Waldorf Math Gnome Sample Stories
updated July 24, 2022

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I found, out of all the enchanting Waldorf curriculum ideas I read about, that the hardest one for me to get concrete information on was the Math Gnome Stories.
It sounded so dreamy in the abstract, but it was confusing when I went to actually teach it. And, of course, I wanted to do it the right way!

WHO are the gnomes? What are their names? What color are they? Do the colors matter?

HOW are they introduced? What verses do you use? What stories?

AND THEN WHAT? What happens after the gnomes are introduced?
What kinds of math problems follow the introductions? What about manipulatives? Do you actually have to buy glass gems?

HOWexactly do these math gnome stories go? How do you write them successfully?

HOW do these characters interact? Are they paired up in the same math problem, one helping
where another has made a mistake? Does Plus bring too much and then Minus gives some away so that the gnome king gets the right amount in the end?

Is there always a story to go with every math problem you give your child?

And what about the main lesson book? What goes in it? How can you possibly fill up an entire big main lesson book with just four little gnomes and their king?

Even after the MLB is done and the block is done, do you still continue to do Math Gnome stories? Or just go back to the mental math and clapping and skip counting games in circle time?

And what about the squirrels? Don't some people do squirrels instead of gnomes? Do you make little squirrel finger puppets with the math symbols embroidered on them? Use piles of acorns?

And etc.

If you haven't yet read my Math Gnomes page, start there. It's where
I began. On this page I will endeavor to lay out how we did the actual Math Gnomes block in the Spring of 2020,
having done Land of Numeria (aka Quality of Numbers) in the Fall of 2019.

This is only my interpretation of the concept of this block, and should not be taken as the be-all and end-all. You must do your
own thinking through what would work best for your child. We were also hindered in our homeschool co-op by a Shelter at Home order
for the state of Illinois during the COVID-19 pandemic, so I was adapting this to teach it to a group of students via Zoom session.

Count and step up to 10.
Count and step up to nine and clap (clap once)
Count and step up to eight, clap, clap (clap twice)

Continue until it is all claps and then reverse until it is all steps.

Fizz Pop, page 111

Start with fizz which replaces all multiples of 3. Only go as far as 36 in the beginning but later you
can go to 100 +. One starts and the next child calls out 2, the next fizz, etc.

1 2 fizz 4 5 fizz 7 8 fizz 10 11 fizz etc.

Now repeat the exercise but leave out fizz and substitute pop for all multiples of 5.

When they're ready, try Fizz Pop:

1 2 fizz 4 popfizz 7 8 fizzpop 11 fizz 13 14 fizz-pop 16 17 fizz 19 pop etc.

Hmmm... are there any more numbers that would be a fizzand a pop?

Skip Counting Patterns to 24 (PDF)
this doesn't always print correctly; make sure your printer is set to Landscape and 100%

Note: If doing this with colored pencil and the Montessori colors, use green for 2, pink for 3, yellow for 4, purple for 6,
and brown for 8. I would suggest orange for 12 and grey for 24. The grey line looks just like a big kangaroo hop! Count
with BIG numbers: by 100s to 1000.

UPDATE: Another nice book for skip counting by 2's is The Lighthouse Cat by Sue Stainton. 12 cats
means 24 glowing eyes!

Day Two

Count & Step as on day one

Trace hands from green construction paper and cut out; attach to piece of white paper

Write number sentences for the different ways fingers can be combined to make 10 as you bend the paper fingers down
(thank you, Gavin McCormack, for sharing this great idea!)

Recall Plantain and Calendula and how we left the story at the end of the Quality of Numbers block

Tell the story of Farmer Plus and act it out.
At the end the king is left with overflowing warehouses!

Day Three

Read Six-Dinner Sid by Inga Moore; how does Sid remind you of Farmer Plus? (the love of
comfort and a good meal,
adding more and more to get lots of dinners)

Get 12 gems and set them out on a board; arrange them in lots of different possible combinations and write
the number sentences; can you find a combination we have not written down yet?

