Expanders
Expanders
1-4 players • 20 min • 7 & up
Focus: Addition
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Ready to expand your number fun? Use your tokens to mark your expansion on the board by connecting a number to its base components. The more components the more tokens used. The first person to place all 32 of their tokens on the board wins the game.
Skills: Addition, Planning
Game Includes
Game Includes
- 128 Plastic Expander Tokens(32 of each color)
- 6 Numbered Double-Sided Circuit Boards
- 2 Circuit Board Fillers
- 1 Mainframe
- 1 Expander Token
- Storage Bag
- 1 Rules Booklet
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How to Play
Educational Standards
Core Standard*: None
Skills
Explore
What Does Child Do To Use Skill In The Game?
Players explore the Expanders board, looking at patterns, openings and options for placing their Tokens either offensively or defensively.
How Parents Can Assist Learning
Encourage children to look closely at where other player's Tokens are and how they are building out their color patterns. This is important for the child to be able to judge whether to make an offensive or defensive move on his or her turn.
Learning Implications and Educator Support
Playing Expanders helps children develop spatial reasoning , situational analysis, planning and perspective changing skills. Encourage children to look closely at where other player's Tokens are and how they are building out their color patterns. This is important for the child to be able to judge whether to make an offensive or defensive move on his or her turn.
Determine
What Does Child Do To Use Skill In The Game?
Players determine where to place Tokens based on the different available Actions in order to use the most Tokens each time. Also, players may be trying to set up defensive positions or offensively pursue other player's positions.
How Parents Can Assist Learning
To help children develop more thoughtful decision-making, parents can ask them to discuss different moves they are considering. Ask questions like, "How will that placing those Token help you reach your goal?"
Learning Implications and Educator Support
Expanders involves examining the board and creating mental models of the consequences of placing Tokens. When first learning to play, players will think about consequences of the immediate move. As they become more proficient, children will think about multiple moves ahead in order to evaluate what Tokens would be best to play on each turn. In addition to determining where to place Tokens on a turn, children need to determine what type of strategic approach, offensive or defensive, to use during the game. They may even take a defensive position against one opponent and offensive against another. Educators can discuss the different moves players make in order to understand different strategies and the logical thinking the children are utilizing.
>Compare
What Does Child Do To Use Skill In The Game?
Players need to compare the different locations of their Tokens on the board and number associated with those locations in order to determine possible moves.
How Parents Can Assist Learning
When children are learning the game, parents may want to help children to verbally describe their options prior to comparing and deciding which to select. As the game proceeds, there are numerous comparisons to make and verbalizing is a good way to examine the different consequences of different potential moves.
Learning Implications and Educator Support
Expanders involves a high level of spatial reasoning and strategic thinking. Educators can help children develop these skills by carefully examining a range of comparison issues such as the position of other players' Tokens, the strategies being used by other players, the areas for easier expansion of their color Tokens, and opportunities for the most number of Tokens to use. The educator can help children learn by observing and commenting on why certain moves were good choices. Avoid commenting on bad choices, so as not to embarrass players.
Remember
What Does Child Do To Use Skill In The Game?
Players may remember moves from prior games of Expanders that were successful or not.
How Parents Can Assist Learning
Adults can remind children of similar situations from prior games. Encouraging children to wait and think also helps with impulse control and logical reasoning.
Learning Implications and Educator Support
Adults can remind children of similar situations from prior games. Encouraging children to wait and think also helps with impulse control and logical reasoning.
Predict
What Does Child Do To Use Skill In The Game?
Players predict where they think opponents will play their colored Tokens.
How Parents Can Assist Learning
Playing Expanders helps children develop spatial reasoning skills, situational analysis, risk assessment and perspective changing. As other players make moves and create patterns and lines of colored Tokens, point this out to younger players to help them predict what their opponent(s) might do next, which can help them strategize their next move.
