Common Core

Helping Early Learners Conquer Those Pesky Vowels

When young children have mastered the alphabet letter names and know more than half of the letter sounds, hooray! But with that sigh of relief comes the reteaching and reteaching of those pesky vowels!

Vowels are most easily mastered if the reteaching is thorough and strategic. To begin this strategic teaching, review the alphabet letter that represents the vowel and the sound-card that you are using in your classroom or homeschool setting. If you don’t have defined sound-card you can check out ours in the product section below.

There are many great videos that are great and kids love them. Heidi's Songs is one of my favorites! She has been remastering all of her videos so if you think you know them, be sure to look again!


When revisiting the vowels, I recommend spending at least two days on each vowel for review. Because this is a review and all sounds have been previously introduced, be sure to talk about both the long and short sounds of the vowel.

Provide a visual and auditory (sound song) link for A E I O and U. There are many available, my favorite is Have Fun Teaching, my students LOVE it!

I also love the Talking Words Factory, kids really get the "glue" concept that is presented in this video.

 

Be sure to add further supports. Using hand cues to teach short vowel sounds adds a kinesthetic link. Teach your students these signs as each vowel is reviewed, then continue to use this cues as vowels are continually reviewed (I love how these signs actually match the mouth formation we will discuss below). 

Teach children the linguistic characteristics of these vowels. I found that even though I was scared to take linguistics as an undergrad, and then terrified of advanced linguistics as part of my masters program, I loved these courses! I found the knowledge I gained to be crucial in regards to the effective teaching of reading. Here are the characteristics that one must know to better teach those pesky vowels.


The /a/ sound /æ/

The vowel is a jaw vowel made with the voice on. (Have students feel the sound made by touching their throat).

 

 

 

 

 

 

The /e/ sound /ɛ/

This vowel is a tongue vowel (it rises ever so slightly) made with the voice on. (Have students feel their mouth widen and tongue lift as they feel the sound made in their throat).

*The /a/ and /e/ are often confused by young children. Calling attention to tongue placement helps demonstrate differences.

 

 

The /i/ sound /ɪ/

This vowel is a tongue vowel (it rises ever so slightly) made with the voice on. (Have students feel the sound made by touching their throat and feel the tongue placement).

 

 

 

 

 

The /o/ sound /ɔ/

This vowel sound is a jaw vowel made with the voice on. (Have students feel the sound made by touching their throat and place hand under chin to feel the jaw drop).

 

 

 

 

 

 

The u sound /ʌ/

This vowel sound is a jaw vowel made with the voice on. (Have students feel the sound made by touching their throat, call attention to the differences between the o and u jaw placements).

 

 

 

 

 


Using mouth cards and hand signals as mentioned above help children learn the correct mouth placement as they practice and practice voicing vowel sounds. The differences become clear as students feel the changes that happen within their own mouth. Make sure to pass out mirrors so students will be able to visually see the differences. 

Be patient. It takes a lot of listening and voicing practice to conquer these separate and distinct (pesky) vowel sounds. And remember that with all phonemic awareness practice, English Language Learners will get it, don't give up on them! But it will take added patience and practice as some of these sounds are not even made in their native tongue. Your patience and continued practice will pay off. As with all pre-reading skills, if added emphasis is placed on oral-phonemic practice until mastered, the transference to the written word will be very easy.

As you spend a week or two reviewing vowel sounds, you might want to check out our new vowel practice early learning essential. This packet also contains the sign language hand cards, mouth placement cards, vowel sound cards, and a vowel song poster and pocket chart cards. With the great low price of $4.00, you will be on your way to vowel sound victory.


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All Kindergarten Kiosk Products are also available on Teachers Pay Teachers!

All Kindergarten Kiosk Products are also available on Teachers Pay Teachers!

Here are some of our other great vowel practice products:

The Perfect Kindergarten and Preschool Assessments

Are you Looking for the Perfect Assessments?

I use the assessments below in my classroom. I have used and perfected these assessments for over 15 years, and I truly believe them to be the perfect kindergarten and Pre-K assessment packets. And yes, they are strategically linked to Core Standards.

A few years ago I found ESGI and it completely transformed the administration and data collection of these assessments. Before ESGI, I ran a copy of the assessments for each student, had an organized assessment binder for both math and reading, and then spent hours transferring the data to a spreadsheet that automatically color-coded the students to red, yellow and green. This took me HOURS of time! But ESGI has changed all of that, it is literally Click Click Done!

Now, I test my students on the iPad or my computer using my tried and true authentic assessments, have immediate data results and all of the tools necessary to utilize this data to improve student learning. I can even access built-in RTI and SLO data at the touch of a button.

