CHAPTER 2 — I CAN COUNT TO 5!

Prerequisite: Your child has the ability to count to 5 comfortably and has a sense of those quantities. Your child also has some knowledge of properties of objects such as color, shape, and texture.

— WHERE YOU'VE BEEN —

Wow! Your child is now able to count to 5! These numbers are not just being repeated in order like a parrot — they represent quantities that your child is gaining a feel for. You are ready to assign properties to objects that you describe and talk about. Think how far your child has come in understanding the world!

Your child is becoming more verbal and better able to reason and explain. You can discuss mathematical things and this allows you to start playing games and doing puzzles together.

— NEW IDEAS IN THIS CHAPTER —

Your child will be learning many things in the coming months beyond counting to 10 and above. Here is a quick list of topics that will be covered in this chapter.

• Counting forward and backward to 10. Don't ignore backward counting - it is important for understanding number relationships as well as being an aid for subtraction.

• Include 0 in your counting sometimes. Including 0 now makes it a familiar number and keeps it from feeling exotic.

• Reasoning with properties and numbers. Understanding properties and reasoning with them is a key part of developing mathematical ability.

• Deepening understanding of shapes, especially circles, triangles, and squares. Keep using descriptive shape names as your child interacts with them.

• Comparing and ordering numbers. How quantities compare and interact with each other is central to understanding them.

• One more, one less, two more, two less. These concepts are relatively easy to pick up, and they will form the basis for addition and subtraction.

• Learning to use manipulatives, especially fingers, to understand adding and subtracting.

• Adding and subtracting 0.

• Subtracting a number from itself.

*SECTION* — COUNTING UP TO 10

Prerequisite: Counting up to 5. Having Number Cards with numerals or dot quantities.

GAME — BINGO WITH CARDS

Play this with Number Cards, or if there are many players, with numbered regular playing cards. Reserve two suits worth of cards for a draw pile, and divide the remaining cards among the players.

Each player will randomly select 16 cards to place in a 4 by 4 grid face up in front of them. Cards are then drawn from the draw pile and the number is called out. Each player may turn over one card from their grid that matches the number drawn. If a player has more than one card that matches, the player must choose which one to turn over.

The first player to get four cards flipped over in a row horizontally, vertically, or diagonally wins the game and calls out "Bingo!"

PUZZLE — ISLAND HOPPING — COUNTING

These puzzles have numbered islands (circles) connected by bridges (lines) drawn on paper. The challenge is to find a path that connects the islands in order. The easiest versions have numbers that go from 1 to the number of islands.

To add challenge, leave out some of the numbers so your child figures out what is missing and where it belongs. Also, instead of starting at 1, design the puzzles to start at 0 or other numbers (usually noting this at the top of the puzzle).

PUZZLE — NUMBER SUDOKU

This is similar to the Shape Sudoku puzzles, only now it uses numbers (or quantities of dots). To avoid erasing, use numbered (or dotted) slips of paper to solve the puzzles.
For a 4 by 4 puzzle, each row and column has the numbers from 1 to 4 once. Also, each marked subregion has the numbers from 1 to 4 once. That's it! Create these puzzles for your child by starting with a completed puzzle and removing some of the pieces of paper.

For variety, you can use irregularly-sized subregions. You can also create puzzles of larger size (two 5 by 5 puzzles are shown).

*SECTION* — BIGGER AND SMALLER NUMBERS

Prerequisite: Can compare single-digit numbers; Number Cards

GAME — WAR — SINGLE-DIGIT COMPARING

Remove the cards from two, four, or six Number Decks outside your child's comfort range. Split the cards evenly in two piles face down. Flip over the top cards and the player with the larger card keeps both cards. If the cards match, flip the next two cards and the winner gets all four cards. The player with the most cards after one or more runs through all the cards is the winner. To change things up, sometimes play that the smaller of the two cards wins.