Learning Implications and Educator Support
Playing Expanders helps children develop spatial reasoning skills, situational analysis, risk assessment and perspective changing, all skills that can be used to make more accurate predictions of opponents' moves. Additionally, making predictions requires analysis, observation, empathy and interpretation. Educators can encourage children to discuss their options and to declare whether they want to make an offensive (ex: move into an opponent's territory) or defensive (ex: create a boundary of their own colored tiles that prevent other players from encroaching into a space) move prior to playing their Tokens.
Plan
What Does Child Do To Use Skill In The Game?
Planning is a key skill used and developed in this Expanders. Players are constantly examining the board and the moves of opponents in order to decide on their next move and subsequent moves.
How Parents Can Assist Learning
To be successful in this game requires thinking about consequences beyond a player's immediate move. Parents can remind children to think about what could happen next so children will plan accordingly. This type of long-term, sequential thinking is important in life well beyond game play.
Learning Implications and Educator Support
Educators can encourage children to look at options for reaching a goal. Ask questions like "Are you trying to create a boundary?" or "How can you set yourself up on the next turn to use at least 4 Tokens?" Also, Expanders is a good game for helping children develop organizational skills as they plan moves, and adaptive skills as they creatively respond to moves of opponents. Organizing is essential to effective planning and is an important executive functioning skill. To be successful in this game requires thinking about consequences beyond a player's immediate move. Educators can remind children to think about what could happen next so children will plan accordingly. This type of long-term, sequential thinking is important well beyond game play.
Experiment
What Does Child Do To Use Skill In The Game?
Players may try different strategies during the game or against different players. The player that finds the right balance will likely win the game.
How Parents Can Assist Learning
Expanders allows for different approaches such as trying to build expansions in other players' areas or creating protected areas that you can fill in as the game proceeds. Discuss these approaches and others, and compare the advantages and disadvantages. Once children understand different strategies, they can shift and adapt strategies within a game.
Learning Implications and Educator Support
Expanders is good for experimenting with strategy and tactics. Discuss different strategies prior to starting the game and encourage the child to select one. Play the game and discuss. Then, play again with the child trying a different strategy. Discuss again and compare the advantages and disadvantages. Further, educators can help children with their strategic thinking by encouraging them to change perspectives, i.e. imagine what an opponent might do. This will help them anticipate which is essential to planning and prediction.
Practice
What Does Child Do To Use Skill In The Game?
The more players play Expanders, the more they will build strategy and predictive capacity.
How Parents Can Assist Learning
When learning this game, play several rounds collaboratively. Talk about different moves and the consequences of each.
Learning Implications and Educator Support
Expanders has several implicit levels of mastery. Therefore, the more children play the more capable they will be in developing and executing increasingly sophisticated or compound strategies. Also, as they become proficient, they will be able to teach others. Teaching others demonstrates mastery, the final stage of learning, and is wonderful for building self-esteem, confidence and intrinsic motivation.
Solve
What Does Child Do To Use Skill In The Game?
As the game progresses, players will learn new information and adapt their strategies to the moves of opponents. The winning player will solve the game by playing all of his or her Tokens first.
How Parents Can Assist Learning
This game involves uses of visual spatial problem solving, directionality and if/then problem solving. After children have mastered the rules and functions of the pieces, they learn new information constantly during game play. This information directly effects how children strategize an approach for placing Tokens, and ultimately solve the game. The ability to shift strategies based on new information can help children cope with the stresses of change in other areas of their life.
Learning Implications and Educator Support
This game involves uses of visual spatial problem solving, directionality and if/then problem solving. After children have mastered the rules and functions of the pieces, they learn new information constantly during game play. This information directly effects how children strategize an approach for placing Tokens, and ultimately solve the game. Educators can talk to children about alternative approaches and help them think about choices. It is important for adults to not create the approaches, but help the children come to their own conclusions. Adults can encourage both offensive and defensive game strategy. The ability to shift strategies based on new information can help children cope with the stresses of change in other areas of their life.
