**Essential Questions: **

**Lesson Plans and Seeds**

Lesson Plan A1: Measurable Attributes

**Download Seeds, Plans, and Resources (zip)**

Content Emphasis By Clusters in Grade PK

Progressions from Common Core State Standards in Mathematics

Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.

### Unit Overview

In this unit, Prekindergarten students participate in hands-on experiences and discussions that allow them to describe and compare measurable attributes of objects, such as length or weight. Students also directly compare two objects and tell how they are comparing. For example, students may compare two buildings made of blocks. One building may be taller (greater in height) and another may be made up of more blocks and, therefore, heavier. These conversations and comparisons help students learn to discriminate and name these measureable attributes. As they discuss these situations and compare objects using different attributes, they learn to distinguish, label, and describe several measureable attributes of a single object. This allows teachers to listen for and extend conversations about things that are “bigger” or “smaller” as well as “longer” “taller” or “shorter,” and name, discuss, and demonstrate with gestures the attribute being discussed.

**Teacher Notes:**

- Review the Progressions for K-5, Geometric Measurement at:
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.*http://commoncoretools.files.wordpress.com/2012/07/ccss_progression_gm_k5_2012_07_21.pdf* - When implementing this unit, be sure to incorporate the Enduring Understandings and Essential Questions as the foundation for your instruction, as appropriate.
- Students should engage in well-chosen, purposeful, problem-based tasks. A good mathematics problem can be defined as any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific correct solution method (Hiebert et al., 1997). A good mathematics problem will have multiple entry points and require students to make sense of the mathematics. It should also foster the development of efficient computations strategies as well as require justifications or explanations for answers and methods.
- Some key areas of focus for measurement development that should occur in the elementary grades include:
- Helping students understand the attribute being measured.
- Developing and understanding of how measuring tools work.
- Assisting students in developing personal benchmarks and the ability to use estimation of measures to prevent errors and to build conceptual understanding of measurement (measurement sense).
- Building a foundation of measurement understanding for students that will eventually allow them to participate in the development of some standard formulas beginning in the Intermediate grades, and to use these formulas on a regular basis.

- Estimation in measurement is important in building measurement sense, or conceptual knowledge of measurement. Estimations helps build familiarity with the units being measured. It is also an enjoyable, real-world element in the process of learning about measurement.
- Students should be provided with a wide variety of meaningful measuring experiences throughout the school year. The concepts in this Unit should not be taught in isolation. It is imperative that students’ experiences with measurement are enhanced by conversations with peers and teachers in order to facilitate understanding.
- Jean Piaget describes conservation of length as knowing that even if an object changes its shape, the length is the same (for example, a piece of string is balled up). Piaget and his colleagues concluded that most children become conservers of length and area between the ages of 7 and 9. Recent researchers have reported that with careful questioning, some children display the ability to conserve at an earlier age; this required participating in and reflecting on measurement activities.

**Enduring Understandings: **

- Objects have distinct attributes that can be measured.
- Measurement is the process of assigning a number to a magnitude of some attribute shared by some class of objects, such as length, relative to a unit.
- Standard units provide common language for communication about measurements.
- The choice of measurement tools depends on the measurable attribute and the degree of precision desired.
- Measurement instruments are tools or devices that help determine accurate measurements.

**Focus Standards **

*(Listed as Examples of Opportunities for In-Depth Focus in the PARCC Content Framework documents for Grades 3-8):*:**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.C.8**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).

**Possible Student Outcomes: **

The student will:

- 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.
- Build measurement sense through the use of hands-on activities that involve estimation, as well as through classroom discussions.

**Evidence of Student Learning: **

**Fluency Expectations and Examples of Culminating Standards:**

**Common Misconceptions: **

- Predicting that the larger the object, the more it weighs. Likewise, assuming that the smaller an object it is, the less it weighs. For example, the views a large stuffed animal and a cantaloupe. The student predicts that the stuffed animal is heavier than the cantaloupe based on their relative sizes. This is why repeated experiences, coupled with estimating the weight or size of an object before measuring is crucial to developing measurement sense.
- Misusing terms such as ‘bigger, smaller, taller, shorter, heavier, and lighter’. Students often incorrectly hold undifferentiated views of measurable attributes, saying that one objects is ‘bigger’ than another when in fact it is longer, or greater in area, or greater in volume, and so forth.
- Counting units incorrectly when measuring a object.
- Using units of different sizes when measuring.