I have partnered with ESGI and my perfect assessments are available both traditional paper or with ESGI, digitally with no extra cost to you. If you want to try ESGI using a free 60 day trial. Remember to enter the promo code B7227. You will find all of the paper assessments below already loaded on ESGI.

All of these assessments are also available on TPT.


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Measurement-Data and Common Core Standards

In addition to working with numbers, kindergarten students should also be introduced to measurement and data. As students work to meet three standards of Measurement and Data, they note measurable attributes such as length and weight, make comparisons, as well as sort and categorize information. Through exploration in these areas students gather, organize, analyze, and interpret information about the world around them.

There are some great books to get you and your students going. with my affiliate links.


STEM Center

If you haven't tried a full-blown science or in this case STEM center before, try setting up a center on measurement. Start simple with some rice and measuring cups, then build from there. Over the years I have accumulated materials from Lakeshore and others, but regular every-day measuring items for the center are easy to find.

The cornerstone for learning in kindergarten is formed by hands-on investigations. This is especially true in STEM. Touching, moving, and manipulating objects helps students gain a better understanding of mathematical concepts. 

Take measurement for example. Most workbooks adequately address length, weight, and volume, but students gain a deeper and more complete understanding of these measurable attributes when given an opportunity to measure, weigh and examine volume with measuring tools. 

Set up your area with a variety of standard and non-standard tools. Rulers, measuring tapes, craft sticks, and/or linking cubes are all effective means for measuring length. A balance and a tub of classroom objects allows students to compare objects by weight. A tub of colored macaroni and a set of measuring cups is a great way to learn more about volume.

Hands-on activities are engaging and interesting to students. “Discovering” the answer is exciting and satisfying to young learners. Whether the hands-on exploration is guided or independent, you will find that it enhances student learning.


Supporting Curriculum

Awesome resource! Thank you!
Using these this year. Thank you!
Good ideas, I haven’t tried them out yet.

The lessons vary in style and format. Many lessons can be used with small groups while others can be completed with a large group. All lessons can be adapted to support struggling students or to challenge high-achieving students. It can also be found on TPT.


For some great cross-curricular thematic fun, enjoy the measuring lessons found in our comprehensive thematic unit, Giants, Trolls and the Big Bad Wolf.


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Used it last year in May, and my students (kindergartners) loved every activity in this unit! Very engaging and fun! Planning on using it again this year. Thanks!
This was an absolute lifesaver! I used multiple products for my formal observation and was given great compliments! Thank you!!!
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Twelve Steps to Parent Reporting

Twelve Steps to Parent Reporting

Are you looking for a time saving report card option?

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Are you looking for a wide variety of already made, time-tested assessments?

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Best Ever Kindergarten Assessments

These “best selling” assessments offer both paper and digital options! 


These documents serve as organizational tools for gathering information about language arts and math strengths and weaknesses of kindergarten students. Using these assessment, you will learn more about your students and will more easily determine the focus of your instruction.

 

If using the paper version, one assessment form should be copied for each student. (I then place all of the assessments in an easy to grab binder). Due to the necessity of assessing students at regular intervals during the school year, the documents provide a space to record information for different assessment periods.

The first assessment is in a trimester format (with benchmarks provided). Following this assessment format is one that is generalized, to fit the format of varying school years.

The next pages of the assessment packets are student copies and examples of a checklist or report card that you may wish to use when reporting to parents.

If you wish to save paper and go digital, I have partnered with ESGI

You will love the ease that ESGI gives this product. I have done the work for you; all of these tests are there: click, click, done. Simply click on the test explorer tab (within ESGI) and look for my name:Kathy Crane

to find the correct tests. (Important: At the very end of the testing documents are screen shots of how to organize your tests on ESGI to correlate with the paper copy).

 Even if you are not sure whether paperless testing and data retrieval is for you, you will want to take advantage of their free 60 day trial!

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Teaching Young Children to Write and Spell Their Name & Names of Others

PicMonkey Collage.jpg

Children who are in the early stages of literacy development are well served if they are familiarized with the letters that make up their own names. This will not only provide an important link between speech and print, it will help them attend to sequencing, orientation and details within the construction of a word. Repetitive practice will not only allow students to master proper handwriting conventions, but will establish a word-meaning connection. 

I particularly love do name activities as part of the morning meeting as the classroom is being established at the beginning of the year. Using this Name chart game will also fulfill Common Core standards RF K1 and RF K.1.D. Demonstrating the understanding of print organization and features as well as recognition of alphabet letters.

