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There are 5 domains of Kindergarten Math standards including: Counting and Cardinality, Operations and Algebraic Thinking, Numbers and Operations in Base Ten, Measurement and Data, and Geometry.

Within these domains, students use numbers including written numbers to represent quantities and to solve quantitative problems such as: counting objects in a set, counting out a given number of objects, comparing sets or written numbers, and modeling simple joining and separating situations with sets of objects and eventually with written equations (students should see written equations and student writing of equations is encouraged). Students choose, combine, and apply effective strategies for answering quantitative questions.

Students also describe their physical world using geometric ideas (shape, orientation, spatial relations) and vocabulary. They identify, name, and describe basic two-dimensional shapes (such as squares, triangles, circles, rectangles, and hexagons) and three-dimensional shapes (such as cubes, cones, cylinders, and spheres), presented in a variety of ways. Students use these basic shapes to model objects in their environment and to create more complex shapes.

What’s Inside?Pg. 2-5: Standards and MaterialsPg. 6: Concrete to AbstractPg. 6: TechnologyPg. 7: Mathematical PracticesPg. 8: Classroom LayoutPg. 9-10 Materials ListPg. 11: References

Kindergarten Math!

Domains of CCSSDear Parents and Teachers of the PTA,

I would like to thank you for the $1,500 you provided for the Kindergarten math program! Math instruction is very important and providing the foundations for math skills and ideas in Kindergarten is particularly important. Young students developmentally need hands-on materials to understand, perform, and explain or show their thinking and understanding of the math skills and ideas within the Common Core State Standards (CCSS). Especially in Kindergarten, the use of manipulatives is most effective in math instruction as most of their learning is hands-on, which helps to make the meaning more solid. Students practice many ways of using these materials to make their learning concrete especially when learning about abstract concepts such as addition and subtraction.

I have provided you with a report of what the Kindergarten CCSS are, the materials (manipulatives, books, and technology) I purchased with your generous funds, and how students will use these materials to learn and have fun with math!

Sincerely,Ms. Bockel

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Counting and Cardinality (K.CC)

Know number names and the count sequence:1) Count to 100 (by 1s and 10s).2) Count forward from a given number other than 1.3) Represent a number of objects with a written number from 0-20.

What are the materials? Manipulatives : hundred poster chart, number chart dry erase boards, craft sticks, chain links,

white boards, expo markers, unifix cubes, 2-color counters, bear counters, bean counters. Books : “Let’s Count to 100!” – shows students a pictorial of objects counted to 100.

How do we learn with them?The hundred poster chart would be used as a reference to practice counting to 100 by 1s and

10s all together as a class. Students have individual number chart dry erase boards for their own use and practice. Students can circle numbers 10, 20, 30… up to 100 to visually see the numbers and practice skip counting. These charts also help students count forward from a number other than 1 because they can see the numbers in front of them and if given a number to start from, they can find that number on the chart and count up from there. Students would group together objects into groups of 10 (craft sticks, chain links, unifix cubes) to have a concrete material to count by 10s by. Students would start here and then work their way to the more abstract counting of numbers on the chart.

Students could use unifix cubes and a variety of counters (2-color, bear, and bean) to practice counting with concrete objects and representing the number counted in written form from 0-20. They would use white boards and markers to practice writing their numbers 0-20.

Count to tell the number of objects:4) Understand the relationship between numbers and quantities

(counting and cardinality). a. Say the number names in order, pairing each object with 1

number name and each number name with 1 object.b. Understand the last number name tells the number of objects counted. The number of

objects stays the same- arrangement and order counted doesn’t matter. c. Understand each succeeding number name refers to a quantity 1 larger.

5) Count to answer “how many” for as many as 20 objects organized different ways (in a line, rectangular array, circle); given a number from 1-20, count out that many objects.

Compare numbers:6) Identify if the number of objects in 1 group as more than, less than,

or the same as the number of objects in other group (by counting and matching).

7) Compare 2 written numbers between 1 and 10.

What are the materials? Manipulatives : unifix cubes, 2-color counters, bear counters, bean

counters, chain links. Books : “Ten Black Dots,” “The M&Ms Counting Book,” “From 1 to 10,” “Teddy Bear Counting,”

“Math for all Seasons,” “The King’s Commissioners”

How do we learn with them?

