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How to Play

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Educational Standards

#### Core Standard*: Math

##### Math

- Operations and Algebraic Thinking
- Represent and solve problems involving addition and subtraction Grade Level 2
^{nd} - Add and subtract within 20. Grade Level 2
^{nd} - Represent and solve problems involving multiplication and division. Grade Level 3
^{rd} - Understand properties of multiplication and the relationship between multiplication and division. Grade Level 3
^{rd} - Multiply and divide within 100. Grade Level 3
^{rd} - Solve problems involving the four operations, and identify and explain patterns in arithmetic. Grade Level 3
^{rd} - Use the four operations with whole numbers to solve problems. Grade Level 4
^{th} - Mathematical Practice
- Make sense of problems and persevere in solving them. Grade Level 3
^{rd}, 4^{th} - Model with mathematics. Grade Level 3
^{rd}, 4^{th} - Look for and make use of structure. Grade Level 3
^{rd}, 4^{th}

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Skills

** Explore**

**What Does Child Do To Use Skill In The Game?**

Players explore their tiles to see various equation options.

**How Parents Can Assist Learning**

Parents can encourage children to rearrange tiles in their hand in order to explore different math functions and numerical combination options.

**Learning Implications and Educator Support**

Sum-ol-o-gy requires children to think about different math function and numerical combinations options. Educators can encourage children to move the dice around to visualize multiple options. Also, children need to consider which tiles to use for maximum scores, or to hold on to for the next turn. Help children by asking them to "Wait. Look. Think." This will help with impulsivity and planning. Also, using such cues can give children a model for future play.

** Determine**

**What Does Child Do To Use Skill In The Game?**

Players determine what options they have within their set of tiles to make an accurate equation.

**How Parents Can Assist Learning**

Parents can encourage children to rearrange tiles in their hand in order to explore different math functions and numerical combination options. Also, have them add up the scoring value of each option in order to determine the best one to use.

**Learning Implications and Educator Support**

Sum-ol-o-gy requires children to think about different math function and numerical combinations options. Educators can encourage children to move the dice around to visualize multiple options. Also, children need to consider which tiles to use for maximum scores, or to hold on to for the next turn. Help children by asking them to "Wait. Look. Think." This will help with impulsivity and planning. Also, using such cues can give children a model for future play.

** Compare**

**What Does Child Do To Use Skill In The Game?**

Players explore the equations on playing area to find a place to put their equation or a place to make a new equation

**How Parents Can Assist Learning**

Parents can encourage children to not only look within their own set of tiles, but also look at tiles on the table that they may be able to use to make an equation.

**Learning Implications and Educator Support**

Sum-ol-o-gy allows children to compare different equation options for maximum scoring, as well as for managing how many tiles they use on a turn. For advanced comparison practice, educators can encourage children to not only look within their own set of tiles, but also look at tiles on the table that they may be able to use to make an equation.

** Remember **

**What Does Child Do To Use Skill In The Game?**

Players need to remember how to make an equation that includes an = sign. They also need to remember addition, subtraction and multiplication and division facts.

**How Parents Can Assist Learning**

Parents should explain all symbols prior to playing the game, if children do not remember how all the functions work. If a child has difficulty, show them how to make an equation and discuss the results together.

**Learning Implications and Educator Support**

Educators should explain all symbols prior to playing the game, if children do not remember how all the functions work. Have children say their equation aloud as the place it on the game area. Verbalizing helps develop memory.

** Predict**

**What Does Child Do To Use Skill In The Game?**

Players can predict what the equation is that is being placed by other players.

**How Parents Can Assist Learning**

Remind children that their score is based on adding the numerical value of the tiles played, not the sum of the equation. This will help children strategize for optimal scoring.

**Learning Implications and Educator Support**

Educators can encourage children to follow the placement of tiles by another player and try to predict what the other player will place next. For exmaple, "Joe placed a 2 x 4, what do you think is next? Oh, a surprise! It is not "= 8"! He placed a "+ 3". He is making a longer equation! Keep watching..."

