Build & Learn Mathematics

Seven Operations. Six Structures.

How much mathematics could that possibly contain?

Most elementary math curricula spend years teaching number sense: math facts, algorithms, rules, decomposition strategies, benchmark numbers, mental-math strategies, and particular ways to move from one number to another.

Build & Learn takes a different approach.

We teach children seven operations and six Cuisenaire rod structures. As they manipulate those structures, they learn the rules for navigating them and how to record what they do in symbolic form.

Then we leave number sense to the child.

There are infinitely many numbers and an inexhaustible number of relationships among them. We cannot teach children every path through that landscape. What should we do instead?

Teach them how to navigate.

---

What Do Children Actually Learn?

Children learn to use seven operations:

Addition, subtraction, multiplication, division, roots, exponents, and fractions as operators.

They manipulate the structures using these operations and discover what is possible. They learn the rules that govern those manipulations and how to record what they have done with mathematical symbols.

As their fluency grows, they can reverse operations, repeat them, combine them, nest them, substitute expressions for expressions, and transform relationships while preserving what is true.

The structure has not changed. What the child can see and express has.

---

What If We Left Number Sense to the Child?

Start with a deceptively simple question:

What is 10?

You can tell me that ten comes after nine. That it is 8 + 2. Or 2 × 5. Half of 20. √100. One ten in our base-ten place-value system.

All of those are true. But every one tells us about a relationship in which ten participates.

There are infinitely many such relationships.

Most number-sense curricula select useful relationships for children to learn. They build highways, major roads, and country roads between numbers.

Build & Learn gives children the tools to build roads.

The numbers themselves do not express the relationships. The operations do.

Once children know how to use the operations and manipulate the symbols, they can generate relationships nobody thought to teach them. They can go somewhere mathematically because they noticed there was somewhere to go.

Mind the symbols and the numbers take care of themselves.

Caleb Gattegno

What Does the Work Look Like?

Mostly, it looks like play.

Children build. They compare. They play games. They make predictions. They try something. They talk about what happened. They change something and try again. They write relationships. They substitute. They hunt for everything they can find in a structure.

Through Notice–Wonder–Discover, we give children something worth attending to, something to do, and something to talk about.

---

This Is Normal.

These are examples of normal student work in Build & Learn when children do the work.

And most of the work is play.

This is normal in Build & Learn
when children do the work.

---

How Do They Get There?

Children begin by working with the rods and mathematical language.

1. Build and read
2. Build from oral language
3. Translate into symbols
4. Read symbols
5. Write from oral language
6. Translate back to rods

We do not rush children into written mathematics before the language and relationships are available to them. Symbols are part of the landscape from the beginning.

That is why algebra does not suddenly arrive as a new subject years after arithmetic. Children have already been playing with mathematical relationships from the very first explorations.

---

Everyone Begins With Cuisenaire Rod Structures

Build & Learn: Cuisenaire Rod Structures is the foundation of the curriculum. Everyone starts here.

Children learn the six foundational structures while developing fluency with mathematical language, operations, equivalence, unknowns, substitution, and symbolic manipulation.

Games and investigations give them repeated opportunities to use what they know in new situations.

Then: Build & Learn Numbers 1–100

After Cuisenaire Rod Structures, children can continue into Numbers 1–100.

They take the tools they have acquired and go exploring the landscape of numbers 1–100: relationships involving doubling and halving, factors, multiples, squares, primes, and much more.

Numbers 1–100 is not sold as a standalone starting point because it builds on the mathematical language, structures, and symbolic work established in the first course.

---

What You Receive

• 80+ short video lessons so you can open the course and begin without hours of preparation.
• Parent guides and task cards with enough guidance to understand the investigation and support your child while leaving the mathematics for them to discover.
• Games and investigations that give children mathematics to do and talk about.
• Skills checklists so you can see what your child can do without reducing progress to pages completed.
• Family access so the curriculum can be used with the children in your household.
• Community support where you can ask questions, share student work, see what other families discover, and get help when you need it.

Choose Your Build & Learn Curriculum

Everyone begins with Build & Learn: Cuisenaire Rod Structures. Families can enroll in Cuisenaire Rod Structures alone or purchase Cuisenaire Rod Structures + Numbers 1–100.

---

Still Wondering If Build & Learn Is Right for Your Family?

Come into the community and ask. That is exactly what it is there for.