Standards and

Materials

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Students would use the variety of concrete materials to learn how to count the number of objects by saying the number names in order and pairing each object with 1 number name and each number name with 1 object. According to the mathematical variability theory, to learn numbers, students need to see and learn it in various ways (Young). Students would practice counting different objects arranged in a variety of ways to gain understanding of number sense and cardinality – the last number name tells the number of objects counted, the number of objects stays the same regardless of the arrangement, and the succeeding number name is 1 quantity larger. We would move from concrete to pictorial and abstract learning by counting pictures of these objects on paper and representing them with a written numeral.

Students would use these materials for counting and matching strategies to compare 2 groups to see if the groups have more than, less than, or the same number of objects. They can pair red and yellow counters and if for every red counter there is a yellow counter, they can see that the 2 groups have the same number (1-to-1 correspondence). To test if students are at the preoperational or concrete operational stages of Jean Piaget’s cognitive development stages, I can spread out one color group of counters (Young). If they are able to tell me that there are still the same number of counters in the yellow and red counter groups even though one group is longer in length/takes up more space, that would tell me that they can conserve number and are in concrete operational. Eventually students can abstractly compare 2 written numbers.

Operations and Algebraic Thinking (K.0A)

Understand addition as putting together and adding to; subtraction has taking apart and taking from:1) Represent addition and subtraction in various ways (with objects, fingers, mental images,

drawings, sounds, acting out, verbal explanations, expressions, or equations).2) Solve addition and subtraction word problems;

add/subtract within 10 (use drawings/objects).3) Decompose numbers within 10 into pairs in more than

1 way (drawings/objects); record decompositions (drawing/equation).

4) Find the number that makes 10 when added to a given number 1-9 (use drawings/objects); record answer (drawing/equation).

5) Fluently add and subtract within 5.

What are the materials? Manipulatives : Hundred poster chart, number chart dry erase boards, chain links, white boards,

expo markers, unifix cubes, 2-color counters, bear counters, bean counters, dominoes, 10-frame dry erase cards, dice.

Books : “Math for All Seasons,” “The King’s Commissioners,” “Mission Addition,” “Subtraction Action”

How do we learn with them? Students would perform addition and subtraction by modeling situations with a variety of sets of

objects (concrete) then eventually with written equations (pictorial and abstract). 2 different colors of the same object would be used so that students can easily see the 2 numbers they are putting together or taking apart. To model 2 + 3 = 5 students put 2 blue unifix cubes together with 3 red unifix cubes for 5 unifix cubes altogether. To show their thinking abstractly, students record their steps with written numbers and eventually symbols (+, –, =). This is done pictorially with pictures of their manipulatives.

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Students can practice counting forward from a number other than 1 (K.CC 2) by “counting on” with unifix cubes – when adding 2 + 3 they’d say “2” then “3, 4, 5” and can clap this out too.

Students would use 10-frame cards and 2-color counters to find the number that makes 10. If students are given the number 6, 6 yellow counters are placed on the frame and students fill the rest of the frame with red counters to find they need 4 more to make 10. These frames are dry erase so students can practice this skill pictorially by drawing counters.

For more practice with pictorial and abstract learning students would use white boards and markers to record their answers with drawings and equations. Addition could be done pictorially with dominoes where the dots on each side are added (helps to see turnaround facts – different order of the numbers added together gives the same answer). The hundred poster chart and number chart dry erase boards can be used to count up (add) and count back (subtract) for abstract practice.

Number and Operations in Base Ten (K.NBT)

Gain foundations for place value by working with numbers 11-19:1) Compose and decompose numbers 11-19 into 10s and 1s (use

drawings and objects); record compositions and decompositions (drawing/equation).