To do the activity, you can prepare the cards or simply print the cards found in our name packet below.

Next, prepare a pocket chart with the selected student name on top and then one job and icon in each succeeding pocket.

Choose a different student daily or weekly. (You may want to tie this to your star student, helper, or caboose). To do the activity. Chose the student. Place the name card at the top, and another cut as a puzzle at the bottom. Complete the activities, one by one. As a name is completed, put the name and puzzle in a manilla envelope, labeled with the student’s name or picture and keep near the pocket chart for student independent practice. This is a very popular independent center!

To find the other 16 activities for teaching names, you might be interested in the complete packet.

Table of Contents:

Water Cap Names: Ordering letters in names and transferring knowledge. 

Name Puzzles: Building familiarity with alphabet letters and their function when spelling one's own name.

Name Cheer: (A variation of Name Puzzles): Identifying and sequencing the letters in names. 

Shave a Name: Using correct handwriting technique to write names.

Rainbow Names: Spelling and writing names.

The "Nameapillar": Ordering letters in names.

Trace A Name: Tracing names using correct letter formation. 

Name Fishing: Reading the names of classmates, then sorting according to beginning capital letter.

Name Dictionary: Alphabetizing classmates' names.

Names: A Guided Reading Book

Name Fun: Ten Additional Name Conquering Ideas

Name Game: Studying names of classmates

Name Chart: Studying names in a Morning Meeting routine

Mosaic Names: Spelling and writing names

Name Necklace: Spelling name

Spell-a-Name: Spelling own name and names of others.


Or purchase the product directly at our Squarespace store by clicking on the icon below.

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Play-based Teaching

I just returned from a trip to Disneyland with my family, and while the sights and sounds of the magical land were amazing, my favorite thing to do was watch the faces and reactions of my grandtots ages 3-7 as they were simply experiencing.

Because brains are built over time through the development of neural connections, you can almost see brain growth as young children experience, see, touch, taste, and hear. This brain growth will affect the architectural development that is creating the very foundation of their future brain power!

As neurons grow and connections are formed, they become more powerful and permanent. Well-used circuits become ready to access as a child learns.

So how can parents and teachers best build that necessary brain power and allow for development of well-used circuits? Not worksheets (that's for sure)! Worksheets limit the use of the brain. They typically use only the sense of seeing. Worksheets typically only have one right answer so demands limit thinking. They lead children to the thinking that there is only one way of doing, thinking, or answering. 

"Worksheets do not allow for students to experiment and/or take risks. Conversely, they dampen enthusiasm for learning. Those who can, quickly complete the task because they already know the material. Those who can’t are frustrated. Simply stated, Young children do not learn from (worksheets) what teachers and parents believe they do" (Kostelnik, Soderman, & Whiren, 1993). I would agree. Worksheets are for the adults.

So what can we do instead to teach crucial academic skills? We can provide powerful opportunities for guided play-based learning. Rather than a worksheet that asks students to circle the pictures that start with the /b/ sound, a container of objects or pictures can be provided the student to sort into piles of /b/ or other. I have watched students do this very activity with amazement as they not only complete the task, practicing the sound of /b/, but they talk about the objects with each other to expand their learning and vocabulary. 

Because I want my students to “experience” in my classroom, I have a myriad of guided lessons that teach core-standards in a playful way. After participating in a guided lesson, the lessons can then be used as independent centers for continued practice through play. The homework I send home mirrors those lessons. I do not want parents to falsely believe that worksheets are the best way for their child to learn, so I limit the amount I send home to about zero. 

The following lesson “Teddy Bears" is an example of such a guided play activity.


Teddy Bears

Objective: Solving story problems.

Common Core K.OA.2: Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Materials: Copy on tag two sets of card backs and then the story cards on the opposite side; laminate and cut apart. Gather a set of teddy bear counters and a bowl, box, or small container for each student. If using paper teddy bear counters, after cutting the bear counters apart, place each set in a bowl or some kind of container. If you are having students write the equations, provide pencils and blank sheets of paper.*


Seat students at a table and give each a bowl or container with a set of real or paper teddy bear counters. Keep the story cards in front of you. Place the story card, 3+2 at the top of the stack for demonstration of the lesson.

Teddy Bears love to play and have adventures. Today we will listen to stories about some teddy bears.  We will use the teddy bear counters to act out the stories.

Let’s begin. Read the 3 + 2 bear card. Three bears sat in the pool. Lay three bears in front of you. Two more bears joined them in the pool. Count out two more bears. How many bears are now all together in the pool? Count all of your bears. Three bears and two bears make five bears. Allow students opportunity to swim the bears around the pool.

