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IM 8 Ch3 Closure
CPM Materials modified by Mr. Deyo
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.
IM 8 Ch3 Closure
By the end of the period, I will apply different problem‐solving strategies and reflect on what I have learned in this chapter.
I will demonstrate this by compleng Four‐Square notes and by solving problems in a pair/group acvity.
Learning TargetTitle: IM8 ‐ Ch. 3 Closure ‐ What Have I Learned? Date:
IM 8 Ch3 Closure
Home Work: Ch. 3 ClosureDesc. Date Due
What Have I Learned?
10 Problems CL 3‐118 through 3‐127
IM 8 Ch3 Closure
IM 8 Ch3 Closure
Chapter 3 Vocabulary ReviewCombining Like Terms
Continuous Graph
Dependent Variable
Discrete
Distributive Property
Evaluate
Independent Variable
Order of Operations
Parabola
Solution
Term
Variable
Vertex
xintercepts
yintercepts
IM 8 Ch3 Closure
IM 8 Ch3 Closure
SUMMARIZING MY UNDERSTANDING
Multiple RepresentationsYour Task:• In this chapter, you learned about how data can be
shown in one of four representations. These include a situation or tile pattern, a graphical display, a table of values, and a symbolic rule. Show what you know about these representations by doing the following activity with your team. While you have not fully investigated all of these representations so far, this exercise will prepare you to make important connections in Chapter 4.
• Pick a pattern or problem from the chapter that you think can best demonstrate your understanding of these four representations.
• Obtain a Chapter 3 Closure Resource Page: Multiple Representations GO (Graphic Organizer) from your teacher, a reduced copy of which is shown at right.
• In the middle of the page, copy the problem that you have selected. Then represent it using each of the four different representations shown on the page.
• Use color or other means to show any connections that you see between each of the representations.
IM 8 Ch3 Closure
IM 8 Ch3 Closure
CL 3118. For the x → y table below, fill in the missing values and find the rule.
What is the rule?
y = (___)x + (___)
Input (x) Output (y)
IM 8 Ch3 Closure
3119a,b,c
One year ago, Josie moved into a new house and noticed a beautiful vine growing on the back fence. She recorded the data in the table.
Assume that the vine continues to grow at a constant rate as you answer the questions.
a) How tall was the vine 7 weeks after Josie moved in?
b) How tall was the vine 3 weeks after Josie moved in?
c) How tall was the vine when Josie moved in? How do you know?
IM 8 Ch3 Closure
3119d,e
One year ago, Josie moved into a new house and noticed a beautiful vine growing on the back fence. She recorded the data in the table.
Assume that the vine continues to grow at a constant rate as you answer the questions.
d) Predict how tall the vine was 19 weeks after Josie moved into her house. Justify your answer.
e) Predict when the vine reached the top of the garage (94 inches tall). How did you find your answer?
IM 8 Ch3 Closure
CL 3120
Define a variable and then write and solve an equation for the problem below. Use the 5D Process, if needed. Show your work in an organized way and state your solution in a sentence.
Clifford is making a really big white cake for his sister’s birthday. The recipe calls for 1.5 times as much flour as sugar. It also calls for one half as much butter as sugar. All the butter, flour, and sugar together total 7.5 cups. How much butter, sugar and flour does Clifford need?
IM 8 Ch3 Closure
CL 3121
Simplify and Evaluate
a) Simplify the expression. b) Then evaluate the result of part (a) if x = −1 and y = 6
3x2 − 5x − 4 + xy − (2xy + 2x2)
IM 8 Ch3 Closure
CL 3122
a) 62 − (5 − 4) + 2(8 − 22) ÷8
Follow the order of operations to simplify each expression.
2(9 6)2 18
b)
IM 8 Ch3 Closure
CL 3123
Raphael had 5 hits in 7 at bats. If he continues this pattern, how many hits will he have in 210 at bats?
Hint: Make a proportion. Then, "butterfly crossmultiply" to solve for the unknown.
IM 8 Ch3 Closure
3124
Explanation
• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative InverseSolve for the variable. Record
your work & check the solution.
6 − x − 3 = 4x − 12
IM 8 Ch3 Closure
What is the rule?y = ( )x + ( )
3125
x y
Create an x → y table using at least eight points from the graph. Write the rule for the pattern in the table.
IM 8 Ch3 Closure
CL 2126
Jessica was solving an equation. After she finished simplifying, her result was 0 = 2. This result confused her. Explain to Jessica what her result means. Explain your reasoning thoroughly.
IM 8 Ch3 Closure
CL 3127a For each of the previous problems (CL3118 to CL3126), 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 3118CL 3119CL 3120CL 3121CL 3122
CL 3124CL 3123
CL 3125CL 3126
IM 8 Ch3 Closure
CL 3127b 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 3____
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 Ch3 Closure
CL 3127c 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 3____
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 Ch3 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 3.1.6 – Qualities of a Complete GraphLesson 3.1.7 – Graphing ErrorsLesson 3.2.2 – How Many Solutions?
Math NotesLesson 3.1.1 – Patterns in NatureLesson 3.1.3 – Discrete and Continuous GraphsLesson 3.1.4 – ParabolasLesson 3.1.5 – Independent and Dependent VariablesLesson 3.2.1 – Complete GraphLesson 3.2.2 – Circle Vocabulary, Circumference, and AreaLesson 3.2.3 – Solving a Linear EquationLesson 3.2.4 – Solutions to an Equation with One VariableLesson 3.2.5 – The Distributive Property
IM 8 Ch3 Closure
Chapter 3 Vocabulary ReviewCombining Like Terms
Continuous Graph
Dependent Variable
Discrete
Distributive Property
Evaluate
Independent Variable
Order of Operations
Parabola
Solution
Term
Variable
Vertex
xintercepts
yintercepts
IM 8 Ch3 Closure
Chapter 2 Vocabulary ReviewAdditive Identity
Additive Inverse
Associative Property
Combining Like Terms
Commutative Property
Equation
Evaluate
Expression
Multiplicative Identity
Order of Operations
Term
Variable
IM 8 Ch3 Closure
Chapter 1 Vocabulary Review5D Process
DDDDD
area
box plot
coordinates
dependent variable
histogram
independent variable
integer
input
mean
median
ordered pair
origin
output
perimeter
proportion
proportional relationship
quadrant
stemandleaf plot
unit rate
variable
xaxis
yaxis