What are the materials? Manipulatives : Craft sticks and rubber bands, chain links, unfix

cubes, 10 frame cards and 2-color counters. Books : “The King’s Commissioners”

How do we learn with them? Students would use craft sticks, chain links, and unifix cubes to count and form a group of 10

objects to represent “tens” and singles of these objects to represent the “ones” when given a number to compose or decompose. If I gave them the number 18, students would group 10 craft sticks together with a rubber band to show the “tens” and count out 8 single sticks to show the “ones.” 10 frames could also be used by filling up the 10 frame with red counters and counting out the “ones” place on the side of the frame with yellow counters. Students could represent this abstractly at the same time with written numbers 10 + 8 to show their work and would eventually move away from manipulatives to show their work with drawings of ten objects in the “tens” place and some ones in the “ones” place.

Measurement and Data (K.MD)

Describe and compare measureable attributes:1) Describe measurable attributes of objects (such as length/weight). 2) Compare and describe 2 objects with a measureable attribute in

common to see which has “more/less of” the attribute. Classify objects and count the number of objects in each category:

3) Classify objects into given categories; count the objects in each; sort the categories by count.

What are the materials? Manipulatives : Chain links, bear counters, assorted small buttons, aquatic counters, attribute

blocks, sorting trays.

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How do we learn with them?All of the objects come in different colors; bear counters, buttons, and attribute blocks come in

different sizes; and attribute blocks come in different sizes and thickness. Students will sort the variety of manipulatives into the sorting trays based on similar attributes (length, size, color, shape) and compare and describe the attributes of the objects. They will count the number of objects in categories and compare categories or objects to see which category or object has more/less of the attribute.

Geometry (K.G)

Identify & describe shapes (square, circle, triangle, rectangle, hexagon, cube, cone, cylinder, sphere):1) Describe objects in the environment using names of shapes;

describe relative positions (above, below, beside, etc.). 2) Correctly name shapes regardless of orientation and size. 3) Identity shapes as two- or three-dimensional.

Analyze, compare, create, and compose shapes:4) Analyze and compare two- and three-dimensional shapes (in

different orientations/sizes); describe similarities, differences, parts, and other attributes.

5) Model shapes in the world by building and drawing shapes.6) Put together simple shapes to form larger shapes (2 triangles make a

rectangle).

What are the materials? Manipulatives : Attribute blocks, pattern blocks (2-D shapes), pattern

block picture cards, geo boards and rubber bands, wooden geo solids (large 3-D shapes) and geo blocks (small 3-D shapes).

Books : “The Greedy Triangle,” “A Cloak for the Dreamer,” “Sea Shapes,” “Windows, Rings, and Grapes: A Look at Different Shapes.”

How do we learn with them? For students to practice correctly naming and identifying shapes as 2-D and 3-D we would

explore and play games with pattern blocks, geo solids, and geo blocks for student use. We would sing fun shape songs and watch shape videos to help students remember the names and describe attributes of shapes (sides, corners, faces, 2 or 3D).We would explore shapes with geo boards and play games where I’d show students a picture card of a shape and they’d mimic that shape with the rubber bands on their boards. “Fill the hexagon” is a game where students use the pattern blocks to fill the hexagon in different ways – with 1 hexagon, 2 trapezoids, 6 triangles, etc., allowing students to name shapes and practice putting together simple shapes to form larger shapes. Pattern block picture cards are a fun way to help students use 2-D shapes to make pictures out of shapes such as cats, boats, and rocket ships.

For pictorial learning, reading shape books and doing art projects with paper shapes helps students to describe and model objects in the environment using the names of shapes, such as a skyscraper as a rectangle. We would move from using manipulatives to using pattern blocks in paper form to explore the geometry concepts pictorially so students can get used to seeing shapes on paper and still be able to correctly name and describe them. Moving

from

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Concrete: Students engage in math with a variety of objects. Young students developmentally need hands-on materials to understand, perform, and explain/show their thinking and understanding of math concepts. It helps to make the meaning more solid especially when learning about abstract concepts such as addition and subtraction.

Pictorial: Students engage in math with a graphic representation of objects. Students perform skills and show understanding of math concepts with a picture of concrete materials. They also draw materials such as cubes to represent unifix cubes.

Abstract: Students engage in math with written numerals and symbols (+,-,=). Abstract work and thinking can be done alongside concrete and pictorial math then students work their work their way to being able to do math without pictures or objects.

