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Number Sense: Cardinality Principle



Developing Number Sense: Principles of Counting

All concepts of number sense need to be actively taught. Cardinality principle is one of the higher order concepts of number sense that children in kindergarten learn. 

Cardinality Principle

Cardinality is the ability to understand that the last number which was counted when counting a set of objects is a direct representation of the total in that group.

A child who understands this concept will count a set once and not need to count it again. They will automatically remember and know how many are represented.

Students who are still developing this skill need constant repetition of counting and explicit teaching through modelling that they do not need to count over and over again when it will result in the same number. Students who have difficulty with their working memory may have difficulty with this concept.

Practice

Simply counting objects that are meaningful to children's lives will help them develop a basic understanding of cardinality. How many candies do you have? How many blocks are in your tower? etc.

Practicing to develop subitizing skills helps students develop cardinality. When children automatically recognize a number they know how many are the set. These two principles are closely related but not the same.

These are some of the activities we use to teach cardinality.

Number Line Fluency
I love this activity as it allows me to choose various representations of numbers based upon what concepts I know students already know. They then need to count the objects in order to know how many are in the set/representation if they don't already know the representation of the number. Then they need to hold that number in their working memory in order to put the numbers in order.

Subitizing Activity
This is a simple tally game. Students flip over a variety of different representations of numbers (sets of bears, tally marks, finger representations etc) and then mark off which number they found. This is a fantastic game to teach cardinality!
  

Number Puzzles
I place out a variety of different puzzles which represent different numbers and students need to match the numbers to make a puzzle. Students need to count various objects (such as ten frames, fingers, tally marks etc.) and hold that number in their head. 

If they play enough or understand the concept of cardinality, they will hold the number in their memory and it will help them solve the puzzles!
  
Number Talks
Number Talks are a huge support to develop students ability to understand cardinality.

We use Number Talks on a regular basis in our classroom and it has made huge gains in our students understanding of numbers and has helped to solidify their fluency of numbers.

If you want to check it out there is a link to an Amazon affiliate if you click the image below.

Books to Teach Feelings and Emotions

I love to explore feelings with young children through books and through the arts, such as puppets. 

It is a safe way for children to explore emotions and develop empathy in a safe situation as they realize others feel emotions just like they do.


How Do You Feel?

By: Anthony Browne
This is a simple book for young children which includes a monkey showing a variety of different feelings in relation to simple concepts that children will understand. This is a perfect book to introduce emotions to students.

When the monkey is bored there are no colors to engaged the children. When the monkey is lonely it is very small on the page filled with white empty space.

When the monkey is hungry he has a banana. When the monkey is full there is a picture of a banana peel!


How Are You Peeling? Foods With Moods

By: Saxton Freymann and Joost Elffers
This is a hilarious book for young children to explore feelings using a wide variety of fruits and vegetables. The creators of this book carved unique shaped food, sculpted them with an Exacto knife and then used natural materials like beet juice to add details like mouths to add realistic feelings!



Grumpy Goat

By: Brett Helquist
Goat is the grumpiest animal at Sunny Acres farm until he remembers that there is more the life than eating and being alone.


Tough Guy

By: Keith Negley
This is a perfect book to show that everyone has emotions - even superheroes, ninjas, and wrestlers! They face challenges, frustrations, and concerns no matter how brave, fast or strong they are! 




Get Happy

By: Malachy Doyle
This is a book about opposites. It is a very simple book for very young children to think about what behaviors they can change to help them be happy!



Do Unto Otters: A Book About Manners

By: Laurie Keller
This is a story about Mr. Rabbit. He wonders if he will be able to get along with his new neighbors, who are otters, until he is reminded of the golden rule.


What are your favorite books for teaching emotions to young children?

Weekly Round-Up: December 29th, 2017


I'm so excited that we have had so much fun the last week of school. This is a late reflection of it but it was so much fun I had to write a blog post about it.

It's been busy. One holiday concert for the whole school and two for our community. We had a PJ day and kid made ugly sweater day on Friday. Plus, all the hustle and bustle of the end of the year prepping to send everything home made for a busy week.

1. Measurement

Snap cubes have been a hit in our classroom all year long.

Last week we explored measurement using gingerkids which were taped to the wall (see this in my last blog post here). To extend our students understanding of non-standard measurement we added some holiday-themed activities to let them practice measuring! If you want to grab your own copy, click here or on the image below.

To ensure that a number of measuring cubes would be used I printed these pages on 11"*18" paper. I was shocked that almost every child independently chose to visit this activity without prompting and all were able to accurately measure using the snap cubes!

I love simple activities like this as it provides meaningful activities for young children to write numbers.


2. Painting

Our paint table was quite busy with interest with live poinsettia flowers as a provocation. I'm always amazed how engaged students are at representing the world around them when they are inspired by real-life objects!


3. Dramatic Play

On Tuesday the kids decided that they wanted to create a train station in our dramatic play area.