Now, put your bears back in your (container). Listen to this story. Draw another card and repeat the process.

Continue reading cards and acting out the problems. Make up additional stories if you complete all story cards.

*NOTE: Early in the school year, you will want to focus on mental math, the ability to solve story problems by using manipulative, fingers, or drawings. If you are doing this lesson later in the school year, you may wish the students to write the equation after each story on blank sheets of paper. 

Extension 1: Have students act out the story problems as if they were the bears. 

Extension 2:Have students illustrate the story problems to make a class book!


Following are the cards needed to play the game. Print them double sided for a deck of fun bear story problems!


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The Three Bears and a Family Thematic Unit

Thanksgiving is the perfect season to talk about the importance of families, and to celebrate the importance they play in our lives.

To begin my unit study on families, I love to start with two of my favorite books, "Hairy Bear," and  "The Three Bears." 

After discussing fantasy stories, where animals talk, we move to the discussion to the families of each of my students. This unit always seems to be a favorite for all! And it should be, who is more important to each of us than our families!


Family Unit Contents:
This developmentally appropriate thematic unit: The Family offers a variety of family themed activities that will connect all facets of the Kindergarten, Pre-K, or Homeschool curriculum.

Contents Include:

Literacy Games/Activities:

Family Vacation: Segmenting Words
The Family Reunion: Producing and Generating Rhyming Words
Family Camping: Identifying Upper and Lowercase Alphabet Letters
Family Camping: Identifying Sight Words
Animal Families: Fluently Naming Upper and Lowercase Alphabet Letters
Animal Families: Fluently Naming Sight Words

Math Games/Activities:

Birth Order: Gathering, Sorting, and Interpreting Data
Family Counting Tree: Addition and Subtraction
Cookie Jar: Counting On
The Family Tree: Matching Quantity and Numerals


Guided Reading Books

The Family

Songs/Fingerplays

With My Family
Families
My Family Tree

Writing

My Family Tree: Scaffolded Writing Lesson
Family Word Wall
My Family: Writing Prompt

Social Studies

Family Traditions: The Patchwork Quilt
Birth Order: Family Combinations
My Family: A Family Home-Connection Activity

Art

My Family: Shape People

Thanksgiving: Teaching Thematically

Looking for a great Thanksgiving Song?


    I'm a very fine turkey and I sing a fine song.
    Gobble, gobble, gobble, gobble, gobble.
    I strut around the barnyard all the day long.
    And my head goes bobble, bobble, bobble.

    And when Thanksgiving Day comes round,
    Gobble, gobble, gobble, gobble, gobble.
    I'll go and hide so I can't be found.
    Then my head will still bobble as I gobble.

And check out this great Thanksgiving Unit:

This Thanksgiving unit is strategically linked to the Common Core Standards! It is divided into areas of literature, media, music, art, literacy activities, math activities, worksheets, science activities, creative writing, word wall words, and guided reading. The activities are clearly written, easy to use, and need limited amounts of preparation. 



Literacy Activities:
Hop To It: Identifying Letters and Sounds
Turkey Lurkey: Producing and Generating Rhymes.
Turkey Twist: Kinesthetic Practice With Letter Recognition
Dinner Rush: Naming & Generating Beginning Sounds
Thanksgiving Races: Developing Fluency
Rhyming Worksheet


Math Activities:
Turkey Guesses: Making Estimates
A Feast For All: Counting Objects to Show Physical Representation of Numbers
Thanksgiving Feast: Counting Forward From a Given Number in a Set of 10
The Turkey Dance: Identifying Numbers and Recording Results.
Thanksgiving Parade: Ordering 1-10 Ten Frames
The Turkey Bowl: Comparing Groups of Objects

Songs
Gobble Gobble Gobble
5 Fat Turkeys
I Like Turkey
A Very Fine Turkey


Writing Prompts/Word Wall (Style Choices)
Thanksgiving
I am Thankful For
Thanksgiving Word Wall

Art Projects
Handprint Turkey
Easy Construct Pilgrim
Construct Indians
Tangram Indian
Draw a Turkey

Guided Reading Books
Happy Thanksgiving

Social Studies
Pilgrim Kids: Compare and Contrast Facts

Rhyme Away!

When students are familiar with a few nursery rhymes, you can help them develop a greater awareness of rhymes by having them complete a well known line. For instance, start the first line of Jack and Jill, then pause to have the students name the missing rhyming word: Jack and Jill went up the _________. By highlighting the rhyming words of familiar rhymes, students will tune in more to the word play of rhymes.

