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Gr. PK Unit PK.NBT.A.1: Work with 0-10 to gain foundations for place value

Essential Questions:

How do I determine the most efficient way to represent a number (pictorial, symbolic, with objects) for a given situation?

In what ways can numbers be composed and decomposed?

In what ways can items be grouped together to make counting them easier?

How does the position of a digit in a number affect its value?

How are place value patterns repeated in numbers?

How does using the base ten system make it easier for me to count?

How does the place value system work?

Lesson Plans and Seeds

Lesson Plan A.1-2: MEASURABLE ATTRIBUTES

Lesson Seed A.1-2: BUBBLES

Lesson Seed A.2: DRESS UP

Download Seeds, Plans, and Resources (zip)

Unit Overview

Content Emphasis By Clusters in Grade PK

Progressions from Common Core State Standards in Mathematics

Send Feedback to MSDE’s Mathematics Team

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, students investigate the beginning foundations of place value by exploring the relationship between ten ones and ten through real-quantity representations that fit their world (e.g. 10 pennies in a dime, ten fingers on each hand and ten toes on each foot, ten acorns collected on a walk, etc.). In order to begin constructing an understanding of base-ten concepts and procedures, it is important that students have a variety of experiences in counting quantities of objects in several different ways, followed by opportunities to discuss their mathematical thinking with their peers. It is also important to note that students’ work in the base-ten system is intertwined with their work on counting and cardinality.

Teacher Notes:

Review the Progressions for Grades K-5, Number and Operations in Base Ten at: http://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf to see the development of the understanding of number and operations as stated by the Common Core Standards Writing Team, which is also the guiding information for the PARCC Assessment development.
When implementing this unit, be sure to incorporate the Enduring Understandings and Essential Questions as the foundation for your instruction, as appropriate.
Since students at this age come to their development of base-ten concepts with a count-by-ones idea of number, teachers must begin there. In Prekindergarten, the goal is to gain an initial foundation for place value. Using five, and then ten as a benchmark should be encouraged. Students at this age should not be asked to explain that the 1 in 10 represents “one ten”. Their exploration of the relationship between ones and ten in Prekindergarten and Kindergarten leads to this understanding in Grade 1.
Students investigate the relationship between ten ones and ten by building the number concretely. This allows them to more easily make initial sense of foundations of the place-value system. In Prekindergarten, students should use multiple models to develop initial understandings of place value and the base-ten number system. This includes the use of real world objects as well as groupable base ten models (e.g., fingers, toes, groups of objects found in the classroom, at home, or in nature, Digi-Blocks, snap cubes, pennies, etc.). Groupable models most clearly reflect the relationships of ones and tens, for which the ten can actually be made or grouped from ones. Pre-grouped base ten models, such as base ten blocks, are not recommended for Prekindergarten students.
Playing games that relate to real-life situations can help students build their knowledge of place value and enrich their number sense. It is Important students build conceptual understanding prior to working with basic algorithms, whose representations rely on a place-value foundation.
It is important to add estimation to grouping activities when working with place value so that students think about total quantities.
Teachers should strive to create a classroom environment in which students are encouraged to freely share their thinking about number and quantity.

Enduring Understandings:

There are many ways to represent a number.
Numbers can be composed and decomposed in a variety of ways
Items can be grouped together to make them easier to count.
Place value is based on groups of ten (10 ones = 10; 10 tens = 100).
The digits in each place represent amounts of tens, or ones (e.g. 18 is 1 group of ten + 8 ones).
There are patterns to the way numbers are formed. For example, in the teen numbers, the one remains fixed and the units change.

Focus Standards

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

PK.CC.b.4 Understand the relationship between numbers and quantities to 5, then to 10; connect counting and cardinality
PK.NBT.A.1 Work with numbers 0-10 to gain foundations for place value.

Possible Student Outcomes:

The student will:

Investigate the relationship between ten ones and ten.
Gain an understanding that the numbers 0-10 are composed of zero, one, two, three, four, five, six, seven, eight, nine, or ten ones.
Explore and represent numbers 0-10 using representations, such as manipulatives or drawings. Using groupable models such as Digi-Blocks, snap cubes, or connecting cubes allows students to clearly reflect the relationships of ones and tens.
Construct the concept of place value through exploration and discussion rather than having the concept of place value shown to or told to them.

Evidence of Student Learning:

Fluency Expectations and Examples of Culminating Standards:

No fluency recommendations are included for Prekindergarten.

Common Misconceptions:

Inadequate part-part-total knowledge for the numbers 0 to 10 and/or an inability to trust the count.
Little or no sense of numbers beyond 5.
Lack of one-to-one correspondence.
Zero is not a number.

