Five Tips for Powerful Math Stories
There’s no better way to capture the attention of students than to tell a story! Stories are the gateway to learning in the Waldorf classroom, and it’s no exception when teaching math.
However, stories can have different purposes in the classroom; and not all stories are effective for teaching math.
Some stories provide food for the soul. These are typically the stories that are identified developmentally as curriculum content for each specific grade. They would include the fairy tales of first grade, or the Norse myths of fourth grade. These stories nurture the inner life of children in powerful ways. And because they delve into grand and noble themes and show us what it means to be human, it is often easier to weave the academics of language arts blocks around them.
While these great stories of the human experience over the ages could be used in math blocks, it can be challenging to make them foundational material for developing mathematical thinking and number sense.
What makes a good math story?
Below are five guidelines I have found helpful in creating effective math stories.
1. Keep it short and simple.
A math story must guide the children to a specific math concept embedded within the story’s imagery. It needs to be short enough to get quickly to the point, with a simple plot line so the math concept can be drawn forth quickly and easily. Often the math stories I tell don’t have much of a plot line at all . . . . they are more designed to build specific imagery around number concepts.
2. Make the imagery in the story clear and relatable to the math concept.
We want the students to be able to create mental pictures and connect these pictures to numbers and math. The problem of the story should have something to do with the math concept you want to teach. The solution to the story will involve solving using the newly discovered math concept you are featuring.
3. Make the story about a practical activity the child can easily picture.
Stories that include seasonal themes and familiar objects from nature provide especially good material for creating strong math stories. We want the children to be able to “see” in their mind’s eye the concrete objects that support them in building understanding and number sense.
For example, an effective first grade math tale might be about a king who needs help in counting and grouping the different colors of jewels in his treasury. This could easily be a foundational story for introducing the four operations. The children can easily envision the colorful jewels that need to be counted in the story.
After this story has been told, the children can enthusiastically count their own colorful glass jewels from a basket in the classroom, deepening their number sense and bringing the story to life.
On the other hand, a story about the noble king giving up all of his beloved and treasured jewels as a sacrifice in order to save his kingdom from the poisonous fire of the dragon would likely not serve a math lesson so easily. Though it does bring in the lovely themes of generosity, kindness, and selflessness, it does not lend itself to picturing familiar objects to solve a problem using developing number sense.
4. Create variations of your original story for more complex versions of your math concept.
Your foundational math story can be easily adapted to develop increased complexity of the math concept. You can add interesting twists and new dilemmas that require math to solve.
You can tweak a story and introduce harder numbers, build in number challenges, and slowly deepen the understanding of the original math concept, step by step..
5. Relate the pictures in the math story to the abstract number symbols slowly.
Once you have told a math story, you will slowly want to connect it with the number symbols. Start with main lesson book drawings that illustrate the story pictorially. Then, gradually shift from pictures to the numbers that represent the pictures.
As you introduce the numbers that represent the math concept, remember that to start with, these numbers are purely abstractions to the students. The children need us to repeatedly refer them back to visual representations of the problems.
Repetition and allowing plenty of time to practice reinforces understanding. We can slowly move towards using the numbers alone, but quite a few children may need the scaffolded support of the pictures and counting objects for a long time before they really can show mastery of the concept in its abstract number form alone.
A Sample Math Story with Main Lesson Book Drawings
Here is an example of a simple math story I recently created to teach place value and vertical addition with regrouping (carrying) to my young, third grade class with some accompanying main lesson book pages.
When I used this story with the students, I introduced only a small portion of it at a time. For example, I introduced the sacks of apples one day, and waited until the next day, when we had done review, worked with the concept of grouping by 10s, and counted out some groups of 10s ourselves, before I introduced the concept of crates and counting by 100s.
The Story of Farmer Macintosh
Farmer Macintosh had a large orchard, filled with many apple trees. Every autumn his good and clever neighbor, Granny Smith, came to help him pick the apples. So many delicious, red apples grew on the trees that it took many days to pick them all. After the apples were picked, Farmer Macintosh brought them into his apple barn, where he counted them before he loaded them in his wagon to take to market.
Farmer Macintosh was very good at counting, but it was hard for him to remember how many apples he had at the end of the day. One day, Granny Smith looked at all the apples piled up in the apple barn, and she said, “Let’s organize the apples and put them into sacks so they aren’t just rolling around on the barn floor.”
Farmer Macintosh thought that Granny Smith had one of her very clever ideas, so together they began to fill sacks up with apples. They discovered that each sack could hold 10 apples. Once they had filled up a sack, they put it in a special Sack Room to the left of the room where they counted the loose apples.. Soon the Sack Room was filled up with sacks and sacks, each holding 10 apples.
The next day, clever Granny Smith said, “There are so many sacks! Let’s see if we can fill up a wooden crate with some of these sacks!”
Farmer Macintosh thought this was another excellent idea. They discovered that they could fit 10 sacks of apples into one wooden crate. When they had one crate filled with 10 sacks, they put it in the Crate Room, to the left of the Sack Room.
First Story Variation:
One day, Farmer Macintosh picked 143 apples before lunch and put them in rooms on the first floor of his barn. After lunch he picked 256 apples and put them on the second floor of his barn.
Granny Smith showed Farmer Macintosh how to keep track of all the apples by writing the numbers down on a big chalkboard with sections to show the crate number, the sack number, and the loose apple number.
She showed Farmer Macintosh how to add together the loose apples (the ones column) from the morning and afternoon and write that number down below.
She showed him how to add together the sacks from the morning and afternoon and write it down below.
And finally, she showed him how to add up the number of crates filled from the morning and afternoon.
Second Story Variation:
One day when Farmer Macintosh was counting by ones and adding up the loose apples, he had more than 10 . . . enough to fill an extra sack with one left over. He carefully counted out 10 apples, put them in a sack, and carried them up to the attic above the Sack Room.
After he filled up a new sack and carried it to the attic, he could add it on as he counted all the sacks of apples for the day. There was now just one apple left over. He carefully wrote the numbers on his chalkboard so he could remember how many he had picked that day.
Let Your Creativity Flow!
This is just one example of how a simple seasonal story can support learning a math concept, with main lesson book pages that second graders can draw to illustrate the concepts as they move from picture to abstract number algorithms.
With stories like this one, the children are enthusiastic about learning and, along with hands-on activities to support this math concept of place value, they are gaining solid understanding.
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