** Plan**

**What Does Child Do To Use Skill In The Game?**

Players need to plan what they need to make various equations. They can also plan for longer equations to make more points.

**How Parents Can Assist Learning**

To facilitate planning and organizing for maximum scores, educators can encourage children to not only look within their own set of tiles, but also look at tiles on the table that they may be able to use to make an equation. Also, when it is not their turn, encourage children to make alternative equations so they have options depending on moves of other players.

**Learning Implications and Educator Support**

Sum-ol-o-gy allows children to examine different equation options for maximum scoring, as well as for managing how many tiles they use on a turn. To facilitate planning and organizing for maximum scores, educators can encourage children to not only look within their own set of tiles, but also look at tiles on the table that they may be able to use to make an equation. Also, when it is not their turn, encourage children to make alternative equations so they have options depending on moves of other players.

** Experiment**

**What Does Child Do To Use Skill In The Game?**

Players experiment by moving their tiles to see various equation options.

**How Parents Can Assist Learning**

Parents can model experimentation by using various types of equations. They should verbalize what they are doing. "I've got a simple equation here, but I'm going to see if I can make it longer by adding another operation."

**Learning Implications and Educator Support**

Educators can model experimentation by using various types of equations. They should verbalize what they are doing. For example, "I've got a simple equation here, but I'm going to see if I can make it longer by adding another operation." Use math terminology so children learn the appropriate vocabulary concepts.

** Practice**

**What Does Child Do To Use Skill In The Game?**

Players are practicing math operations with each turn.

**How Parents Can Assist Learning**

Parents can check children's equations to see if they are accurate. If they are not correct, the parent helps the child break down the problem to see where there was an error in thinking. For example, say, "Tell me how you got this answer." (Don't say, "That's wrong. The answer is..." That will discourage learning.)

**Learning Implications and Educator Support**

Educators can focus the math content on addition, subtraction, multiplication, division or a combination to meet the skills and needs of the child. Check children's equations to see if they are accurate. If they are not correct, the educator helps the child break down the problem to see where there was an error in thinking. For example, say, "Tell me how you got this answer."

** Solve**

**What Does Child Do To Use Skill In The Game?**

Players solve equations with every turn and experiment with options in between turns. They also solve addition of numerous numbers when they add the sum of all digits in the equation for a score.

**How Parents Can Assist Learning**

Parents can check children's equations to see if they are accurate. If they are not correct, the parent helps the child break down the problem to see where there was an error in thinking. For example, say, "Tell me how you got this answer." (Don't say, "That's wrong. The answer is..." That will discourage learning.)

**Learning Implications and Educator Support**

Educators can check children's equations to see if they are accurate. If they are not correct, the educator helps the child break down the problem to see where there was an error in thinking. For example, say, "Tell me how you got this answer."

** Review**

**What Does Child Do To Use Skill In The Game?**

Players may review if encouraged. See Implications for Learning and Adult Support.

**How Parents Can Assist Learning**

Part of the game is to review what other players have placed on the board. If equations are inaccurate, the tiles are returned for another try. This gives children additional practice in solving problems.

**Learning Implications and Educator Support**

Part of the game is to review what other players have placed on the board. If equations are inaccurate, the tiles are returned for another try. This gives children additional practice in solving problems.

** Demonstrate**

**What Does Child Do To Use Skill In The Game?**

Players demonstrate knowledge through accurate creation of equations.

**How Parents Can Assist Learning**

Parents can demonstrate how to approach a problem by verbalizing for the child what they did. For example, "I had a 4, 5, 2, =, and 0, and I know that 4 X 5 = 20, so I looked on the board for an open X." or "I had 2, 5, 3, 7, = and a X. I know that 5 X 7 is 35, so I looked on the board for an open 3 or 5."

**Learning Implications and Educator Support**

Educators can evaluate children's mathematic skills by observing the accuracy and complexity of their equations. To determine children's problem solving approach, educators should ask children to demonstrate understanding by verbalizing their thinking as they lay tiles down.

** Create**

**What Does Child Do To Use Skill In The Game?**

Long equations require creative thinking about the various ways numbers can be combined.

