Monday, April 19, 2010

Maths Block II: Gnome Share (Divide)

Last week, I introduced the girls to the character of Gnome Share through an extensive story here. We continued through the week with various exposure to the concept of division. Here is some of what we did that tied into math...

In our first Maths Block, I had several stories going for the qualities of numbers that I thought I would weave number stories into this block. So for the number One, I told the girls the story of "Offerus the Giant" by Jakob Streit found in "The Easter Story Book" (the legend is actually of St. Christopher and is found in many books by various authors. Here is a very short version of it more appropriate for young ones, which takes out the devil section and the section in the end where St. Christopher goes Home to Heaven.) One represents God.

We then went into the living room and Gnome Share revealed his sign in nature.

I showed the girls the chalkboard drawing and read the verse to them. We then drew it in our main lesson books together.

Gnome Share told the story for number 2, which was "The Two Kings' Children" by the Brothers Grimm.

For number 3, he told, "The Three Sons of Fortune" by the Brothers Grimm.

All week we've had fun *sharing* things together. For the first exercise, I took the basket of eggs we painted and counted out 12 of them in one basket. I presented two empty baskets next to it as follows:

I told Elena that I'd like her to count the eggs and then divide them evenly so that she and her sister would have an equal amount.

She loved this! I then made up a story of some squirrels who were hungry and gathered around her, hoping she would share some nuts. So she worked within the confines of the story and was dividing them equally among the squirrels. I then would increase or decrease the number of squirrels so that she could see that 24 divided by 4 equals 6 and 24 divided by 6 equals 4. Or 24 divided by 2 equals 12, etc.

Then Charley finished what she had been working on and came to try, too.

I started her with the 12 eggs divided into two baskets, then told her I wanted some eggs, too - so she divided 12 by 3. And then Daddy wanted some eggs, as well so she divided 12 by 4.

They had so much fun with this and started to see some patterns. I wrote down the equations on a dry erase board. And we made a second MLB drawing to represent our equations.

We also worked with bean bags and rhythms. We were counting by two's and passing our bean bag to the next person on the 2's and then jazzed it up by alternating the bean bag from hand to hand while passing on the 2's. That was a bit of a challenge for them as it involves the thinking and the movement on the appropriate number. I wrote down the numbers on a board so they could see a pattern.

2, 4, 6, 8, 10
12, 14, 16, 18, 20
22, 24, 26, 28, 30
32, 34, 36, 38, 40

When they could see the pattern emerging, they could count by 2's up to 144 (and then they kept going even though we're focusing up to 144)...

This week, we'll be meeting the next process gnome...


  1. Jen, this is fantastic! I am amazed at how magical and beautiful the learning in your home is! I find this so very, very inspiring! Your chalkboard drawings are gorgeous! Do you make them in front of the girls or do you make them the night before?

  2. Thank you so much, Catherine! You're so sweet :D In Grade 1, I think it's preferred to make the chalk drawings privately so I usually do them the night before and turn the board around or cover it with a cloth so they can't see it until the proper time. It also ends up being something they get really excited to see so it builds a nice anticipation.

    We draw our MLB's together, though. One daughter needs to see something on the page before diving in while the other can create her own visions. I do try to encourage her to copy at least the basic elements of the main drawing, but she does like to embellish. HTH :D

  3. So you draw in the MLB in front of them before they do their own or you just start drawing and they start their own while you draw?

    Thanks so much for this information!!

  4. I've done it both ways. When we just started first grade and they were being introduced to the block crayons, I would draw in my book and have them watch. It was hard for them to wait, but I wanted them to see how to use them properly while I was learning, myself. Now that we're almost done with Grade 1, I've gotten more flexible, though we'll talk about what we're going to be drawing in the books first. I've even let them use the stick crayons once in a while when it's a harder drawing, but in the beginning, I was very strict about no stick crayons and no outlining. I think some grade 1 teachers wouldn't introduce sticks until Grade 2 (except for writing letters, but even then...)

    This summer, I'm going to have them practice more on plain paper with the block crayons. They adore the MLB's and get upset when a drawing gets messed up so I figure this will help for next year. :D

  5. Hello Jen!
    This is so beautiful! You are doing such a wonderful job of homeschooling.
    We are working on our 4 processes block right now, as well : )

  6. That's interesting, Jen. I think this is what I will aim for (re: using only blocks first and reinforcing no outlining).

  7. Dear Jen,
    as always your homeroom is just great! I will try te Division Gnome with my girl, who still needs a big bunch of visualization.
    Do you have an idea how to help with addition over 10? Katarina has the problem, that she still counts with her fingers and does not get the step on f.ex. 6+8, or 9+5. Searched on your site, but couldnt find. Thank you for helping! I do try with stones and pearls, but somehow dont find the click button in her imagination.
    Thanks again!!

  8. Thanks Lynn!

    And sounds great Catherine! Work from the inside out with the block crayons :D

    Gabriele, I'm going to pull some things together for you. The girls are counting objects now - no headmath just yet. What comes to mind is using bean bags to learn addition facts, though. You could try that or hopscotch of jump rope to get her moving to cement the facts better.