Review
What Does Child Do To Use Skill In The Game?
Children may review if encouraged. See How Parents Can Assist Learning.
How Parents Can Assist Learning
This game involves uses of visual spatial problem solving, directionality and if/then problem solving. As the game is being learned, children may place Tokens in non-strategic ways. If parents see this, ask children to explain their thinking and discuss what they might do differently next time. It is also important for parents to discuss their thinking, as this can help children learn a new strategy.
Learning Implications and Educator Support
This game involves uses of visual spatial problem solving, directionality and if/then problem solving. As the game is being learned, children may place Tokens in non-strategic ways. If teachers see this, ask children to explain their thinking and discuss what they might do differently next time. It is also important for other players to discuss their thinking, as this can help children learn a new strategy.
Demonstrate
What Does Child Do To Use Skill In The Game?
Children may demonstrate if encouraged. See How Parents Can Assist Learning.
How Parents Can Assist Learning
This game involves uses of visual spatial problem solving, directionality and if/then problem solving. As the game is being learned, children may place Tokens in non-strategic ways. If parents see this, ask children to explain their thinking and discuss what they might do differently next time. It is also important for parents to discuss their thinking, as this can help children learn a new strategy.
Learning Implications and Educator Support
Demonstrating knowledge, skills and abilities is an important step in the learning process because it 1) allows a children to show their mastery, i.e. that they have learned something thoroughly enough to share and even teach it to another, and 2) is the beginning of the next level of learning.
*Data compiled from CCSSI ELA Standards, WA Science Standards, and Washington Social Studies Standards
Special Needs
Cognitive
Suggestions for How to Modify Play Experience
Eliminate the option for diagonal addition. This will make it easier for children with cognitive delays to see options.
Help children examine the board for options. Other players can help the child see where they might be able to play.
Change the rules to find only pairs.
Communication
Suggestions for How to Modify Play Experience
Children do not need to talk during the game, but should be encouraged to verbalize their thinking.
Ask questions to encourage thinking and communicating among players. "What do you think I should do?" "You want to use as many tokens as you can. Where can you use more?"
Play in teams to encourage discussion of potential moves.
Sensorimotor
Suggestions for How to Modify Play Experience
The tokens in this game are small and somewhat tricky to maneuver because they are smooth. Children with fine motor control issues may have difficulty with accurate placement on the spots on the board.
If needed, the child can point to the spots they want their tiles placed, and another player can assist them. The child can use a finger to push the needed tokens close to the area of the board where the child wants them placed.
Social Emotional/Behavioral
Suggestions for How to Modify Play Experience
Expanders requires focus of attention. To help children reduce impulsivity, require that each player take 20- 30 seconds to examine the board for options. Let players determine how long the time frame should be for studying the board.
If a child gets easily frustrated, the game can be played in teams. This allows ideas to be pooled and creates a greater chance of finding the best options. Team play also encourages cooperation.
Vision
Suggestions for How to Modify Play Experience
Expanders may be difficult for children with vision impairments to play, as the numbers and board spots are small and play requires scanning the whole board for play options. In addition, each player has lightly colored tokens that may be problematic for some children to differentiate.
Hearing
Suggestions for How to Modify Play Experience
Children who are hard of hearing should be able to play this game, as know communication is needed. Sign language can be used if desired.
*Data compiled from CCSSI ELA Standards, WA Science Standards, and Washington Social Studies Standards
Autism
Autism Strengths & Interests
Short Summary of Strengths & Interests
- Has a strong spatial reasoning skills.
- Likes using math in playing games.
- Enjoys strategy games like checkers or chess.
Is good at matching visual items
This game is not appropriate
Has a good memory for sensory details, including visual, touch, taste and smell
This game is not appropriate
Has a good memory for words, phrases and dialouge
This game is not appropriate
Has a good memory for pictures, numbers and patterns
Is This Game Appropriate? Yes
Description
Like checkers or traditional chess, the more you play Expanders the more easily you can see options for using multiple tokens to expand a number, as well as anticipating the moves of other players or playing matching numbers. Children who are good at patterning games and spatial reasoning will be able to use and sharpen that ability playing Expanders.