**How Parents Can Assist Learning**

Give teams the same numbers and see how many different equations they can make. Long equations require creative thinking about the various ways numbers can be combined. Parents can encourage children to try to use as many of their numbers and operations as they can

**Learning Implications and Educator Support**

Educators can use this game to give children practice in conceptualizing how numbers can be combined in different ways to form an equation. Encourage children to use trial-and-error to "think of another way" to use the numbers. Children can then visualize how different combinations of operations have the same total. Educators can encourage children to try to use as many of their numbers and operations as they can.

*Data compiled from CCSSI ELA Standards, WA Science Standards, and Washington Social Studies Standards

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Special Needs

**Cognitive**

**Suggestions for How to Modify Play Experience**

Eliminate the multiply and divide operation for children who have cognitive delays until they have mastered the addition and subtraction.

Lower functioning children can practice counting by finding the number tiles and placing them in a sequence, one after the other. The adult can help the child use the visual cues provided by the tiles to show them how to count by 2's, 5's, and 10's.

**Communication**

**Suggestions for How to Modify Play Experience**

Have children read out each other's equation and solve it verbally to check if the child who laid down the equation is right.

**Sensorimotor**

**Suggestions for How to Modify Play Experience**

Provide space between the numbers when they are placed so children with fine motor difficulties do not knock the numbers out of place on the playing area when they lay down their numbers.

Children with severe motor problems may verbalize where they want a peer to put their numbers.

**Social Emotional/Behavioral**

**Suggestions for How to Modify Play Experience**

Have children read out each other's equation and solve it verbally to check if the child who laid down the equation is right.

Work in pairs to make an equation. This requires communication and collaboration.

**Vision**

**Suggestions for How to Modify Play Experience**

Some of the numbers are difficult for children with vision impairments to see. Increase the contrast by tracing around each letter with a black marker.

**Hearing**

**Suggestions for How to Modify Play Experience**

No modification required.

*Data compiled from CCSSI ELA Standards, WA Science Standards, and Washington Social Studies Standards

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Autism

Autism Strengths & Interests

Short Summary of Strengths & Interests

- Likes math and math operations.
- Is good at visualizing options, particularly with numbers.
- Likes to use their dexterity in play.

**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**

Players need a good memory for addition, subtraction, multiplication, and division facts. They may also be able to use sets of numbers to create equations.

**Likes to put things in order or a sequence**

Is This Game Appropriate? Yes

**Description**

Players can combine different mathematical operation in one equation. This requires ordering subsets of smaller equations (A + B = C, then C-D = E, then E+F = G) so that they are translated into A + B - D + E = F) in order to make one equation. In addition, the players need to order their equations on the board to build the entire game area into a connected grid.

**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**

The rules for reading and interpreting math operations are needed to make an accurate equation. Children who understand the rules and can accurately conduct the operations will do well with Sumology.

**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**

Some children are strong in learning by "chunks", e.g. they assemble information into a single concept and then combine that with other concepts to create and/or remember something more complex. Each part of an equation represents a "chunk" of the larger equation. 2 + 5- 3 = 4 is actually (2+5 = 7 )and (7- 3 = 4)

**Is good at nonverbal reasoning and logic**

Is This Game Appropriate? Yes

**Description**

Nonverbal reasoning is needed to determine how to get most points. Points are counted by the values of the numbers contained within the equation placed on the board. Therefore, selection of tiles both in the play set and on the board is important for a higher score. This requires players to be able to shift perspectives and think of numerous options for each turn.

**Likes spatial problem solving**

Is This Game Appropriate? Yes

**Description**

Using the space on the board to advantage is important for winning. Strategic tile placement is key.

**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**

Fine motor skills are needed for building the grid on the board. Tiles also need to be manipulated in various ways to try out equations before they are finally laid on the board.

**Likes established routines or set ways of doing things**

This game is not appropriate

**Likes manipulating, constructing or building things**

Is This Game Appropriate? Yes

**Description**

The arrangement of tiles on the board results in the construction of a grid that expands the game area. This is not the intent of the game but placement of tiles makes a difference in equation possibilities.