Draw Plus for the MLB with his 12 gems at his feet and some of your favorite number sentences

Day Four

My students were very familiar already with the idea of Minus as "take away," so I immediately wanted
to replace that with the more specific understanding that we use subtraction to find the difference between two numbers.
We began by reading Let's Get Turtles by Millicent E. Selsam.

Then we discussed, where in the story do you find examples of subtraction? They came up with the turtle eating the worms,
and the boys spending money at the pet store. Worms eaten. Money gone.

Then I clarified that you use subtraction whenever you want to find out the difference
between quantities; where in the story do we see examples of people measuring two things and then looking to see how they are different?

That brought us to LOTS of new examples for subtraction: the difference in temperature between Billy's body
and his bathwater,
the temperature in the turtles' bowls being hotter or colder than it should be
and figuring out what to change to correct it,
the six pieces of food that Jerry's turtle wasn't eating, the size of each turtle after the experiments that the zookeeper wanted
them to try (and why they should have measured the turtles beforehand). Considering the shopping at the pet store again:
the amount of money the two boys spent was different because Jerry bought a turtle bowl but Billy didn't need to. And, as one little girl
pointed out, there were a bunch of turtles in the tank at the petshop and Billy and Jerry bought four out of the group, leaving some turtles
behind.

Discuss today's temperature compared to yesterday's (it is 30 degrees colder today!)

Discuss how your age now and your age before you had your last birthday are different by 1

Tell the story of the king calling for a council meeting, having a new advisor come in, and what happens with Mr. Minus.
Act it out. At the end the king is left with empty echoing warehouses, frustrated and confused subjects, and nothing to eat for breakfast but a stale leftover breadcrust!

Day Five

More work with the boards and gems!

This time I told them little stories with problems
in them and they used their gems to solve them, then the children each shared
their answers and their strategies. Some lined up the two quantities in two straight rows
side by side very carefully, and then counted how many gems were different. After a while, I showed
them that you get the same answer faster by making the large number and then removing the smaller number. But I thought it
was wonderful that they were looking so intently at the numbers as being different from one another, and not only as "take away."

It's
also nice to make sure Minus is presented as a helping figure, for the child who acted him out yesterday... instead of just as the character
in the story who made the king's problem even worse!

In my storytelling, I focused on the different ways that a subtraction problem can present itself:

At the Easter Egg Hunt, Zac (age 4) found 14 eggs and Natalie (age 18) found only 3 eggs. How many more Easter eggs did Zac find?

I went to two grocery stories in search of bread. At the first store a loaf of bread was 6 dollars but at
the second store a loaf of bread was 4 dollars. How much less was the bread at the second store?

I went to visit my grandfather and he showed me his vegetable garden. I saw 4 lovely tomato plants, but he told me
that he had 17 tomato plants in all and the rest were planted behind the shed. How many tomato plants were behind
the shed? (I would strongly recommend drawing a picture of a shed with four plants in front of it. This problem is
much harder for children than it seems.)

The Gnome King announced one day that he wanted each gnome to collect 15 gems. But Plus just kept getting more and
more until he realized that he had collected too many. He had 20! And
he didn't know what to do! Plus only knows how to make numbers bigger. He doesn't know how to make them smaller. Minus
offered to help (he's really good at taking away when there is too much). How many gems did Minus take away so that Plus
had 15?

The next day the Gnome King announced that he wanted each gnome to collect 7 gems. Poor Plus. You know what happened... Again, he got carried
away with all the beautiful gems and this time he collected way way too many. He had 19! Kind Minus offered to help. He knew
how to fix everything. How many gems did Minus
take away so that Plus had 7?

Draw Minus for the MLB (pockets with holes in them) and some of your favorite number sentences:

Read these aloud as follows: "11 is the same asthe difference between 14 and 3"

Read Seven Little Rabbits by John Becker; how does this book remind you of subtraction?

Listen to Tap Your Sticks by Hap Palmer (link to free YouTube video),
play rhythm sticks in patterns

Tell the story of the king calling for a council meeting, having a new advisor come in, and what happens with Tommy Times.
Look at examples of the multiplication symbol in the story (wheels of cart, bell, suspenders, cartwheel). At the end
the king is back to overflowing warehouses!

