Patterns, Functions & Algebra A B A B Y=x +30-(x-2) X=2(y +5)
Vocabulary List Patterns, Relations and Functions Equation- an equation is a mathematical statement, in symbols, that two things are the same (or equivalent). Equations are written with an equal sign, as in 2 + 3 = 5. Inequality- In mathematics, an inequality is a statement about the relative size or order of two objects. Patterns- Commutative property- order does not matter when we add two or more numbers Associative property For all real numbers a, b, and c: (a + b) + c = a + (b + c)the associative property is a lot like the commutative property, except that it involves three or more numbers, not just two. We can only operate on two numbers at one time, but we have the choice of which two to choose first, next, and so on. Just like the commutative property, the associative property tells us the outcome will be the same no matter in which order we choose to use the numbers. Distributive property For all real numbers a, b, and c: a(b + c) = ab + ac (a + b)c = ac + bc The distributive property means that we can break up one factor of a multiplication problem into its addends, multiply them by the other factor, and then add the products together to get the whole answer. Variable-variable often represents an "unknown" quantity that has the potential to change;
GRAPHIC ORGANIZER Name Date Tell me what you know about the properties of addition, subtraction, multiplication and division. List the four math properties in the squares and then tell something about each in the ovals connecting. PROPERTIES
WHAT A DEAL (Hands on Activity) Materials: Deck of cards for every two students (Face cards removed) Teams of two students Procedure: This game will allow student creativity in finding relationships between a random set of playing cards Divide the class into teams of two and give each team a deck of cards. Each team should pick five cards. From these five, the students will need to create a function chart and from this function chart they will generate an equation (function) which can be represented by the cards. X Y 3 4 6 9 10 For example, if a team were dealt: 3, 4, 6, 9, 10, they might create a function chart (as shown). From this function chart, they can create a function which says, X + Y = 1
At this point, they should stack the five cards into a pile, and write the function on a slip of paper. Teams should trade playing cards and functions and see if they can discover the function table which represents the first team s equation. Other five card sets might be organized as follows: X Y X Y 6 1 3 5 7 _ 8 3 X 5 = Y 6 8 8 X + 2 = Y * DO SEVERAL EXAMPLES AS A WHOLE CLASS FIRST BEFORE DIVIDING INTO TEAMS
Dear Abby Writing Assignment Bring in and read a few samples of a Dear Abby or Ann Landers column and read aloud to the class. In this activity, students will be writing to Dear Abby to explain a problem a math problem which is bothering to them and will ask Abby for advice. The ultimate goal is to put all of the Dear Abby letters together into a column and let the students solve the problems (equations) presented in the letters. Begin by reading a sample problem and putting on the overhead. Dear Abby, I have a problem about our school playground. There are several groups of students that like to play different games, but we don t ever seem to have enough room. The playground is 54 meters wide and 125 meters long. There is an area which is blacktop which is 24 meters by 50 meters. Our principal says that one third of the students must play on the blacktop and two thirds must play on the grass. My problem is that if we have 240 students at school, how many square feet of grass area does each student have of his own? If you can help, please write. Have each student write a math problem in letter form and then distribute these to the class, having them create formulas and solutions for each letter.
On A Roll Game Materials: Four dice for each group of two students, cards for writing greater than, less than, equal to, +, -, x, symbols. Teams of two students Procedure: This game gives students practice in creating equations from random numbers. Since the lesson is somewhat difficult, you may wish to divide the calls into groups of four with two students working together on each team. Give each set of players four dice and several cards. They should make two cards for each of the symbols described in the materials. Player 1 begins by rolling the four dice. The object is to use the numbers on the dice to create a number sentence. If the student can create a sentence which uses an equal sign (and it is correct), player receives 5 points. If the student creates a sentence using or, then student 1 receives 3 points. Once student 1 has finished the sentence, player 2 repeats the process. The first student to receive 25 points is the winner. To create these sentences, the students can use each die individually, or can place them together in a place value format (ex: 2 and 3 could become 23 or 32). Original roll: Student rolls 1, 2, 3, 4 3 + 2 = 1 + 4 5 point play 4 x 3 = 12 5 point play 1 + 2 + 3 4 3 point play
MINUTE DAILY REVIEW PATTERNS, FUNCTIONS AND ALGEBRA 1. Write what comes next in the pattern. 1.2, 2.4, 4.8, 9.6. 2. If a = 1, b = 2, and c = 3, then abc =. 3. If a = 8 and b = 2, then a / b =. 4. 2, 12, 22, 32,,, 5. 1, 4, 9, 16,, 36, 49, 64, 6. If 5x + 1 = 21, then x = 7. Use,, or = 5/8 ¼ 8. If a = 2 and b = 7, then b a = 9. 1, 4, 9, 16,, 36, 49, 64 10. Name the property in math where is doesn t matter the order in which you add two or more numbers