Austin ISD Instructional Planning Guide – Mathematics
Austin Independent School District Six Weeks IPG- November 10th – December 17th, 25 days; (2 days for 6 weeks review/test) 8th Grade
Major Concept #1: Transformations 6 DAYS
Overarching Idea Transformations describe change and motion in the coordinate plane.
How are congruence and similarity related to transformations?
Teacher
How are algebra and proportionality connected to transformations?
Guiding Questions
How do dilations help solve two-dimensional measurement problems?
Matrix TEKS TAKS Time/
Matrix # Student Expectation Resource Teacher Tools
Strand Knowledge & Skill OBJ Pace
Foundation Activity:
Holt: Alt opener 7-7 p. E 53
Vocabulary: generate, similar, figures, dilation, enlargement,
Focus TEKS Student
Core Lesson(s): reductions, reflections, translations, coordinate plane
Expectations
APIE: TEXTEAMS
Geometry Across the TEKS Teacher Notes: For ideas on questioning and building
The student is expected
Transformations p. 167-187, 207- understanding, Read Teaching Student Centered Mathematics
Focus TEKS to graph dilations,
224 in Grades 5-8. John Van de Walle, p. 217-220
Knowledge and Skill reflections and
Statement translations on a
Holt Hands –On Lab 5-6 Differentiation Strategies: Use foldable for organizing ideas
coordinate plane (8.6B)
p. 242-243 on the different translations. Use geoboard with the quadrant
The student uses
Holt Hands-On Lab 7-7 grid and build the triangles in Holt Lab p. 242-243. For
transformational Supporting TEKS
p. 262-263 students that are struggling learners use patty paper to help
geometry to develop Student Expectations
Geometry and Spatial Reasoning
them see the translations and reflection. Use large polygons
spatial sense (8.6)
Classroom Practice: and one-inch grid paper (large sheet) to explore
The students will
Holt p. 246 transformations on a coordinate grid.
generate similar figures
Supporting TEKS using dilation, including Holt: p. 360
Extension Notes: The quilt project is an engaging project that
enlargements and
Homework Practice: allows students to apply their artistic side to using math.
313 The student reductions (8.6A)
3 Holt Lab Manual p. L29-L30 6 days Students are engaged and take pride in their work. The check
314 communicates about
off stages are to keep the student on task and you get a better
Grade 8 math through The student is expected
Centers: success for completion
informal and to communicate
mathematical mathematical ideas Super Source: Geometry
Penticube and Hexacube Twins p. Materials: Centimeter Grid Paper, Pattern Blocks, Coordinate
language, using language, efficient
74-77 Plane
representations, and tools, appropriate units,
models. (8.15) and graphical,
Extension: Guiding Questions:
numerical, physical, or
AISD The Quilt Project What happens to the x- coordinate and y- coordinate after a
The student uses algebraic mathematical
Bt the Sea, Middle School point is reflected across the x –axis?
logical reasoning to models. (8.15A)
Mathematics Assessments, How is dilation different than other transformations?
make conjectures and
Charles A. Dana Center, How are scale factors determined in dilations?
verify conclusions. The student is expected
http://www.utdanacenter.org/matht Why are similar shapes the result of dilation?
(8.16) to validate his/her
oolkit/downloads/msassess/ms_ch How will using a scale factor greater than one affect the size of
conclusions using
3.pdf the figure?
mathematical properties
How will a scale factor less than one affect the size of the
and relationships.
figure?
(8.16B)
How is congruence related to transformations?
DRAFT 8th Grade Page 1 of 5 11/23/2011
MIC: Mathematics in Context by Holt Holt: Holt Mathematics Course 3 CMP: Connected Mathematics by Dale Seymour Publications 8th Sense: Region XIII LTF: Laying the Foundations
RIV: Region IV Accelerated Curriculum MGA2: Math Games and Activities V2 APIE: Austin Partners in Ed. HOM: Hands On Mathematics NCTM: NCTM Navigation Series
Austin ISD Instructional Planning Guide – Mathematics
Austin Independent School District Six Weeks IPG- November 10th – December 17th, 25 days; (2 days for 6 weeks review/test) 8th Grade
Major Concept #2: Real Numbers: Squares and square roots and irrational numbers 2 DAYS
Overarching Idea Rational numbers and irrational numbers comprise the set of real numbers.
How do equivalent forms of rational numbers assist in the problem solving process?
Teacher
How do algorithms for operating with rational numbers compare to the algorithms for operating with integers and how do you know?
