Shared Wealth

Tutoring Activities from Math 222

Fall 2002 GVSU
Permission granted for educational use.

Game

# Name

Content

1

Sums to Ten

2

3

Sums to Ten

4

5

Doubles +1 or 2

6

Sums to Ten, adaptable to other families

7

Sums to Ten, Mental Strategies

8

Fact Practice

9

Fact practice

Goals :   This game works on facts to 10 while demonstrating the communicative property of addition.   The concept that addition and subtraction are inverse operations is also illustrated.

Materials:

• Game board (any game board with blank spaces will work)
• 10-sided die (good luck) OR cards, with numbers 1-10 on them, to draw from.
• Some kind of marker / piece for players to move along the game board.
• Record sheets.

Rules:   Players take turns rolling the die or drawing a card from the stack.   Each player moves the difference between 10 and the number rolled / drawn.   Then writes down the record.   For instance: If a 6 is rolled, the player moves 4 spaces. Depending on the sheet that is being used, the player will write down either 6+4=10 or 10-6=4.

Method:   This game meets these goals because every turn requires the player to deal with a fact to 10.   Upon examining the record sheet, players can see how A+B=B+A and 10-A=B and 10-B=A.   To help see the connections between certain numbers, may want to color the different facts.   For instance, color all the problems involving 3, 7, and 10 yellow, color 4, 6, and 10 orange, etc.

Variations: The different record sheets allow a different focus for the game.   If addition is what needs to be focused on, use the Record Sheet #1.   If subtraction is the goal, Record Sheet #2 is appropriate.   Record Sheet #3 is designed to help with the relationship between addition and subtraction - how they are inverse operations.

This game could also be played up to 12 with a pair of dice.   Then, different strategies for each fact could be discussed, especially bounce-off ten.

Questions:

• How many more do you need to get to 10?
• How many different problems / facts are there?
• Have we seen this combination of numbers before?   How was it recorded, the same or different?
• Can you switch the numbers in addition?   In subtraction?   Why?
• Are addition and subtraction connected?   How can we see that in this game?
• Can you out the “10” anywhere?
• How do you know what operation this problem should be?
• Can you tell what the sign is just by looking at the 10?

Ó 2002, Heather Lillie

Record Sheets #1-3 for “Move to Ten”

 Number Rolled + Number Moved = 10 1. + = 10 2. + = 10 3. + = 10 4. + = 10 5. + = 10 6. + = 10 7 + = 10 8. + = 10 9. + = 10 10. + = 10

Record Sheet #2 – Subtraction

 10 - Number Rolled = Number Moved 1. 10 - = 2. 10 - = 3. 10 - = 4. 10 - = 5. 10 - = 6. 10 - = 7. 10 - = 8. 10 - = 9. 10 - = 10. 10 - =

Record Sheet #3 – You pick the operation!

Suggestion : Fill-in the “10’s” on the other player’s record sheet before starting this game.

 + or - = 1. = 2. = 3. = 4. = 5. = 6. = 7. = 8. = 9. = 10. =

Ó 2002, Heather Lillie

 10 2 3 4 5 8 6 12 10 7 9 11 14 18 13 12 16 10 17 15 6 9 5 7 10

 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9

Play begins with each player covering a number from 1 to 9 at the bottom.   The 2 nd player then covers the sum of those two numbers on the game board.   The 1 st player can then select one new number from 1 to 9 at the bottom and cover the sum of those two numbers.   Play continues until one player has covered four squares in a row, horizontally, vertically, or diagonally.

Goal: The sums game is a variation of the product game provided in class. The game is designed to help students become fluent in single digit addition.

Materials: Game board, two different color/type of markers for covering the board, addition fact sheet if needed.

Rules: Provided on attached game board.

Method: This game meets the stated goal by allowing students to see the two numbers to be added and then finding the sum on the game board.

Variations: The game could be modified to allow students to chose addition or subtraction, depending on which action would benefit them most. Also, the board could be modified to allow double digit addition or addition of smaller groups of numbers (1-5, 5-10).

Questions: the tutor could ask questions to encourage the student to find different ways to reach the same sum.
Examples:
-How can you make 10 using a six or a three?
-Is there more than one set of numbers that add up to six?
-What sum is the easiest to make (has the most combinations)?

