What Are the Four Processes in Waldorf Grade 1 Math?

The four processes are addition, subtraction, multiplication and division. In Waldorf grade 1 your child meets all four in the same year, usually in the same block, rather than one after another over several years. Before that comes a block on the quality of numbers, where each number from 1 to 12 gets its own story and picture. And the sums themselves usually start from the whole: your child sees 12 stones and finds that they can be 5 and 7, before learning that 5 and 7 make 12.

For the whole grade 1 year, see What's in Waldorf grade 1?. This article stays with the maths.

What are the four processes in Waldorf grade 1 math?

They're the four operations of arithmetic, given a Waldorf name. Addition puts things together. Subtraction takes away. Multiplication makes equal groups. Division shares out fairly.

What's different is the order. Many school programs teach addition and subtraction in the first year or two and leave multiplication and division for later. Waldorf grade 1 introduces all four together, with whole numbers. Waldorf teachers treat grades 1 to 3 as one arc. The processes are introduced in grade 1 and practised with bigger numbers in grade 2. Grade 3 takes them into long multiplication, measurement and money.

Most Waldorf curricula bring the four processes in as characters. Many families know them as the maths gnomes, and What are Waldorf math gnomes? tells their stories. Some curricula use a king and queen or other figures instead. Whatever the characters, they let your child know what each process does before the sign appears.

The quality of numbers comes first

Before any sums, most Waldorf grade 1 years give a whole block to the numbers themselves. The question is less "how many?" than "what is this number like?"

A Waldorf teacher might bring:

• One as the sun, whole and single.
• Two as day and night, or left and right.
• Three as head, heart and hands.
• Five as the five petals of a wild rose.
• Seven as the colors of the rainbow.

Your child draws the story picture in the main lesson book and writes the numeral on the facing page. Many teachers add the Roman numeral too, so a child sees that I, II and III are made the same way as a tally.

It helps to look for the number outside. On the day you meet three, go and find clover leaves. On the day you meet five, count the petals on an apple blossom or the points of a starfish. The block usually covers 1 to 12 over three or four weeks.

Why Waldorf goes from whole to parts

This is the part of Waldorf grade 1 maths that surprises parents most.

In most programs, a child adds 5 and 7 and gets 12. Steiner suggested doing it the other way round. In his first talks to Waldorf teachers in 1919, he described a heap of 24 scraps of paper. He divided it into piles of 9, 5, 7 and 3. The child starts with the whole heap and finds its parts. He said teachers should go from the whole to the separate parts, and begin with the sum rather than the numbers that make it.

At your table, it looks like this:

1. Put 12 chestnuts on a cloth.
2. Ask your child to split them into two piles. Write down what they find: 12 = 5 + 7.
3. Put them back and ask for another way. 12 = 6 + 6. 12 = 10 + 2.
4. Keep going for 10 minutes, or until the fun runs out.

Your child finds that one number holds many answers. Twelve is 7 and 5, and also 6 and 6, 3 groups of 4, and 2 groups of 6. That's a first taste of multiplication, straight out of addition.

Why does Waldorf teach all four operations in first grade?

Because the four processes explain each other. Prerana Waldorf School puts it simply: multiplication is fast addition, and division is fast subtraction. When your child makes 3 groups of 4 chestnuts, they can see it's the same as 4 + 4 + 4. When they share 12 between 3 bowls, they can see each bowl ends up with 12 take away 4, then 4, then 4.

Meeting all four early also keeps maths flexible. A child who knows 12 can be split or shared can come to see numbers as things to play with.

How is subtraction taught in Waldorf first grade?

Steiner applied the same whole-to-parts idea to subtraction. Rather than "24 take away 3", he suggested starting from the remainder. The child sees 21 left and asks what was taken from 24 to leave it.

At home, give it a story. "There were 12 apples in the basket this morning. Now there are 8. How many did the squirrel carry off?" Your child looks at what's left, counts up to the whole and finds the 4. Many children find this easier to picture than taking away from a pile, because the missing apples have a reason to be missing.

When do Waldorf students learn multiplication and division?

They meet them in grade 1, as ideas you can see: equal groups and fair sharing. Your child might share 15 beans between 3 gnomes, or count the legs on 4 stools. The times tables come in grade 1 too, but as movement and rhythm, not as tables on a page.

That's where Waldorf maths moves. Prerana Waldorf School describes children clapping and stamping through the facts of all four processes, much as a musician learns scales. You might:

• Walk around the garden counting in 2s, with a stamp on every second step.
• Clap the 5s while saying them, then whisper the numbers in between.
• Toss a beanbag back and forth counting in 10s.

Five minutes in morning circle is plenty. Grade 2 brings longer practice and bigger numbers, and long multiplication and division usually come in grade 3.

Is Waldorf grade 1 math behind conventional math?

In some ways it can look it. Your child may not write many sums in grade 1, and there are no timed drills. In other ways it's ahead: the US Common Core, for example, starts multiplication and division in grade 3. By the end of the year many Waldorf children can add and subtract within 20 in their heads, and understand the other two processes as ideas.

If you're worried, Is Waldorf math rigorous enough? compares the Waldorf sequence with the Common Core, grade by grade. Will my Waldorf child be behind in math? takes the same question year by year.

How many math blocks are in Waldorf first grade?

Usually two to four, taking turns with language arts. A common pattern:

• The quality of numbers, often the first maths block of the year.
• The four processes, one or two blocks.
• Number patterns or word problems, in some curricula, later in the year.

Between blocks, maths doesn't stop. It moves to 10 minutes of daily practice and to circle time, where the counting and clapping keep going.

Starpath's grade 1 has free guides for the Quality of Numbers block and the Four Operations block, each with an example story, movement game and main lesson page. For other curricula, see the best Waldorf homeschool curriculum for grade 1.

What to do this week

1. Gather things to count. A bowl of chestnuts, stones or dried beans is enough.
2. Pick one number a day and find it outside: three clover leaves, five petals.
3. Try one whole-to-parts game. Twelve chestnuts, as many ways to split them as your child can find.
4. Tell one subtraction story from the remainder. The squirrel and the apples works well.
5. Add five minutes of counting with movement to your morning circle.