Talk about how Times skip counts; listen to and sing the 2 table
from Waldorf Skip Counting Songs
(link to free YouTube video)

by 2 to 24 -- London Bridge (start at 0:21)

by 3 to 36 -- Row, Row, Row Your Boat (start at 0:49)

Celebrate the fact that Zac lost his second baby tooth today; talk about the Tooth Fairy
as being an example of multiplication (the same amount over and over); skip count dimes by 10

More work with the boards and gems!

Recall how Times helped the farmers to grow more produce. Arrange 4 gems ("cabbages") in a row. Have Times come
over and suggest 3 rows of four. Make them with the gems. Count how many cabbages that is. Then rearrange the 12 to another
garden arrangement (again an array: orderly rows all containing the same number) containing 12 (2 x 6 or 6 x 2).

Add another 3 gems, making 15. How can you arrange your cabbages? (3 x 5 or 5 x 3)

Add 3 gems, making 18. How can you arrange your cabbages? (3 x 6, 6 x 3, 2 x 9, 9 x 2)

Of course, it is important that Times have a chance to help out his fellow gnomes as well. The Gnome King announced one day that he wanted each gnome to collect 12 gems.
Plus got carried away (as always) and collected 16. How many did Minus have to take away for Plus to have 12? Now, Plus is happy
because he has 12 gems but Minus is sad because he has only 4 and he is supposed to bring 12 to the king. Along comes Times, who
suggests multiplying the gems by making an additional row of 4. Count the gems Minus has now to see if it is the correct number. Realize
that it is not and add another row of 4. 12!

Draw Times for the MLB and the array of 3 x 4 gems. Write the number sentence. Sing the 3 table.

Read The Great Molasses Flood by Beth Wagner Brust; how does Maggie remind you of Tommy Times; where
do you see multiplication in this story?

More work with the boards and gems!

The story never tells us how tall Maggie is... only that the molasses flood is first four times her height, then three times her height,
then the same height as she is. Have Maggie be two gems high. How high is the molasses flood when it is four times her height? Build it
and count the gems. Then three times, then her height.

Then have Maggie be four gems high. How high is the molasses flood when it
is four times her height? Build it and count the gems. When it is three times her height, how many fewer gems do you need? When it is her height,
how many fewer gems do you need? Discuss that any number times 1 is itself and any number times 0 is 0.

Tell the story of the king calling for a council meeting, having a new advisor come in, and what happens with Mr. Divide.
At the end all is well!

As we did with the symbols for more (x is speed addition... looks like a + rolling down a hill), look at the visual relationship between the symbols for less (-, ÷).
The division symbol
indicates that you will also have less, but the dot above and below is a reminder that you are sharing it out fairly.

Sing the 4 table.

UPDATE: I just fond another story that is perfect for multiplication, and also covers estimating too. It is Lucky Beans
by Becky Birtha. I would suggest giving it its own day after The Great Molasses Flood.

Read chapter 5, "Happy Jack Squirrel's Stolen Nuts," from Mother West Wind's Neighbors
by Thornton W. Burgess; where do you see division in this story?

UPDATE: I just fond another story that I think would work
better for first introducing division, which is
The Little Mouse, the
Red Ripe Strawberry, and the Big Hungry Bear by Don and Audrey
Wood. It is shorter and easier to follow, so it makes for a nice introduction to sharing
out fairly (and introduces halves)... plus the strawberry is red! Eat strawberries afterwards!

Then you could do the Old Mother West Wind story on the following day,
to delve into division a bit further. It is a really fun story
to do with three little finger puppets (grey squirrel, red squirrel, chipmunk). Go out and
collect acorns, or
use walnuts or pecans or chestnuts!

Encourage students to share stories they find which have one or more of the operations in them

Flicka, Ricka, Dicka and the Big Red Hen by Maj Lindman
6 chickens + 1 rooster is how many? when Maisie gets lost, how many are there now? when Maisie is found
(along with her six baby chicks), how many are there now?

More work with the boards and gems!

