(Referring back to two previous math posts)
When I did the spring workshop about frugal curriculum, I found it very hard to fit everything in to the hour available (it went so fast!. Some people think I'm quiet, but not when I get started on this!). But anyway, I think some people still felt shortchanged on the "how." This is for them, and I'm sorry to still be going on about math, but it is one of the easiest examples to use when you're talking about "teaching the child, not the book."
Here's a typical week of math work for a first or second grader, based on the common items in the math cupboard. This is the quick version:
Monday: Practice skip counting, play a dice game, do a workbook page.
Tuesday: Addition flash cards, card game.
Wednesday: Workbook page, practice telling time
Thursday: Addition on the hundred chart; play store
Friday: Story problems with real objects; then make up a story problem for Mom to solve.
This is the detailed version:
"Practice skip counting": There are all kinds of ways to do this, starting with no materials at all: you start counting and the child follows you. Two, four, six, eight (who do we appreciate?). Or you can count Cheerios, raisins, pebbles, coins. Or you can take paper plates and mark them up as follows: the "2" plate has a big "2" in the centre, and the following numerals written around the outside (all vertical so you can read them like a clock): 2, 4, 6, 8, 0, and then those five repeated again. What you do is start at the top and go around the plate clockwise; you can keep on going around till infinity if you want, and the last digit will always be whatever numeral you're pointing to. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 and so on.
You can make other plates the same way. The "3" plate has these numbers spaced around the rim: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0. The "4" plate has 4, 8, 2, 6, 0 on it twice; the "5" plate has just 5's and 0's. (I saw counting circles like this in the Miquon First Grade Diary, and the paper plates are just to make them sturdier.)
And you can practice skip counting lots of other ways too: songs (commercial or free online); playing Buzz (scroll down there or do a search on the page for Buzz); making jumps on a number line; counting pairs of eyes and ears, or wheels on cars; colouring multiples on hundred-chart printouts and then using them for practice; and so on. You don't have to do the same thing all the time!
And look at that, we're only on Monday...
"Dice game": Here are some typical games from Marilyn Burns. If you really can't think of any others, how about Bug? (That was around long before Hasbro turned it into Cootie.)
"Workbook page": depends on the child and on what you have available; if you don't have any workbooks, you can search online for pre-made or custom-made worksheets--here's one worksheet generator you can use.
"Addition flashcards": Commercial or homemade, regular or triangle, straight up or used in a board game (you have to answer a question before you make a move). Just don't overdo it on these: math isn't all about memorizing facts.
"Card game": again, there are all kinds of games, including the schoolish kind and the just-for-fun kind. Maybe Math War, or The Greatest Number (from Ruth Beechick's Arithmetic booklet).
"Telling time": we use the cardboard clock and set the hands to a certain time, and Crayons uses it as a guide for copying onto a clock worksheet. Or we use the toy clock as a flashcard--I show her the clock, she tells the time; or I say the time and she moves the hands.
Or I just ask her occasionally what time the wall clock says!
"Hundred chart": Ruth Beechick has many suggestions for making good use of this. With Ponytails, I did a bit of hundred chart work almost every day during grade 1. I would just ask her several addition and/or subtraction questions, sometimes random and sometimes following a pattern. Then she would ask me some.
"Play store": Bring out coins, label real or pictured objects with prices, decide what to buy, figure out what coins you need to pay for it. Later buy two or three things at a time and figure out your total, or order from a "menu." Later still, make change.
"Story problems with real objects": that can mean symbolic objects, too! For instance, several coloured cubes become swimmers in bright-coloured bathing suits. Some of them go into the water (a sheet of blue paper) and some stay on the beach (brown paper). You can make up questions: if there are three in the water and four on the sand, how many are at the beach?
Our children, for some reason, have always understood cookies-on-the-plate questions and handful-of-candy problems very well! ("If you bake 10 cookies, and your selfish sister comes and eats up 6 of them...")
And there are all kinds of other activities to do in other weeks: play with pattern blocks; do rod activities if you have rods; use bundled popsicle sticks and single sticks to show 2-digit numbers (once a child is clear on those, you can try adding groups of them together or even--much later--unbundling some of them to subtract); jump on the number line; jump up stairs while counting, reading numbers on file cards (placed on the stairs) or doing flash cards (placed on the stairs); practice sums on paper or chalkboard; write down a large number you dictate, or read a large number you write. And if all else fails...you can make cookies.