Download direct_inverse sorting activity

 Direct vs. Inverse Variation Card Sorting BCS Learning Targets Addressed: Outcome 1.a: I can create equations in one variable to describe inverse relationships Outcome 1.b: I can interpret the components of a variation function. Outcome 1.c: I can compare two variation and/or simple power functions given tables, graphs, and rules. NC SCOS Standards Addressed: A-­‐CED.1: Create equations and inequalities in one variable and use them to solve problems. A.SSE.1: Interpret expressions that represent a quantity in terms of its context. F.IF.9: Compare properties of two functions each represented in a different way. Directions: 1. Have students work in partner to sort the following cards into three piles: Direct Variation Inverse Variation Neither 2. After direct variation and neither piles are complete and correct, have students just work with the inverse variation stack. 3. With this subset (Inverse Variation) have the students arrange the cards in order of constant of variation (k) from increasing to decreasing. Students will have to reason with multiple representations to arrive at constant of variations. 4. For differentiation, some cards may be removed or scaffold based on group dynamics. Not all students need to do all cards but purposeful selection may be appropriate for some students. Answers: Inverse Variation: Alphabetical Order: B, F, G, I, N, Q, R, S, T, U, V, W In order of constant of variation (k) value: U(k=3), R(k=5), N(k=10), B(k=10), F(k=12), G(k=15), W(k=16), I(k=25), T(k=30), S(k=300), V(k=500), Q(k=200) Direct Variation: C, D, E, H, J, K M Neither: A, L, P A
B C
The number of calories in a cup of
orange juice varies with the amount of
orange juice in the cup. There are 45
calories in a 4-ounce cup of orange juice.
There are 135 calories in a 12-ounce cup
of orange juice.
E The radius of a circle can be found
according to the formula:
D
The length of a diagonal, d, in a square
varies according to the formula:
G
F
Ohm’s Law states that in a 10 amp
circuit the voltage can be found
according to
H
I
J
x
y
-5
-5
-1
-25
0
Undefined
1
25
10
2.5
25
1
KThe graph represents the volume of a
sphere with various radi.
M
y
-5
-1
0
1
10
25
125
-25
0
25
250
625
P
A rental company charges a flat delivery
fee of $15 dollars plus an additional $5
dollars per day for the rental of a tent.
y
0
1
2
5
10
0
5
40
625
5000
x
y
-10
-1
0
5
8
17
1
3
13
19
L
N
x
x
Q
R
S
x
y
-10
-5
1
5
10
20
-0.5
-1
5
1
0.5
0.25
T
The relationship between a pendulum
arm length, L, and the frequency of a
swing, F can be expressed by the
equation:
x
y
-2
-1
0
1
2
75
300
Undefined
300
75
U
xy=3 V
W
The cost per person to rent a beach house The length and width of a rectangle with
is inversely proportional to the number
area of 16cm2 are shown in the table:
of people who share the rent. The cost is
$62.50 if 8 people share.