for and express regularity in reasoning
   1. Use the unit patterns illustrated in measurement to justify solutions.

Content Standards with Essential Skills and Knowledge Statements and Clarifications:

Standard	Essential Skills and Knowledge	Clarification
PK.MD.A.1 Describe measurable attributes of objects, such as length or weight. PK.MD.A.2 Directly compare two objects with a measurable attribute in common, using words such as longer/shorter; heavier/lighter; or taller/shorter.	Essential Skills and Knowledge Ability to use vocabulary specific to measurable attributes of objects Essential Skills and Knowledge Knowledge of length/weight as absolute descriptors Ability to physically align two objects to determine which is longer, shorter, or if they are the same length Ability to physically align two objects to determine which is taller, shorter, or if they are the same height Ability to compare the weight of two concrete objects to determine which is heavier, lighter, or if they are the same weight.	A variety of real world objects and manipulatives are useful in helping students develop the ability to describe measurable attributes. These can include, but are not limited to shoes, buttons, lids, and attribute blocks. Exploring measurement presents additional opportunities for students to compare objects in different ways. These experiences are important for students' understanding of mathematics. Students connect these understandings later to more abstract ideas, such as numeration. Providing students with everyday objects to measure first (before pictures) is beneficial in developing students' measurement concepts. Several examples of comparing familiar objects are: Comparing the length of a piece of string to other objects (longer, shorter, bigger, smaller). Finding objects in the classroom to compare height (shorter or taller than the student). Collecting classroom or familiar objects found in the home to compare weight or size. Comparing the weight of objects in the classroom to a box of crayons. Asking students to model a long and short line. These authentic experiences help students to develop meaningful understandings of comparative language, essential to understanding later measurement concepts.To assist in making the transition from non-standard units towards standard units (in future grades) easier, teachers can sometimes provide manipulatives that are a standard size. These include Cuisenaire Rods, Base Ten blocks, one inch color tiles, one-centimeter cubes, and “inchworms” links). “Bigger” and “smaller” are words students use when they do not differentiate the various measureable quantities. Descriptors need to be related to the attribute you are comparing, e.g., “longer” and “shorter” when comparing length. Students need to be able to physically align two objects to determine which is longer, shorter, or if they are the same length. Students also need to be able to physically align two objects to determine which is taller, shorter, or if they are the same height. Students need to be able to physically compare the weight of two concrete objects to determine which is heavier, lighter, or if they are the same weight. Students should provide verbal descriptions about how they measured and what they determined when comparing the common measureable attribute of the objects. The classroom environment should encourage student interaction and conversation that will lead to mathematical discourse. Students should present their solutions and ideas on a regular basis.