Chapter 3 — I CAN COUNT TO 10!

Prerequisite: Ability to count to 10 and have a sense of those quantities. The child can add the numbers from 0 to 5 using manipulatives, especially fingers. The child can add or subtract 1 and 2 to any single-digit number. The child can reason with properties of objects such as color, shape, and texture.

— WHERE YOU'VE BEEN —

Your child can now count up and down between 0 and 10 and understand what all those quantities mean. Beginning addition and subtraction skills are developing. An important foundation for those skills is confidence with adding and subtracting 1 and 2 (and maybe 3) with other small numbers. Your child also understands small quantities, and can reason with those quantities to do addition and subtraction for small numbers.

In addition to that wonderful stuff, your child is able to reason so much better now! They understand that objects and numbers have properties, and they can reason and do beginning problem solving. Your child is now a full member in family math games and puzzles and exploring the mathematical world around them.

— NEW IDEAS IN THIS CHAPTER —

• Counting On — This refers to counting upward starting at any number, rather than always starting at 1. This is useful for addition and for finding differences.

• Counting Down — This refers to counting downward starting at any number. It is useful for subtracting, as well as for developing a sense for the relationships between numbers.

• Number Bonds — The number bonds for a number are all pairs of numbers that add up to that number.

• Ten Frames — This represents a number from 0 to 10 as the appropriate number of dots inside a 2 by 5 rectangular grid. For numbers greater than 4, the upper group of 5 squares is always filled.

• Expanded Form — This refers to writing a multi-digit number broken down into the contribution of each of its digits. For example: 25 = 20 + 5 and 317 = 300 + 10 + 7.

• Fact Families — This refers to a group of closely related math facts. For example, 2 + 5 = 7 is in the same family as 7 - 2 = 5 and 7 - 5 = 2.

• Adding twins and near twins — An adding twin is adding a number to itself, such as 4 + 4. A near twin is one away from a twin, such as 4 + 5.

• Doubling, multiplying by two, and halving, two equal parts, dividing in two — Children usually enjoy adding twins. With that comes the idea of doubling and multiplying by 2. Also associated with that is halving, splitting something into two equal parts, and dividing by two.

• Even and Odd numbers — Even numbers can be split into two equal parts. Odd numbers have one left over when split into two matching parts. Even numbers are the results of adding twins.

• Skip counting by 2's — This means counting up or down by 2's — such as, 0, 2, 4, 6, 8 or 13, 11, 9, 7, 5.

*SECTION* — FACT FAMILIES

Prerequisite: Some comfort adding and subtracting small single-digit numbers

ACTIVITY — MYSTERY CHANGE

Have your child count some small number of objects. While they look away, change the number of objects. When they look back, ask what change you made. They can test their theory by reenacting what they think happened.

Once this becomes easy, you can have them be more creative with their answers. For example, if 4 became 6, the answer might be that you doubled the 4 and then took 2 away.

GAME — CHOPSTICKS HAND GAME

All players start with one finger raised on each hand. During a turn, a player has the choice of either "attacking" or "splitting."

To attack, a player takes a live hand and attacks a live hand of an opponent. The result is that the opponent's hand has the sum of the two hands and the attacking player's hand is unchanged. If a hand ends up with exactly five fingers, it is dead. If the hand has over five fingers, its count is either reduced by five (in one set of rules) or is dead (an alternate set of rules).

To split, a player bangs their hands together and redistributes the fingers between the two hands. A split may not reverse the two finger counts.

A player wins when both hands of everyone else are dead. In one variation, the first player to have two dead hands wins.

PUZZLE — SHAPE SUMS

Numbered circles are connected in an upward fashion, and every circle is the sum of all the circles directly below and connected to it.

The easiest puzzles have most of the circles filled in. For older children, there are variations that involve larger numbers and cleverer solutions.

One option is to use non-circular shapes. While the value in a circle may duplicate the value in some other circle or shape, the value in a non-circular shape must match the value in all other places with the same shape. For example, all squares have the same value. Use matching to practice adding twins, near twins, and halving.