As students continue to develop a better sense of rhymes, they need opportunities to match rhymes. Games can provide the practice needed to help students move from matching to producing rhymes. As students master the production stage of rhyming, they can then focus on reading rhymes within word families.


Rhymes help develop the foundation for reading. Capitalize on the “fun” of rhymes through books, songs, and games to help your students progress through the stages of rhyming. For games, activities, and supporting materials, check out these products.

  


Animal Zoo: Early Reading Games

If you love teaching letters and sounds using lovable animal characters, you will enjoy this product: Animal Zoo: Early Reading Games.

Contents Include:

Animal Alphabet Flashcards
Alphabet Zoo Match-up: Matching Animal to Beginning Letter
Alphabet Zoo Beginning Sounds
Zookeepers: Letter Recognition
Write the Room: Alphabet Zoo
Alphabet Zoo Bingo


Kindergarten And Preschool Math and Language Arts Common Core Assessments

Are you looking for assessments that are authentic, strategic, and linked to Common Core Standards?  Are you looking for assessments that will lead you to be organized, effective, and powerful in your teaching.

These assessments gather information about the language arts and mathematic strengths and weaknesses of your students. You will be able to immediately use important information to guide your classroom instruction, strategically target intervention groups, and inform parents of individual student progress.

Additionally consider using ESGI, a secure assessment platform to digitally conduct your one-on-one tests, score, and report your assessments.  The digital and paper format are a great way for you to visualize your assessments and keep yourself organized!

You will love the ease that ESGI gives this assessment product. I have done the work for you; all of these tests are there: click, click, done. Simply click on the test explorer tab (within ESGI) and look for my name: Kathy Crane to find the correct tests. (Important: At the very end of the testing documents are screen shots of how to organize your tests on ESGI to correlate with the paper copy).

Even if you are not sure whether paperless testing and data retrieval is for you, you will want to take advantage of their free 60 day trial! Simply go to  https://www.esgisoftware.com/ESGI/ click on the orange button!

Please remember to enter promo code B7227 to receive $40.00 off the already low price.

             




                                      



    












Reading Words in Kindergarten

Throughout the second semester of kindergarten, students work on reading words. For teachers, this emphasis on words can be a challenge. We need a variety of methods to keep word reading engaging and interesting. 



Try this approach to involve all students. Use large letters - magnetic letters on a white board or a set of flashcards in a pocket chart. Put the vowels in a column down the middle of the board or chart; use all or some of the vowels, placing them in alphabetical or random order.  Next have two or more students each choose a consonant letter. Arrange them before and after one of the vowels, then have the class (or an individual student) sound the word out. Continue with more students choosing letters for another vowel. With your guidance, letters can be arranged so you can work on CVC or CVCe words. You can also focus on digraphs or blends. If you allow students to put the letters around any vowel, you will definitely have a lot of nonsense words to read!


Your students will enjoy the variety of this activity and their added involvement in creating words. Give it a try for a fun word-reading experience!

The Little Red Hen

One of my favorite tales to tell.. The Little Red Hen
Here is a link to some writing center activities.





Making The Red Hen: Collage Portrait

Writing the Hen's Biography

Finished Product!


Acting out the Story at the Drama Center




                    
Learn The Process

Grinding the Wheat


                 









Constructing The Elements as a Team.
            
Constructing The Elements: Building Teamwork

 

Adding Finishing Touches 

Our Story Element Mural



The Development of Mathematical Representation

According to the research of David Sousa, children progress through three stages of mathematical understanding as they develop an understanding of concepts. The stages are Concrete, Representational (Pictorial), and Abstract. It will be important to remember that each of our children will be in a different stage of development for each concept that we are teaching, and, therefore, it is important to differentiate the method by which the children are allowed to work with problems. Differentiating in this way is sometimes known as the CRA (or CPA) approach. First, let's define the different stages of development:

Concrete

All children must start here when learning mathematical concepts. Concrete models tie mathematics to the real world and include anything that the child can use physically to represent a problem.

Representational/Pictorial

The representational stage provides the mental scaffolding for children to move their mathematical understanding from concrete to abstract. In this stage, children are able to use visual or pictorial representations to represent concrete examples. Teachers deliberately help children see how pictorial representations tie to concrete examples.

