Math Skills Mastery: CRCT Review, Jeopardy, Algebraic Thinking, Geometry, Applications, Numbers

1. CRCT ReviewJEOPARDY Algebraic Thinking Geometry Applications Numbers Sense Algebraic Relations Data Analysis/Probability Problem Solving

2. Number Sense/Numeration • Find square roots of perfect squares • Understand that the square root of 0 is 0 and that every positive number has 2 square roots that are opposite in sign. • Recognize positive square root of a number as a length of a side of a square with given area • Recognize square roots as points and lengths on a number line • Estimate square roots of positive numbers • Simplify, add, subtract, multiply and divide expressions containing square roots • Distinguish between rational and irrational numbers • Simplify expressions containing integer exponents • Express and use numbers in scientific notation • Use appropriate technologies to solve problems involving square roots, exponents, and scientific notation.

3. Geometry • Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically • Apply properties of angle pairs formed by parallel lines cut by a transversal • Understand properties of the ratio of segments of parallel lines cut by one or more transversals. • Understand the meaning of congruence that all corresponding angles are congruent and all corresponding sides are congruent • Apply properties of right triangles, including Pythagorean Theorem • Recognize and interpret the Pythagorean theorem as a statement about areas of squares on the side of a right triangle

4. Algebra • Represent a given situation using algebraic expressions or equations in one variable • Simplify and evaluate algebraic expressions • Solve algebraic equations in one variable including equations involving absolute value • Solve equations involving several variables for one variable in terms of the others • Interpret solutions in problem context • Represent a given situation using an inequality in one variable • Use the properties of inequality to solve inequalities • Graph the solution of an inequality on a number line • Interpret solutions in problem contexts. • Recognize a relation as a correspondence between varying quantities • Recognize a function as a correspondence between inputs and outputs for each input must be unique

5. Algebra, cont. • Distinguish between relations that are functions and those that are not functions • Recognize functions in a variety of representations and a variety of contexts • Uses tables to describe sequences recursively and with a formula in closed form • Understand and recognize arithmetic sequences as linear functions with whole number input values • Interpret the constant difference in an arithmetic sequence as the slope of the associated linear function • Identify relations and functions as linear or nonlinear • Translate; among verbal, tabular, graphic, and algebraic representations of functions • Interpret slope as a rate of change • Determine the meaning of slope and the y-intercept in a given situation

6. Algebraic, cont. • Graph equations of the form y = mx +b • Graph equations of the form ax + by = c • Graph the solution set of a linear inequality, identifying whether the solution set in an open or a closed half plane • Determine the equation of a line given a graph, numerical information that defines the line or a context involving a linear relationships • Solve problems involving linear relationships • Given a problem context, write an appropriate system of linear equations or inequalities • Solve systems of equations graphically and algebraically • Graph the solution set of a system of linear inequalities in two variables • Interpret solutions in problem contexts.

7. Data Analysis & Probability • Demonstrate relationships among sets through the use of Venn diagrams • Determine subsets, complements, intersection and union of sets. • Use set notation to denote elements of a set • Use tree diagrams to find number of outcomes • Apply addition and multiplication principles of counting • Find the probability of simple independent events • Find the probability of compound independent events • Gather data that can be modeled with a linear function • Estimate and determine a line of best fit from a scatter plot.

8. Problem Solving • Build new mathematical knowledge through problem solving • Solve problems that arise in mathematics and in other contexts • Apply and adapt a variety of appropriate strategies to solve problems • Monitor and reflect on the process of mathematical problem solving • Recognize reasoning and proof as fundamental aspects of mathematics • Make and investigate mathematical conjectures • Develop and evaluate mathematical arguments and proofs • Select and use various types of reasoning and methods of proof • Organize and consolidate mathematical thinking through communication • Communicate mathematical thinking coherently and clearly

9. Problem solving cont. • Analyze and evaluate mathematical thinking and strategies • Use language of mathematics to express mathematical ideas precisely • Recognize and use connections among mathematical ideas • Understand how mathematical ideas interconnect • Recognize and apply mathematics in context • Create and use representations to organize, record and communicate mathematical ideas • Select, apply and translate among mathematical representations to solve problems • Use representations to model and interpret physical, social and mathematical phenomena

10. Mathematics Categories Geometry CRCT2 Algebra CRCT1 Numbers CRCT3 Relations CRCT4 Probab CRCT5 Prob Solv CRCT6 100 100 100 100 100 100 200 200 200 200 200 200 300 300 300 300 300 300 400 400 400 400 400 400 500 500 500 500 500 500

11. CRCT1 • What is the value of • A. 36 • B. 1,728 • C. 2, 187 • D. 531,441

12. Answer • D. 531,441

13. CRCT1 What is/are the square root(s) of 36? • 6 only • -6 and 6 • -18 and 18 • -1,296 and 1,296

14. Answer • B.-6 and 6

15. CRCT1 How is 5.9 x 10-4 written in standard form? • 59,000 • .0059 • .00059 • 5900

16. Answer • C. 0.00059 • Scientific notation with negative exponents are smaller numbers….. • Move the decimal 4 places to the left.