Likes to put things in order or a sequence
Is This Game Appropriate? Yes
Description
Players can "expand" a number by connecting as many numbers together that add up to the "expanded" number. Thus, children who are good a simple addition and enjoy finding sequences will hone those skills playing Expanders. In addition, players may try to build barriers to prevent other player's from scoring points. Thus, children need to analyze the board for possible moves that all players may take and plan potential future moves accordingly.
Learns through visualizing or "replaying" actions in their mind
This game is not appropriate
Likes activities with rules, such as math and phonics
Is This Game Appropriate? Yes
Description
Expanders involves simple addition as players deconstruct a number into smaller numbers that add up to the original. For example, 8 can be broken down into 5, 2, 1. Additionally, Expanders has very simple rules that govern the play. Thus, children who are good at following rules and simple math will likely enjoy playing the game.
Is very concrete and literal
This game is not appropriate
Learns in small "chunks" (for example, phone numbers are 3 chunks of number xxx-xxx-xxxx that are combined together)
Is This Game Appropriate? Yes
Description
Expanders involves simple addition as players deconstruct a number into smaller numbers that add up to the original. For example, 8 can be broken down into 5, 2, 1. Thus, the more children understand different number combinations, the more successful they will be at playing the game.
Is good at nonverbal reasoning and logic
Is This Game Appropriate? Yes
Description
Some children are good at logic and reasoning, but do not like to discuss or verbalize their thinking. Expanders is a good match for these children, since players demonstrate their reasoning through action. Namely, they place their tokens to create defensive positions, expand numbers correctly and attempt to use all of their tokens first.
Likes spatial problem solving
Is This Game Appropriate? Yes
Description
Like checkers or traditional chess, the more you play Expanders the more easily you can see the patterns of tokens on the board and recognize the move options such as "expand a number" or play matching numbers for yourself and other players. Children with autism who are strong at logic, patterning and examining sequential options will uses those skills playing Expanders.
Can read well with good vocabulary, though may not fully comprehend content
This game is not appropriate
Likes to use and has good fine motor skill
Is This Game Appropriate? Yes
Description
Children who like playing with small game pieces, such as in checkers, mancala or chess, will enjoy utilizing that skill playing Expanders.
Likes established routines or set ways of doing things
This game is not appropriate
Likes manipulating, constructing or building things
This game is not appropriate
Likes to use and has good musical abilities
This game is not appropriate
Likes to use and has good drawing skills
This game is not appropriate
Autism Special Considerations
Appears to ignore other's communication and/or has difficulty giving eye contact to a communication partner
Is This Game Appropriate for Child with Characteristic? Yes
Can Child with Characteristic Play Game w/o Modification? Yes
Strategies for Developing Compensatory Skills:
No eye contact is needed to play the game. Children can concentrate on the number options on the board.
Has difficulty understanding complex verbal directions
Is This Game Appropriate for Child with Characteristic? Yes
Can Child with Characteristic Play Game w/o Modification? No
Strategies for Developing Compensatory Skills:
The directions are complex, as there are multiple options available for a player to do within a turn. However, other players can remind them of the options. If needed, the child with autism can play the game with a partner. Use demonstration of options so the child can visualize the directions.
Uses vocabulary inaccurately or demonstrates echolalia (repeating another's speech)
Is This Game Appropriate for Child with Characteristic? Yes
Can Child with Characteristic Play Game w/o Modification? Yes
Strategies for Developing Compensatory Skills:
Echolalia should not be an issue in this game. Even if the child repeats others' phrases, it will not detract from the game.
Gets stuck repeating a verbal topic or physical actions and/or has difficulty attending to others' actions or topic.
