Preparing for Algebra

1. Preparing for Algebra Chapter 0

2. 0.1 Plan for Problem Solving • Pg. P5-P6 • Obj: Learn how to use the four-step problem-solving plan.

3. 0.1 Plan for Problem Solving • Four-Step Problem-Solving Plan • Understand the Problem • Read the problem and explore what the problem is about • Identify the information given • Identify what you need to find • Plan the Solution • Strategy example: write an equation • Solve the Problem • Check the Solution • Check your answer in the context of the original problem • Does your answer make sense? • Does it fit the information in the problem?

4. 0.2 Real Numbers • Pg. P7 – P10 • Obj: Learn how to classify and use real numbers.

5. 0.2 Real Numbers • Positive Numbers – values greater than 0 • Negative Numbers – values less than 0 • Natural Numbers – 1, 2, 3, … • Whole Numbers – 0, 1, 2, 3, … • Integers - …, -3, -2, -1, 0, 1, 2, 3, … • Rational Numbers – numbers than can be expressed as a fraction • Square Root – one of two equal factors of a number

6. 0.2 Real Numbers • Principal Square Root – the nonnegative square root of a number • Perfect Square – a number like 64, with a square root that is a rational number • Irrational Numbers – numbers that cannot be expressed as a fraction (cannot be written as a terminating or repeating decimal) • Real Numbers – irrational and rational numbers • Graph – means to draw or plot the points named by those numbers on a number line

7. 0.2 Real Numbers • Coordinate – the number that corresponds to a point on a number line

8. 0.3 Operations with Integers • Pg. P11 – P12 • Obj: Learn how to add, subtract, multiply, and divide integers.

9. 0.3 Operations with Integers • Absolute Value – the distance a number is from zero on the number line (always positive) • Opposites – pairs of positive and negative numbers • Additive Inverses – a number and its opposite

10. 0.3 Operations with Integers • Addition • Like Signs • Add and keep the sign • Different Signs • Subtract and keep the sign of the larger • Subtraction • Change subtraction to addition and change the sign of the number immediately after • Follow addition rules

11. 0.3 Operations with Integers • Multiplication and Division • Like Signs • Positive Answer • Different Signs • Negative Answer

12. 0.4 Adding and Subtracting Real Numbers • Pg. P13 – P16 • Obj: Learn how to compare and order; add and subtract rational numbers.

13. 0.4 Adding and Subtracting Real Numbers • Follow the same rules for adding and subtracting integers • Adding and Subtracting Fractions • Like Denominators • Add or subtract the numerators • Simplify • Unlike Denominators • Find a common denominator • Rewrite the fractions using the common denominator • Add or subtract the numerators • Simplify

14. 0.5 Multiplying and Dividing Rational Numbers • Pg. P17 – P19 • Obj: Learn how to multiply and divide rational numbers.

15. 0.5 Multiplying and Dividing Rational Numbers • Use the same rules for multiplying and dividing integers. • Method • Cancel where possible • Multiply numerators and multiply denominators • Simplify if necessary • Multiplicative Inverses or Reciprocals – two numbers whose product is 1

16. 0.6 The Percent Proportion • Pg. P20 – P22 • Obj: Learn how to use and apply the percent proportion.

17. 0.6 The Percent Proportion • Percent – a ratio that compares a number to 100 • Percent Proportion

18. 0.7 Perimeter • Pg. P23 – P25 • Obj: Learn how to find the perimeter of two-dimensional figures.

19. 0.7 Perimeter • Perimeter – the distance around a figure • Rectangle – P=2(l + w) or P=2l + 2w • Parallelogram – P=2(a+b) or P=2a+2b • Square – P = 4s • Triangle – P = a + b + c • Circle – the set of all points in a plane that are the same distance from a given point • Diameter – the distance across the circle through its center

20. 0.7 Perimeter • Circumference – the distance around the circle – C=2πr • Center – the given point • Radius – the distance from the center to any point on the circle

21. 0.8 Area • Pg. P26 – P28 • Obj: Learn how to find the area of two-dimensional figures.

22. 0.8 Area • Area – the number of square units needed to cover a surface • Rectangle – A=lw • Parallelogram – A = bh • Square – A = s² • Triangle – A = ½ bh • Circle – A = пr²

23. 0.9 Volume • Pg. P29 – P30 • Obj: Learn how to find the volumes of rectangular prisms and cylinders.

24. 0.9 Volume • Volume – the measure of space occupied by a solid • Rectangular Prism – V = lwh • Cylinder - V = пr²h

25. 0.10 Surface Area • Pg. P31 – P32 • Obj: Learn how to find the surface area of rectangular prisms and cylinders.

26. 0.10 Surface Area • Surface Area – the sum of the areas of all the surfaces, or faces, of a solid • Prism – S = 2lw + 2lh + 2wh • Cylinder – S = 2пrh + 2пr²

27. 0.11 Simple Probability and Odds • Pg. P33 – P36 • Obj: Learn how to find the probability and odds of simple events.

28. 0.11 Simple Probability and Odds • Probability – the ratio of the number of favorable outcomes for the event to the total number of possible outcomes • Sample Space – the list of all possible outcomes • Equally Likely – when there are n outcomes and the probability of each one is 1/n • Complements – the events for rolling a 1 and for not rolling a 1

29. 0.11 Simple Probability and Odds • Tree Diagram – a method used for counting the number of possible outcomes • Fundamental Counting Principle • Odds – the ratio that compares the number of ways an event can occur to the number of ways it cannot occur

30. 0.12 Measures of Center, Variation, and Position • Pg. P37 – P40 • Obj: Learn how to find measures of central tendency, variation, and position.

31. 0.12 Measures of Center, Variation, and Position • Variable – a characteristic of a group of people or objects that can assume different values • Measurement or Quantitative Data – data that have units and can be measured • Categorical or Qualitative Data – data that can be organized into different categories • Univariate Data – measurement data in one variable • Measures of Center or Central Tendency – measures of what is average

32. 0.12 Measures of Center, Variation, and Position • Mean – the sum of the values in a data set divided by the total number of values in the set • Median – the middle value of the mean of the two middle values in a set of data when the data are arranged in numerical order • Mode – the value or values that appear most often in a set of data. A set of data can have no mode, one mode, or more than one mode.

33. 0.12 Measures of Center, Variation, and Position • Measures of Spread or Variation – describe how widely the data values vary • Range – the difference between the greatest and least values • Quartiles – common measures of position that divide a data set arranged in ascending order into four groups • Lower Quartile – the median of the lower half (Q1) • Upper Quartile – the median of the upper half (Q3)

34. 0.12 Measures of Center, Variation, and Position • Five-Number Summary – the three quartiles, along with the minimum and maximum values • Interquartile Range – the difference between the upper and lower quartiles • Outlier – data values that are beyond the upper or lower quartiles by more than 1.5 times the interquartile range

35. 0.13 Representing Data • Pg. P41 – P46 • Obj: Learn how to represent sets of data using different visual displays.

36. 0.13 Representing Data • Frequency Table – uses tally marks to record and display frequencies of events • Bar Graph – compares categories of data with bars representing the frequencies • Cumulative Frequency – each event is the sum of its frequency and the frequencies of all preceding events • Histogram – a type of bar graph used to display numerical data that have been organized into equal intervals

37. 0.13 Representing Data • Line Graph – usually shows how data change over a period of time • Stem-and-leaf plot – the digits of the least place value usually form the leaves, and the rest of the digits form the stems • Circle Graph – a graph that shows the relationship between parts of the data and the whole • Box-and-Whisker Plot – a graphical representation of the five-number summary of a data set