**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:

Sit or stand at an angle to the child, so direct eye contact is not needed, if you are playing in teams.

Look at the game instead of each other.

Use unusual or exaggerated inflection to begin a communication about the game. This attracts the child's attention.

**Has difficulty understanding complex verbal directions**

Is This Game Appropriate for Child with Characteristic? Yes

Can Child with Characteristic Play Game w/o Modification? Yes

Strategies for Developing Compensatory Skills:

Break down directions into small steps. Don't go through all the directions at once.

Combine short verbal instructions with visual and physical examples of each step.

Use photos to illustrate what needs to be done. These can be taken ahead of time. The combination of pictures and actions reinforces learning the steps. Also, take pictures during the game for use in later discussions about the game and what happened.

Check for comprehension by doing an equation wrong and asking the child to fix it.

Let children read the directions as they are explained. Visualizing the words is often a stronger learning method for children with autism.

**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:

Respond to immediate echolalia (repeating what was just said) by rephrasing the child's response into a correct format, so the child can hear and repeat that phrase. For example, assume you are playing with a child named Andy and you say, "Your turn," and Andy repeats, "Your turn." You can say, "It's Andy's turn. You say, my turn." This allows the child to hear and repeat the correct response. Eventually, the child will pick up the pattern of response.

Delayed echolalia (repetition of previously heard comments) may have a hidden meaning or association. Look for connection in the phrase used to the current situation. For example, the child says, "After these messages we'll be right back!" Think what the repeated phrase is associated with for the child. Try to interpret what is meant and rephrase it for the child. For example, you might respond by saying, "It sounds like you want a break for a few minutes. Is that what you mean? You can tell me, 'I need a break.'"

**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? Yes

Strategies for Developing Compensatory Skills:

Remind children about listening and watching others' before making their own comment or action.

Extend the child's action to make a correct response. For example, if the child persists in placing the same type of simple equation, you can suggest adding more. For example say, "You can include more. How can you include subtraction?"

Reinforce attention and actions by commenting on what was done correctly. For example, "You combined two different operations. Good for you!"

**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:

Use gestures and sign language to illustrate actions or concepts. For example, use the sign for 'finished' (turn two hands facing down, then to the side from the middle of the body), point to the next player and say, "I'm done. It's your turn." The signs and gestures add a visual component to support understanding.

Provide at least 10 seconds wait time for the child to process or produce responses. It may take longer to formulate a thought or response for children with special needs.

**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? No

Strategies for Developing Compensatory Skills:

Use physical actions to walk through steps numerous times. Practice simple equations first, then add in two-step equations.

Playing as a team is recommended, so the child with special needs can be coached or encouraged to higher level thinking.

**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? No

Strategies for Developing Compensatory Skills:

Develop a social story to be read at the start of a game. A social story is a short booklet that illustrates how a child can use positive social skills. It includes two to five descriptive statements and a directive statement. For example: "When I watch others, I will know when it is my turn. Others like me when I take turns. I will watch what others do with their pieces and listen to what they say. Others like it when I talk about the game." Add photos or drawings of the child doing the actions described in the story.

As the child feels comfortable with what the game requires, add partner play. Explain to the partner how to support the child with special needs to do the thinking and not provide the answers. For example, the child could do one part or one side of an equation and ask the child with special needs to add another part. Alternatively, they could take turns experimenting with adding a tile. Encourage partners to talk about what they are thinking out loud. Children with special needs benefit from hearing what others are thinking.

Use video feedback of positive social behaviors. Video of actual play enables children to see what they or others did. Appropriate actions and interactions can then be discussed.

**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? No

Strategies for Developing Compensatory Skills:

Reduce extraneous noise or allow the child to wear head phones or ear plugs if loud sounds cause anxiety.

A weighted vest worn during the game may provide additional pressure input and thus reduce fidgeting due to sensory needs. Pressure can be calming when used for no more than 20 minutes at a time.