They lined up chairs to make a train, created tickets, money and served each other on the train or took turns driving the train as an engineer. We found a box and some of them wanted to paint it as the engine of our train. They worked hard to create this masterpiece and enjoyed playing with it!


4. Sensory

We added some sensory items to our water table this week. Cut up oranges, cranberries and cinnamon sticks became a hit! We added a few spoons and small cups and the children enjoyed counting how much they could fit into the different cups. There was lots of exploring of movement and gravity!


5. Number Sense

By simply adding a string to our fence outside we were able to enjoy creating a number line. We used shirt board to create our numbers for the number line.

We played games, guess the missing number, created a number line and explored numbers with this fun activity. I will admit, this game would be easier to play without the snow and mittens!


Check out my other Round-Ups here or  Follow me on Bloglovin' to see more ideas for learning activities in kindergarten!

How to Customize Your Desktop Images on a Mac

Have you ever wanted to customize your folder images on your MAC? 

I just learned how to do it this week and I am super excited to share it with you! 

It is super easy to do!

First of all I create my images in powerpoint. 

The image size I use is 5" * 5".  I made a shape, filled it in with a background that I wanted and then added my text.

Next you need to highlight everything that you want to include in your image. 

Double click on the border surrounding it and click on "Group" and then "Group" again.  The image will look like the one below without showing the lines for the text. It is now one image. 

Right click on this image and copy it (command C) or click file and copy.

Double click on the file that you want to pick and click on "Get Info."

Now you must click on the blue "folder" at the top left of the Info that appears on your screen. As soon as you have done that press copy by either clicking on "File" and then "Paste" or using the Command V shortcut to paste it to replace that blue image! 

Instantly the image at the bottom and top will be replaced and it will look like the image below and your done!


Have fun making your customized desktop!

Number Sense: One-to-One Correspondence


Developing Number Sense: Principles of Counting

All concepts of number sense need to be actively taught.

The one-to-one correspondence principle ensures we accurately count objects one at a time.

One-to-One Correspondence Principle

When children first learn to count a set of objects they often will randomly touch the objects in any order and will count the same object more than once or even multiple times.

When students understand the concept of one-to-one correspondence, they understand that each object is counted only once and that each object represents one number.

Practice

Touch counting helps students develop this skill and it usually has to be modelled for students to learn how to do it properly.

We can either simply touch an item or move it away from the group being counted in order to ensure that we have counted all of the objects in the set. Moving objects away is a skill for children to learn at the beginning of understanding this concept. When a child has a stronger working memory they do not need to rely on this skill.

Math Journals in Kindergarten


We use journals as a part of small group instruction in our classroom. Specifically, to cover problem-solving in math. There are many ways to demonstrate problem-solving but one way I love is to use math journals.

Math journals can be used as a diagnostic, formative or summative assessment. Journals are simple, easy, and kids can represent their ideas with pictures, numbers, and words. And if they cannot do that I can scribe for them!

Whenever possible, I always try to provide hands-on manipulatives for students to hold and manipulate while writing journals. This allows their learning experiences to be more meaningful and students can draw what they know afterward. Not all students choose to use them, but offering manipulatives is extremely important to learning math concepts!


Number Sense
Mental math, representing numbers, ten frames, printing numbers, and even math talk concepts can all be represented through journals! Addition, subtraction and even word problems are perfect concepts to be used as a journal as it allows students to represent what they know in a way that they can show it!

Graphing & Patterning
I use journals for engaging graphing activities, especially for students who need visual prompts to keep them focused and for students who cannot draw or write!  They still can engage in meaningful graphing activities but do not need to be stressed by their limited fine motor skills. Students often can create their own patterns. Many young children cannot manipulate writing materials enough to feel successful. By providing real-life objects for them to color, students can quickly demonstrate their knowledge!

Sizes & Shapes
Cut and paste activities allow students to demonstrate their understanding of big and small while also supporting their fine motor development! Students can tally and/or color the number of shapes presented to them to show their answers. It is so simple and easy to differentiate!


If you're interested in checking out the journal prompts that I use, click here or on the image below. I love this set as it does not use a lot of ink and I can quickly run off a class set without using a lot of paper for my classroom!

Number Sense: Abstraction Principle


Developing Number Sense: Principles of Counting

All concepts of number sense need to be actively taught.

The conservation principle is one of the first few principles children learn when developing their understanding of number sense.

Abstraction Principle

Is the ability to understand that the number of objects in a group remains set regardless of the composition of the sizes of the objects in the group.

So five large blocks are five.

Three large blocks and two small blocks are also five.

One small, two medium and two large blocks are five.

Practice

We practice this on a regular basis throughout our normal play activity. When we get balls out for outdoor learning we might ask the children how many are out when there are a variety of different sizes presented.

Block play provides an easy opportunity to practice this skills. Sometimes we challenge students to build a structure using a certain amount of blocks. Other times we challenge our students with counting the blocks used and/or drawing a representation of their building.

We love to bring a real life connection to building and to expand their knowledge of the world around them. We often use this building activity to get students to represent their ideas the quantity of blocks used and to represent their creations in writing.

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