Number+Sense+and+Operations

Number Sense and Operations

 * INTRODUCTION**

Teachers have discovered an easy to setup game for students with a wide range of mathematical operation comprehension. The best dynamic of this game is that students will continue to be challenged regardless of their proficiency. The game can be played by two players or teams with two sides for students to gain confidence in using operations. Several game boards can be played at the same time to provide a large number of students ample opportunity to develop their skill.


 * OVERVIEW**

Tiguous is an excellent game for students struggling to remember their math operations. Especially for students that need to develop speed with multiplication and division when coupled with addition or subtraction. This game provides students with a wide variety of strategies for problem solving.They are able to make conjectures that are convincing to illustrate their techniques. The connections are multifaceted to other games and real world examples. Students will verbalize their proficiency with mathematical language and common language. Students will be able to show multiple representations on paper during games and as final assessment with a multiple operations test.




 * TIGUOUS.....NUMBER SENSE AND OPERATIONS **

 Students will be able to fluently add, subtract, divide, and multiply single digit numbers; this game is intended to increase mental math capabilities, both in speed, function, and accuracy.


 * LEARNING OBJECTIVES **

7.1b Represent addition, subtraction, multiplication, and division of positive and negative integers visually and numerically. 7.1c Fluently and accurately add, subtract, multiply, and divide rational numbers.

State Middle Level Math Endorsement Standards


 * MATERIALS **


 * Tiguous Board (link below)
 * 3-5 dice per board
 * 8 of each colored chip (two colors per board)


 * INSTRUCTIONAL PLAN **

 Tiguous should be introduced to students to increase their mental math abilities. Tiguous is intended to accelerate a students skills through application and repetition.


 * Roll a die to see who gets to start the game
 * The winner of the role gets to roll all three dice at once
 * Using the numbers that were rolled on the dice the player has to perform any two operations (addition, subtraction, multiplication, division) to get an answer equal to one of the available numbers
 * <span style="font-family: Arial,Helvetica,sans-serif;">The players continue this process, taking turns, until one player gets three consecutive colored chips vertically, horizontally, or diagonally
 * <span style="font-family: Arial,Helvetica,sans-serif;">If a player cannot reach an available number on the board, then they receive one re-roll. If a number is not reached at that point the next player goes
 * <span style="font-family: Arial,Helvetica,sans-serif;">Each operation must be discussed verbally during each players turn so all players benefit from the number operations exercise


 * <span style="font-family: Arial,Helvetica,sans-serif;">MODIFICATIONS **

<span style="font-family: Arial,Helvetica,sans-serif;"> If number operation skills are not fluent in all areas (addition, subtraction, multiplication, division) the operations my be reduced to addition and subtraction only.

<span style="font-family: Arial,Helvetica,sans-serif;"> Another option is to decrease the number of dice to two, or increase the dice to four.


 * <span style="font-family: Arial,Helvetica,sans-serif;">QUESTIONS FOR STUDENTS **

<span style="font-family: Arial,Helvetica,sans-serif;"> Prior to start
 * <span style="font-family: Arial,Helvetica,sans-serif;">What is your grade level?
 * <span style="font-family: Arial,Helvetica,sans-serif;">Which mathematical operations are you comfortable performing mentally?

<span style="font-family: Arial,Helvetica,sans-serif;"> During the game
 * <span style="font-family: Arial,Helvetica,sans-serif;">How can you rearrange the numbers on the dice to create another number?
 * <span style="font-family: Arial,Helvetica,sans-serif;">What happens if you try subtracting/taking away the number?
 * <span style="font-family: Arial,Helvetica,sans-serif;">If you divide the larger number by the smaller number, how many groups can you make?
 * <span style="font-family: Arial,Helvetica,sans-serif;">What number is needed to create a row, column, or diagonal of three?
 * <span style="font-family: Arial,Helvetica,sans-serif;">Does the order of the operations we perform effect the outcome?