Concrete Pictorial Abstract

1 + 5 = 6

2 + 4 = 6

3 + 3 = 6

Document Camera: This would be used to model the use of manipulatives such as modeling the use of unifix cubes to perform addition and subtraction problems.Video Projector: This would be used to show academic videos related to the content of the standards and instruction. In Geometry students would watch fun educational videos to help them remember the names and attributes of 2D and 3D shapes.

DreamBox and Computers: DreamBox is a Prek-8 math online program aligned to the Math CCSS. The game keeps track of the students’ progress and moves students forward as they progress. This would be used during free time to for a fun way to get extra practice with the math concepts we learn.

The 8 Standards for Mathematical Practice describe important skills (“processes and proficiencies”) that math educators at all levels should seek to develop in their students.

Technology in the Mathematical Practices

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1: Make sense of problems and persevere in solving them. Before students start working on a problem, they first make sense of what it’s asking then think of entry points to solving it. When given an addition problem, students might first think “how many bears am I putting together to find how many bears there are altogether?” then might think “I need to get 2 different colors to show the 2 different numbers I’m adding.”

2: Reason abstractly and quantitatively. Young students mostly reason/show their thinking with concrete materials. Once they show understanding of concepts, we can move to reasoning abstractly with use of materials with written numerals and symbols so that students understand how using manipulatives relate to actual math problems.

3: Construct viable arguments and critique the reasoning of others. Students justify their actions by explaining their actions and thinking as they solve problems. Students can use words (math language), pictures, or objects to explain/show their thinking.

4: Model with mathematics. Students can use the math they know to solve problems in everyday life. Teachers can help students develop and solve addition and subtraction problems that describe a real-life situation, such as adding apples at the grocery store.

5: Use appropriate tools strategically. Teachers help students choose strategies and materials that would be most appropriate for the content or problem being solved and help them to understand why these tools are more useful. When adding 5 + 3 it would be more useful to start at 5 and count on 6, 7, 8 rather than start counting from 1.

6: Attend to precision. Students give careful and clear explanations in discussion with others and in their own reasoning. When explaining/showing their thinking, students try to keep their steps in order and explain their thinking clearly.

7: Look for and make use of structure. Students look for patterns to identify more efficient strategies for solution. Young students might see that 5 plus 3 more is the same amount as 3 plus 5 more. They might see patterns when sorting objects into categories according to attributes.

8: Look for and express regularity in repeated reasoning. Students make connections and notice if patterns are repeated and look for shortcuts. Teachers look out for these “noticings” and share them with the class so other students can gain strategies.

Storing Materials: Materials will be stored in either the shelves in the classroom or in the upper cabinets (storage). The materials needed for the unit, week, or month will be stored in the shelves around the classroom and the extra materials or

Classroom

Layout

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materials not needed at the moment will be stored in the classroom’s upper cabinets.

Managing Materials: I will mostly be in charge of distributing materials needed for that day’s instruction. However depending on the lesson and the material (how heavy it is, etc.), students may demonstrate responsibility by getting the needed material for their group.

Manipulatives Standards Quantity Cost (in dollars)

Page #

Hundred Poster Chart

Number Chart Dry Erase Boards

K.CC 1, 2,K.OA 1-5

1 poster

1 pkg. of 30

10.95

24.95

17-18

Craft Sticks (Rubber bands not included)

K.CC 1K.NBT 1

3 boxes of 1,000 (2,000) 11.85 26

Chain Links K.CC 1 ,4a-c, 5, 6-7 2 pkg. of 1,000 (2,000) 44.9 26

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K.OA 1-5K.NBT 1K.MD 1-3

Double-Sided White BoardsExpo Markers

K.CC 3K.OA 1-5 practice

30 boards3 packs of 12 (36)

106.835.25

2020/95

Unifix Cubes K.CC 1, 3, 4a-c, 5, 6-7K.OA 1-5K.NBT 1

Bulk set of 3,000. 10 colors, 300 each, in container.