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:

verbal counting: : counting while aligning each number said to an object, picture, etc. in order to solve a problem.

cardinality: is the understanding that when counting a set, the last number represents the total number of objects in the set

Example: This is a set of 3 stars.

one-to-one correspondence: linking a single number name with one object--and only one--at a time

subitizing : the ability to recognize the total number of objects or shapes in a set without counting. Example: Recognizing that this face of a cube has five dots without counting them.

decomposition: breaking a number into two or more parts to make it easier with which to work. Example: When combining a set of 5 and a set of 8, a student might decompose 8 into a set of 3 and a set of 5, making it easier to see that the two sets of 5 make 10 and then there are 3 more for a total of 13.

Decompose the number 4; 4 = 1+3; 4 = 3+1; 4 = 2+2

Beginning in Grade 3: Decompose the number ⅗ ;⅗ = ⅕ + ⅕ +⅕

Part II – Instructional Connections outside the Focus Cluster

rote counting: reciting numbers in order from memory without aligning them to objects, pictures, etc.

Part-Part-Total Mat: a mat used to organize concrete materials to make sense of a problem.

Examples:

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://illuminations.nctm.org/activitydetail.aspx?id=75 activity that reinforces counting and place value with ten frames
https://www.yourtherapysource.com/freestuff.html Simple activities to encourage physical activity in the classroom
https://mathsolutions.com/classroom-lessons/?crid=56 Free lesson plan ideas for different grade levels
https://www.digiblock.com/ Lesson plans for using Digi-Blocks
https://www.nctm.org/ National Council of Teachers of 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
https://www.nctm.org/standards/mathcommoncore/ Math Common Core Coalition
https://mathstory.com/mathstory.com/multimediapage/multimediapage.html Songs for learners of all ages.
https://www.illustrativemathematics.org/ Tasks that align with the MD CCSS.
https://www.brighthubeducation.com/preschool-crafts-activities/64559-physical-fitness-theme-and-activities-for-preschoolers/ Fitness fun ideas for young learners.
https://www.the-best-childrens-books.org/10-Little-Rubber-Ducks.html Activity to go with Ten Little Rubber Ducks.

Math Related Literature:

Carle, Eric. Ten Little Rubber Ducks.
Notes: This story is based on an actual cargo ship accident that set 29,000 plastic ducks, turtles and frogs adrift in the ocean. The book focuses on ten ducks that went adrift.
Dee, Ruby. Two Ways to Count to Ten: A Liberian Folktale.
Notes: King Leopard plans a contest; the winner is to be named a prince and marry his daughter.Contestants must throw Leopard's spear up in the air and count to ten before it comes to earth again.
Feelings, Tom. Moja Means One: Swahili Counting Book.
Notes: This book is the winner of numerous awards. Readers learn to count to ten as well as learn how to pronounce Kiswahili numbers.
Fox, Mem. Ten Little Fingers and Ten Little Toes.
Notes: Simple picture book with rhyming text that can be used to reinforce the concept of ten through pictures of babies’ fingers and toes.
Grossman, Bill. My Little Sister Ate One Hare.
Notes: A hungry little sister eats everything from one hare to ten peas.
Murphy, Stuart J. Double the Ducks.
Notes: Count down from ten to one while learning that every kind of truck has an important job.
Sloat, Terry. From One to One Hundred.
Notes: Students first count by 1s from 1-10, and then by 10s from 10-100. They can also count the objects listed at the bottom of each page along with the teacher.
Ward, Jennifer. Over in the Garden.
Notes: This is a lively one to ten counting book is set in a garden.

References:

------. 2000. Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
------. 2006. Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics: A Quest for Coherence. 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.
Chalk Talk: Teaching Ideas and Tips for Early Childhood Teachers. Web. January, 2012.
http://larremoreteachertips.blogspot.com/2012/01/using-ten-frames.html
Clements, D. “Subitizing. What is it? Why Teach it?” Teaching Children Mathematics. March 1999: 400-05. Print.
The Common Core Standards Writing Team (12 August 2011). Progressions for the Common Core State Standards in Mathematics (draft), accessed at:http://commoncoretools.files.wordpress.com/2011/08/ccss_progression_nf_35_2011_08_12.pdf
Copley, J. (2010). The Young Child and Mathematics. Reston, VA: National Council of Teachers of Mathematics.
Sullivan, P, & Lilburn, P. (2002). Good Questions for Math Teaching: Why Ask Them and What to Ask, K-6. Sausalito, CA: Math Solutions Publications.
Tennessee Early Grades Math Toolkit. Web. 2012. http://www.readtennessee.org/math/teachers/teachers_mathematics_toolkit/integrating_mathematics_throughout_the_daily_curriculum.aspx
Thompson, C.S. 1990. “Place Value and Larger Numbers.” In Mathematics for the Young Child, edited by J.N. Payne, 89-108. Reston, VA: National Council of Teachers of Mathematics.
Van de Walle, J. A., Lovin, J. H. (2006). Teaching Student-Centered mathematics, Grades K-3. Boston, MASS: Pearson Education, Inc.

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Last Updated 7/21/2019 10:20 PM