Is This Game Appropriate for Child with Characteristic? Yes
Can Child with Characteristic Play Game w/o Modification? No
Strategies for Developing Compensatory Skills:
It is important to watch other players' moves, as they can maneuver in such a way as to block another player's ability to make a move. Other players can support the child with autism by pointing out how moves may affect the child's options. For example, "Look, he is starting to block you in. You need to move further this way." They can also point out possible plays if needed.
Has difficulty producing speech/communication
Is This Game Appropriate for Child with Characteristic? Yes
Can Child with Characteristic Play Game w/o Modification? Yes
Strategies for Developing Compensatory Skills:
Players do not need to talk during the game, although it makes the game more fun. Comment on the child's play, modeling something the child could say. "You used four tokens! That was great."
Has difficulty sequencing multi-step actions and/or doing complex abstract tasks
Is This Game Appropriate for Child with Characteristic? Yes
Can Child with Characteristic Play Game w/o Modification? Yes
Strategies for Developing Compensatory Skills:
Players just need to select a move to make during their turn. They need to be able to add simple numbers and analyze spatial options for the best move. Encourage player to examine the whole board to see options.
Demonstrates difficulty initiating and maintaining social interactions
Is This Game Appropriate for Child with Characteristic? Yes
Can Child with Characteristic Play Game w/o Modification? Yes
Strategies for Developing Compensatory Skills:
Children do not need to have discussions during the game. Players do need to observe other players' moves to help them make the best moves in their own turn. Encourage the child to "Watch what she does", "Was that a good play?", and " Tell her what you think."
Acts out or demonstrates avoidance behaviors when frustrated, overwhelmed, or needs more sensory input.
Is This Game Appropriate for Child with Characteristic? Yes
Can Child with Characteristic Play Game w/o Modification? Yes
Strategies for Developing Compensatory Skills:
If blocked in or not able to make a move, the child may become frustrated. Try to keep the board open while the child is learning to play the game, and encourage other players to support the child by explaining their strategies as they play. Once the child feels more confident, the child and other players can be encouraged to try different strategies.
Has short attention span for non-preferred activities
Is This Game Appropriate for Child with Characteristic? Yes
Can Child with Characteristic Play Game w/o Modification? Yes
Strategies for Developing Compensatory Skills:
If the child does not like simple math activities, this might not be a preferred game. Play only a few turns at a time instead of a whole game until the child is comfortable and enjoying the game. Use a preferred activity as a break between turns if needed, until the child understands the game.
Needs sameness or consistent routines and/or has difficulty with transitions from one activity to another
Is This Game Appropriate for Child with Characteristic? Yes
Can Child with Characteristic Play Game w/o Modification? Yes
Strategies for Developing Compensatory Skills:
Although different moves and strategies are used in each turn and there is no predictable path for a child to follow as in some games, the game has a predictable pattern to follow.
Encourage the child to think about looking in all directions for a possible addition pattern. Transition to the game may be easier if the child likes math and puzzles. If needed, describe Expanders as a" math puzzle" to interest the child in playing.
Has difficulty understanding others' feelings, intentions, and the reasons for others' actions.
Is This Game Appropriate for Child with Characteristic? Yes
Can Child with Characteristic Play Game w/o Modification? Yes
Strategies for Developing Compensatory Skills:
Players need to pay attention to what other players are doing to anticipate potential moves and places they can play defensively or offensively. Remind the child to "Think about where you can move to stop him from moving your way."
*Data compiled from CCSSI ELA Standards, WA Science Standards, and Washington Social Studies Standards
Extended Play
Extra Ways to Play the Game
In ordinary play, you are not allowed to place your token on top of another player's token. In this variation, players may place their tokens on top of others in order to Expand a Number. However, after their turn is over, any tokens placed on top of another token must be removed, and the player must also remove an equal number of their tokens from anywhere on the board.