ACTIVITY — FITTING IN

Give your child some number of small objects, say seven, and count them together. Pick a target number, say five. Ask your child to take five objects out of the original group of seven objects, if it is possible. This helps your child learn the relative sizes of numbers and how much they are bigger or less than each other.

At first, the target number should be less than or equal to the total number. Later on, giving numbers that are too big provides practice with the relative size of quantities, as well as providing practice checking that requests are reasonable.

GAME — I'M THINKING OF A NUMBER

This is an introductory, warmup version of a fun game we will revisit again soon.

There are two people involved. The Puzzler thinks of a number and the Questioner discovers the number. The Puzzler declares, "I am thinking of a number from 0 to 8" (or whatever upper limit they like). The Questioner then asks questions of the form "How does your number compare to 3?" The Puzzler answers that the number is smaller, equal to, or larger than that number.

Here is an example of a game with a target of 5:

Puzzler: I'm thinking of a number from 0 to 8. Question: How does your number compare to 3?
Puzzler: My number is larger than 3.
Question: How does your number compare to 6?
Puzzler: My number is smaller than 6.
Question: How does your number compare to 5?
Puzzler: Well done! My number is equal to 5.

With younger children, you can play this game with counting cards from 0 to 8 (or whatever the limits are) placed face up in order on the table. Under one of the cards you hide a star or whatever is fun. After each guess, the child (Questioner) turns over all the cards that have been eliminated until the star is discovered.

For older children who can play this in their heads, this is a good game to play while traveling.

You can make a competitive game of this by seeing how many questions it takes the Questioner. Add up all the tries over several rounds to determine the winner.

*SECTION* — GAMES WITH DOMINOES

Prerequisite: Counting up to 5; Dominoes Cards or commercial Dominoes set

GAME — STEALING BONES

Place all the dominoes, also known as bones, face up between the players. For a turn, a player rolls two dice. If the domino that matches the two dice is available, the player claims it and moves it to their own pile — an alternative rule is that, even if a domino has already been claimed by one player, it can be stolen by another player.

For two players, the first player to claim ten dominoes wins. For more than two players, the first player with six dominoes wins.

GAME — DOMINOES

The game of dominoes has a long and rich history with many versions. If you play with others, make sure you all use the same rules before you start! The game starts by placing all the tiles (bones) face down and mixed up — this is called the boneyard. Take seven tiles apiece for two players, and five tiles apiece for three or four players.

Play starts with the player with the highest double putting it on the table. If no one has a double, the game is started over. After this first play, play passes to the player to the right. A turn consists of placing a tile that matches one of the two available ends of the string of dominoes. If the placed domino is a double, place it crosswise to the previous domino.

If the player has no matching tile, the player is "blocked," and there are two possible rules to use. One option is that the player's turn is over. The other option is that the player must keep drawing tiles from the boneyard until there is a match (one version restricts this to a single draw whether or not there is a match). If the boneyard is emptied before there is a move, then play passes on to the next player.

The game is over when a player runs out of bones, or when all players are blocked. At this point, the winner is the player with the lowest total of dots on their remaining bones (which will be 0 if they have used up all their bones).

The winner's score can be calculated in two ways. The traditional way is to use the sum of the dots on all the other players' tiles. With this scoring, rounds are played until a player reaches a target of 50 or 100. For little ones just learning to count, a better scoring system is to let the winner have the score which is the count of all the other players' tiles. Alternatively, you can just have a winner and not bother with doing any scoring.

One variation, useful later when your child starts adding, is to change the rule for matching. In this variation, two tiles match if their numbers add up to six — if you are using dominoes up to a larger number, such as nine, matching numbers would add up to nine.

*SECTION* — NEARBY NUMBERS

Prerequisite: Can count forward and backward between 0 and 10; Number Cards; Number line

GAME — WITHIN ONE OR TWO

Create a stack of Number Cards with a range of quantities your child is comfortable with. Split the cards evenly between two players and place the cards face down. The players take turns placing a single card on the stack in the middle between them. If the card is one more, same, or one less than the previous card, the first player to yell out the relationship claims the whole pile.