Abstract

The abstract level of thinking represents mathematical thinking symbolically. It is important to realize that this is the final level of understanding for children, and that we must help each child through the first two stages before they will be able to grapple with abstract representations. "Numerals were developed to signify the meaning of counting. Operational symbols like + and - were constructed to represent the actions of combining and comparing. While these symbols were initially developed to represent mathematical ideas, they become tools, mental images, to think with. To speak of mathematics as at mathematizing demands that we address mathematical models and their developments. To mathematize, one sees, organizes, and interprets the world through and with mathematical models. Like language, these models often begin as simply representations of situations, or problems, by learners... These models of situations eventually become generalized as learners explore connections between and across them" (Fosnot and Dolk, 2001)

.

Many lessons in kindergarten can be specifically designed to move children from one stage of understanding to another. For example, one lesson could ask groups of children to count out objects from a bag and then draw a picture of the objects they found (Concrete to Pictorial). The teacher could then write the number each group found in their bags on the board (Pictorial to Abstract). Lessons can also be designed where each stage of development can be used to answer the question.

Here is such a lesson: The teacher places a container in view of the children and tells them their are five bears inside. Some of the bears are red and some are blue. How many of each color could be inside? Children can use their own sets of bears to answer the question. They could draw a picture. They could use numbers and equations. The important part of the lesson is that each child is developing an understanding of the part/whole relationships of the number 5, and allowing each child to work within his own stage of understanding will better strengthen his mathematical knowledge.

Number Sense and the Common Core: Compensation, Unitizing, and the Landscape of Learning

In Part 1 of this series I discussed how important number sense is to a child's development along with early number sense skills and how they relate to the Common Core. In Part 2 I discussed the importance of hierarchical inclusion, magnitude, and subitizing. In Part 3 I discussed part/whole relationships (a concept which will probably fill the entire kindergarten year). The whole of the math Common Core (except for geometry and measurement) fall under the umbrella of number sense, and today we will discuss some of the concepts of number sense that are on the horizon for kindergartners.

Compensation

Compensation is the ability to play with numbers. It is the understanding that if 5+5=10 then 6+5 must be 11 because 6 is one greater than 5 and so the sum must be one greater than 10. Or that if 5+5=10 then 6+4 must also equal 10 because 4 is one smaller than 5 and 6 is one larger than 5. This is a complex skill that some kindergartners will not be ready for, but some children may begin to use compensation, and teachers should feel free to conduct Number Talks introducing compensation.

The following video is an example of a 2nd grade Number Talk involving compensation. Number Talks involving compensation in kindergarten would obviously be less complex.

Compensation strategies can be used in the following Common Core standards:

CCSS.MATH.CONTENT.K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

CCSS.MATH.CONTENT.K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

CCSS.MATH.CONTENT.K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

CCSS.MATH.CONTENT.K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

CCSS.MATH.CONTENT.K.OA.A.5 Fluently add and subtract within 5.

Unitizing

Unitizing is a child's ability to see numbers in groups. It is an ability they use to see that there is simultaneously 1 chair with 4 legs, to count by 2's with understanding, to hold one number in their head when counting on, or to begin grouping numbers into tens.

Grouping numbers into tens is especially significant, because "A set of ten should play a major role in children's initial understanding of numbers between 10 and 20. When children see a set of six with a set of ten, they should know without counting that the total is 16. However, the numbers between 10 and 20 are not an appropriate place to discuss place-value concepts. That is, prior to a much more complete development of place-value concepts (appropriate for  second grade and beyond), children should not be asked to explain the 1 in 16 as representing "one ten". The concept of a single ten is just too strange for a kindergarten or an early first grade child to grasp. Some would say that it is not appropriate for grade 1 at all. The inappropriateness of discussing "one ten and six ones" (what's a one?) does not mean that a set of ten should not figure prominently in the discussion of the teen numbers"  (Walle and Lovin 2006).

 

(This book by Walle and Lovin is one of my very favorites for teaching mathematics. You can get it through this affiliate link)

 

In kindergarten, the goal is not to formalize unitizing, but to begin to help students see numbers in groupings. The following standard requires unitizing:

CCSS.MATH.CONTENT.K.NBT.A.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Let's dissect this standard to figure out exactly what it is and what it is not asking you to evaluate. According to the standard, children should compose and decompose a number in the teens into a group of tens and some ones. Nowhere in the standard is it required for the teacher to use place value language (as Walle and Lovin discourage) but to make representations of the teen numbers using objects and drawings. Although the language of the standard includes the terms "ten ones and one, two, three, four, five, six, seven, eight, or nine one" this vocabulary is there for the teacher, the standard itself specifically requires "understanding" from the student.

Watch the following videos, if kindergartners can see the images and identify the teen number that is represented, then they have met the conditions of the Common Core Standard.

The Landscape of Learning

We should keep in mind that these concepts of number sense do not describe a linear progression of understanding. 