 * <span style="font-family: Arial,Helvetica,sans-serif;">ASSESSMENT OPTIONS **

<span style="font-family: Arial,Helvetica,sans-serif;">Some assessment options associated with Tiguous include:
 * <span style="font-family: Arial,Helvetica,sans-serif;">Tournament: The students would set up and play a round-robin tournament. This would be a successful formative tool in order to assess the students' overall understanding of the objectives.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Create a New Game: The students would create, produce, and teach a new game based on the same objectives as Tiguous. They would teach their peers how to play the game. The teacher could then host a series of Game Days, in which the students teach and play their unique games.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Math Bee: The class would participate in a mental math tournament, the Math Bee. Set up similarly to a Spelling Bee, the students would compete in a progressively more difficult series of equations, solving them verbally.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Tiguous vs. Teacher: On a Game Day, each student (or two students) would play Tiguous against the teacher. The teacher could extend the questions asked to more difficult and applicable topics associated with the assessment of the objectives.
 * <span style="font-family: Arial,Helvetica,sans-serif;">Quiz/Test: This summative assessment is always an option, however it may not be the most beneficial to the concept of mental math. In order for a quiz or test to fully meet the needs of the objectives, the students would not be able to use any paper nor would they be able to express their calculations in any other format than mentally and/or verbally. A verbal quiz could work if executed successfully to the needs of each student.


 * <span style="font-family: Arial,Helvetica,sans-serif;">Tiguous (Printable versions) **

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 * <span style="font-family: Arial,Helvetica,sans-serif;">EXTENSIONS (Pre and Post Activities) **

<span style="font-family: Arial,Helvetica,sans-serif;">Tribulation

<span style="font-family: Arial,Helvetica,sans-serif;">This game also challenges students to find equivalent names for numbers. In Tribulation, students must search the game board for 3 numbers in a row (vertically, horizontally or diagonally as in a word search) that combine to make the target number. In this game, however, there is a prescribed formula for combining the numbers. Students must multiply the first two numbers then add or subtract the third number to produce the target number. <span style="font-family: Arial,Helvetica,sans-serif;">Students quickly learn that any string of three numbers produce four different results since the string of numbers can be considered both forwards and backwards as in word searches. Consider that the numbers 3, 5 and 8 are in a horizontal row. These three numbers produce the following results when combined in the formula: <span style="font-family: Arial,Helvetica,sans-serif;">Note that the student may not begin with the middle number. Once again, students will perform many mental calculations in a search for a viable solution on the game board. <span style="font-family: Arial,Helvetica,sans-serif;">This game was originally a board game in the 1980s but has been developed into a classroom game using a game board template designed to be inserted in a sheet protector and used with dry-erase pens so that students can easily circle and record solutions. Two different approaches are effective in using this game: (1) students search for one solution for 6-8 different target numbers, and (2) students search for many different solutions for one number. Samples of both types of activities are included in the Tribulation directions packet for teachers.
 * <span style="font-family: Arial,Helvetica,sans-serif;">3 x 5 + 8 = 23
 * <span style="font-family: Arial,Helvetica,sans-serif;">3 x 5 - 8 = 7
 * <span style="font-family: Arial,Helvetica,sans-serif;">8 x 5 + 3 = 43
 * <span style="font-family: Arial,Helvetica,sans-serif;">8 x 5 - 3 = 37

[|Math Factoring Games]

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 * <span style="font-family: Arial,Helvetica,sans-serif;">Game Board **

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 * <span style="font-family: Arial,Helvetica,sans-serif;">Teacher Guide **


 * <span style="font-family: Arial,Helvetica,sans-serif;">TEACHER REFLECTION **

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<span style="font-family: Arial,Helvetica,sans-serif;">Reflecting back on the “Math Game Night” at Selah Middle School, we expected to be playing the game we designed for 6-8th graders. Unfortunately, there were nary but a few. This was good; it forced us as a group to reevaluate our game playing strategy and thus adapt it to the droves of first and second graders that sat at our table. Upon asking the children what their level of math comfort was, we then as a group took on the task of introducing the game, to them and their families. Most of the mathematics played involved addition and subtraction of three dice, and eventually some of the children ventured into small portions of the multiplication table, like the (2x, 3x). It was refreshing to see the children learning new ways of thinking about how the answers can vary if you move the numbers (dice) around while performing the addition and subtraction properties with the dice. Once the children were engaged with the game, it seemed to spark a real and healthy competition amongst the parents and children as well as the CWU teachers and children. A very enjoyable evening spent doing math connected to a game with children, who seemed to enjoy learning. ======