PROBLEM SOLVING WITH SLOPE TRIANGLESpkeenan.weebly.com/.../45670275/unit_5_topic_14_sab_2014.pdf · 2019-09-17 · 1. Create the following representations of the problem situation

Topic 14: Problem solving with slope triangles 49

Copyright © 2014 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc.

PROBLEM SOLVING WITH SLOPE TRIANGLES Lesson 14.1 Checking for understanding

14.1 OPENER A car rental company charges $35.50 plus 9¢ per mile for each mile you drive. You are charged $60.25 for the rental. You want to know the number of miles you drove.

Represent the situation with an equation and solve the equation using any of the methods you learned in the last topic.

14.1 MID-UNIT ASSESSMENT Today you will take the mid-unit assessment.

14.1 CONSOLIDATION ACTIVITY 1. Examine the graph and the slope triangle.

a. What is the slope of the line shown?

b. Use the slope triangle idea to list two other points that are on the line. (You will need to visualize the graph extending beyond what is presently shown.)

c. Write an equation for the line in slope-intercept form.

50 Unit 5 – Linear equations and inequalities


2. Examine the graph and the slope triangles.

a. What is the slope of the line shown?

b. Use the idea of slope triangles to determine if the line passes through the point (−1,−4). (You will need to visualize the graph extending beyond what is presently shown.)

c. Write an equation for the line in slope-intercept form.

3. A linear function is represented by this equation.

–2x + 7 = y

a. Sketch the graph for this function on the coordinate grid.

b. Use slope triangles on your graph to solve these equations.

–2x + 7 = 9 –2x + 7 = –3

4. A linear function is represented by a line that passes through the point (0,–2) and has a slope of

43

.

a. Sketch the graph of this function on the coordinate grid.

b. What is the value of x when the value of y is –6 for this function? Show or explain how you know.

c. Does the line representing this function pass through the point (21,28)? Explain how you know. Use a graph, a table, or an equation to help with your explanation.



HOMEWORK 14.1

Notes or additional instructions based on whole-class discussion of homework assignment:

1. A line passes through the point (3,−5) and has a slope of −3. Graph the line on the coordinate grid and list one other point the line passes through.

2. Use slope triangles to help you solve these equations.

a. -3x + 4 = -2

b. -3x + 4 = 10

3. A line passes through the point (−4,5) and has a slope of . Graph the line on the coordinate grid and find one other point

the line passes through.

4. Use slope triangles to help you solve these equations.

a. x – 1 = −1

b. x – 1 = −10

5. Your class came up with a definition for good communication in Unit 1. Describe a situation where you felt that you and

another person practiced good communication.



STAYING SHARP 14.1 Pr

actic

ing

alge

bra

skill

s & c

once

pts

1. Solve the following equation for j: j – 4 = −12

Answer with supporting work:

2. Consider the equation 18x + 12y = 72.

a. If x = 0, find the value of y that satisfies the equation.

b. If y = 0, find the value of x that satisfies the

equation.

Prep

arin

g fo

r upc

omin

g le

sson

s

3. Two numbers have a sum of 19 and a difference of 5. Find the two numbers. Use whatever method you like. Answer with supporting work:

4. Solve the shape equation puzzle:

+ + + + = 20

+ + = 13

= =

Revi

ewin

g pr

e-al

gebr

a id

eas

5. Sana is buying a car. She wants either a coupe (2-door) or a sedan (4-door). Each type of car is available in red, white, or blue. List or draw a tree diagram of all Sana's possible choices of cars.

6. Manny flips a coin three times in a row. List or draw a tree diagram of all the possible sequences of flips he could get. (For example, flipping a head and then two tails would be "HTT".)



Lesson 14.2 Slope triangles and linear equations

14.3 OPENER

The slope and a point on the line is given for three lines. Graph each line by plotting the given point and constructing slope triangles to find other points on the line. Then use the graph you created to write the equation of the line in slope intercept form.

1. Point: (-3,1) Slope: −

23

2. Point: (1,-1) Slope: 2

3. Point: (-3, 0) Slope: 12



14.2 CORE ACTIVITY

Follow these criteria as you play the game.

• It is important that the speaker is the only one who sees the card.

• The speaker will read the sentence next to the card letter.

• The listener may ask questions of the speaker.

• The speaker can respond to the questions, but cannot look at the listener’s work.

• Go in order from card A through card F.

1. Listeners will use this space to sketch graphs and write equations.

Card A or B

Card C or D

Card E or F



2. Circle the communication skills that you and your partner used in this activity.

14.2 CONSOLIDATION ACTIVITY 1. Use slope triangles to find the slope of each graphed line.

a.

Slope:

b.

Slope:

c.

Slope:



2. Use each table of data to find the slope and y-intercept of the line that passes through the data. Then find a function rule for the line. Write the function rule in slope-intercept form.

a. x y slope = y-intercept =

-1 -8

0 -4

1 0

2 4

3 8

4 12

Function rule for the line in slope-intercept form:

b. x y slope = y-intercept =

-4 43

-2 23

0 3

2 -17

4 -37

6 -57


c. x y slope = y-intercept=

0 3

2 13

3 18

6 33

9 48

10 53


d. x y slope = y-intercept =

3 5

6 6

9 7

12 8

15 9

18 10


3. Review the communication skills associated with being a giver and getter of information. In each column, identify one skill at which you would like to improve. Write a goal statement for each of these skills.



HOMEWORK 14.2

Notes or additional instructions based on whole-class discussion of homework assignment:

Homework Assignment

Part I: Complete the online More practice in the topic Problem solving with slope triangles.

