*SECTION* — SUM COMBINATIONS

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

GAME — SHUT THE BOX

Each player writes the numbers from 1 to 9 on a piece of paper. To start a turn, a player finds the sum of the roll of two dice. Using only numbers that have yet to be crossed out, the player crosses out a group of one or more numbers that add up to that sum. If this can't be done, nothing changes. A player may decide in advance to use just one die. The first player to get all numbers crossed out wins.

One way to vary this game is to use a larger range of numbers, such as going to 10 or even 12. Another way is to give each player a single turn — the turn continues with new rolls until the first time the player is stuck. At the end, the player's score is the sum of the numbers not crossed out. The player with the lowest score wins.

GAME — HIT THE TARGET

From a deck of playing cards, remove the face cards and any numbers that are larger than what the children are comfortable with. Shuffle the cards and turn over five cards to use and a sixth card that is the target. Leave the remaining cards as a draw pile to fill in cards as they get removed.

During a turn, if a player can use the sum or difference of two of the five cards to equal the sixth, the player gets all three cards and they are replaced from the draw pile. If the player fails, then a new sixth card is turned over and the turn moves to the next player. The player with the most cards at the end of the game wins.

There are several variations you can use. You can allow a player to use three cards, instead of just two, to add up to the sixth. You can even allow any number of cards to be used to add up to the sixth.

GAME — HOT POTATO WITH SUMS

Use a regular deck of playing cards, have a target number of 5, and remove all cards above the target, except for one card — the hot potato, which can be anything else, such as a Joker or face card. Deal the entire remaining deck to all players — it's okay if some players get one more card than others.

All players start by placing on the table from their hands 5's and any pairs that add up to 5. On your turn, you can pick a random card from any other player's hand (a simpler rule is that it is always the player on your right). If this new card gives you a pair of cards that add up to the target sum, place the pair on the table; otherwise, keep the card in your hand. Play then moves to the next player on your right.

When play ends, the player holding the hot potato loses. Alternatively, you can play that the first player to run out of cards wins.

As your child's adding skills improve, use larger target numbers up to 10. Varying the target number will provide practice with the various number bonds.

*SECTION* — LET ME COUNT THE WAYS

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

ACTIVITY — ANY WHICH WAY

The players agree on a target. A useful target is 10, but other numbers are fine. Each player is dealt five cards from a deck without face cards. Players then find as many ways as they can to get the target total using addition and/or subtraction with any of their cards to reach the target.

Do this as a group activity where the whole group is given five cards to use to cooperatively come up with ways to achieve the total.

INVESTIGATION — HOW MANY WAYS

Counting the number of ways of doing something involving choices can lead to some interesting investigations. Here are a few possibilities — have fun thinking of many more with your child.

Investigation 1: Drawing with only red and blue, how many ways can you draw a monster with a hat, eyes, and cape? How does this change if you only colored the hat and the cape? How would it change if you used three colors, or if you could only use each color once?

Investigation 2: You have a row of 5 identical candies. How many ways can you color them so that there are 2 red ones and 3 blue ones?

Investigation 3: Find all the ways to get a sum using a small set of numbers. Do this with and without considering order. If you use 1 and 2, there are 1+1+1+1 = 2+1+1 = 2+2 ways without considering order, and 1+1+1+1 = 2+1+1 = 1+2+1 = 1+1+2 = 2+2 ways considering order.

ACTIVITY — HOW CAN I MAKE

One person gives the other person a target number and challenges them to come up with different ways of adding and/or subtracting to get that number. If the target is 3, it might start with 1 + 2, but then become 1 + 5 - 3 and so on. As your child learns more mathematics, additional skills can be added, such as doubling and halving. For example, 5 is 2 doubled plus 1 or two 10's minus three 5's.

ACTIVITY — NUMBER SCRAMBLE

Roll five dice to create numbers to work with. Roll two more dice to create a two-digit target number — the first die will be the tens place digit and the second die will be the ones digit. The challenge is to use addition, subtraction, and forming two-digit numbers to get as close as possible to the target number — the score is how close they come. You can either have a winner for each round, or you can add up the scores over several rounds and have an overall winner with the lowest score. Allow multiplication once your child knows how to double or triple numbers.