"Historically, curriculum designers... analyzed the structure of mathematics and delineated teaching and learning objectives along a line... [f]ocusing only on the structure of mathematics leads to a more traditional way of teaching--one in which the teacher pushes the children toward procedures or mathematical concepts because these are the goals. In a framework like this, learning is understood to move along a line. Each lesson, each day, is geared to a different objective, a different "it." All children are expected to understand the same "it," in the same way, at the end of the lesson. They are assumed to move along the same path; if there are individual differences it is just that some children move along the path more slowly--hence, some need more time, or remediation. As the reform mandated by the National Council for Teachers of Mathematics has taken hold, curriculum designers and educators have tried to develop other frameworks. Most of these approaches are based on a better understanding of children's learning and of the development of tasks that will challenge them."  (Catherine Twomey Fosnot and Maarten Dolk 2001)

 

(Cathy Fosnot is an excellent resource for mathematics teaching. Here is her book in this affiliate link.)

 

According to Cathy Fosnot, a child's development of number sense looks less like a line and more like the following chart, developing in a way that she describes as the "Landscape of learning".

https://jessicapartridge.files.wordpress.com/2014/02/fosnot1-e1393552630905.jpg

"The paths to these landmarks and horizons are not necessarily linear. Nor is there only one. As in real landscape, the paths twist and turn; they cross each other, are often indirect. Children do not construct each of these ideas and strategies in an ordered sequence. They go off in many directions as they explore, struggle to understand, and make sense of their world mathematically... Ultimately, what is important is how children function in a mathematical environment (Cobb 1997)--how they mathematize." (Fosnot and Dolk 2001)

Because number sense development is nonlinear, the best activities we can use in our classrooms will weave together different components of number sense and engage children on multiple planes of development. Many of the links in these posts will lead you to some excellent books with activities in them, that do exactly that. 

But we must be honest, many of the textbooks that have been adopted are more concerned with checking off the Common Core standards than developing the understanding behind them, much less teaching in a non-linear fashion. Therefore, we, as teachers need to be more discerning lesson planners using textbooks and workbooks only as a resource to teach the Core in the way we know best, instead of letting textbook companies dictate to us how the Core should be taught. 

In our next post we will discuss the development of mathematical representation. Be sure to check it out!

Number Sense and the Common Core: Part-Whole Relationships

part-whole-relationships

In Part 1 of this series I discussed how important number sense is to a child's development along with early number sense skills and how they relate to the Common Core. In Part 2 I discussed the importance of hierarchal inclusion, magnitude, and subitizing. The whole of Common Core math (except for geometry and measurement) fall under the umbrella of number sense, and today we will discuss the aspect of number sense that should be the major focus of any kindergarten math program.

Part/Whole Relationships

"Count out a set of eight counters... [a]ny child who has learned how to count meaningfully can count out eight objects as you just did. What is significant about the experience is what it did not cause you to think about. Nothing in counting a set of eight objects will cause a child to focus on the fact that it could be made of two parts. For example, separate the counters you just set out into two piles and reflect on the combination. It might be 2 and 6 or 7 and 1 or 4 and 4. Make a change in your two piles of counters and say the new combination to yourself. Focusing on a quantity in terms of its parts has important implications for developing number sense. The ability to think about a number in terms of parts is a major milestone in the development of number" (Walle and Lovin 2006).

All of the following Common Core standards involve an understanding of part/whole relationships. Notice that the word equation is mentioned in only three of these standards, and in those standards it is only one option that students can use to represent addition and subtraction. In actuality, using an equation may not be developmentally appropriate for most kindergartners. What they should be doing in order to meet the standard, is show addition and subtraction in terms of the part/whole relationships of numbers. 

For example, if you ask a child to show combinations of 10 with colored plates, as shown in the previous video, and he/she can tell you all of the different combinations that make ten, they have just solved a problem involving addition to 10 or subtraction from 10 using a drawing. This meets Core Standard K.OA.A.3 without solving any abstract equations.

"To really understand addition and subtraction, we must understand how they are connected... By modeling addition and subtraction situations and then generalizing across these situations, children are able to understand and represent the operations of addition and subtraction... Children who commit the facts to memory easily are able to do so because they have constructed relationships among them and between addition and subtraction in general, and they use these relationships as shortcuts. When relationships are the focus, there are far fewer facts to remember, and big ideas like compensation, hierarchical inclusion, and part/whole relationships come into play. Also, if a child forgets an answer, she has a quick way to come up with it" (Fosnot and Dolk 2001)

CCSS.MATH.CONTENT.K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

CCSS.MATH.CONTENT.K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

CCSS.MATH.CONTENT.K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

CCSS.MATH.CONTENT.K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

CCSS.MATH.CONTENT.K.OA.A.5 Fluently add and subtract within 5.

