Algebra in Kindergarten? Absolutely!

 "Pure mathematics is, in its way, the poetry of logical ideas."

Albert Einstein

 

When you think about algebra you might have memories of sitting in a high school math class, searching for unknown values in linear and quadratic equations. Those long ago math courses may seem far removed from today's kindergarten classrooms but did you know that it is essential for educators to promote algebraic reasoning in early childhood education?

I devoured the most recent issue of Young Children (Volume 77, Number 3), especially the article Promoting Algebraic Reasoning in the Early Years by Lindsey Perry. 

In her work Perry advocates for algebra in early math programs that explore two main ideas: composition and decomposition of numbers and properties of operations. According to Perry (2022) algebraic reasoning "involves seeing and describing patterns and relationships between quantities that may be unknown...which builds upon students' understanding of patterns and relationships with known quantities and values" (pg. 17). Perry posits that if children can observe and describe number relationships they can begin to symbolically represent relationships between numbers. 

Composition and Decomposition of Numbers

When children compose they understand that a number can be put together using its parts (e.g., 5 plus 5 equals 10). Decomposition is the opposite where a number can be broken apart in different ways (e.g., 10 can be broken into 8 and 2 or 7 and 3). When children compose and decompose numbers they understand how to manipulate numbers in different ways, which helps them become flexible when solving calculations. For example mentally adding 68 + 22 can become easier when children realize that the ones values total 10 and then add this to the tens value (10 + 60 + 20). Adding 68 plus 22 is the same as adding 10 plus 60 plus 20 but the second strategy may be easier to mentally calculate for many people.

Properties of Operations

Properties of operations encourage children to work flexibly with numbers in order to recognize and manipulate their relationships. This helps them simply calculations in order to more efficiently and accurately solve them. For example the order of addends (numbers added together) does not matter in order to arrive at a sum. 

a + b = b + a 

6 + 4 = 4 + a therefore a must be 6.

The commutative property applies to addition and multiplication. The order of numbers can be switched and it does not change the answer of the operation.

2 + 7 = 9 and 7 + 2 = 9

4 x 5 = 20 and 5 x 4 = 20

The inversion property states that all integers have an inverse number that when added equal zero. 

3 + (-3) = 0

Although complicated young children can play with inversion when they become interested in, and work flexibly with equations.

3 + 2 - 2 = 3

So how can early childhood educators encourage children to participate in activities that promote early algebra? Here are some simple activities that can be used regularly to build children's confidence, ability and interest in number sense.

Equation Line

 

Provide children with a variety of subitizing cards and math symbols (addition sign, subtraction sign, equal sign). Encourage children to arrange the cards in different ways in order to create equivalencies.

 Make 5 (or 10)

Show children a total number of cubes (starting with 5 and then 10 is helpful). Hide the cubes behind your back and remove some. Show children the remaining number of cubes and encourage them to calculate how many are hiding.

Singing Songs with a Five/Ten Frame

When singing popular songs and finger plays with children (e.g., 5 Little Monkeys, 10 in the Bed) add a five or ten frame as a visual and manipulate the number of counters in the frame to match the number being sang. 

Counting Beads

   

A string of counting beads can easily be made using two colours of wooden beads secured on a pipe cleaner. Encourage children to use these when playing number games or engaging in number talks.

Domino Sort

Provide a mat for children (here a foam shamrock has been used but any shape will work). Write numbers on individual mats. Encourage children to sort dominoes and match their quantities to the mats in order to represent the many different dot arrangements possible for each number.

Roll a Ring

 

Seasonal rings are a fun tool to use in math games. Provide children with dice and encourage them to roll and add (or subtract) the numbers. Children can then wear the corresponding number of rings on their fingers. If two players play the game, they can each roll and wear rings and then compare hands to see who has more or less.

Name Equations

 

We enjoy representing children's names with boxes and encouraging them to think about the number, size and shape of the letters. These boxes are also fun to represent at equations so that children can play with their names and integrate a bit of math into literacy.

Calendar-based Number Talks

Morning message is a great time to encourage a daily number talk. We often represent the date in different ways (e.g., dice faces, dominoes, tallies, frames) and then encourage children to calculate the number by paying careful attention to the representations and operation signs used.

Which One Is Wrong?

 

Another favourite number talk is 'Which One is Wrong'. Different equations are displayed and children are challenged to explore each one using manipulatives (e.g., cubes, bead strings) to find the incorrect one. 

What other activities do you use to help children with early algebra? Let's connect on social media @McLennan1977!

Creating a Sensory Wall for Children

In our classroom we have a discovery area where children are invited to explore materials that focus specifically on the senses. We enjoy including resources that support exploration of light and colour (e.g., light table, sensory jars). Many loose parts are also in this area (e.g., stones, shells). The materials are stored on a small wooden shelf so they are easily accessible for children.

The shelf floats in the middle of the room as an anchor for the space. The back was covered in blue felt. We wanted to maximize all areas of this space and because there are many children with sensory needs in the class we decided to turn the felt area into a sensory wall.

The first step was to measure the space and plan out how the materials would fit together. I found this easiest to do on a flat working space. This way I could piece the material together like a puzzle and ensure they were diverse and interesting to explore.

Once I was satisfied with the way it looked I attached each piece to the felt wall using hot glue. I know that over time as children explore the pieces may fall off, but I am hopeful that I will be able to quickly and easily reattach them. I love how the sensory wall is low enough for all children to access. They will be able to sit and explore, or touch it while they walk by. The materials also match the colour scheme and decor in this calming space and do not stand out.

I found myself enjoying the materials and know that the children will too!