Suppose the roll is: 1, 2, 5, 6, 4 and 63. A player gets close with 65 - 4 + 2 + 1 = 64. Another one gets it exactly with 56 + 4 + 2 + 1 = 63. A third says 52 + 6 + 4 + 1 = 63 also works. Have a chat about why some problems have lots of solutions.

*SECTION* — Solitaire Puzzles

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

— INTRODUCTION —

While these puzzles are described as solitaire puzzles, they are best done together as a family.

PUZZLE — CARD DECK ORDERING

The challenge is to stack a deck of numbered cards, say 1 to 5, so that the following happens:

The top card is 1. Remove the top card and set it aside. Move the next card to the bottom of the deck. The next card is 2 and is set aside. Move the next card to the bottom of the deck. Continue until all cards are set aside in order.

Once your child finds it easy for 1 to 5, challenge your child to do it for larger number ranges.

PUZZLE — PYRAMID SOLITAIRE

Remove all cards above a target number, say 10. Make a 21-card pyramid with 6 rows. Place the cards in the pyramid face up with each lower row half-overlapping the smaller row above it. The remaining cards create a draw pile.

A group of one or more cards summing to the target may be used if each card is not covered at all. This group can include the top card of the draw pile or the discard pile. These cards are then moved aside. If there are no matches, move the top draw pile card to the discard pile.

The game is over when the draw pile is empty. Your goal is to use as many cards as possible from the pyramid.

If you use a target less than 10, reduce the pyramid size by a row or two so that you have a big enough draw pile. For example, for a goal of 8 use 15 cards in 5 rows.

Instead of using addition, use subtraction. If you use the cards up to ten, a good target number is 5. For this, remove pairs of cards whose difference is 5. When you have a card with a 5, you can either remove it or pair it with a 10.

PUZZLE — DIFFERENCE PYRAMID

The challenge is to place the numbers from 1 to 6 in a pyramid with one card in the top row, two cards in the second row and three cards in the third row, where each number is the difference of the two numbers below it.

Let your child take time and play around with this. Most likely, just by playing with it, your child will happen upon a solution. However, if your child gets anxious, here are two tips that help. The 6 must be in the bottom row because it cannot be the difference of any pair of numbers. Similarly, the 5 must either be in the bottom row or in the middle row above the 6 and the 1.

If your child finds this easy to do, challenge them to find how many ways it can be done. Another challenge is to solve the harder puzzle of putting the numbers from 1 to 10 in a pyramid.

*SECTION* — STRATEGY GAMES

Prerequisite: Reasoning and problem solving skills

— INTRODUCTION —

Playing strategy games will help your child immensely with many reasoning, planning, and problem solving skills. There are dozens of such games - such as tic-tac-toe, 9 Men's Morris, Fox and Geese, Dara, Connect Four, Mancala, Checkers, Go, Chess - far too many to cover here.

GAME — TAPATAN

There are many games similar to this one — games such as Rota, 9 Holes, and 3 Men's Morris. In this version, there are 9 points connected in a grid by 3 horizontal and 3 vertical lines. Each player has three identical tokens to play with. The goal of the game is to get your three tokens in a line.

There are two phases of play. During the first phase, the placement phase, the players take turns placing their tokens one at a time on vacant points. After all the tokens have been placed, the second phase, the movement phase, begins. During this phase, players take turns moving their tokens to empty adjacent points. An alternative rule is that pieces can be moved to any empty point, not just adjacent points.

The game is over when one player wins or when the same position occurs three times, in which case it is a tie game.

GAME — DOTS AND BOXES

This satisfying game starts with a rectangular grid of dots — say 3 by 4. During a turn, a player draws a horizontal or vertical line connecting two unjoined adjacent dots. If the new line completes a 1 by 1 box, the player earns a point and draws another line. When no more lines can be drawn, the player with the most points wins. An easy way to keep track of points is to put an initial inside each earned box.

Although this is traditionally played with little squares, it can also be played with dots in a pattern to produce triangles or hexagons — it's just a bit harder to draw.

GAME — PENTE OR GOMOKU

There are a cluster of games played with similar rules. Rather than use any of the detailed official rules, a simpler version should work just fine for young players. Although the official games are played on a 19 by 19 rectangular grid of points, a 13 by 13 grid produced by 13 horizontal and vertical lines should work well.

Players take turns placing their tokens on grid points - you can use raisins and cheerios, or any other tokens you have lots of. The first player to get five of their tokens in a row wins.