Three swans were gliding on a pond. Four swans joined them, and then three more. How many swans were now on the pond?
These swans then flew off in two groups of equal numbers. How many swans were in one of the groups?

Four woodchucks came out of their underground home to forage for seeds. Two went towards the river and two went towards
the old oak tree, where they met up with seven squirrel friends. How many animals are now by the old oak tree? The
animal friends split up into three equal groups. How many are in each group?

Listen to and practice Kookaburra tune for the 4 table.

Day Ten

Play Fizz Pop, introduce Clap

More work with the boards and gems! Have students create math stories for the rest of us to solve:

M has eight frogs. For her birthday she gets six more; for Christmas she gets another one. How many frogs does she have now?
Then her mother tells her that she needs more frog homes because the frogs are too crowded in their one little habitat. She gets
two more frog habitats and divides the frogs evenly between them. How many frogs are in each?

A's family is making an angel food cake recipe which calls for twelve eggs, but they only have four in their fridge. How many eggs
do they need?

C's little brother has five pieces of paper in his art area. On his birthday he gets ten times that amount! How many pieces
of paper did he get for his birthday? How many pieces of paper does he have all together?

Sushi the monkey (who wears a top hat) has eighteen bananas. The wind blows away 7. Oh no! How many bananas does he have left?
His three children decide to help the family out, so they each go out and collect 4 bananas. How many did they bring back? How many bananas does
the family have in all? His children are hungry, so
Sushi wonders if he can divide the pile of bananas evenly among the three of them. Can he? How many
more does he need for things to be fair? How many bananas does each little monkey get in the end?

R and her mom and her dad and their two dogs go for a walk. When they were walking down the street they saw
five other people walking their dogs. Each person had two dogs. Then they saw a dog walker with six dogs! How
many dogs did they see in all that day?

student responses: two dogs died, the journey was 800 miles and the train did 100 miles of it, Gunner and Balto and their
team did the last two legs of the journey instead of their planned distance, medicine was expected to arrive in 15 days and they made it in 5 1/2

Solve several of the problems in the story. We used the gems to each represent 100 miles and calculated
how many miles the dog sled teams traveled. We also made a circular paper gem which could be cut in half
and swapped it out for one of the glass gems, made 15 using 14 glass gems plus the paper one, and then calculated
that by taking just 5 1/2 days for the journey they cut 9 1/2 days off the expected time!

Note: For drawing this in the MLB, draw a 5 x 3 grid to show 15 days on the calendar, and then cross off 5 1/2. I think
this makes it easier for students to see how it is still a whole day and
yet it is two halves, and to count off the nine days plus the remaining half. Plus it makes a nice MLB page.

Work on patterns. Find the 12 combinations of two addends (specify that they must be whole numbers) that equal a sum of 11. Sing the 2, 3, and 4 table and listen to the
6 table.

Day Twelve

Solve a word problem which uses division, draw Mr. Divide with four sets of seven gems organized neatly, and notice
the relationship between his artwork and Tommy Times. They both have neatly organized the gems into sets! The difference
between them is just that Division asks the question "how much does each one get?" and Times answers the question "how much
do they have in all?"

C's little brother is having a birthday! His family makes 28 cups of punch. They want to divide it evenly
between 4 pitchers. How many cups will they put in each pitcher?

Play the Silks Game (this is a simple game which I just invented and which was a huge hit). I read a word problem aloud and the children had to listen
and try to figure out what operation it was. They did not solve the problem. They showed which operation they thought it was by
putting on the color silk of that math gnomes. Or, if they didn't have a set of green / blue / yellow / red playsilks (21 inches square is a good size for wearing as a cape)
at home,
they simply began acting out the part of that character.

It was a blast! I loved to see them walk slowly with the hunched over back of
Mr. Minus searching for his gems, cartwheeling enthusiastically around like Tommy Times, or standing cross-armed and bossy (but kind) like Mr. Divide.
Farmer Plus, of course, is just constantly bending down to pick up more and more stuff and put it in his pockets.

Today's problems are adapted from one of the books I gave to Becca when she was little.
My kids used to love to play school and used my extra workbooks and textbooks from my classroom stash to do it.
This is Understanding Math
Story Problems 2 by Martha McGlothlin, pages 22-23.

