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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:_______________________________________________________________________________________