234.95 30

2-color counters (chips) K.CC 3, 4a-c, 5, 6-7K.OA 1-5

Pkg. of 1,000 22.5 29

Bear Counters K.CC 3, 4a-c, 5, 6-7K.OA 1-5K.MD 1-3

96 bears (4, 8, 12g. Each weight- Each weight has 8 bears each of 4 colors)

11.70 27

Bean Counters K.CC 3, 4a-c, 5, 6-7K.OA 1-5

2 pkg. of 400 (2 colors) (800) 33.5 29

Double-Nine Wooden Dominoes K.OA 1-5 Bucket of 275 14.9 4310 Frame Cards (dry erase) K.OA 1-5

K.NBT 1Pkg. of 25 9.75 73

Dice K.OA 1,2, 4 3 pkg. of 12 (36) 4.65 45Sorting Trays K.MD 1-3 25 trays 181.25 26Assorted Small Buttons K.MD 1-3 2 Container of 400 each (800) 21.9 26Aquatic Counters K.MD 1-3 4 containers of 84 (336) (6

colors each of 14 animals)49.8 28

Attribute Blocks (shapes- different width, size, color)

K.MD 1-3K.G 1-6

3 sets of 60 (180) 70.35 39

Pattern Blocks (shapes- same size)(paper form not included)

K.G 1-6 Pkg. of 250 12.25 34

Pattern Block Picture Cards K.G 1-6 Set of 20 cards 9.75 35Geo Boards andRubber Bands

K.G 1-6 Classroom 7” Set (30 double sided boards, 1 transparent board, 250 geobands)

59.95 41

Wooden Geo Solids (3-D shapes) K.G 1-6 Set of 12 different shapes 9.95 119Geo Blocks (small 3-D shapes) K.G 1-6 Set of 330 51.75 120

Books Standard Quantity Cost (in dollars)

Source/Page #

Ten Black Dots (by Donald Crew) K.CC 4a-c 1 6.99 AmazonThe M&Ms Counting Book (Barbara McGrath)

K.CC 4a-c 1 3.99 Amazon

From 1 to 10 (Richard Scarry) K.CC 4a-c 1 6.26 AmazonTeddy Bear Counting (Barbara McGrath)

K.CC 4a-c 1 7.95 Amazon

Let’s Count to 100! (Masayuki K.CCC 1 1 7.16 Amazon

Materials List

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Sebe)Math for all Seasons (Greg Tang) K.CC 4a-c

K.OA 1-51 5.95 194

The King’s Commissioners (Marilyn Burns)

K.CC 4a-cK.OA 1-5K.NBT

1 14.95 195

Mission Addition (Loreen Leedy) K.OA 1-5 1 7.54 AmazonSubtraction Action (Loreen Leedy) K.OA 1-5 1 7.52 AmazonThe Greedy Triangle (Marilyn Burns)

K.G 2-4 1 5.95 195

A Cloak for the Dreamer (Marilyn Burns)

K.G 2-4 1 14.95 195

Sea Shapes (Suse MacDonald) K.G 1-4 1 6.75 196Windows, Rings, and Grapes: A Look at Different Shapes (Brian Cleary)

K.G 1-4 1 6.88 Amazon

Total Cost: $1496.66 (including technology)

* Technology purchased: DreamBox math game

$12.5 per student/year (reduced rate for school district) = $312.5 (25 students) Video Projector: &47.75 (Amazon – UC28 Pro HDMI Mini Home LED Projector)

* Technology have access to: Few computers ACTIV Board Document camera Overhead Projector TV/VCR/DVD player

References

OSPI. "Mathematics Common Core State Standards." OSPI. Web. 24 Nov. 2014.

<http://www.k12.wa.us/Mathematics/Standards.aspx>.

"Outline Your Classroom Floor Plan." Classroom Architect. ALTEC, 2000-2008. Web. 24 Nov.

2014. <http://classroom.4teachers.org/>.

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Van De Walle, John A., Karen S. Karp, and Jennifer M. Bay-Williams. "Developing Early Number

Concepts and Number Sense." Elementary and Middle School Mathematics: Teaching

Developmentally. 8th ed. Pearson, 2013. Print.

Young, Sharon. "How Do Children Learn to Make Sense of Numbers?" EDMA 3000: Math

Methods 1. Seattle Pacific University, Seattle. 30 Sept. 2014. Lecture.

Young, Sharon. "Strategies for Memorizing Basic Addition and Subtraction Facts." EDMA 3000:

Math Methods 1. Seattle Pacific University, Seattle. 7 Oct. 2014. Lecture.