Goals:   Reinforces and expands on the learner’s knowledge of sums to ten to prepare the learner to use the mental strategy of making tens to add large numbers.

Equipment:   Numbered cards from Rack-o game, by Parker Brothers.

Object:   Pairs are made of any two cards that add up to a multiple of 10.
(EX: 10, 20, 30, etc,)   The player who lays out the most pairs is the winner after all the cards have been used up.

Rules:   Deal out 5 cards to each player.   Place the rest of the cards face down in the middle of the table.   Flip the top card of the pile face up next to the pile of cards.   If the first player has two cards that add up to a multiple of 10, s/he lays those cards down on the table in front of her/himself, and picks up two new cards from the top of the pile to replace the cards laid out.   Play continues until the player can no longer lay out a pair of cards that adds up to a multiple of 10.   If the player cannot lay out on the first turn, s/he may pick a card off the top of the pile; if s/he is still unable to lay out, s/he can discard any card and her/his turn is finished.   At the end of their turns, each player should always have five cards in her/his hand.

Method:   It meets these goals by requiring the student to concentrate especially on the numbers in the ones place as s/he adds two numbers to make multiples of ten.   For example, if a player has a 23 and a 57, s/he can quickly realize that these numbers add up to a multiple of ten because the 3 and 7 in the ones place add up to 10.   Then, the student can skip count by tens to find the sum of the cards laid out, either to keep a record or at the prompting of the tutor.   For example, using the numbers 23 and 57 again, the student can skip count starting at 50, so s/he counts 60, 70 because of the 20 of 23, and since the student knows that 3+7 makes one more 10, s/he skip counts from 70 to 80 to find the answer.   This will help to develop number sense in the learner and prepare her/him for more complex mental strategies.

Questions:   Examples of questions the tutor could ask while playing are:

1.       What card do you need to be able to lay out a pair?

2.       What does the pair of cards you laid out add up to?   (This will have to be figured for each pair if a record is kept.)

3.       Do you have a strategy for which is the best card to discard?
-Possible strategy:   If you have two cards with the same number in the ones place, one should be discarded before discarding any other card

4.       What are the different combinations of numbers in the ones place that will add up to a multiple of ten?
-Possible answers:    0+0, 1+9, 2+8, 3+7, 4+6, 5+5

Record:   If you want the student to make a record of the cards laid out, a table like the following could be used. Writing the larger numbered card first may encourage the learner to count on from the larger number when adding two numbers together.

 Larger numbered card Smaller numbered card Total of cards when added 57 23 80 19 31 50

### Thinker, Thinker

Goals: The goal of this game is to help students practice their addition facts in a fun and different way.

Materials: 1 deck of cards

How to Play: This game requires three players to play. Two of the players are called thinkers, and the third player is called the calculator. The two thinkers each draw a card without looking at it and place it on their forehead so the other thinker sitting opposite can not see the card. The calculator then adds the two cards up mentally and says out loud the sum of the cards. The two thinkers than race to figure out the card they have on their own forehead. Whoever figures out what their card is first, gets that pair of cards. Once the deck is gone through, the thinker with the most pair of cards wins.

Meeting the Goals:

This activity is meant for students to practice their addition skills. When playing and one thinker sees that the other thinker has a four, and the calculator says the sum is six, then the think knows that they have a two. It allows for the students to practice their addition facts in a fun, and different way.

Variations:

-Instead of adding the two cards drawn by the thinkers, you can multiply them and have students work on multiplication.

-When only playing with two players you only have one thinker and one calculator. The thinker stills draws a card and puts it on his/her forehead. The calculator then draws a card and holds it so only he/she can she it. The calculator then says the sum of the two cards and the thinker has to figure out the card on their forehead. If they get it right they keep that pair of cards. Each time you switch who gets to be the thinker and the calculator. Whoever gets the most pairs at the end of the game wins.

How did you get that answer?

Is there a different way you could have gotten that sum?

What to record:

You could record this game in a variety of different ways. You could have the calculator record all the thinkers’ pairs, or you could have each thinker record their own pairs.

Goal: The goal is to strengthen student’s use of fact families by using doubles and then adding +1/+2.