Materials Needed
No additional materials needed
Developmental Benefits
This version allows players to make different risk and reward choices by deciding whether the cost (removal of tokens from the board) is worth the benefit of being able to extend a number by playing on top of another player's tokens. Additionally, this variation of the rules may cause players to adopt different defensive or offensive strategies as the game proceeds.
*Data compiled from CCSSI ELA Standards, WA Science Standards, and Washington Social Studies Standards
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How to Play Video & Transcript
Today we’ll use our math and thinking skills to fill the Mainframe in Simply Fun’s Expanders.
Expanders is a great game for people ages 7 and up. You can play Expanders all by yourself, or play with up to 4 players.
Learning to expand numbers is a great way to practice early addition math facts. We learn addition from 1 + 2 = 3, but now let’s work in reverse….we start with 3, now what numbers can add up to 3? Expanding and contracting numbers will be steps performed countless times as kids move up into more advanced equations and algebra. Expanders is a great tool to help them start practicing this at a very early stage.
Every Expanders game box contains:
One Mainframe that holds six numbered, double-sided circuit boards. On one side of the circuit board, you’ll see numbers 1 through 8. On the other side, you’ll see numbers 1 through 12. The higher numbers provide a more challenging game experience.
You’ll also find two circuit board fillers for the mainframe. These are used when the game is played with fewer than four players.
There are 128 clear plastic expander tokens, 32 of each color: blue, pink, purple and orange. Tokens can be stored in the Expander Token storage bag included when not in use.
To set up the game, place the Mainframe where everyone can reach it.
Choose the level of game difficulty by selecting which side of the circuit boards to use: one to eight…. Or one to twelve. Again, the higher numbers are more challenging.
Assemble the Mainframe and circuit boards based on the number of players.
For 4 players, use all 6 circuit boards, randomly placed in the Mainframe, as shown. For 3 players, use 5 circuit boards and 1 circuit board filler, like this. For 2 players, use 4 circuit boards and 2 circuit board fillers.
Finally, give one set of 32 Expander Tokens to each player. The token color should match the color on the side of the Mainframe board closest to each player.
During a players turn, they may do one of three actions:
Action 1 -Find a single open number. Place ONE token on an unoccupied number that is either in the first row on your side of the board OR connected horizontally, vertically or diagonally to any of your tokens already on the board.
Action 2 -Find two matching numbers. Place TWO tokens on any two unoccupied matching numbers that share the same specifications as the first action.
Action 3 - Expand a number. This action has two steps: first, place ONE token on an unoccupied number with the requirements from Action 1. Then, say that number out loud – it’s the number you’re expanding – and place tokens on the adjacent numbers that, when you add them up, equal the number you said out loud. These numbers must be connected as the others so they form a single connected group. Like this.
SPECIAL STARTING RULE:
Note that for the first three turns of every game, the actions are limited to the following Special Starting Rule:
The player taking the first turn can only complete Action 1. For example, if the first player is Orange, he may place a token on the number 3. [as shown in book]
The player taking the second turn can only complete Action 1 or Action 2. For example, if the Magenta player is next, and selects Action 2, he may choose to place two tokens on two 5s.
The third player of the game can complete any of the three Actions, but may place no more than three tokens on the board. For example, if the third player is Orange, and selects Action 3, he may place a token on the number 8 and expand it by two tokens on the numbers 5 and 3, because the 5 and 3 add up to 8.
From the 4th turn on, players may choose any action they wish, and place as many tokens as they can. So if the fourth player is Magenta again, all options are open, so she may choose action 3 and place one token on the number 8, as shown, but then expand it by four tokens, placing them on 2, 1, 2, and 3, which add up to 8. Like this.
Players should attempt to place as many tokens on the board as possible when choosing to expand a number.
If a player is unable to place ANY tokens on a turn, he is out of the game and the remaining players continue the game.
Things can get tense when tokens begin to fill the Mainframe and players drop out one by one…
The games ends when there is only one player left!
For variations on the game, including how to play with only one player, and how to play multiple round games like best of three, see the instruction booklet included with Expanders.
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