Course 1 Unit 3
Lesson 2 Investigation 1-Stretching Things Out
Name: ______
Date: ______Pd:______
Page 182
MATH Toolkit: The Greek letter deltais used in mathematics to represent the “change in” the value of a variable. For example Weight indicates the change in weight.
1 a. Complete the table.
Weight Change / Rubber Band Length Change / Rate of Change0 to 1 ounce
1 to 3 ounces
5 to 9 ounces
What are the units for the rate of change in each case? ______
- How is the rate of change pattern in Part a illustrated by the shape of the graph?
c. The length of the rubber band with no weight attached is 3 inches. Use that fact and the rate of change pattern discovered in Part a to find the length of the stretched rubber band when the weight is:
2 ounces: ______
4 ounces: ______
10 ounces: ______
W ounces: ______
- Write the NOW-NEXT equation, include the START value.
Next =
Start at
- Using the letters L (for length in inches) and W (for weight in ounces), write an equation (rule) that shows how the two variables are related:
L = ______
- How is the rate of change shown in the equations of:
- Part d
- Part e
- How is the length of the rubber band with no weight attached shown in the equation
for Part e?
h. Use your equations to predict stretch lengths for each of these weights:
4.5 ounces: ______17 ounces: ______
0.25 ounces: ______
2. a. Complete the table
Weight / Length A / Length B / Length C0
1
2
3
4
5
6
7
8
9
10
- According to the table, how long were the
different springs without any weights attached?
- How is that information shown on the graphs?
- Looking at data in the table, estimate the rates of change in length as weight is added to the three springs.
- How are those patterns shown on the graphs?
- Write NOW-NEXT equations for each linear model.
A: ______
Start at______
B: ______
Start at______
C: ______
Start at______
- Using letters L (length in inches) and W (weight in ounces), write equations that show how the two variables are related in each case.
A: L =______
B: L =______
C: L =______
- How can you use the equations from Part e to find lengths of each spring with no weight attached?
- How are the rates of change in length of the various springs related?
- How is this fact shown in the equations?
- a. Complete the table.
0
1
2
3
4
5
6
7
8
9
10
- According to the table, how long were the springs without any weights attached?
- How is that information shown in the graph?
c. Rate of Change for A: ______Rate of Change for B: ______
Rate of Change for C: ______Rate of Change for D: ______
- How do you determine these rates from the graph?
- How do you determine these rates from the table?
- Write NOW-NEXT equations for each linear model.
A: ______
Start at______
B: ______
Start at______
C: ______
Start at______
D: ______
Start at______
- Using letters L (length in inches) and W (weight in ounces), write equations that show how the two variables are related in each case.
A: L=______B: L=______
C: L=______D: L=______
f. What do the numbers in your equations tell you about the graph?
g. What differences in the springs could cause the differences in graph, tables, and
equations that model the data from the experiments?
- a. Complete the table.
0
20
40
60
80
100
- How long are the springs with no weight applied?
- Give the rates of change for each spring.
A: ______B: ______
C: ______D: ______
- How can you calculate these rates of change using points on the lines?
- How can you calculate these rates of change using pairs of values in the tables?
dWrite NOW-NEXT equations for each linear model.
A: ______
Start at______
B: ______
Start at______
C: ______
Start at______
D: ______
Start at______
e.Using letters L (length in cm) and W (weight in kg), write equations that show how the two variables are related in each case.
A: L=______B: L=______
C: L=______D: L=______
- Which linear model might correspond to springs in an extra-firm mattress? Explain your choice
- Which linear model might correspond to springs in an medium-firm mattress? Explain your choice
- For each of the tested springs, estimate the length of the spring with a weight of 30 kg.
- Estimated length for spring A: ______
- Estimated length for spring B: ______
- Estimated length for spring C: ______
- Estimated length for spring D: ______
- Which do you prefer to use in making estimates: a graph, table, or equation?
- Complete the table below for each equation given in your text. (pg. 185)
Equation / Initial Length / Rate of Change / Stretch or Compression?
a
b
c
d
MATH Toolkit: Enter defintions for slope and y-intercept for a linear graph.
- Study the two linear models on this graph.
a. y-intercept for A: ______
b. y-intercept for B: ______
Explain how to find the y-intercept using:
- Tables of (x, y) values.
- NOW-NEXT equations.
- Equations relating x and y
b. Find the slope of each graph.
Slope for A: ______Slope for B: ______
Explain how to find slopes using:
- Tables of (x, y) values.
- NOW-NEXT equations.
- Equations relating x and y
- Look back over the examples of linear models for (weight, length) data from experiments with rubber bands and springs.
a. How are the linear graphs related when they have the same slope?
- How are the linear graphs with the same y-intercept, but different slopes, related to each other?
Checkpoint: pg 187
Linear models relating any two variables x and y can be represented using tables, graphs, or equations. Important features of a linear model can be seen in each representation.
- How can the rate of change in two variables be seen:
- In a table of (x, y) values?
- In a linear graph?
- In an equation relating NOW and NEXT for the model?
- In an equation relating x and y?
- How can the y-intercept be seen:
- In a table of (x, y) values?
- In a linear graph?
- In an equation relating NOW and NEXT for the model?
- In an equation relating x and y?
Course 1 Unit 3 Lesson 2 Investigation 1Page 1 of 12