# Math

## Patterning Activities in Google Slides

Click on the image below to see the activities we have used so far.

## Patterning Videos on YouTube

## Number Sense: Principles of Counting

## Developing Number Sense: Principles of Counting

This is a round up blog of various posts which I have blogged about over the past few months regarding principles of counting.

These concepts are extremely important for children to develop a fluency in number sense.

8 principles are covered below. Feel free to check them out by clicking on the image you are curious to learn more about and discover some activities to support students understanding of these basic math concepts.

These skills are especially important for students in kindergarten or with students in the primary division who do not have a solid understanding of numbers.

## Number Sense: Unitizing Principle

## Developing Number Sense: Principles of Counting

All concepts of number sense need to be actively taught.

The unitizing principle helps students develop the understanding of place value. This principle of counting is the last to be taught when all of the other principles are understood.

### Unitizing Principle

When students have developed the understanding that our math system uses base ten units. Objects are grouped into ten once a number is bigger than 9. And then, into sets of 100 when the number is bigger than 99.

When this occurs, students are aware of the concept that a one appears in the tens column and a zero in the ones column.

### Practice

Hands on manipulation of objects, especially base ten or snap cube manipulatives, help students learn this concept.

Have students play games together with manipulatives and have them build the numbers to represent their ideas. For instance,”I had 5, but now I have 5 more. What number do I have?” Playing number games like this help children see this principle concretely and helps them to understand it in a deeper way.

## Number Sense: Movement is Magnitude

## 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.

### Movement is Magnitude Principle

### Practice

Building towers with blocks, lego or any type of manipulative that is of a consistent height helps teach kids the visual concept of movement is magnitude.

Graphing with charts is a visual representation where children can see this concept. Especially when the topic is related to their personal lives. For example, how many people walk to school versus how many people take the bus?

For children ready for skip counting, moving manipulatives two at a time while they are counting can help them understand the consistency of this principle.

## 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**

**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.

## 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

**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**

**Sizes & Shapes**

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.