Materials: Rekenrek, spinner, game chips, one quarter and a sheet to record

How to Play: This game requires two players each player will compete for the most game chips. You will need to create a spinner that has doubles starting with 2+2 and continuing until 10+10 (or if your student needs larger doubles do so) also include a space that says give five chips to your opponent. You will also need to assign a value to the head and tail of the quarter. For example, in this game we are working on +1 and +2, so we will assign +2 to the head and +1 to the tail. After the player spins the spinner they will then add the doubles by using the rekenrek, if they do not already have the fact memorized. They will then flip the quarter and will add plus one or two depending on if the flip is heads or tails. Player will then add on +1 or +2 on the rekenrek to come up with their final sum for that round. There will be one hundred game chips placed in the middle the player will then take the total of there sum, in chips. The player who has the most chips after all the chips are taken, wins.
Note: In order to make the game fair you need to have an opportunity for opponent to be able to “steal” some of your chips. Other wise if one player has obtained fifty chips he has already won unless the other player has an opportunity to steal his chips. This is why you will need to have a spot on the spinner that calls for the relinquishment of some of other player’s chips. But if player has not obtained any chips yet just spin again.

As each player takes their turn they should record their work on a sheet of paper.

Questions you can ask: Do you know that double without adding? Can you figure out what one more is without using the rekenrek. Does it make sense to add on one or two? Do you think you can use this when doing other math problems?

Goal:
The goal of this game is to make sums to ten more automatic by having fun and playing a game

Materials:
One Aggravation board
The marbles that go with the game (one set of colors for each person)
One die

Object:
To be the first person to get all of his/her marbles from base to home using sums to ten to travel.

Rules:
All the marbles start on the base. In order to get a marble out you must roll a 5. Once you have a marble out whatever you roll on the die you get to move the number of spaces it takes to make ten, for example if I roll a 4 then I get to move 6 spaces, if I roll a 1 then I move 9 spaces because 9 and 1 make ten. You have two options if you roll a 5, you can either get a marble out, or you can move the 5 spaces it takes to make ten. Only one marble can reside on a spot at a time, meaning that if I was on a spot and the next person rolled and got the number of spaces it takes to land on my spot they would send my marble back to base and I would have to start that marble all over again. The first person to get all of his/her marbles home wins!

Variation:
-You could use any kind of board as long as you only had one die and the student had to use sums to ten to move
-You could also work on things like doubles by whatever number is showing on the die you get to move twice that amount for example if you roll a 5 you get to move 10, or if you roll 6 you move 12.

-Always remember to ask if the student knows how many spaces they get to move after rolling the die, like: "So you rolled a 4, 4 plus what equals 10?"
-Toward the end of the game and each of us are close to winning ask the student what he/she needs to roll in order to win, remember they don't get to move the number on the die, they move what it takes to make ten.

How it meets the goal:
This game works on fact families because the student is working on sums to ten by moving the number it takes to make ten.

# First Down!

Drive Chart

 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 Touch down!

Goal:   To work on sums to ten, landmark numbers.

Materials:   At least one die, up to three dice.   One drive sheet for each player.

To win:   Be the first person to score a touchdown, one first down at a time.

To play:   Each player starts on the goal line.   They get three rolls to get a first down.   If they don’t get a first down, the other player gets a turn and they will start their next turn on the next multiple of ten.   After each roll, they record the yard line they’re on and how far to go for a first down.

Example:   I’m on the 20, and roll a 3, then a 4, then a 2.

 20 23 27 29 30 7 3 punt

My next turn I’ll start on the 30 in the next row.

Example:   I’m on the 60, and roll a 5 then a 6.

 60 65 70 5 1 st down

I got a first down and will continue my drive starting at the 70 on the next row.

Note:   the numbers are based on how many yards you’ve driven, not the yard lines on a football field.

Variations:   You get every yard you roll, and start from where you left off.   Circle where you are on first down, then know you have to get ten more yards for another first down.   In the first example, I’d start my next series on the 29 and have to get to the 39.   In the second example, the 6 rolled would take me to 71, so I would have to get to the 81 in three more rolls.

This variation would be for students who know their sums to ten and are working more on mental strategies for addition and subtraction.