**Interdisciplinary Connections:** *Interdisciplinary connections fall into a number of related categories:*

*Literacy standards within the Maryland Common Core State Curriculum*

*Science, Technology, Engineering, and Mathematics standards*

*Instructional connections to mathematics that will be established by local school systems, and will reflect their specific grade-level coursework in other content areas, such as English language arts, reading, science, social studies, world languages, physical education, and fine arts, among others.*

**Sample Assessment Items: ***The items included in this component will be aligned to the standards in the unit and will include:*

*Items purchased from vendors*

*PARCC prototype items*

*PARCC public released items*

*Maryland Public release items*

*Formative Assessment*

**Interventions/Enrichments: ** *(Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)*

**Vocabulary/Terminology/Concepts: ** *This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.*

*Part I – Focus Cluster:*

** absolute descriptors: ** characteristics of objects and shapes that are common among them and used for comparison. Examples: length, height, and weight

**positional relationships: **comparing objects or shapes by their placement to each other. Descriptive words would include above, below, next to, in front of, behind, near, far, beside, etc.

*Part II – Instructional Connections outside the Focus Cluster*

** congruent:** having the same size and shape, but not necessarily the same orientation. All corresponding parts of congruent figures have the same measure

Example:

** similar:** a mat used to organize concrete materials to make sense of a problem.

Example:

** examples and non-examples of shapes: ** Examples are polygons that are all the same shape but may be different sizes and orientations, while non-examples are shapes that are different from the type named.

**Resources:**

**Free Resources: **

- http://wps.ablongman.com/ab_vandewalle_math_6/0,12312,3547876-,00.html Reproducible blackline masters
- http://lrt.ednet.ns.ca/PD/BLM_Ess11/table_of_contents.htm mathematics blackline masters
- http://yourtherapysource.com/freestuff.html Simple activities to encourage physical activity in the classroom
- http://www.mathsolutions.com/index.cfm?page=wp9&crid=56 Free lesson plan ideas for different grade levels
- http://sci.tamucc.edu/~eyoung/literature.html links to mathematics-related children’s literature
- http://www.nctm.org/ National Council of Teachers of Mathematics
- www.k-5mathteachingresources.com Extensive collection of free resources, math games, and hands-on math activities aligned with the Common Core State Standards for Mathematics
- http://elementarymath.cmswiki.wikispaces.net/Standards+for+Mathematical+Practice Common Core Mathematical Practices in Spanish
- http://mathwire.com/ Mathematics games, activities, and resources for different grade levels
- http://www.pbs.org/teachers/math/interactive online and offline lesson plans to engage students. Database is searchable by grade level and content
- http://www.k8accesscenter.org/training_resources/MathWebResources.asp valuable resource including a large annotated list of free web-based math tools and activities.
- http://www.cast.org/udl/index.html Universal Design for Learning

### Math Related Literature:

- Lioni. L.
__Inch by Inch__.

Notes: An inchworm is proud of his ability to measure anything under the sun. - Hoban, T.
__Is it Larger? Is it Smaller?__.

Notes: Photographs show large and small leaves, pigs, fish, bowls, beads, tea sets, boats, balls, dolls, snowmen, cars, shoes, and toys. - Reed, Margarette S. The Button Box.

Notes: An little boy explores the many pleasures that can be found in--and made from--his grandmother's button box.

### References:

- ------. 2000.
*Principles and Standards for School Mathematics*. Reston, VA: National Council of Teachers of Mathematics. - Arizona Department of Education. “Arizona Academic content Standards.” Web. 28 June 2010
__http://www.azed.gov/standards-practices/common-standards/__ - Bamberger, H.J., Oberdorf, C., Schultz-Ferrell, K. (2010).
*Math Misconceptions: From Misunderstanding to Deep Understanding.* - Burns, M. (2007 )
*About Teaching Mathematics: A K-8 Resource.*

http://larremoreteachertips.blogspot.com/2012/01/using-ten-frames.html - Christinson, J., Wiggs, M.D., Lassiter, C.J., & Cook, L. (2012)
*Navigating the Mathematics Common Core State Standards. Englewood, CO: Lead, Learn Press.* - Copley, J. (2010).
*The Young Child and Mathematics.*Reston, VA: National Council of Teachers of Mathematics. - Gelman, R., & C.R. Gallistel. 1987.
*The child’s understanding of number.*Cambridge, MA: Harvard University Press. - North Carolina Department of Public Instruction. Web. February 2012. North Carolina Department of Public Instruction. Web. February 2012 http://www.ncpublicschools.org/acre/standards/common-core-tools/#unmath
- Piaget, J., B. Inhelder.[1941] 1974.
*The child’s construction of quantities: Conservation and atomism.*Translated by A.J. Pomerans. London: Routledge & Kegan Paul. - Progressions for the Common Core State Standards in Mathematics (draft). Web. June 2012. K-5, Geometric Measurement. http://commoncoretools.files.wordpress.com/2012/07/ccss_progression_gm_k5_2012_07_21.pdf
- Van de Walle, J. A., Lovin, J. H. (2006).
*Teaching Student-Centered mathematics, Grades K-3.*Boston, MASS: Pearson Education, Inc.