An airplane ticket from Houston to New Orleans is $70. A ticket from Houston to Dallas is $45. What is the difference
in the cost of the tickets?

James, Robert, and Luther are newspaper boys. Each day James delivers 58 papers, Robert delivers 61, and Luther
delivers 45. How many papers do the boys deliver all together?

A bag of beef-flavored dog treats has 9 treats in it and you have three dogs. You want to divide the treats equally between them.
How many treats does each dog get?

A small jar of pecans costs 97 cents. A small jar of peanuts costs 83 cents. What is the difference
in price between a jar of pecans and a jar of peanuts?

Laurie brushes her teeth 3 times each day. How many times will she brush her teeth in a week?

The Tigers football team scored 31 points in their first game. The Raiders football team scored 17 points. How many
more points did the Tigers score than the Raiders?

Mrs. Simpson wants to give some flowers to her friends. She has 5 vases to put the flowers in. She will put 3 flowers in each
vase. How many flowers will she need in all?

75 people watched Tad's baseball game. 56 people watched Steven's baseball game. How many fewer people
watched Steven's game than watched Tad's game?

Bess' suitcase weights 31 pounds. Her brother Frank's suitcase weighs 45 pounds. Her mom's suitcase weighs 53 pounds. How
much do all the suitcases weigh together?

A circus has 24 monkeys and 12 horses in it. The circus wants to combine the monkeys and horses and then
sort the animals out into three even groups. How many animals are in each group?

Mr. Hawkins is a barber. He works every day. He gives 7 haircuts each day. How many haircuts will Mr. Hawkins give
in a week?

Mr. Simpson needs to have his car brakes fixed. At Brake-Fix it will cost $97. At Frank's Brakes it will cost
$83. What is the difference in the cost at Brake-Fix and Frank's Brakes?

Mrs. Barker is taking dancing lessons. She takes 4 lessons each month. If she goes for 7 months, how many
lessons will she take altogether?

Francis lives 37 miles from the airport. Kelly lives 18 miles from the airport. How many fewer miles
does Kelly live from the airport than Francis?

Mr. Jacobson owns a dairy farm that had 162 cows. Then he bought 38 more cows. What is the total
number of cows Mr. Jacobson has now?

Talk about checking your answer for reasonableness (my big focus here is building math sense). In this workbook
Becca wrote 11 as the answer to the problem about Mrs. Barker's dancing lessons. I can tell in my gut that just doesn't
feel right. It doesn't feel right that 4 taken 7 times would be 11. So we talked about the importance of knowing
what the operation is before diving into the problem.

We got out our boards and gems and solved the Mrs. Barker problem correctly. Then we looked at
all the ways we could divide 28 evenly into groups and made a list of the number sentences. Then I showed
them how to put all the factors in order and make a list of the factors (1, 2, 4, 7, 14, 28). We are starting
to use correct terminology like "factor," "multiples," "sum," and "addend."

Solve some multi-step word problems with the gems; continue to have each child share his/her strategy
for manipulating the gems as well
as the solution to the problem:

Bianca decided to build a gnomie house near her home. She gathered 6 good-sized sticks for a strong tipi-like structure;
then she gathered 8 smaller sticks to put in-between the larger ones. Finally, she used 10 small, bendable sticks to wrap
around the standing sticks. How many sticks did she use altogether? If she was to take all those sticks and separate
them into 2 equal piles, how many would be in each pile? If she was to separate all the sticks into 4 equal piles, how many
would be in each pile?

Ryan has two very frisky cats named Thunder and Lightning. They love to get into mischief with many things
around Ryan's house. Thunder and Lightning have a cat tree with a ladder, a platform to climb up onto, and a railing.
Besides their other adventures around the house, they love to go up and down the cat tree ladder. If the ladder has seven
steps and Thunder climbed up just three steps, how many more steps does he need to climb to get to the top? If the ladder
had ten steps and Thunder climbed five steps, how many more steps would the cat need to get to the top? If Lightning
jumped up every other step of the ten-stepped ladder, how many rungs (steps) did she touch? Lastly, if Thunder climbed a
total of fourteen steps and Lightning climbed a total of twelve steps, how many steps did they climb altogether?