This can be extended to include the relationships of two more or two less as options. Another variation is to use a target sum, say 10 — yell out whenever the top two cards add up to the target.

ACTIVITY — ESTIMATION GAME

Develop a sense of quantities by seeing who can make the best estimate for the size of a group, such as a group of people standing in line. Force yourselves to make a quick estimate so no one gets an advantage by doing a partial count. After everyone gives an estimate, count the objects and reward the person who is the closest.

ACTIVITY — INVISIBLE ADDING AND SUBTRACTING

Have your child count a small number of objects and put them in a box. Next, ask your child to put up the same number of fingers as there are objects in the box. Finally, show your child that you are adding (or removing) one or two objects to the box, and then ask how many objects there are in the box. When this becomes too easy, you can add or remove more than two objects.

GAME — NIM WITH ONE AND TWO

A target number, say 10, is chosen. Let your child choose whether to go first or second. The total starts at 0. During a turn, a person chooses to add 1 or 2 to the current total. The first person to reach the target wins. Once children learn to play this verbally, it is a great travel game.

For younger children, use an actual pile of objects to play with instead of writing anything down. In this case, a player would add one or two objects to the pile on their turn until the target quantity is reached. Similarly, a number line to the target number could be used and a marker could be advanced along the line one or two spaces during each move.

This game can also be played with subtraction. In this version, the starting total starts at the target, which in this example is 10. On a given turn the player chooses whether to subtract 1 or 2. The first person to reach 0 wins.

There are many variations to this popular game. You can use larger target numbers as your child's skills improve. One variation is that instead of winning, the player forced to hit or go beyond the target number loses. You can also experiment with what happens if you allow a player to add (or subtract) 1, 2, or 3 for each turn.

*SECTION* — ORDER AND SIZE

Prerequisite: Can count forward and backward between 0 and 10; Number Cards, Number line

GAME — THE IN-BETWEEN GAME

Use one set of cards from 0 to 10. Use either Number Cards or playing cards with Queen as 0 and Ace as 1. Each player also gets 20 tokens.

For the player whose turn it is, deal two cards face up and a third card face down between them. The player decides to bet 0 to 3 tokens that the third card is between the two cards. If the player is right, the player gets that many tokens from the other player. If the player is wrong, that many tokens go to the other player.

You can either play five rounds or until one player runs out of tokens. The player with the most tokens at the end wins.

GAME — GET OUT OF MY HOUSE — 1 MORE/LESS

Use a deck of cards with numbers from 1 to 10. On a shared piece of paper, have boxes, or simple drawings of houses, numbered from 0 to 11. To provide practice figuring out order, do not put these boxes in order on the page. Each player has 7 tokens distinct from the other player's tokens - using different colors is one way to do this.

On a turn, a player picks a card and puts their token in any house that is one more or one less, as long as it does not have 3 or more of the other player's tokens in it already. If the house has one or two of the opponent's tokens, those are given back to the opponent and the player says "Get out of my house." The first player to place all their tokens wins.

If your child is not ready for numerals yet, use Number Cards and boxes with quantities of dots.

ACTIVITY — STRING NUMBER LINE

In addition to putting a number line on a piece of paper on a wall, create a number line using a string. Tie or clip a section of string between two objects. Use paper clips to attach sliding Number Cards from 0 to 10 along the string in order.

Here are some things you can do with this. You and your child will probably discover many more.

• Switch two numbers and have your child find the mistake.
• Leave out a number and have your child find which one is missing.
• Have your child remove every other card and skip count by 2's.
• Have your child pair up the cards to see that 10 is made up of five pairs.
• Practice adding. For example, to do 4 + 2, slide over the first 4 numbers and then slide over the next 2.
• Practice subtracting. To do 6 - 2, slide over to the left the first 6 cards and then slide 2 of those back to the right.