Practice a phrase to ask for help and role play situations in the game where it is needed.

Provide techniques for self-calming, such as holding a special toy.

Allow time for movement. For example, a child who needs to move frequently can be given an opportunity to 'celebrate' their turn by running around the table or jumping up and down 10 times.

**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? No

Strategies for Developing Compensatory Skills:

Provide a break when needed.

Frequently remind the child of the goal of the game. "Let's see how high a number you can make on this side of the equation."

Incorporate a motivating activity as part of the play. For example, each player gets to manipulate a fun 'fidget' toy, such as a stress ball or squeeze toy.

**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:

Play games at the same time every day, so the child anticipates the game routine.

Change the location of the game, so the child may play in different rooms, at the table, or on the floor. This will build tolerance for variation.

Prepare the child ahead time for the introduction of a new game. Talk about aspects that will be motivating for the child, and let them explore the parts of the game before setting out the whole game.

Provide a structure for placement of game pieces that can be the same each time the game is played. For example, have a specific location for where the board goes, the pieces, etc.

Involve the child verbally and with actions for the transition to the game table or at the end of game play. For example, you might say, "Let's look at the pictures on the game box and guess how to play it or what it might be about."

**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:

If playing in teams, it is important for the teammate to talk through what they is thinking and to ask questions to understand what the child with special needs is thinking.

*Data compiled from CCSSI ELA Standards, WA Science Standards, and Washington Social Studies Standards

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Extended Play

**Extra Ways to Play the Game**

Memory game. Turn over all the tiles. Each player turns over 2 tiles to try to find a match. Extras: There are 5 of each operator, so either remove one of each operator tile or let the extra be a spoiler that they have to remember is an extra. There are 6 of each number tile, so either 2, 4, or 6 of each can be turned over. You may give extra points for finding 4 or six of a number.

**Materials Needed**

No additional materials needed.

**Developmental Benefits**

This modification builds visual spatial memory, a cognitive skill.

**Extra Ways to Play the Game**

A player creates the beginning of an equation with the tiles but does not provide the answer. Each other player tries to solve the original equation with as many additional equation pieces as possible resulting in the same answer. Each person gets 1 point for each tile added to the equation. For example, the first player writes: 8 x 2 =. another player can get 2 points for answering 16 (2 number tiles) or he/she can add on 4 x 2 + 8 for 5 points (3 number tiles and 2 operation tiles). Add multiplication and/or division to make the game harder. Give extra points for a X or a divided by operator.

**Materials Needed**

Paper and pencils for practicing.

**Developmental Benefits**

Children need a basic ability to add and subtract for an easy level of this game, and the ability to multipy and divide for a harder variation. This game variation requires ability to retain a number in the mind and then perform operations on that number that result in the same number. This ability to perform different operations in sequence requires higher level cognitive thinking. With assistance and support, children will gain self confidence about their math abilities.

**Extra Ways to Play the Game**

Let children work in pairs or as a group to solve the problem. Draw a number tile. See how many equations the children can create with this number as an answer.

**Materials Needed**

Paper and pencils.

**Developmental Benefits**

In addition to cognitive skills, this activity allows children to learn collaborative problem solving skills. The will also practice leadership and communication skills by teaching others and discussing options.

**Extra Ways to Play the Game**

Experiment with how to make domino-like falling runs. Stand up the tiles in a line and knock over the first one. See what happens. Make a new line, curve, etc. Try it again. Try putting one tile on top of another. What else can you try?

**Materials Needed**

None. If you have dominoes at home, try adding those.

**Developmental Benefits**

This activity builds fine motor skills, as well as reinforcing a wide range of thinking skills. Also, depending on what other materials kids add and the different types of runs they make, this can be a very imaginative and creative activity.

**Extra Ways to Play the Game**

Player 1 says a number between 1-100. Each player has 2 minutes to make the longest equation that equals the number. The longest equation wins.

**Materials Needed**

A timer or watch

**Developmental Benefits**

This modification expands on the core math learning in Sum-ol-o-gy, by encouraging kids to make increasingly complex equations.