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# bingo number range

## Number After Bingo 1-15

Each student will need a different Number After Game Board (a 5×5 grid with numbers from 2 through 15 randomly arranged, one in each square), 15 each of two different color counting chips and a set of 2-3 each of number cards with the numbers 1 through 15 on them.

Begin whole group by discussing what “number after” means. Next have the students identify and point out on a large number line the number after various numbers selected by the teacher. Initially keep these numbers in the range of 1-15. After the group seems to have an understanding of what “number after” means and how to locate them on the number line, have students play Number After bingo on the 5×5 bingo board in pairs. Students will take turns drawing a number card, stating the number after and placing his/her counter on that number on the game board. The first student with 3 counters in a row on the grid is the winner. As students progress the practice range should be increased by changing the numbers on the grid and the corresponding numbers on the cards.

### IM Commentary

Student work with number after is important because it increases student flexibility with the number sequence and the ability to start counting sequences at various points.

Initially students may need a number line to locate the number after; students may also do some “sub-vocal” counting (sort of like counting under their breath) from another number to give them a “running start” which helps them carry on the sequence.

Sub-vocalization is a common student strategy that should be noted when assessing a studentâs facility with number after. The students should reach a point when they “just know” the number after orally and do not need the number line support or the additional counting. This should occur naturally through targeted and repeated exposure and practice.

Repeating the initial whole group activity daily by having students identify the number after a given number as a sponge activity will be very supportive for students.

Once students have become facile with the number after, it is important to work on number before following a similar process.

If the students have not played games much, they may need the teacher to model what “3 in a row” on the game board looks like. If students are struggling with the “3 in a row” concept, they can also play blackout and just cover the board completely, which is often easier for young students to understand initially.

### Solution

Possible ranges for practice identifying the number after: 1-15, then 1-21, then 10-31, then 20-40 and 50-80. Initially, the whole class can work on the same range, but over time some students may still need to work on 1-15 while others will be ready to move on to 1-21 etc. In this way, all students can be doing the same activity but it is differentiated for individual student needs.

Possible ranges for practice identifying the number before: 1-10, then 1-15, then 1-21, then 10-31, then 20-40 and 50-80.

This game can also be modified to support crossing into the next family or “crossing the decade” forward or backward by doing the number after “_9” numbers or number before “_0” numbers. You would need to have 19, 29, 39, 49, 59, 69, 79, 89, 99 on cards and 20, 30, 40, 50, 60, 70, 80, 90, 100 on the 5×5 grid to practice crossing the decade forward. The teacher would need to have 20, 30, 40, 50, 60, 70, 80, 90, 100 on cards and 19, 29, 39, 49, 59, 69, 79, 89, 99 on the 5×5 grid to practice crossing the decade backward.

### Number After Bingo 1-15

Each student will need a different Number After Game Board (a 5×5 grid with numbers from 2 through 15 randomly arranged, one in each square), 15 each of two different color counting chips and a set of 2-3 each of number cards with the numbers 1 through 15 on them.

Begin whole group by discussing what “number after” means. Next have the students identify and point out on a large number line the number after various numbers selected by the teacher. Initially keep these numbers in the range of 1-15. After the group seems to have an understanding of what “number after” means and how to locate them on the number line, have students play Number After bingo on the 5×5 bingo board in pairs. Students will take turns drawing a number card, stating the number after and placing his/her counter on that number on the game board. The first student with 3 counters in a row on the grid is the winner. As students progress the practice range should be increased by changing the numbers on the grid and the corresponding numbers on the cards.

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## Bingo number range

Traditional BINGO is played in person in a large hall. Players meet at the hall, pay a fee to get in, then the games begin. A night of BINGO consists of many BINGO games played continuously, one after another.

A single BINGO game proceeds like this: Each player has a number of BINGO cards (players can usually play any number of cards). Each BINGO card has 5 rows and 5 columns thus providing 25 spaces.

The columns are labeled from left to right with the letters: ‘B’, ‘I’, ‘N’, ‘G’, ‘O’. With one exception (the center space is “free”) the spaces in the card are assigned values as follows:

• Each space in the ‘B’ column contains a number from 1 – 15.
• Each space in the ‘I’ column contains a number from 16 – 30.
• Each space in the ‘N’ column contains a number from 31 – 45.
• Each space in the ‘G’ column contains a number from 46 – 60.
• Each space in the ‘O’ column contains a number from 61 – 75.

Furthermore, a number can appear only once on a single card.

Here’s a sample BINGO card:

 B I N G O 10 17 39 49 64 12 21 36 55 62 14 25 FREESPACE 52 70 7 19 32 56 68 5 24 34 54 71

The number of unique BINGO cards is very large and can be calculated with this equation:

While perhaps interesting to a statistician, the number of possible BINGO cards has nothing to do with player’s chances of winning.

You will note that there are 75 possible BINGO numbers:

When a player has a BINGO (5 marks in a row, column, or diagonal), he or she calls out BINGO. The game pauses while the card is verified. If indeed a winner, the game stops and a new game begins. If the card wasn’t a winner, the game proceeds where it left off. Each BINGO game proceeds until someone wins (there’s always a winner).

The first line of input contains n, the number of BINGO games that you will analyze. n game descriptions follow. Each game description specifies a card to be played followed by a sequence of BINGO numbers. You are to determine, when the holder of the card will win the game, assuming the player has just this one card and there are no other players.

Each card description consists of five lines, giving the numbers on the card row by row. All but the 3rd row contain 5 numbers; the 3rd contains 4 because of the free space. One or more lines follow that represent some ordering of all 75 bingo numbers. All bingo numbers are simply integers between 1 and 75 – the one-letter prefix is redundant. For each game, ouput the line “BINGO after n numbers announced” as appropriate.

##### Chances of Winning

Every BINGO game has a winning card, so a player’s chances of winning depend on the number of cards in the game and how many cards s/he is playing. For example, if a player has 12 cards in a game with 1200 cards, the chances of winning for that player is 1 in 100.

Bingo number range Traditional BINGO is played in person in a large hall. Players meet at the hall, pay a fee to get in, then the games begin. A night of BINGO consists of many BINGO games played