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IM 8 Ch9 Closure
The activities here offer you a chance to reflect about what you have learned during this chapter. As you work, look for concepts that you feel very comfortable with, ideas that you would like to learn more about, and topics you need more help with.
CPM Materials modified by Mr. Deyo
IM 8 Ch9 Closure
Title: IM8 ‑ Ch. 9 Closure ‑ What Have I Learned?
Date:
Learning Target
By the end of the period, I will apply different problem‑solving strategies and relect on what I have learned in this chapter.
I will demonstrate this by completing Four‑Square notes and by solving problems in a pair/group activity.
IM 8 Ch9 Closure
Home Work:
Ch. 9 Closure
Desc. What Have I Learned? Date Due
9 Problems CL 9‑155 through 8‑163
IM 8 Ch9 Closure
IM 8 Ch9 Closure
Chapter 9 Vocabulary
AA (Triangle Similarity) Corresponding Angles
Acute Angle
Exterior Angle (of a Triangle)
Adjacent Angles
Hypotenuse
Alternate Interior Angles
Legs(of a right triangle)
Complementary Angles
IM 8 Ch9 Closure
Chapter 9 Vocabulary
(Continued)
Obtuse Angle
Radical Sign
Parallel
Remote Interior Angles
Perfect Square
Right Angle
Perpendicular
Square (of a number)
Pythagorean Theorem
Supplementary Angles
IM 8 Ch9 Closure
Chapter 9 Vocabulary
Straight Angle
Transversal
Vertex
Vertical Angles
(Continued)
IM 8 Ch9 Closure
IM 8 Ch9 Closure
SUMMARIZING MY UNDERSTANDING
http://www.cpm.org/pdfs/stuRes/CC3/chapter_09/CC3%20Ch%209%20Closure
%20RP.pdf
This section gives you an opportunity to show what you know about properties of triangles and applying the Pythagorean Theorem, two of the main ideas of this chapter.
Triangular Treasure Hunt
Jasmine and Mason are spending the summer with their Uncle Simon. He lives in an old castle that has many interesting doors, not all of which are rectangles. One day, while looking through the books in the castle library, Jasmine found an unusual piece of paper in a book. “Look, Mason! This looks like some kind of a treasure map,” she exclaimed. Mason looked at the paper and read, “A valuable secret is hidden inside. But beware – danger lurks behind the other doors. Only those who can follow the clues will succeed in the search.” He also saw that it had a series of clues and pictures of triangular doors. Read the clues below and, with your team, help Jasmine and Mason find the secret door and the treasure.
• My sides are not congruent.
• My angles are not congruent.
• I am similar to another door.
units long.
• One of my sides is a) Look at the doors on the Chapter 9 Closure Resource Page.
b) Using what you have learned in this chapter, decide which door is the secret door. Justify your answer. c) List the triangles that were not the secret door and justify why each did not fit the clues. IM 8 Ch9 Closure
IM 8 Ch9 Closure
http://www.cpm.org/pdfs/stuRes/CC3/chapter_09/CC3%20Ch%209%20Closure
%20RP.pdf
Triangular Treasure Hunt
Read the clues below and, with your team, help Jasmine and Mason find the secret door and the treasure.
• My sides are not congruent.
• My angles are not congruent.
• I am similar to another door.
units long.
• One of my sides is a) Look at the doors on the Chapter 9 Closure Resource Page.
b) Using what you have learned in this chapter, decide which door is the secret door. Justify your answer. c) List the triangles that were not the secret door and justify why each did not fit the clues. IM 8 Ch9 Closure
CL 9­155. Solve for x.
a)
b)
IM 8 Ch9 Closure
CL 9­156. Solve for x.
a)
b)
IM 8 Ch9 Closure
CL 9­157. Determine the length of side x. Give the answer in radical form and as a decimal.
IM 8 Ch9 Closure
CL 9­158. Simplify the following exponential expressions. Give answers without negative exponents.
a)
b)
4­3·47
(5x4)3
b)
d)
37
34
(4x5)(3x­8)
IM 8 Ch9 Closure
CL 9­159. Visualize a line that goes through the two points on the graph here.
a) What is the slope of the line?
m = b) What is the rule for the line?
y = ( )x + ( )
IM 8 Ch9 Closure
CL 9­160. Casey was building a rectangular pen for his pigs. He has 62 feet of fencing. The length of his pen is 9 feet longer than the width. Write and solve an equation to find the dimensions of the pen.
IM 8 Ch9 Closure
CL 9­161. Clay and his friend Lacey are making cookies for the school dance. Clay started early and has already made 3 dozen cookies. He can make an additional 2 dozen cookies an hour. Lacey has not started making cookies yet, but she has a bigger oven and can make 4 dozen cookies an hour. If Lacey starts baking her cookies right away, how long will it take for her to have made as many cookies as Clay? How many cookies will they each have made?
IM 8 Ch9 Closure
CL 9­162. Sarah loves to order paperback mystery books. Some of her recent orders are shown in the table here.
a) Draw a scatterplot with this information.
b) Fully describe the association.
c) Determine the equation of the line of best fit.
y = ( )x + ( )
d) Based on the equation, estimate the total cost of an order of 10 books.
IM 8 Ch9 Closure
CL 8­163a
For each of the previous problems (CL9­155 to CL9­162), do the following:
Color or shade in a portion of the bar that represents your level of understanding and comfort with completing that problem on your own.
CL 9­155
CL 9­156
CL 9­157
CL 9­158
CL 9­159
CL 9­160
CL 9­161
CL 9­162
IM 8 Ch9 Closure
CL 9­163b
If any of your bars are less than a 5, choose one of those problems and complete one of the following tasks:
Which problem did you choose? CL 9­____
Write two questions that you would like to ask about that problem.
