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Activity #1: Best Strategy (Ratios) Directions: For each problem below, decide what the best strategy for solving the problem is. Then, use your strategy to solve each problem. Strategies: (1) Multiplication (2) Tape Diagram (3) Ratio Table (5) Proportion (6) Other Valid Strategy (4) Double Number Line A. The ratio of red marbles to blue marbles in a bag is 4 to 9. If there are 45 blue marbles in the bag, how many red marbles are there? The best way to solve this problem is ________________________________ because _________________________________________________________________ ___________________________________________________________________________. B. The ratio of apples to oranges in a basket is 4 to 7. If there are 18 more apples than oranges, how many apples are there? The best way to solve this problem is ________________________________ because _________________________________________________________________ ___________________________________________________________________________. C. The ratio of slices of turkey to slices of cheese on sandwiches in the cafeteria is 2:3. If the cafeteria has 9 slices of turkey, determine how many slices of cheese they should buy. (Use a double number line ) The best way to solve this problem is ________________________________ because ___________________________________________________________ ___________________________________________________________________________. Activity #2: Your BEST Method (Distance vs. Pythagoras) For each of the problems below, decide the best way to solve for the distance between the given points--Distance Formula or Pythagorean Theorem (by drawing in legs for a right triangle). Provide a warrant for your claim. Then solve the problem using what you think is the best method. 1. 2. Distance between (3, 24) and (-14, 33). 3. S (-7,8) G (5,3) Activity #3: Your BEST Method (Systems of Equations) In each system of equations below, decide on the best method for solving the system (substitution, elimination, graphing). State your argument with a complete claim and warrant. Then solve the system. 1. x y 11 3x y 5 Claim: ________________________________________________ Warrant: _____________________________________________ _____________________________________________________ 2. y x 1 Claim: ________________________________________________ y 12 x 3 Warrant: _____________________________________________ _____________________________________________________ 3. 5x 4 y 6 y 2x 3 Claim: ________________________________________________ Warrant: _____________________________________________ _____________________________________________________ Activity #4: Make an Argument (Is It a Triangle?) Determine if each set of three numbers below could be the sides of a triangle. If they could form a triangle, classify what type of triangle they would make (scalene, isosceles, right, etc.). BE SURE to give a complete argument (claim + warrant) for your answer. 1. 9,40,41 2. 7,5,13 3. 6 5 4. 8,1,8 , 3 5 , 53 Activity #5: Matching Deduction (Sin/Cos) Match each expression in the left hand column with its closest approximation in the right hand column. You may NOT use a calculator. Use only your knowledge of the unit circle to deduce the answers. Be sure to convince your partners with solid arguments (claim + warrant). Be careful, each section gets a little bit harder! Section 1 1. sin(π/6) A. -0.71 2. cos(π/4) B. 0.50 3. sin(-π/2) C. -1.00 4. cos(-3π/4) D. 0.71 Section 2 1. cos(-3π/6) A. 0.31 2. cos(π/22) B. -0.87 3. sin(5π/6) C. 0.99 4. sin(9π/10) D. 0.50 5. cos(5π/6) E. 0.00 Activity #6: Which is Bigger? (Fraction Number Sense) Each problem below has a set of fractions. Determine which of the fractions is largest WITHOUT using a calculator. Be sure each claim (which is bigger) has a warrant! 1) 1 5 1 9 Claim: ________________________________________________ Warrant: _____________________________________________ _____________________________________________________ 2) 8 10 10 8 Claim: ________________________________________________ Warrant: _____________________________________________ _____________________________________________________ 3) 8 15 9 20 Claim: ________________________________________________ Warrant: _____________________________________________ _____________________________________________________ 4) 7 8 11 12 Claim: ________________________________________________ Warrant: _____________________________________________ _____________________________________________________ Activity #7: Always/Sometimes/Never (Equations) Directions: Consider each equation below. Is the equation always true, sometimes true, or never true? Be sure to give a claim and warrant for each response. A. ________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________ B. ________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________ C. ________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________ D. ________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________ Activity #8: Write a Warrant (Experiments) What do you think: Qualitative or Quantitative? – For each property, state whether it is a qualitative or quantitative characteristic. For 1/5/8/10, be sure to give a reason to defend your argument. 