Part II: Complete Staying Sharp 14.2.




actic

ing

alge

bra

skill

s & c

once

pts

1. Solve the following equation for m: −2m + 7 = 11


2. Plot the x- and y-intercepts of the line with the equation 5x + 3y = 30, then sketch the line.

Prep

arin

g fo

r upc

omin

g le

sson

s

3. Mohammed and Timothy ask you to order sodas for an end-of-school-year party. Mohammed says they need 60 sodas in all. Timothy says they need twice as many diet sodas as regular sodas. a. State a soda order you could place that satisfies

Mohammed’s condition.

b. State a soda order you could place that satisfies Timothy’s condition.

4. Consider the situation in question 3 again. State a soda order you could place that satisfies both Mohammed’s and Timothy’s conditions.


Revi

ewin

g pr

e-al

gebr

a id

eas

5. A six-sided number cube has faces with the numbers 1 through 6 marked on it. If each number has an equal probability of being rolled, what is the probability that, on one toss of the number cube, you would roll: a. The number 5

b. Any number OTHER than 5

c. A number less than 3

d. A number no more than 3

e. An even number

6. If the probability that it will rain on Monday is ,

what is the probability that it will NOT rain on Monday?

Explain. Answer and explanation:



Lesson 14.3 Communicating while problems solving

14.5 OPENER

Study the graph and answer the questions.

1. How many hours did each student work for each job?

a. Marcus

b. Isabel

c. Jaelynn

d. Benjie

2. What additional information do you need in order to find who earned the most money?



14.3 CORE ACTIVITY

Suppose you are a helicopter pilot who provides emergency relief to victims of natural disasters. Today you are transporting food and clean water to victims of a recent earthquake. Your helicopter can transport 400 pounds or less of supplies. A gallon of water weighs 8 pounds and a box of food weighs 5 pounds.

1. Create the following representations of the problem situation.

• Make a table that shows some possible combinations of the number of boxes of food, f, and gallons of water, w, that your helicopter can carry, given the weight restrictions.

• Make a graph to show the data from your table. Each point on your graph is an ordered pair, with gallons of water represented on the horizontal axis and boxes of food represented on the vertical axis.

2. What patterns do you notice in your graph? Describe where the allowable combinations on your graph are located, compared to where the impossible combinations are located. (You may need to find some more data points to help you see patterns.)



3. Find a way to figure out whether or not your helicopter can carry a load of supplies for any combination of gallons of water and boxes of food. You may want to use tables, graphs, or equations to show your method.

14.3 REVIEW MID-UNIT ASSESSMENT

Today you will review your mid-unit assessment.



HOMEWORK 14.3

Part I: Fundraiser

The Math Club will sell rolls of wrapping paper and ribbon as a fundraiser. They must spend less than $600 to purchase the fundraiser items. Each roll of wrapping paper costs the club $2. Each roll of ribbon costs the club $3.

1. Is it possible to buy 250 rolls of wrapping paper and meet the conditions above? Why or why not?

2. Is it possible to buy 250 rolls of ribbon and meet the conditions above? Why or why not?

3. Is it possible to buy a combination of 100 rolls of wrapping paper and 100 rolls of ribbon and meet the conditions above? Why or why not?

4. Find three other combinations of wrapping paper and ribbon that will meet the conditions above.

Wrapping paper

Ribbon

5. Plot the three combinations from question 4 on the grid.



Part II: Summer staffing The school board is investigating ways to hire staff for the summer school program. They can hire teachers and aides. There can be no more than 50 staff members altogether. The graph below represents this situation.

1. Find three points on the graph that satisfy the conditions of the problem and explain why they satisfy the conditions.

2. Find three points on the graph that do not satisfy the conditions of the problem and explain why they do not satisfy the conditions.

3. What is different about the locations of the points you listed for question 1 and question 2?




actic

ing

alge

bra

skill

s & c

once

pts

1. Solve the following equation for p:

+ 5p =


2. Plot the x- and y-intercepts of the line with the equation 12x + 14y = –84 in standard form, then sketch the line.

Prep

arin

g fo

r upc

omin

g le

sson

s

3. Nidia keeps ants and grasshoppers as pets. She has 186 insects in all, and twice as many grasshoppers as ants. a. Identify the two variables in this situation.

First variable (a):

Second variable (g): b. Write an equation to represent each condition.

She has 186 insects in all:

There are twice as many grasshoppers as ants:

4. Raymond and Godwin go to a bakery. Raymond buys 2 donuts and 3 cookies for $3.30. Godwin buys 5 donuts and 2 cookies for $4.95. All the donuts have the same price and all the cookies have the same price. Using the variables d for the price of a donut and c for the price of a cookie, write two equations to represent the situation.

Revi

ewin

g pr

e-al

gebr

a id

eas

5. Antonio is drawing marbles from a bag containing 3 green marbles and 2 orange marbles. The first marble he draws is orange. He keeps it, and then draws another marble. On his second draw, what is the probability that he a. draws a green marble?

b. draws an orange marble?

6. Twenty students have been nominated to appear on a local talk show: 4 freshmen, 7 sophomores, 6 juniors, and 3 seniors. Their names are put in a bowl, and one is randomly drawn to select the winner. What is the probability that the winner is a junior or senior? Answer with supporting work:

Documents

PROBLEM SOLVING WITH SLOPE TRIANGLESpkeenan.weebly.com/.../45670275/unit_5_topic_14_sab_2014.pdf · 2019-09-17 · 1. Create the following representations of the problem situation