Have one child write the multiples of 4 and the other watch the digits in the units place to check for patterns. Then
have the second child write the multiples of 6 and the first child watch the digits in the units place. Amazingly, we find the
exact same pattern!!!
Sing the 4 and 6 table.

potential for math problems in this story: she had 12 eggs and they all broke, she spent some (or all) of her money at the store, she and her dad and her
mom each picked apples, they each carried a portion of the apples home, some of the apples were used in the pie

Do some informal assessment using the multiple choice questions from Understanding Math
Story Problems 2, pages 25-26. Which one of these is the correct ending to the problem?

For a Fourth of July party, Everett blew up 20 red balloons, 20 white balloons, and 15 blue balloons.

a. How many firecrackers did Everett have?
b. How many balloons did Everett blow up in all?
c. How many people came to the party?

Mrs. Conklin makes clothes for her grandchildren. She needs 4 spools of thread to make each dress. She made 6 dresses.

a. How many spools of thread will Mrs. Conklin need to make all 6 dresses?
b. How many buttons did Mrs. Conklin need?
c. How many shirts did Mrs. Conklin make?

Mrs. Martin spent $61 at the grocery store. Mrs. Davidson spent $37 at the grocery store.

a. Which grocery store did Mrs. Martin go to?
b. What did Mrs. Martin buy?
c. What is the difference in the amount Mrs. Martin spent and the amount Mrs. Davidson spent?

There are 6 beds in Tony's house. Each bed has 3 pillows on it.

a. What is the total number of pillows on all the beds?
b. What color are the pillowcases?
c. What size are the pillows?

A large package of bandaids has 64 bandaids in it. A small package has 30 bandaids in it.

a. How much do the bandaids cost?
b. How many more bandaids are in the large package than in the small package?
c. What color are the bandaids in the small package?

Mrs. Tyler bought 21 tomato plants for her garden. She has planted 15 of the tomato plants.

a. How many pepper plants did Mrs. Tyler get?
b. When did Mrs. Tyler buy the plants?
c. How many tomato plants does Mrs. Tyler have left to plant?

Tonya drank 4 glasses of water every day for a week.

a. How many glasses of water did Tonya drink in a week?
b. How big are the glasses of water Tonya drank?
c. How many glasses of milk did Tonya's brother drink?

Todd has 15 cows on his farm. George has 11 cows on his farm, and Joe has 13 cows.

a. How many pigs does Sandy have?
b. How many cows do Todd, George, and Joe have altogether?
c. What do the cows eat?

Do some informal assessment having each child create a math story which involved all four operations working together to bring a set
quantity of gems to the Gnome King. For example,

The Gnome King asked everyone to bring him 20 gems, and if they did so they would be invited to the great feast held that
evening.

(Go on and on about the feast, and how delicious all of the foods were and how anyone
who didn't have 20 gems would have to stand in the cold outside the gate, etc.)

Plus got too many of course, and he ended up with 25.

Minus helped him by taking away 5. (Add in dialogue, etc.) Now Plus could go into the feast, and he did so with his mouth watering.

Minus only had 5 and he was sad, but up bounced Times with bell jingling and quickly turned that 5 into 60!

Times and Minus were standing by this massive pile of gems trying to figure out what to do (since they
still couldn't go into the feast), when up marched Divide. He quickly sorted the gems into three piles of 20,
and Minus, Times, and Divide each gave 20 gems to the palace guard and entered the feast. And they all feasted and feasted until late into the night, and it
was the most delicious meal anyone ever tasted.

Sing 7 and listen to 8.

Day Sixteen

Wrap up our block with games! Play Fizz Pop Clap to 20

1
2
fizz
clap
pop
fizz
7
clap
fizz
pop
11
fizz-clap
13
14
fizz-pop
clap
17
fizz
19
clap-pop

Sing 8, write and look at patterns in 9 table, and sing 9

for Grade 1 & Grade 2 practice, and finding number patterns:

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