Guiding Questions
How can the value of irrational numbers be estimated and the reasonableness of the estimate be verified?
TEKS
Matrix Matrix TAKS Time/
Knowledge & Student Expectation Resource Teacher Tools
# Strand OBJ Pace
Skill
Vocabulary: square root (length of the side of a square), rational number,
irrational number, perfect square, real numbers, radical sign
Teacher Notes:
Use examples and non-examples when working with rational and irrational
numbers. Have students model squares and square roots with square tiles
Foundation Activities: and grid paper. Build the concept of irrational through the use of models
Building Squares and Square before moving to a number line. Have students use inverse relationships to
roots determine the approximate location of square roots between whole numbers
on a number line. 27 is a little more than 5 because 5² = 25
Holt Alt Opener 4-5 E28
Holt E4-6 Estimating Square
Real Numbers, Teaching Student Centered Mathematics, John Van de
Numbers and Operations and Algebraic Thinking
Focus TEKS roots E29
Focus TEKS Student Walle, p. 150-151
Knowledge
Expectations
and Skill Core Lesson(s):
Statement APIE: MIC: Revisiting Differentiation Strategies: Build the understanding of square root as the
The student will length of the side of a square by having students find the area of the color
Numbers pp. 50-52 and
approximate (mentally and tile square and the length of its side – or use grid paper to build squares and
The student Patterns and Figures p. 20-25
with calculators )the value determine length of side. Foldable is to use grid paper and build the perfect
understands
of irrational numbers as squares stapling them in one corner – example in notebook in teacher
that different Classroom Practice:
they arise from problem notes.
8th Sense Teacher p.75-77
situations (such as ,
forms of 1 and 2
112 numbers are 6 8th Sense Student Page p.79
days Materials: Calculators, color tiles, number line cards with rational and
appropriate for 2 ) (8.1C)
different Homework Practice: irrational numbers to add to existing number line in classroom.
situations (8.1) Holt PS 4-5, PS28
Supporting TEKS Extension Notes: Using map colors the students can find the area of the
Student Expectations squares on the grids and then determine the length of the side of the
Supporting Centers:
TEKS Super Source Measurement square. Then on centimeter grid paper the students draw the squares with
8.15A areas (2, 5, 8, 10, 20) and measure the sides with a centimeter ruler and
The Squarea Challenge p.
8.16B test using a calculator to find and justify the square roots of the squares.
8.15 63-66
8.16
Extension: Technology Application: Include a demonstration on how you use the
MGA2 p. 217 Lengths of square root button on the graphing calculator. Understanding Math
Edges of Squares Understanding Exponents Topic #5
Guiding Questions: How do you determine the difference between rational
and irrational numbers?
How do you estimate the value of an irrational number?
How does the square root relate to the area of a square?
DRAFT 8th Grade Page 2 of 5 11/23/2011
MIC: Mathematics in Context by Holt Holt: Holt Mathematics Course 3 CMP: Connected Mathematics by Dale Seymour Publications 8th Sense: Region XIII LTF: Laying the Foundations
RIV: Region IV Accelerated Curriculum MGA2: Math Games and Activities V2 APIE: Austin Partners in Ed. HOM: Hands On Mathematics NCTM: NCTM Navigation Series
Austin ISD Instructional Planning Guide – Mathematics
Austin Independent School District Six Weeks IPG- November 10th – December 17th, 25 days; (2 days for 6 weeks review/test) 8th Grade
Major Concept #3: Modeling the Pythagorean Theorem 6 DAYS
Overarching Idea In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs.
Teacher How do the squares around the sides of a right triangle relate to one another?
Guiding Questions What are various models which can represent and prove the Pythagorean Theorem?
TEKS
Matrix Matrix TAKS Time/
Knowledge & Student Expectation Resource Teacher Tools
# Strand OBJ Pace
Skill
Vocabulary: Pythagorean Theorem, right angle, right triangle, leg
hypotenuse, squares, square roots, area, models
TAKS Information: See released TAKS items to confirm that
Foundation Activities:
understanding of the Pythagorean theorem is tested on TAKS by
Focus TEKS Student CMP Looking for Pythagoras
using models and pictures and not by solving the formula with this
Expectations Investigations 2.1 – 2.3
student expectation. This student expectation is tested under the
Include the Mathematical
Geometry Objective 3.