The next game is included because several people used it and seemed to find it worthwhile.   I think it needs some variation to be improved, but the premise is interesting.

```Number Tick Tack Toe:

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```A Math Game for Primary Grades

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```

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```AUTHOR:

Ann James, Klawock Elementary; Klawock, AK

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```GRADE LEVEL:

1st - 3rd

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```

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```OVERVIEW:

As surely as the sun rises and sets, kids will learn how to play tick tack toe.

They do not have to be taught the game.

Kids learn it the way they learn jump-rope rhymes and knock-knock jokes.

Yet, kids lose interest quickly because tick tack toe is not challenging enough.

There are only about a dozen different outcomes.

By changing the rules and symbols slightly, you can give the game new life while giving students extended practice in basic addition and subtraction facts.

```
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```OBJECTIVE(s):

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```1.

Students will practice basic addition and subtraction facts to twelve.

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```2.

Students will use high level thinking skills to win at the game of tick tack toe.

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```

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```RESOURCES/MATERIALS: Students will simply need lots of scratch paper and pencils.

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```ACTIVITIES AND PROCEDURES:

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```1.

The class will need to be divided into pairs.

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```2.

Each pair makes a standard tick-tack-toe grid.

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```3.

Instead of using X's and O's, students use the numbers 0 through 9.

Use numbers 0 through 12 for a greater challenge.

Each number can be used only once during a game.

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```4.

The object of the game is to complete any row, column, or diagonal so that two of the three numbers add up to the third.

The order of the numbers does not matter.

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```5.

The first move may NOT be in the center.

(If the first player is allowed to make that move, he or she can always win the game.)

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```6.

The second and subsequent moves, however, can be anywhere on the grid.

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```TYING IT ALL TOGETHER:

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```

There is not any sure fire strategy for winning this type of tick-tack-tow game.

Likewise, there seems to be no advantage in going first.

The games, however, tend to end with a winner rather than in ties.

```
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Most losses result from carelessness.

It's easy to make a mistake after four or five numbers have been played.

That's when the game requires close attention, higher level thinking skills, and accurate adding and subtracting.

```
```

The game is far more complex than tick-tack-toe in that there are thousands of outcomes.

The one constant is good number facts practice in an enjoyable context.

```

Number Tic Tac Toe

Goals: The goals of this game include: using number facts, addition, subtraction and using higher level thinking skills.

How to play: This variation of tic tac toe involves numbers instead of x’s and o’s. The teacher would begin by dividing the class into pairs to work together. Each pair would use a tic tac toe grid that they had made and by using the numbers 0-10. Each player is trying to complete a row, column or diagonal so that two of the numbers add up to the third. Each number can only be used once during each game. The only other rule is that the first person cannot use the center square. Any subsequent move after the first can be in the center.

How this activity meets the goals: By playing this game the students are encouraged to learn how to add and subtract numbers using a variety of numbers. Since they are not allowed to use the same number twice in each game they are encouraged to use higher thinking skills to come up with the answers. It also takes a lot of concentration because once there are a few different numbers on the grid it becomes a lot more challenging.

Variations: This game can be modified to use multiplication and division instead of addition and subtraction. The teacher could also make this a collaborative game by having the students work together to get as many problems in the grid as possible and challenge each other to come with the most problems they can.

Record: If the students are working collaboratively then you can have them write down all of the problems they were able to fit in the grid.

1)What numbers can be added together to make the number you need?

Variations:   rather than just allow1-12 for extension, other possibilities include making a 4x4 grid (1-16) or a different set of numbers (eg.   2, 4, 6, …, 18).

Materials:   paper for the game grid, paper for student records.

This is a variation on the number Tic Tac Toe above.

The best variation I can come up with is to play until the grid is filled, and players get a point for each row, column or diagonal that makes a record.   Players keep track of their points by writing their record.   A sample game is below.   This is without any restriction on numbers.

Plays (in order): 7, 4, 3, 2, 5, 6, 1, 9, 13.   Player One wins 3 points to 2.

 Player 1 Game board Player 2 2+3=5 5 3 2 2+4 6+1=7 13 9 4 9-2 4+9=13 7 1 6

Recommendations:   Make scores cumulative, having players add their points from game to game, taking turns going first.   The game might be fairer with number restrictions like only allowing 1-9, that would have prevented the last Player One score, and makes players try more variations.