    And as far as the stones and pearls, are you creating a story to go along with them? It doesn't have to be elaborate or anything, but if your daughter is in Grade 1, teaching is mainly to their imagination (sorry, I can't remember how old Katarina is). I would use something she is very interested in - for my girls, it's animals, so any story with animals (like the one about squirrels coming to them for some nuts) usually gets them excited and in the moment. If you were doing Grade 2, you could tie in dropping stones into the glass for the crow to drink his water (Aesop Fable), or pearls could be tied into jewelry if she was going to make a necklace for Grandma who wanted five and then a knot and then five more. Or water nixies in the sea collecting pearls to present to the Sea Princess or the Queen of the Mermaids, etc. Try creating a story around the activity and see if that helps (if you aren't already) :D And I'll get back to you with some other suggestions after I get my girls to bed :D

  9. Hi again - just lost a long reply (too long) so I'll try to sum it up:

    - it's important to see patterns, which you are doing already so let her see that 9+5 will always have a 4 in the last column. 9+5=14, 19+5=24, 29+5=34, 39+5=44.

    - if she can round to the nearest 10 or even 5, that can help her compute without her fingers. So 9+6, she would round the 9 to 10 and then take away 1 from 6 to get 15.

    - make watercolor flash cards together with the four processes and an = sign. Make games with them involving movement. So give her a problem and have her run up the stairs to get the answer and bring down to you (she figures it out while she's moving up the stairs).

    - movement with addition facts - swinging on a swing, hopscotch, jump rope, throw bean bags, stomping and clapping, jumping over sticks, lay a jumprope on the floor in a circle and have her run around it with one foot in and one foot out of the circle while she recites facts. Bouncing balls with facts, walking on a 2x4 while she recites facts.

    - what type of learner is she? Appeal to that so for auditory, make up a song or verse or rhyme with the facts. Good book for that is:

    - review math 5-10 min every day in circle time that you aren't doing a block on it.

    - nice yahoo group for living math (not waldorf directly, but can be waldorfized) is

    - Make up a board game with her so that she will imprint what is fun/important to her that centers around math facts.

    - Play math games like Sum Swamp, Dominoes, Monopoly, etc. With dominoes, write out the numbers on the blocks and then add them up together. "Number Jugglers" is popular with the math group. Also the book "Family Math" is widely praised.

    - Present non-elaborate word problems to her centered around her interests. If she likes stuffed animals, let them have a tea party and biscuits. Sally wants 4 biscuits and Susy wants 8 so how many will you bring to the table? Then you both join the party after several minutes of problems and eat together :D

    Not all kids learn traditionally, but to avoid finger counting, she has to understand the process and patterns. I love that math is constant (unlike phonics) so once she gets comfortable with the patterns, it'll be easy for her. It's just a matter of presenting the concrete facts in a creative, imaginative manner that becomes second hand with a real understanding rather than remote numbers that mean nothing to her.

    HTH! LMK if you need more specifics, etc. :D

  10. Dearest Jen,

    I am overwhelmed!!
    Overwhelmed how much of your time you offered to us!!!! Huge big thank you from me for all the wonderful advices you gave me!! Feel a little bit ashamed of having so few phantasy myself.....
    Sometimes this math and her drives me crazy, some days it makes me sad, but that doesnt help at all, isnt it. Since I decided the last winter holidays to get active to support her and not leaving it up to her school, since then we have quite a nice relationship. I can see that she started to trust in me after we got the multiplication to be at least remembered and I see her glowing when she can solve her homeworks.
    Now, her schools teaching style is not what fits to us. Japanese schooling is very academic, with a lot of small letters in black on white in an highly unconcentrated class room. Unfortunately she got an unexperienced young teacher for the second year in a row.... Just by writing this, I feel my heart cringe and maybe I should consider again to move and try another school.....But let me stop here, before doing the big jump, I will continue to at least afterschool her( although its hard for me to not get angry on the school). I will go on with your ideas and will start to trust more in my own abilities. Katarina loves water, all mermaids and fishes, so I will try to make a story out of that and count fishes or shells. To get her moving, helps a lot. Throwing bean bags while memorizing did obviously help. I learned a little bit at the Waldorf School in Germany, which we visit each year, the teacher there made the kids climb on the desks while singing English songs, jumping down and clapping hands, amazing, I thought. Will go forward and let her walk or jump the addition.
    Katarina will turn 10 in May and is already in 4th grade since April. Its time for us, I know! She is not the only one in her class counting with the fingers, I guess, I could open up a sidebusiness teaching creative math!
    Jen, I hardly find words to say enough thank you to you! Thank you so so so much!!! I am absolutely touched and grateful for your generous help!!
    Will go and search immediately for the books and groups you recommended.
    I am so relieved to have asked for help and will for sure have a better sleep this night!
    Your advices mean the world to me!


  11. Gabriele, what a touching response - you just made my day! Thank you so much and I'm so glad I could help. Definitely join the living math group and in the archives, there is a wealth of info. Post your questions there - there are some real math experts in there - sometimes almost intimidating as they almost speak a different lingo :D

    There's also a wonderful summary of a mom who switched to living math here which has great ideas on making your own games and things:

    And please visit this site for a lovely list of math readers and other games/lesson plans from the owner of the Living Math Group:

    Like I said before, not all this is "waldorf" per say, but you can waldorfize and living math is wonderful for really grasping how much we use math in our everyday lives! Cook, bake, knit, build something together, sew together - read patterns, all of that will help her grasp the essence of math :D

    Keep me updated on your progress & you're doing an amazing job balancing out what she is getting in school! What a wonderful mother you are (((hugs)))