17. CRCT1 • The square root of 30 is in between which two whole numbers? • A. 5 & 6 • B. 25 & 36 • C. 4 & 5 • D. 6 & 7

18. Answer • A. 5 and 6 • Use perfect squares to check and see where the square root of 30 falls. • Square root of 25 is 5 and square root of 36 is 6, so square root of 30 falls somewhere in between those two numbers.

19. CRCT1 Write in scientific notation 134, 000

20. Answer • 1.34 x 105 • Larger numbers have scientific notation exponents that are positive……. • Make sure the “c” value is 1 or more, but less than 10….

21. CRCT2 • Lines m and n are parallel. Which 2 angles have a sum that measure 180 • m 1 2 • 4 3 • n 5 6 • 8 7 • A. < 1 and < 3 • B. <2 and <6 • C. <4 and <5 • D <6 and <8

22. Answer • C. <4 and <5

23. CRCT2 • Which angle corresponds to <2 • 1 2 • 3 4 • A. <35 6 • B. <6 7 8 • C. <7 • D. <8

24. Answer • B. <6

25. CRCT2 • What do parallel lines on a coordinate plane have in common? • Same equation • Same slope • Same y-intercept • Same x-intercept

26. Answer B. Same slope

27. CRCT2 • In the figure below, find the missing side. • 4 x • A. x= 9 • B. x= 10 6 12 • C. x = 8 • D. x = 5

28. Answer • C. X = 8

29. CRCT2 • How long is the hypotenuse of this right triangle? • 5 cm • 12 cm • A. 13 cm • B. 15 cm • C. 18 cm • D. 20 cm

30. Answer • A. 13 cm Pythagorean Theorem:

31. CRCT3 • Which mathematical expression models this word expression? • Eight times the difference of a number and 3 • A. 8n – 3 • B. 3 – 8n • C. 3(8 – n) • D. 8(n – 3)

32. Answer • 8(n-3)

33. CRCT3 If a = 24, evaluate 49 – a + 13. • 86 • 60 • 38 • 12

34. Answer C. 38

35. CRCT3 Solve the following equation and choose the correct solution for n. 9n + 7 = 61 • 5 • 6 • 7 • 8

36. Answer B. 6

37. CRCT3 Solve the following and graph on the number line y + 7 > 6

38. Answer • Y>-1 • Make sure there is an open circle on -1 and you shade to the right….. -1

39. CRCT3 Chose the correct solution for x in this equation X + 3 = 12 • 9 and 15 • -9 and -15 • -9 and 15 • 9 and -15

40. Answer • D. 9 and -15

41. CRCT4 Which relation is a function? A. B. C. D. • 5 1 5 1 5 1 5 1 • 10 2 10 2 10 2 10 2 • 15 3 15 3 15 3 15 3

42. Answer C - A relation is a function when each element of the first set corresponds to one and only one element of the second set.

43. CRCT4 What is the slope of the graph of the linear function given by this arithmetic sequence: 2,7,12,17,22… • 5 • 2 • -2 • -5

44. Answer • A. 5 Slope is the common difference of an arithmetic sequence

45. CRCT4 What is the equation of the linear function given by this arithmetic sequence? 7, 10, 13, 16, 19… • y= x + 3 • y= 2x – 4 • y= 3x + 3 • y= 3x + 4

46. Answer • D. y= 3x + 4 • Remember slope is the common difference and the y intercept is the zero term.

47. CRCT4 Which of the following could describe the graph of a line with an undefined slope? • The line rises from left to right • The line falls from left to right • The line is horizontal • The line is vertical

48. Answer • D. The line is vertical

49. CRCT4 • How would you graph the slope of the line described by the following linear equation? y = -5x + 5 3 • A. Down 5, left 3 • B. Up 5, right 3 • C. Down 5, right 3 • D. Right 5, down 3

50. Answer • C. Down 5, right 3 • Rise over Run.