Kindergarten Math

I don’t post as much about what the twins are doing, and I fear this does reflect where my attention tends to run . . . however, there is the trickle-down effect and I hope they are not growing up in complete ignorance.

Dash has been assigned to set the table for breakfast each morning. This is a great chance to deal with concrete quantities. How many people if Papa isn’t here for breakfast? There are three plates in the dishwasher–how many more do you need from the cupboard? If you dropped two forks on the floor, how many would be left in your hand?

Friday nights are our role-playing game nights. The older two are big enough to sit in with the grownups and are even starting to play their own characters, but the twins are sent to play quietly in the other room and then to bed. Last night Dash was playing with Munchkin cards, a game that reduces role-playing to its simplest and silliest aspects. Your character puts on various equipment with bonuses, fights monsters, goes up levels, and gets more treasure. We have played it as a family many times.

Dash can’t read words independently yet, but the cards are vividly illustrated and plainly labeled with numbers that show the size of the monster, the amount of the bonus, etc., and he is very good at reading numbers. (Even 2-digit numbers, which he likes to punch into the scientific calculator and then read off. I have, by the way, no idea when or how he learned this–I guess the trickle-down effect does work.) So he was working it out on his own with a little help.

He got stumped when it came to adding up all the bonuses his character had from equipment to see if he was strong enough to beat a particular monster. Even with small numbers, adding three numbers at once was more than he could do in his head.

Finally I suggested he take the glass gems he was using to keep track of his level and place the appropriate amount on each card–5 counters on the +5 Gatling Gun, 3 counters on the +3 Twenty Gallon Hat. He figured out what I meant from a brief explanation and when I checked on him next, each card was covered with the appropriate number of counters. Then as he battled each monster, he had to compare his total level plus all bonuses with the size of the monster.

It turned out to be the perfect level of challenge for him, as well as keeping him happy through a long evening. And a lot more fun than “Circle the set with more balloons.”


Game Theory

March is here, and I’m ready for spring, as can be easily seen through our memory selections for this month:

Poem: Spring, by William Blake (the twins LOVE this)

Folksong: English Country Garden.

Memory: The Apostle’s Creed (review, it’s being studied in Sunday School)

Hymn: Amazing Grace

I also created a Lenten paper chain with activities for each day until Easter. We are also working on attending the Wednesday evening services at our church, which are beautifully geared for all ages. On Ash Wednesday the pastor helped each of the children plant flower seeds in a purple pot, and talked about the beauty that would grow in the quiet darkness of Lent. Last week there were candles to light and pray, and D1 asked to go up and pray together. They also had the story of Noah (the Wednesday services are going through Hebrews 11) and D1 eagerly told the whole story–that narration is starting to show.

DOB sets aside two evenings each week to play alone with one of the children. They all anticipate their turn eagerly, and he likes the chance to get to know them individually instead of as a collective chaos. He’d had a bit of a struggle finding what to do with D1, though–they each have very different playing styles and both want to do things their own way. Finally he struck on the idea of teaching her chess. It’s been a huge hit. She is studying it closely, reading books, practicing. She challenges D2 (who is a little more tentative) and her oldest cousin.

Meanwhile D2 has discovered one of those jumping-peg boards, as well as a chinese checkers board. Between them, he’s been absorbed creating, modifying, and studying different patterns, the effect of different rules, etc. I also found an amazing book in my sister’s homeschool library, Anno’s Math Games. It’s exactly what I’ve been wanting–a puzzle and game approach to math that works at a conceptually high level but that is appropriate for early elementary. We have had fun working through the first chapter together and I look forward to doing more. And now I see there are two sequels! Anno’s math books are some of the best out there for this age.

Robin Hood maintains his appeal. I tried reading from one of the illustrated simpler editions we had borrowed from the library–very thin and insipid compared to the Howard Pyle audiobook they listen to every night. What’s Robin Hood without varlets and forsooth?

In writing, D1 wrote up a page of instructions for chess and a lengthy letter to her cousin asking him to play chess. She usually has me write out words she thinks she needs help with. I notice a lot of copying poetry has led her to settle on the rule of starting each line with a capital–we probably need a basic lesson on sentences here soon. D2 is sticking to single words, but they are getting longer, like “bobolink” and “cukoo” from “English Country Garden.”

D1 is devouring Tintin books; she also has been reading some of the Flicka, Ricka, Dicka and Snipp, Snapp, Snurr books. D2 picked up some easy-reader joke books and has been browsing picture books, Frog and Toad, Amelia Bedelia, etc.

Everyone has been drawing a lot, mostly on paper. The big kids added on to some maps of imaginary worlds they created several months ago. The twins are showing more variety of strokes. D3 likes to color things in and sticks to the lines pretty well; D4 likes to draw his own things and sometimes verges on recognizable shapes.