It would be difficult to overstate how important part/whole relationships are to a kindergartener's mathematical development. I highly recommend looking into the books that I have used as sources in these discussions if you would like more information as well as some great lessons on teaching part/whole relationships. Our Interactive Math Worksheets for March  and Interactive Math Worksheets for January also include some activities designed to develop this skill. Tomorrow we will discuss some of the number sense skills that are on the horizon for kindergartners.

Number Sense and the Common Core: Hierarchical Inclusion, Magnitude and Subitizing

kindergarten-number-sense

In Part 1 of this series I discussed how important number sense is to a child's development. In fact, number sense could be considered the most important part of the kindergarten year. I also discussed early number sense skills and how they relate to the Common Core. The whole of the math Common Core (except for geometry and measurement) fall under the umbrella of number sense. Here are more of the components of the Core and how they relate to an understanding of numbers.

Hierarchal Inclusion

Hierarchical Inclusion, as explained in the following video, is the concept that a number contains all of the previous numbers. Imagine a number as a Russian nesting doll, if working with the number 4, imagine the largest doll is 4 and inside that doll are the smaller dolls, 3, 2, 1. Without this understanding a child will think that, when counting, the number he points to and names "3" is "3" in of itself without the other objects and when you ask him for "3" he will give you only that object. 

Hierarchical inclusion also helps students understand other number sense concepts, such as part/whole relationships and compensation because a child cannot understand that 4 can be broken up into the parts 3 and 1 without also understanding that the number "4" contains 3 and 1.

In order to complete the following common core standard, a child must understand hierarchical inclusion:

CCSS.MATH.CONTENT.K.CC.A.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

Magnitude

Magnitude is a child's ability to compare groups. Even children who cannot count have the ability to judge the relative size of groups of objects, but as a child's number sense develops, so should the sophistication of her understanding of magnitude. The following Common Core activities depend on a child's understanding of magnitude:

CCSS.MATH.CONTENT.K.CC.B.4.C Understand that each successive number name refers to a quantity that is one larger.

CCSS.MATH.CONTENT.K.CC.C.6 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.

CCSS.MATH.CONTENT.K.CC.C.7 Compare two numbers between 1 and 10 presented as written numerals.

Subitizing

Watch the following video. In it, groups of objects quickly flash on the screen. Can you tell how many objects there are in each grouping?

As explained in the following video, subitizing is the ability of a child to quickly recognize a number visually. Children do this by mentally grouping the objects they see (and you probably did this too, for example, seeing a group of 3 and 3 and 3 and knowing that there were 9 objects).

"Looking at a quantity for a short time and then being able to tell how many are in the group(s) without counting each object in the group begins to develop from small sets of two, three, four, and five objects, to parts of sets of six up to twenty. Generally, this development begins between ages 2 and 6. Later, the subitizer sees objects as groups of 10s and 1s and, combined with an understanding of place value, is able to see the numerosity of a large group of numbers quickly." (Copley 2010).

 
 

Subitizing strengthens a child's understanding of what numbers mean, and how they relate to one another. In fact, when children are taught to subtize, and their attention is drawn to the groups and patterns they see, it becomes a visual representation of addition and subtraction, as seen here

When strengthening a child's subitizing skills, we are teaching the following Core standards:

CCSS.MATH.CONTENT.K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

CCSS.MATH.CONTENT.K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

CCSS.MATH.CONTENT.K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

CCSS.MATH.CONTENT.K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

CCSS.MATH.CONTENT.K.OA.A.5 Fluently add and subtract within 5.

It is important to note that the word equation is present in only three of these Core standards, and in those standards it is only one option for representing addition and subtraction. In actuality, representing addition and subtraction with equations in kindergarten will not be appropriate for most of our students, but if we have the children participate in a subitizing activity where they are shown a variety of images with a quantity of 5 arranged in different ways, and a child can state that each group contains 5 because they saw a group of 1 and 4 or 2 and 3, they are fluently adding and subtracting within 5, and in a way that is more appropriate than asking them to solve 2+3=__, because instead of working from the end result backwards, we are building their foundational knowledge. In fact, testing a kindergartener's understanding of addition and subtraction by asking her to solve an equation, is like testing her phonemic awareness by asking her to read a story!

Tomorrow I will discuss the rest of the components of number sense, including the concept that the majority of your kindergarten math lessons should be focusing on. See you tomorrow!