1)
?
2)
?
Brainstorm two things that you DO know about that type of problem.
1)
2)
IM 8 Ch9 Closure
CL 9­163c If any of your bars are 5 or above, choose one of those problems and do one of these tasks:
Which problem did you choose? CL 9­____
Write two questions you might ask or hints you might give to a student who was stuck on the problem.
1)
?
2)
?
Make a new problem that is similar and more challenging than that problem and solve it.
IM 8 Ch9 Closure
WHAT TOOLS CAN I USE?
You have several tools and references available to help support your learning – your teacher, your study team, your math book, and your Toolkit, to name only a few. At the end of each chapter you will have an opportunity to review your Toolkit for completeness as well as to revise or update it to better reflect your current understanding of big ideas. The main elements of your Toolkit should be your Learning Logs, Math Notes, and the vocabulary used in this chapter. Math words that are new to this chapter appear in bold in the text. Refer to the lists provided below and follow your teacher’s instructions to revise your Toolkit, which will help make it a useful reference for you as you complete this chapter and prepare to begin the next one.
Learning Log Entries
Lesson 9.1.1 – Angle Relationships
Lesson 9.1.2 – Angles in a Triangle
Lesson 9.1.4 – Angle­Angle Similarity
Lesson 9.2.1 – Triangle Inequality
Lesson 9.2.1 – Triangle Side­Length Patterns
Lesson 9.2.3 – Square Roots
Lesson 9.2.5 – Pythagorean Theorem
Math Notes
Lesson 9.1.1 – Angle Vocabulary
Lesson 9.1.2 – Parallel Lines and Angle Pairs
Lesson 9.1.3 – Angle Sum Theorem for Triangles
Lesson 9.1.4 – Exterior Angle Theorem for Triangles
Lesson 9.2.1 – AA Similarity for Triangles
Lesson 9.2.2 – Triangle Inequality and Side­Length Patterns
Lesson 9.2.3 – Right Triangles and the Pythagorean Theorem
Lesson 9.2.4 – The Real Number System
Lesson 9.2.5 – Squaring and Square Root
IM 8 Ch9 Closure
Chapter 9 Vocabulary
AA (Triangle Similarity) Corresponding Angles
Acute Angle
Exterior Angle (of a Triangle)
Adjacent Angles
Hypotenuse
Alternate Interior Angles
Legs(of a right triangle)
Complementary Angles
IM 8 Ch9 Closure
Chapter 9 Vocabulary
(Continued)
Obtuse Angle
Radical Sign
Parallel
Remote Interior Angles
Perfect Square
Right Angle
Perpendicular
Square (of a number)
Pythagorean Theorem
Supplementary Angles
IM 8 Ch9 Closure
Chapter 9 Vocabulary
Straight Angle
Transversal
Vertex
Vertical Angles
(Continued)
IM 8 Ch9 Closure
Chapter 8 Vocabulary
Base of an Exponent
factor Commutative Property
of Multiplication
interest
Compound Interest
linear equation
Exponent
linear function
Exponential Growth
linear growth
(verb)
IM 8 Ch9 Closure
Chapter 8 Vocabulary
period
principal
relationship
scientific notation
simple interest
(Continued)
IM 8 Ch9 Closure
Chapter 7 Vocabulary
association
constant of proportionality
categorical variable
form
central angle
frequency table
circle graph
lattice points
cluster
line of best fit
y = mx + b
y­intercept
IM 8 Ch9 Closure
Chapter 7 Vocabulary
(Continued)
linear equation
positive slope
linear (non­linear) form
outliere
negative association
simple interest
negative slope
slope
positive association
strength (of association)
unit rate
IM 8 Ch9 Closure
Chapter 6 Vocabulary
congruent
enlarge
conjecture
linear equation
corresponding parts
point of intersection
dilation
reduce
IM 8 Ch9 Closure
Chapter 6 Vocabulary
(Continued)
reflection
similar figures
rigid transformation
systems of equations
rotation
translation
scale factor
y­intercept
IM 8 Ch9 Closure
Chapter 5 Vocabulary
coefficient
equivalent
constant term
Fraction Buster Method
counterexample
growth factor
Equal Values Method
linear equation
IM 8 Ch9 Closure
Chapter 5 Vocabulary
(Continued)
point of intersection
term
solution
variable
standard form
y­intercept
system of equations
y = mx + b form
IM 8 Ch9 Closure
Chapter 4 Vocabulary Review
graph
solution
growth factor
tile pattern
parabola
variable
parameter
x → y table
rule
y­intercept
IM 8 Ch9 Closure
Chapter 3 Vocabulary Review
Combining Like Terms
Order of Operations
Continuous Graph
Parabola
Dependent Variable
Solution
Discrete
Term
Distributive Property
Variable
Evaluate
Vertex
Independent Variable
x­intercepts
y­intercepts
IM 8 Ch9 Closure
Chapter 2 Vocabulary Review
Additive Identity
Evaluate
Additive Inverse
Expression
Associative Property
Multiplicative Identity
Combining Like Terms Order of Operations
Commutative Property Term
Equation
Variable
IM 8 Ch9 Closure
Chapter 1 Vocabulary Review
5­D Process
D
D
D
D
D
integer
proportional relationship
input
quadrant
mean
stem­and­leaf plot
median
area
unit rate
ordered pair
box plot
variable
origin
coordinates
x­axis
output
dependent variable
y­axis
perimeter
histogram
proportion
independent variable