Always, Sometimes, or Never True Solve for X Name The Property Algebra Term & Symbols 10 10 10 10 20 20 20 20 30 30 30 30 40 40 40 40 50 50 50 50 Click here for game DIRECTIONS Hardtke Jeopardy Template 2011

10 Always, Sometimes, or Never If x is a repeating decimal, then x is a rational number. Click to check answer ALWAYS Hint: Use 1 3 =0. 3 as an easy way to remember this. Click to return to game board

20 Always, Sometimes, or Never If x is a whole number, then 𝑥 is an irrational number. Click to check answer SOMETIMES Hint: 16 is rational while 17 is irrational Click to return to game board

If x is an integer, then x is a natural number. Click to check answer 30 Always, Sometimes, or Never If x is an integer, then x is a natural number. Click to check answer SOMETIMES Hint: Integers  {… ,-2, -1, 0, 1, 2, …} Natural (or Counting) numbers  {1, 2, 3, …} Click to return to game board

40 Always, Sometimes, or Never If x is a non-negative real number, then 𝑥 <𝑥. Click to check answer SOMETIMES Hint: true when x > 1, but false when 0 ≤ x ≤ 1. Click to return to game board

The solution set of an identity is . Click to check answer 50 Always, Sometimes, or Never The solution set of an identity is . Click to check answer NEVER Hint:  is the solution set of a contradiction. {All real numbers} is the solution set of an identity. Click to return to game board

x = −6 −3 −2 −3 ÷9 Click to check answer 10 Solve for X x = −6 −3 −2 −3 ÷9 Click to check answer – 5 Hint: this becomes (-9)(5) ÷9 Click to return to game board

−5 2 + −3 2 Click to check answer 20 Solve for X −5 2 + −3 2 Click to check answer – 16 Hint: “opposite of 5 squared plus negative 3 squared” This becomes -25 + 9 Click to return to game board

30 Solve for X X is the smallest value from this list of real numbers: 0, −𝜋, −2 2 , − 1 9 , − 0.444… Click to check answer −𝟐 𝟐 Small to large: −2 2 = − 4, −𝜋, − 0.444…,− 1 9 =− 1 3 =−0.333…, 0 Click to return to game board

40 Solve for X | x | > 5 is equivalent to {x| _______or _______}. Click to check answer {x| x < -5 or x > 5} Hint: Where is the distance to the origin greater than five? Click to return to game board

Click to return to game board 50 Solve for X X is the only real number from this list: 6+2 5−5 , 18 −3 2 − 7 , 4 2 − 2 4 𝜋−𝜋 , −9 Click to check answer 𝟏𝟖 −𝟑 𝟐 − 𝟕 Hint: 0 0 𝑜𝑟 𝑛𝑜𝑛−𝑧𝑒𝑟𝑜 0 ,𝑜𝑟 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑎𝑟𝑒 𝑛𝑜𝑡 𝑟𝑒𝑎𝑙, 𝑏𝑢𝑡 0 𝒏𝒐𝒏−𝒛𝒆𝒓𝒐 𝑖𝑠 𝑟𝑒𝑎𝑙 Click to return to game board

6 + 2x = 2(3 + x) Click to check answer 10 Name the Property 6 + 2x = 2(3 + x) Click to check answer DISTRIBUTIVE PROPERTY Hint: recall the full name is “Distributive Property of Multiplication over Addition” and properties can be applied in either order. 5(a + b) = 5a + 5b and 6x + 9 = 3(2x + 3) are both examples of Distributive Property. Click to return to game board

2 + (3 + x) = (2 + 3) + x Click to check answer 20 Name the Property 2 + (3 + x) = (2 + 3) + x Click to check answer ASSOCIATIVE PROPERTY Hint: order of terms stayed the same, only the grouping symbols moved Click to return to game board

For a ≠0, 𝑎∙ 1 𝑎 =1 Click to check answer 30 Name the Property For a ≠0, 𝑎∙ 1 𝑎 =1 Click to check answer INVERSE PROPERTY OF MULT. Hint: this can also be called the Property of Reciprocals Click to return to game board

If a + b = c and c = d + f, then a + b = d + f. Click to check answer 40 Name the Property If a + b = c and c = d + f, then a + b = d + f. Click to check answer TRANSITIVE PROPERTY (of Equality) Hint: Reflexive a = a Symmetric  If a = b, then b = a Transitive  If a = b & b = c, then a = c. Click to return to game board

2 + (3 + x) = (3 + x) + 2 Click to check answer 50 Name the Property 2 + (3 + x) = (3 + x) + 2 Click to check answer COMMUTATIVE PROPERTY Hint: this is same as a + b = b + a Click to return to game board

Name this set of numbers: {0, 1, 2, 3, . . . } Click to check answer 10 Algebra Terms & Symbols Name this set of numbers: {0, 1, 2, 3, . . . } Click to check answer WHOLE NUMBERS Hint: Natural (or Counting) Numbers{1, 2, 3, …} Integer  {…, -2, -1, 0, 1, 2, …} Click to return to game board

20 Algebra Terms & Symbols An equation that has {all real numbers} as its solution. For example: 2x + 5 – x = 1 + x + 4 Click to check answer IDENTITY Hint: Contradiction has no solutions; Conditional equation has a finite number of solutions; Identity has all real numbers as solution. Click to return to game board

30 Algebra Terms & Symbols Write the set {x| -3 ≤ x < 7} in interval notation. Click to check answer [ -3, 7 ) Click to return to game board

40 Algebra Terms & Symbols Write this statement using absolute value symbols: “x is no more than 7 units from -3” Click to check answer | x + 3 | ≤ 7 or | -3 – x | ≤ 7 Hint: Distance from a to b is defined as |a – b | or | b – a| Click to return to game board

50 Algebra Terms & Symbols Write the definition of the absolute value of x as a piecewise definition. Click to check answer 𝒙 = 𝒙 𝒊𝒇 𝒙 ≥𝟎 −𝒙 𝒊𝒇 𝒙<𝟎 Hint: you only need to take the opposite to change the sign when x is negative to begin with. Click to return to game board

Return to main game board Jeopardy Directions Any group member may select the first question and students rotate choosing the next question in clockwise order regardless of points scored. As a question is exposed, EACH student in the group MUST write his solution on paper. (No verbal responses accepted.) The first student to finish sets down his pencil and announces 15 seconds for all others to finish working. After the 15 seconds has elapsed, click to check the answer. IF the first student to finish has the correct answer, he earns the point value of the question and no other students earn points. IF that student has the wrong answer, he subtracts the point value from his score and EACH of the other students with the correct answer earns/steals the point value of the question. (Those students do NOT lose points if incorrect, only the first student to “ring in” can lose points in this game version.) Each student should record a running total of his own score. Good sportsmanship and friendly assistance in explaining solutions is expected! Reviewing your math concepts is more important than winning. Return to main game board