1. Color: ___________________________________ a. Explain why you selected what you did: _______________________________________ _____________________________________________________________________________________ ___________________________________________________________ 2. How heavy something is: ___________________________________ 3. Material something is made out of: ___________________________________ 4. Pattern or design: ___________________________________ 5. Size: ___________________________________ a. Explain why you selected what you did: _______________________________________ _____________________________________________________________________________________ ___________________________________________________________ 6. How hot or cold something is: ___________________________________ 7. Texture (how it feels): ___________________________________ 8. Smell: ___________________________________ a. Explain why you selected what you did: _______________________________________ _____________________________________________________________________________________ ___________________________________________________________ 9. How long something is: ___________________________________ 10. How far away something is: ___________________________________ a. Explain why you selected what you did: _______________________________________ _____________________________________________________________________________________ ___________________________________________________________ 11. How pretty something is: ___________________________________ 12. Someone’s age: ___________________________________ Activity #9: Write a Warrant (Hypotheses) Directions: Fill in the cause and effect statements for each hypothesis statement in two different ways. Be sure to give two different hypotheses that could go along with each scenario. 1. A scientist wants to see if sunlight actually helps a plant grow. He places one plant in the sun and one in the closet. (a) If_________________________________________________________________________________________________________ Then__________________________________________________________________________________________________________ Because______________________________________________________________________________________________________ (b) If_________________________________________________________________________________________________________ Then__________________________________________________________________________________________________________ Because______________________________________________________________________________________________________ 2. A scientist wants to see if chemical X helps mice have a better memory. He gives 10 mice chemical x and 10 water instead. Then he times how fast they can get through a maze. (a) If_________________________________________________________________________________________________________ Then__________________________________________________________________________________________________________ Because______________________________________________________________________________________________________ (b) If_________________________________________________________________________________________________________ Then__________________________________________________________________________________________________________ Because______________________________________________________________________________________________________ 3. A student wants to see how caffeine helps him concentrate. One day he drinks caffeine and then shoots the basketball. The next day he drinks water and shoots basketball. He counts how many baskets he makes on each day. (a) If_________________________________________________________________________________________________________ Then__________________________________________________________________________________________________________ Because______________________________________________________________________________________________________ (b) If_________________________________________________________________________________________________________ Then__________________________________________________________________________________________________________ Activity #10: Which is Stronger (Chemical Bonds) Pairs of chemicals are listed below. Determine the type of bond between them. (You should determine the Electronegativity difference between these atoms. Ionic >1.7 Covalent<1.7) Hydrogen and oxygen CLAIM: WARRANT: ________ ___________________________________________ ___________________________________________ Magnesium and Sulfur ________ ___________________________________________ ___________________________________________ Strontium and fluorine ________ ___________________________________________ ___________________________________________ Carbon and oxygen ________ ___________________________________________ ___________________________________________ Magnesium and nitrogen ________ ___________________________________________ ___________________________________________ Nitrogen and oxygen ________ ___________________________________________ ___________________________________________ Hydrogen and nitrogen ________ ___________________________________________ ___________________________________________ Activity #11: Ordering (Food Chain) Each set of organisms below is ordered from most predator to most prey. Do you agree? Justify your claim. Hawk, Mouse, Snake _______________________________ WARRANT:_______________________________________________________________________________________ :_______________________________________________________________________________________ Fish, Whale _______________________________ WARRANT:_______________________________________________________________________________________ :_______________________________________________________________________________________ Racoon, Fish, Algae _______________________________ WARRANT:_______________________________________________________________________________________ :_______________________________________________________________________________________ Seal, Fish, Amphipod, Phytoplankton _______________________________ WARRANT:_______________________________________________________________________________________