Calendar Math: Daily Date-Inspired Prompts to Inspire Math Talk

Math talks are regular, short conversations about purposeful math problems with children. These are intentionally crafted to invite children into specific math situations, helping them to improve their mathematical confidence and abilities. Math talks are meant to be open-ended opportunities that have multiple entry points and approaches for interpreting and solving the problem. To learn more please read my article Joyful Number Talks in Kindergarten available here:

 

The Journal of Teaching and Learning

Vol. 13, No. 2 (2019) pp.43–54

https://jtl.uwindsor.ca/index.php/jtl/article/view/5684/5082

 

In my classroom I engage children in daily math talks during our first whole group time together. I often use the date as a focus for the number talk. For example, if the date is December 10, I use the number ten as the focal point of our math exploration. 

Over the years I have shared my math talks on social media and have been asked repeatedly to create a guide to support educators who wish to engage their students in math talks. This served as the inspiration my book Calendar Math. This book provides photo prompts and accompanying questions is that educators can use these to engage children in regular conversations in the classroom. In the book each calendar date (numbers 1 through 31) has four different pages with accompanying prompts. Use them for different months and also as sparks for creating your own daily number talks with children. 

 

To help educators get started here is a collection of photos representing the numbers 1 to 31 available as a PDF file. They can be digitally projected or printed and used as part of your morning math talk. Feel free to use them to support and supplement math discussions with your students!

Using Outdoor Discoveries to Inspire Rich Math Talks

"It's the little details that are vital. Little things make big things happen."
John Wooden

Now that spring is emerging muddy conditions are common in our school yard. Although some educators shy away from messy spots, I find they are often one of the best places to notice and name rich, authentic math.

One morning the children were exploring the yard and noticed interesting tracks on the path. They took their time observing the different prints they found. They wondered who had been visiting the space and how the markings were made. They noticed that the prints appeared to be dried in the dirt and preserved in the thick mud. 

 

 

The tracks that fascinated us the most were those made by animals. Our school is located near a wooded trail and our yard is frequented after hours by coyotes, deer, geese, wild turkeys and dogs. The children compared the different tracks and used their prior knowledge to try and identify the animals. We also used a handy animal tracks identifier to help us as the difference between some tracks is minimal.

 

               

The children were also very curious about the shoe/boot tracks that they found alongside the animal tracks. Within each we noticed intricate shape and line details that differentiated them from one another. We identified many shapes including circles, diamonds, hexagons and squares. There were also many different lines in each - straight, wavy, and zigzag.

 

      

     

We wondered if our footwear matched any of the tracks. The children examined each other's feet to see if they could find a match between their shoes and any of the tracks. This inspired rich observation and discussion as small details were noted and comparisons were made. 

 

In order to capitalize on this interest I printed large photos of a shoe and animal print and brought them to our whole group discussion. I asked the children to consider what was the same and different about each print. I also used the thinking routine 'see, think, and wonder' to facilitate math talk and help the children mathematize the photos. 

We also brought this interest in prints to our art center where children were invited to paint our spare classroom boots and stamp them to see what kinds of prints they made. 

Once the tread prints were dry the children brought them to our whole group gathering time and we continued to observe and discuss the shapes and lines we saw in each. The children grouped the prints according to similarities and also compared the size of the marking to their feet in order to see which was the bigger foot. 

 

As spring weather continues to bring rain, the children's interest in tracks endures. The children are now curious about how long an entire track path is, how deep the prints are in the mud and how much space is in between each print. They wonder about how far and fast the person or animal might have been travelling and use these clues to help them hypothesize the speed and distance. Each time a discovery is made in the yard I carefully document the findings using photos and videos so we can bring the information back to our whole group conversations and build our collective knowledge about tracks. 

Our next step will be to record ourselves making tracks in the mud using digital tools. We will use the different recording options on our smart device including time lapse photography and slow motion recording. These will be interesting to watch and will hopefully help us understand more clearly how the distance, pressure and speed of movement will affect the way a print is made in mud. Stay tuned! 

Looking for a resource to support mud play? Check out my book Muddy Math available on Amazon!

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!

Daily Math Talks with Young Children

  “Mathematics is a very broad and multidimensional subject that requires reasoning, creativity, connection making, and interpretation of methods; it is a set of ideas that helps illuminate the world; and it is constantly changing.”
― Jo Boaler

Math talks are a great way to engage children in open-ended explorations that invite them to think critically and creatively about a concept. An effective math prompt to facilitate a rich math discussion will be layered; it should be open-ended with multiple entry points for engagement. Even children as young as kindergarten are capable of participating in complex math conversations. In our classroom I aim to invite children into a math talk at least once a day; I sometimes use the numerical date on our morning message as the spark for exploration. Other times an interesting photo or collection of loose parts will be engaging and incite children into further exploration. I try to vary the invitations I provide in order to diversify the math we discuss and to reach as many learning interests as possible.

Recently I posted two Instagram Reels regarding our daily math talks that has generated many questions regarding how we engage young children in robust discussions about math each morning. There was much interest in these math prompts and many educators reached out with questions regarding how I create these prompts.

 

 

In our program we have a morning circle time. This circle is our first whole group gathering time for the day and helps set a positive atmosphere in our classroom. It is also a time to celebrate being together, and share news from our homes. We often use it as an opportunity to read a story and discuss any new and exciting activities or additions to our classroom space about which the children should know in order to be successful for the day. 

 

When I first started teaching kindergarten many years ago it was expected that the morning circle would begin with 'calendar time' where children would put a sticky number on a large grid to depict the day and there would be an extensive discussion about the calendar (e.g., day of the week, month, year). However over the years I realized that this was a very teacher-directed task and not as meaningful a use of our time. After reading Sherry Parrish's work on number talks I was inspired to use our morning message as an anchor for math talks. Wanting to still introduce the date to students, the numerical representation of the date became the foundation for our number talks most days. Sometimes I would use other prompts depending on the events and interests emerging in our classroom. If you would like to read more about number talks in kindergarten, you can access an article I wrote for the Journal of Teaching and Learning here: Joyful Number Talks in Kindergarten. 

 

I enjoy participating in a professional learning community with educators on social media and often tweet or Instagram my number talk prompts. Many educators have reached out to me how I create these open ended math talks, and to ask if I would consider sharing some ideas to try. Here are some examples of number talks we have used in the classroom. Feel free to share your own ideas in the comment section or tweet/instagram me @McLennan1977. 

 

To help support educators who are interested in starting daily math talks with children, I have published a book called Calendar Math: Daily Prompts for Math Explorations with Children. 

To help give an idea of what this book is about, and to help educators create their own math prompts, here are the first few pages of the book!