Make these puzzles by starting with a diagram that is completely filled in and then removing some numbers. If the puzzle has some repeated numbers, use a square or other shape instead of a circle for that repeated number.

*SECTION* - ADDING AND SUBTRACTING 10

Prerequisite: Comfort counting to 10, some comfort counting to 20

— INTRODUCING 10'S —

Welcome to the world beyond 10 fingers! There are wonderful things to discover here. The next group of numbers from 10 to 20 is 10 more than the numbers your child already knows. But, before this can become easy, your child needs to conquer the crazy names we use for eleven, twelve, and thirteen.

The next games are designed to emphasize the role that 10 plays in connecting pairs of numbers such as 6 and 16. These games also emphasize the idea that 16 should be thought of as 10 plus 6. This view of decomposing numbers using place value will be much more important as your child counts to 100 in the next chapter.

ACTIVITY — MAKING NUMBER CARDS 1 TO 20

If you don't have them already, create some extended decks of counting cards from 0 to 20. One deck will be normal numbers, one deck will have the numbers in expanded form from 0 to 20 as 0 + (0 to 9), 10 + (0 to 9), and 20 + 0, and one deck will use ten frames.

GAME — BINGO WITH 10

Place a random collection of 16 Number Cards from 0 to 20 with expanded form on a 4 by 4 bingo board for each child. Then, mix up a collection of counting cards from 0 to 20. Select one card at a time from this pile until the first child gets four in a row and yells Bingo!

One important variation of this game is to do a "Tens-Reversed" version using cards with numerals. When a card is chosen, if it is 1 to 10, then 10 is added to find the matching value, and if it is 11 to 20, then 10 is subtracted for the matching value.

GAME — MEMORY CHALLENGE — 10'S

This version of the Memory Challenge game uses a Number Card deck from 0 to 20 with the rule that two numbers match if they are 10 apart. If you also have cards from 0 to 20 that use expanded form or ten frames, you should use those too. Deal a 3 by 4 grid of cards out on the table, all face-down.

Players take turns flipping two cards face-up. If the two cards are ten apart, the player gets to keep the cards, replaces the two cards from the draw pile, and continues their turn. If the cards do not match, the player flips the cards back over and ends their turn.

The game ends when the last pair of cards is taken. The player with the most cards wins.

*SECTION* — SHAPES

Prerequisite: Comfort counting to 10, some comfort counting to 20

GAME — SIM TRIANGLE

The two players have different colored markers. Place six (use more for a harder game) dots evenly around a circle. Players take turns drawing lines between the dots using their color. The loser is the first player forced to create a triangle all of whose sides have the player's color and whose corners are on the circle. In the illustrated game, green moves next and must lose.

ACTIVITY — GEOMETRIC ART

Here are some geometric concepts your child can play around with. The first is the idea of similarity. Two shapes are similar if they have the same shape except that one is smaller or larger than the other. Challenge your child to pick a picture and draw it twice as big or twice as small.

Another geometric concept to play with is mirror symmetry. Your child can see this by taking a mirror with a flat side and putting it down along its edge on a drawing or photo and seeing what the mirror image looks like. Once your child has the idea, give your child half of a picture and challenge them to draw the mirror image.

ACTIVITY — NUMBER SHAPES

Using something small, such as pieces of food, challenge your child to make shapes with a given number of pieces. These shapes can be rectangles, triangles, squares, or anything fun.

Investigate which numbers are even and odd by using number shapes. For any number, ask your child to put the pieces into two rows that have the same number in them. This is something you would do if you were splitting the food evenly between the two of you. For which numbers does it work out evenly?

Once your child knows what an odd number is, investigate adding up the first few odd numbers as shown in this diagram. Amazingly, the sum of the first odd numbers is always a square number.

Your child may notice that for some numbers, such as 12, there are different shapes of rectangles that can be made, and that for other numbers, such as 7, only flat rectangles can be made. If you want to, you can tell your child that numbers such as 5 and 7 are called prime numbers because there is no way to break them into normal rectangles.