Read-alouds have mostly been Heidi and various tales from the Brothers Grimm in various forms. I reserved The Apple and the Arrow from the library to supplement the Switzerland study; I hope D2 likes it.

The kids are becoming more pronounced in their different selections–D1 usually wants to choose stories and art; D2 usually wants to choose science and math. They are starting to notice this, and I wonder if they even differentiate for the sake of being different. Regardless, it ensures we get a good variety of activities every week.

In addition to all the games and the wonderful Anno’s Math Book, D2 has been asking to do some math worksheets. I’ve been having a bit of trouble with this. The ones from MEP math have a nice variety of problems, and they stick to smaller, more concrete numbers in Grade 1, but they still are not a perfect fit. Some of the problems really need extensive instruction to do (and I’m just not ready to start in on math lessons), and some just seem too abstract in approach for what they need right now. But no other free pages I have found have the nice mix of problems–most math pages are all-of-a-kind, which is not only boring but I suspect dulls the brain from paying attention. DOB finally suggested the rather obvious solution of continuing to use MEP, but marking any sections that I didn’t think they should be doing as “Play” and letting them write whatever they want on them. Duh.

I’m thinking we may wrap up studying Europe within a couple more weeks–true, we’ve only done a few countries, but we have learned a lot about their neighbors. We have some anchor points. And I still kind of would like to move on to Asia and Africa through the rest of the spring and summer and start a definite chronological history in the fall. We’ll see. I’d also like to be in our own house by then. And have the twins potty trained. I can dream. 🙂

Manipulative Photo Post

Not, of course, photos that will manipulate you, but photos of us using manipulatives.  It took me a while to accummulate these, but they are all the genuine article–showing what the ducklings ask to play with and how they play with them.  These are a mix of homemade items, Christmas gifts, and ones inherited from my mom.  As far as I’m concerned, anything small enough to be handled and different enough to be  sorted or counted can be impressed into service as a toddler manipulative.Beads are always eagerly received, even by those too young to string them. Larger ones would probably be desirable at this age, but I wait to let them play with them until they’re past teething, and then I keep a sharp eye on it and teach them not to put them in their mouth. Even though he can’t put them on the string, D2 likes to pull them off the string. D1 can string them herself, now, and likes sorting them by color. The little cups (old jello molds or something–those are from my mom)  are handy for all kinds of sorting projects. Egg cartons are good, too, especially the eighteen-hole variety. My sister sent them these counting bears and frogs, and they are always a  favorite toy, although we seldom actually count them. Here they are actually being used in a mathematical way–a pattern of alternating bears and frogs. (One-to-one correspondence comes in naturally when you start talking about each bear having a frog friend.) At other times they may get cooked and eaten (actually that fate awaits pretty much anything the ducklings play with).
These rocks I scored at  a  garage sale that was getting rid of everything for free.  They were meant to decorate potted plants, but they’re great for handling, sorting, counting, and comparing sizes. And a natural material, finally! Or you can just sit around and pass them from hand to hand. Mmm . . . nothing like a nice, tactile experience. Note the jello molds making another appearance.The Melissa & Doug magnets were a Christmas present. D2 has a set of vehicles. Sometimes we talk about starting sounds,  but mostly they just arrange them different ways. Shortly after this picture, D1 arranged them all in two rows, larger ones and smaller ones.  Someday we might also sort them by where they live or how many legs they have or things like that, but so far we mostly just have fun putting them on and taking them off.
The shapes are homemade by my sister. (Some of them are inherited and she jazzed up the supply.) I find D2 interacts with them better if I just take a few out in a few colors and we  point to the different shapes or colors, or match ones that are the same, or trace around them on paper and match to the paper shape. Sometimes we have his doggie sit on the blue triangle, or the red square.  D2 loves triangles.

D1 likes to sort them, too, and they make also great sandwiches. These are made of felt; I’ve also seen people suggest making them from craft foam.
These logs (I suspect homemade, but they date from when I was little) are in graduated sizes, to sort out longest to shortest. D1 still finds this quite a challenge, but she likes to try it every once in awhile. I find it a challenge to keep them from rolling under the couches.

Other things we like: puzzles, of course, both the wooden knob variety and the foamy Lauri variety. Bingo-style card games with pictures of household objects or different colors or animals or whatever–we don’t try to play Bingo with them, but we sort them by which card they go on and talk about starting sounds. All different kinds of buttons (those jello molds come in handy again). They love to dip and pour grains, but I don’t often feel up to that much mess, although I usually let them help me grind the grain for bread.