The student uses reflections on pg. 26
pictures or models to
Teacher Notes:
demonstrate the Core Lesson(s):
The Pythagorean Theorem is introduced for the first time in 8th grade
Pythagorean theorem. APIE: CMP Looking for
and should be taught conceptually using models. Continue building
Focus TEKS (8.7C) Pythagoras 3.1-3.2
geometry vocabulary with these lessons and the students’
Knowledge and Holt Hands-on Lab 4-8 page 195
understanding of square roots as lengths of the sides of squares.
Skill Statement Supporting TEKS APIE: MIC: Looking at An Angles
Begin with the CMP lesson so that the students have the opportunity
Student Section E: “Reasoning with Ratios”
to build the squares around the sides of the right triangle using
The student Expectations –Pythagoras pp. 47-50
centimeter grid paper and their recording sheet. Students will be
uses geometry
able to communicate this relationship and have understanding of the
to model and The student is Classroom Practice:
Geometry
concept in order to apply it in the next stage of the curriculum, which
describe the expected to Holt: Labs: L16-L17
331 physical world. communicate
3 and 8th Sense p. 277-280 6 days
is applying the theorem.
(8.7) mathematical ideas 6
Differentiation Strategies: Students use square grids to explore
using language, Homework Practice:
the Pythagorean theorem. Have students construct triangles using
Supporting efficient tools, Holt Exploration 4-8 PS31
the side lengths of the squares to represent the side length of a
TEKS appropriate units, and
triangle. Make sure students construct various triangles including
graphical, numerical, Centers:
non right triangles. Develop the concept of the Pythagorean
8.15 A physical, or algebraic MGA2 p. 213-214 Areas of Similar
Relationship through examples and non-examples.
8.15 B mathematical models. Figures on the Sides of Right
(8.15A) Angles.
Geopolis Materials: Centimeter Grid Paper, Color Tiles, Map colors
The student is
expected to validate Extension:
Technology Application: Understanding Math Understanding
his/her conclusions CMP Looking for Pythagoras
Exponents Topic #6
using mathematical Investigations 3.3 and 3.4 – and
properties and Investigation 4 (Special Right
Guiding Questions:
relationships. (8.16B) Triangles)
How does the hypotenuse relate to the legs of a right triangle?
How is the Pythagorean Theorem used to find a missing side in a
right triangle?
How is the Pythagorean Theorem formula derived from a model?
DRAFT 8th Grade Page 3 of 5 11/23/2011
MIC: Mathematics in Context by Holt Holt: Holt Mathematics Course 3 CMP: Connected Mathematics by Dale Seymour Publications 8th Sense: Region XIII LTF: Laying the Foundations
RIV: Region IV Accelerated Curriculum MGA2: Math Games and Activities V2 APIE: Austin Partners in Ed. HOM: Hands On Mathematics NCTM: NCTM Navigation Series
Austin ISD Instructional Planning Guide – Mathematics
Austin Independent School District Six Weeks IPG- November 10th – December 17th, 25 days; (2 days for 6 weeks review/test) 8th Grade
Major Concept #4: Applying the Pythagorean Theorem 6 DAYS
Overarching Idea Understanding the Pythagorean Theorem helps to apply it to real world situations using indirect measurement
How is the distance between any two points determined?
Teacher
What are characteristics of real world applications involving the Pythagorean Theorem?
Guiding Questions
How does rate of change in linear relationships connect to right triangles?
TEKS TAK
Matrix Matrix Time/
Knowledge & Student Expectation S Resource Teacher Tools
# Strand Pace
Skill OBJ
Vocabulary: Pythagorean Theorem, right angle, right triangle, leg
hypotenuse, squares, square roots, indirect measurement,
distance, similar
Core Lessons:
RIV Making Connections with Teacher Notes: An important concept to remember is that the
Focus TEKS Student
Measurement (7 days) application of Pythagorean Theorem is utilized to find the distance
Expectation
Student pgs 40 – 49 between any two points. Although students have just modeled
Teacher pgs 30 – 39 and been working with the new concept of this Theorem, they
The student is expected to
RIV Unit 6 Lesson 2 may still be struggling with the concept. Application problems
use the Pythagorean
Focus TEKS TE p. 267-272 allow for them to formalize the learning by applying the new
Theorem to solve real-life
Knowledge and SE p. 133-134 concept in a real world context. Please note TAKS released
problems (8.9A)
Skill Statement items to ensure how this concept is tested in application.
