Mental Math Strings

1. Mental Math Strings Start with the number of quarts in one gallon. Add the number of sides in a hexagon. Square your result. Subtract the number of degrees in a right angle. Multiply by the number of eggs in one-half dozen. Divide by the number of degrees in one angle of an equilateral triangle. Share your answer with a partner. How do you feel about your answer?

2. Mental Math Strings Start with the number of feet in one mile. Round your answer to the nearest thousand. Divide by the cube of ten. Add the number of vertices in a rhombus. Add the first odd whole number. Divide by one half. Share your answer with a partner. How do you feel about your answer?

3. Impementing Mental Math Strings 1. Determine extended math facts you want your students to know. 2. Build your mental math strings. 3. Do one string each day. 4. Preview information in the mental math string. 5. Implement the mental math string. 6. Share results, congratulate students who succeed and encourage those who don’t. 7. Invite a student who succeeds to repeat the string in front of the class. 8. Invite students to make their own and share with the class.

4. Reading for Meaning:Galileo’s Pendulum Agree Disagree Statement 1: Mathematics is a tool scientists use to explain things Evidence Support Refute

5. Reading for Meaning:Galileo’s Pendulum Agree Disagree Statement 2: Observing is more than looking. Evidence Support Refute

6. Reading for Meaning:Galileo’s Pendulum Agree Disagree Statement 3: The weight of a pendulum has a direct effect on the periods of the pendulum’s swing. Evidence Support Refute

7. Reading for Meaning:Galileo’s Pendulum Agree Disagree Statement 4: The time it takes for one swing of a pendulum is a result of the pendulum’s length: the longer the length, the faster the swing. Evidence Support Refute

8. Reading for Meaning:Galileo’s Pendulum Agree Disagree Statement 5: For every second it takes a pendulum to swing back and forth, the length of the pendulum is equal to a number the square of the time. Evidence Support Refute

9. Reading for Meaning:Galileo’s Pendulum Galileo Galilei, who lived in Italy from 1564 to 1642, used mathematics to make important contributions to physiscs and astronomy. One of the phenomena he studied was the behavior of pendulums. He noticed that if you tie a weight to the end of a string, hang it from a fixed point, and start it swinging, it will swing in a definite rhythm. Each wing cycle of the pendulum-from one side to the other and back-always takes the same amount of time. As you can see from the table below, in order to slow the period of the pendulum swing from 1 to 2 seconds, you have to more than double the length of the string; you have to quadruple it. In fact, you will note that each number in the length column is the square of the corresponding number in the period column. If you lengthened the string to 25 units, the period would be 5 seconds. The mathematical way to express the relationship between the length (in Galileo’s units) of a pendulum, 1, and its swing period (ins seconds), p, is p=1. Galileo also noticed that the time each swing cycle takes has nothing to do with the weight of the pendulum or where it starts. Instead, the period of a pendulum swing is a function of its length. If you change the length of the string, the period of the swing changes accordingly. The following table expresses, or shows, that function. (In Galileo’s time, they used different units of length from the ones we use today).

10. Reading for Meaning:Galileo’s Pendulum

11. 1. The solution set for any linear equation in x and y is exactly one ordered pair.2. The graph of a linear equation is a line.3. The slope of a vertical line is zero.4. Slope-intercept form looks like: y=mx+b5. Two parallel lines have equal slopes. Anticipation Guides Directions: In the column labeled ME, place a check next to any statement with which you agree. After reading the section, consider the column labeled TEXT, and place a check next to any statement with which the text agree. Selection on Linear Equation in Two Variables Me Text

12. 1. Quadratic equations have at most two solutions.2. The quadratic formula can be used to solve any quadratic equation.3. If x2=25, then the solution set for x is{5}.4. Completing the square is a valid method for solving quadratic equations.5. When using the factoring method to solve a quadratic equation, you must set the equation equal to zero before you factor. Anticipation Guides Directions: In the column labeled ME, place a check next to any statement with which you agree. After reading the section, consider the column labeled TEXT, and place a check next to any statement with which the text agree. Solving Quadratic Equation in One Variable Me Text

13. Anticipation Guides Directions: In the column labeled ME, place a check next to any statement with which you agree. After reading the section, consider the column labeled TEXT, and place a check next to any statement with which the text agree. Measures of Central Tendency Me Text 1. The median is the middle-most value of a data set. 2. The mean = median = mode of every data set. 3. The mode is the most recurring number in a data set. 4. If the median is more than the mean, then the data set is skewed to the left. 5. If a set contains an even number of data, then the median will be equal to the mean of the two numbers in the middle of the data set.

14. Math Concept: Mental Math and Extended Math Facts Teaching Strategy: Mental Math Strings:

15. Mental Math Strings Start with the number of quarts in one gallon. Add the number of sides in a hexagon. Square your result. Subtract the number of degrees in a right angle. Multiply by the number of eggs in one-half dozen. Divide by the number of degrees in one angle of an equilateral triangle. Share your answer with a partner. How do you feel about your answer?

16. Mental Math Strings Start with the number of feet in one mile. Round your answer to the nearest thousand. Divide by the cube of ten. Add the number of vertices in a rhombus. Add the first odd whole number. Divide by one half. Share your answer with a partner. How do you feel about your answer?

17. Implementing Mental Math Strings 1. Determine extended math facts you want your students to know. 2. Build your mental math strings. 3. Do one string each day. 4. Preview information in the mental math string. 5. Implement the mental math string. 6. Share results, congratulate students who succeed and encourage those who don’t. 7. Invite a student who succeeds to repeat the string in front of the class. 8. Invite students to make their own and share with the class.

18. “Phil Jackson will earn 10 million dollars for coaching the Los Angeles Lakers this season. Division I college football coaches regularly earn in excess of 1 million per year. They may all be fine coaches, but the coaching that affects millions of lives every year takes place in smaller, virtually invisible venues: in youth leagues and in junior-high and high schools.”