Game Cards

My sister sent the ducklings a collection of counting bears and frogs, which are now among their favorite toys. Of course, they don't usually turn them to mathematical ends–they are more interested in using them for the study of physics (force and mortion, i.e., throwing them across the room), culinary arts (you'd be surprised how tasty Bear and Frog Soup is, when cooked in a desk drawer), and the like.

However, last week I decided to see if D1 would like to put them to an actual mathematical use, and since she is always delighted to have a new game, I made her one. I got out some colored dot sticker we had and put from one to four dots in red, yellow, and blue on index cards. (This is all stuff that was laying around the house.) D2 amused himself by pulling stickers off the paper and playing with the odd-colored bears and frogs.

To play the game, she drew a card and put the appropriate number and color of animals, setting one animal on each dot. She thought this was quite fun and went through the entire deck, and as she progressed I could see her getting more confident, picking out as many as she would need at a time and then putting them all on the card at once.

Later I wrote the numbers on the card with her and I probably confused her completely because when she pointed out that she was 2 and D2 was 1, I continued the sequence by noting that her friend Julia is 3 and Regan is 4. She's going to think one counts D2, D1, Julia, Regan.

I think I'm an early learning hypocrite. I don't really believe in formal instruction for preschoolers, but sometimes I have a hard time resisting the urge.

The Silly Question Game

One of D1's favorite things to do when we have a little down time–say at the lunch table, or while sitting on the sidewalk playing with leaves, which for some reason they love to do every afternoon–is play a game of asking silly questions. I usually get it started, but she joins in, not just answering the questions, but making up her own. (Which I think is pretty good for two.)


Yesterday it was food, stimulated by their interest in consuming whatever the tree was dropping:


“Do we eat leaves?” “Noooo.”

“Do we eat biscuits?” “Yesss!”

“Do we eat D2?” “Noooo.”


Then she put in a few of her own:

“Do we eat houses?” “Nooo.”

“Do we eat cars?” “Nooo.”


She usually sticks to making up ones with the answer “No.”


At the supper table we got it going again with DOB. After a few more conventional ones, he threw in a curve ball.


“Do we eat radioactive porcupines?” “Nooo.”


“Hmm,” I said, “I wonder what she'd do with other things she'd never heard of. Do we eat escargot?”




“She's a gourmet!” I said.


“I'm not sure,” said DOB, “Maybe she's just a carnivore. Let me try. Do we eat fried possum?”




“See?” I said, “She's a gourmet.”


DOB remained skeptical and tried a few more exotic foods on her, which she rejected. But perhaps she's just selective.

Something’s Cooking

D1's imagination seems to have had a growth spurt in the past two weeks. She now will amuse herself for half an hour or more in usually indecipherable but obviously elaborate plays with  her little “mans” (Duplo), or “cooking” with dishes from the cupboard, accessorized by the ever-useful film canisters and surplus CDs.


Sometimes I wish she had a proper kitchen set. Or maybe not. As DOB's mother pointed out this weekend, careful copies of the real things are often less enjoyable toys than scrounged objects.


Perhaps it has to do with who creates the meaning. If you have a purchased, properly designed, toddler-safety-approved cup and plate, then they're a cup and plate; a cheap plastic cup and plate, at that. But if you have a CD and a film canister, then they can be dishes of gold and silver, if you want. You are the one in charge, not some distant toy designer.


Then again, maybe I'm just cheap.

Keeping them busy

We do not have any way for the children to watch videos. This is good, because at this stage, if I had it as an option, I would abuse it. So these are some things we do when we've all had it and I must find something to keep them busy or lose my sanity.


First and foremost, if the weather is at all agreeable, we go outside. I don't know why this works, but it does. Take two cranky, fretful children outside and the baby will sit happily in the grass for half an hour, looking at a pinecone, while the toddler empties and fills a dumptruck or watches the cars go by. (Not that they are always good outside, but it seems to be a lot easier than being good inside.) Even sitting on the porch and watching the rain is better than nothing. We have appropriated the ten-foot strip of communal grass between our building and the sidewalk and treat it as our own.


If D2 is reasonably well fed and has had sufficient human contact, I fill a large, sturdy basket with an assortment of reasonably safe things–a block, a beanbag, an outgrown shoe, an empty bottle, a scrap of fabric, whatever comes to hand. He will often happily sit or roll around and empty it, contemplating the various items, for half an hour.


For D1, my standby activity is either a sinkful of water or a pan full of flour, and an assortment of measuring cups, spoons, or plastic dishes. Yes, this makes a mess. But I probably needed to scrub the kitchen floor anyway. If I get distracted and leave the dishes or cooking midway, she will probably climb up and start doing this on her own.


For both of them, the bin of Duplos will keep them quiet for fifteen minutes while I vacuum the rest of the house so D2 doesn't eat too much hair.