The student Classroom Practice:
Supporting TEKS Student
uses indirect RIV Unit 6 Lesson 2 Technology Application: Understanding Math Understanding
Expectations
measurement to SE p. 135
Measurement
Exponents Topic #6
solve problems Holt: Reteach 4-8
The student is expected to 4
(8.9) Holt: Problem Solving PS31 Extension Notes:
416 communicate mathematical and 6 days
ideas using language, 6 The Wheel of Theodorus design project
Supporting Homework Practice: (This is an excellent project to have the students discover the
efficient tools, appropriate
TEKS RIV Unit 6 Lesson 2 SE p. 137 – wheel of Theodorus and then use it in an artistic format
units, and graphical,
Knowledge and 141 (four different assignments)
numerical, physical, or
Skill Statement Questions:
algebraic mathematical
Extension: How does understanding the Pythagorean Theorem help us
models. (8.15A)
8.15 CMP Looking for Pythagoras Inv. to find the distance between any two objects?
8.16 5: The Wheel of Theodorus design
The student is expected to If we think about distance, how does understanding the two
project
validate his/her conclusions small sides of the triangle help us to understand how the
ACE questions pgs 22-25 #’s2, 6,
using mathematical hypotenuse relates to them?
7, 9, 10, 15
properties and relationships. Is it possible to draw a right triangle where the sum of the
MGA2: p. 220 Applying the
(8.16B) two short sides is equal to the hypotenuse?
Pythagorean Theorem
How does the hypotenuse help us to understand the shortest
distance between two points?
Why is the Pythagorean theorem contingent upon the
triangle being a right triangle?
DRAFT 8th Grade Page 4 of 5 11/23/2011
MIC: Mathematics in Context by Holt Holt: Holt Mathematics Course 3 CMP: Connected Mathematics by Dale Seymour Publications 8th Sense: Region XIII LTF: Laying the Foundations
RIV: Region IV Accelerated Curriculum MGA2: Math Games and Activities V2 APIE: Austin Partners in Ed. HOM: Hands On Mathematics NCTM: NCTM Navigation Series
Austin ISD Instructional Planning Guide – Mathematics
Austin Independent School District Six Weeks IPG- November 10th – December 17th, 25 days; (2 days for 6 weeks review/test) 8th Grade
Major Concept #5: Scientific Notation 3 DAYS
Overarching Idea Scientific Notation is an example of an exponential relationship
Teacher
How is Scientific Notation is an example of an exponential relationship?
Guiding Questions
TEKS
Matrix Matrix TAKS Time/
Knowledge & Student Expectation Resource Teacher Tools
# Strand OBJ Pace
Skill
Vocabulary: scientific notation, standard notation,
Teacher Notes: Students are building an understanding that the
Numbers Operations, and Quantitative reasoning
scientific notation and standard notation are representations for
the same number. Real world examples help students
Foundation Activity:
understand that very small numbers (0.000007) will have a
Holt Alt Opener E4-4
negative exponent when written in scientific notation where as
very large numbers (10,000,000) will have a positive exponent
Target TEKS Core Lesson(s):
when written in scientific notation.
Knowledge and Target Student Holt 4-4 p. 174-176
Skill Statement Expectation:
Differentiation Strategies: Use a plastic counter to represent
The student The student will express Classroom Practice:
the decimal and physically move the decimal. Ensure that
understands that numbers in scientific Holt p. 176 #1-10
113 1 and 6 3 days students understand that the decimal is able to move because the
different forms of notation, including negative Holt Practice 4-4
number is multiplied by a power of 10. It is important to
numbers are exponents, in appropriate
communicate that the number remains the same quantity but is
appropriate for problem situations using a Homework Practice:
represented by either standard notation or scientific notation.
different calculator. 8.1D Holt p. 177 #11-20
situations Holt Reteach 4-4
Technology Application: Understanding Math Understanding
Exponents Topic #4
Extension:
Holt: Problem Soving 4-4
Guiding Questions:
Why do mathematicians and scientists use scientific notation?
Is it possible to multiply a number while it is written in scientific
notation?
DRAFT 8th Grade Page 5 of 5 11/23/2011
MIC: Mathematics in Context by Holt Holt: Holt Mathematics Course 3 CMP: Connected Mathematics by Dale Seymour Publications 8th Sense: Region XIII LTF: Laying the Foundations
RIV: Region IV Accelerated Curriculum MGA2: Math Games and Activities V2 APIE: Austin Partners in Ed. HOM: Hands On Mathematics NCTM: NCTM Navigation Series