Myths

The Two Bear Cubs Too Greedy and the Fox

Story Summary

Two bear cubs discover a cheese. But when it comes time to share it, things get complicated: each wants the biggest piece. A cunning fox offers to even out the portions. With each attempt, he nibbles a little… then a little more… until only two tiny crumbs remain. In the quest for perfect equality, almost nothing is left after a potentially endless sharing process.

About the Story

This story is short, effective, and follows a spiral progression: a simple conflict (sharing a cheese), a cunning mediator (the fox), and an infinite loop where the problem worsens as one tries to fix it!

With its repeated sequences, it is easy to memorize and works very well for rhythmic and mimed storytelling: children love acting as the frustrated bear cubs or observing the fox’s strategy.

It is an excellent tool for discussing sharing, modeling, and the limits of perfectionism. Sometimes striving for perfection leads to losing everything!

👉 Discover the story

Maths

Fractions, sharing…
and a hungry fox

💬 Pedagogical Commentary

This story deals with comparing quantities, impossible equality in practice, the limit approaching zero in a dichotomy, and the idea that sometimes one must accept unequal shares. The bear cubs’ inability to manage error costs them their cheese.

Doing mathematics is reasoning correctly, even with “incorrect” figures. Modeling a real situation often requires considering quantities as equal even if they differ in reality.

🔢 Mathematical Concepts in Play

Comparison

Empirical: “by eye,” via superposition, cutting, manipulation.
Calculative: using modeling with fractions or discrete quantities.

Sharing

The attempt to equalize portions can continue indefinitely, each correction creating a new inequality.
During the activity, the teacher can choose to end the loop with two very small, roughly equal portions.

🟢 Activity 1: Playing with quantities: empirical comparisons

👦🏻 Target Age: 5–6 years (Kindergarten)

⏰ Duration: 30–45 minutes

🎯 Learning Objectives

Explore the notion of equality through play and manipulation of quantities: lengths, volumes, areas, angles, and numbers.

📝 Principle

Children play at equalizing portions (role-play with 3 children: the fox and two bear cubs) to understand what sharing means:

– in length (goat cheese log)

– in angle (Camembert)

– in volume (Mozzarella with whey, cancoillotte)

– in area (flat cheese)

– in number (Apéricubes, goat cheese caps).

Materials to Prepare

Type of Cheese	Object to Manipulate	Quantity Worked
Goat cheese log	Paper strip to cut	Length
Camembert	Paper disc to color	Angle
Mozzarella	Modeling clay ball	Volume
Flat cheese	Cardboard piece to cut	Area
Apéricubes	Tokens or cubes	Number

Procedure

1. Share by Eye

In groups of three (two bear cubs, one fox), distribute a “cheese.”

Children must share “by eye”, without rules or tools, each taking a portion.

Observe their strategies: folding, cutting by sight, tactile comparison, discussion…

Children agree on informal ways to share each cheese and check if portions are equal.

2. Formalize a Possible Equalizing and Removing Strategy

Ask the children: “How can we make the portions equal?”

Possible answers:

– Superimpose them

– Align starting points and cut the excess

This is not what the fox does!

❗ For volume (modeling clay as mozzarella), it is more complex. Initially, it’s unclear.

Based on the mozzarella whey: immerse both portions in a liquid and compare height (with a mark on the container). But this is complicated.

The fox teaches a lesson; the bear cubs may be satisfied with what they have next time or try to solve the problem themselves.

🟣 Activity 2: Calculative comparisons to approach the concept of fractions

👦🏻 Target Age: 10–11 years (Grade 5)

🎯 Objectives

Compare two angles using fractions or without using fractions, though fractions make it easier by reducing the problem to integers.

Start by imagining or drawing what happens in the story.

Represent successive sizes of the cake.

Modeling with fractions is not the only method: one can compare angles without fractions, but fractions simplify modeling by converting to comparable integers.

Materials

Use similar materials to illustrate the story when it is read a second or third time to deepen concepts.

Provide enough identical portions. The number of portions can vary depending on children’s ages.

1 - Start by imagining or drawing what happens in the story.

2 - Represent the successive sizes of the cake.

3 - At each stage of the story, children can materialize the portions of the two bear cubs and the fox.

Fair sharing: If the cheese were divided into 16 parts, each bear cub should get 8 portions:

$$\frac{1}{2} = \frac{8}{16}$$

Step 1

But in the story, one bear cub (green) takes a larger portion.

The division goes:

Green cub $\frac{9}{16}$

Blue cub $\frac{7}{16}$

We have $\frac{9}{16} + \frac{7}{16} = 1$

Step 2

Now we must account for the fox’s portion:

Green cub $\frac{6}{16}$

Blue cub $\frac{7}{16}$

Fox $\frac{3}{16}$

We have $\frac{6}{16} + \frac{7}{16} + \frac{3}{16} = 1$

Step 3

Green bear $\frac{6}{16}$

Blue bear $\frac{5}{16}$

Fox $\frac{5}{16}$

Total check: $\frac{6}{16} + \frac{5}{16} + \frac{5}{16} = 1$

Step 4

Green bear $\frac{4}{16}$

Blue bear $\frac{5}{16}$

Fox $\frac{7}{16}$

Total check: $\frac{4}{16} + \frac{5}{16} + \frac{7}{16} = 1$

Step 5

Green bear $\frac{4}{16}$

Blue bear $\frac{3}{16}$

Fox $\frac{9}{16}$

Total check: $\frac{4}{16} + \frac{3}{16} + \frac{9}{16} = 1$

Step 6

Green bear $\frac{2}{16}$