Course: 8th grade Math 1st Nine Weeks Instructional Guide
Unit 1: Simplifying and Evaluating Expressions / Estimated Time: 2 weeksGLE: 0806.3.1 Recognize and generate equivalent forms for algebraic expressions
0806.1.1 Use mathematical language, symbols, and definitions while developing mathematical reasoning.
0806.1.2 Apply and adapt a variety of appropriate strategies to problem-solving, including estimation, and
reasonableness of solution.
0806.1.4 Move flexibly between concrete and abstract representations of mathematical ideas in order to
solve problems, model mathematical ideas, and communicate solution strategies.
0806.1.6 Read and interpret the language of mathematics and use written/oral communication to express
mathematical ideas precisely.
0806.1.7 Recognize the historical development of mathematics, mathematics in context, and the
connections between mathematics and the real world.
0806.1.8 Use technology/manipulatives appropriately to……facilitate problem solving….
Prerequisite Skills: follow standard order of operations; understand meaning and use of variables and variable expressions
Essential Question: How are the properties of real numbers useful when simplifying expressions?
Why is there a standard order of operations when simplifying expressions
Unit Vocabulary: perfect square, evaluate
Checks for Understanding / State Performance Indicators / Assessments / Instructional Resources/
Strategies / Connections
0806.3.1 Perform basic operations on algebraic expressions (including grouping, order of operations, exponents, square/cube roots, simplifying and expanding)
0806.3.12 Represent situations and solve real-world problems using symbolic algebra / As closure items:
-foldable with terms
-“create a problem” activity
Quiz on Order of Operations- thatquiz.org
(create own quiz) / Everything Balances Out In The End:
http://illuminations.nctm.org/ActivityDetail.aspx?id=33
Order of Operations: tutorial with pre-test, practice, and post-test
http://amby.com/educate/ord-op/
SpeedMath Deluxe:
writing a problem to match a solution
http://education.jlab.org/smdeluxe/index.html
Game 24
PH Sect. 1.1, 1.2, 1.3, pg. 15 / Steps in the Scientific Method- science
Write “story” problems- language arts
Unit 2: Rational and Irrational Numbers / Estimated Time: 2.5 weeks
GLE:0806.2.1 Extend understanding of the real number system to include irrational numbers.
0806.2.3 Solve real-world problems using rational and irrational numbers.
0806.1.1 Use mathematical language, symbols, and definitions while developing mathematical reasoning.
Prerequisite Skills: operations with integers
Essential Question: Why is it important to understand properties and operations involving rational and irrational numbers?
Unit Vocabulary: rational number, irrational number, infinite
Checks for Understanding / State Performance Indicators / Assessments / Instructional Resources/
Strategies / Connections
0806.2.4 Use a Venn Diagram to represent the subsets of the real number system.
0806.2.5 Identify the subset(s) of the real number system to which a number belongs. / 0806.2.1 Order and compare rational and irrational numbers and locate on a number line. / Venn diagram group activity and presentations (see appendix)
“clothesline” ordering relay (see appendix) / Ordering Rational Numbers and Finding Their Approximate Location On a Number Line
http://www.uen.org/Lessonplan/preview.cgi?LPid=23484
PH Sect. 4.6 / Compare and Contrast Reading Selections- language arts
0806.2.2 Square numbers and simplify square roots.
0806.2.3 Solve contextual problems involving powers and roots. / 0806.2.2 Identify numbers and square roots as rational and irrational. / Math Menu: skills from Units 1 and 2 as mid-9 weeks review/assessment / Square activity using color tiles/ Cube activity using unifix/multilink cubes (see appendix)
PH Sect. 11.1
Appendix for Unit 2:
Venn Diagram Group Activity and Presentations: Students will classify numbers into the subsets to which they belong using a Venn diagram. The students will then present this Venn diagram to the class with explanation.
OR
As students enter the classroom the teacher hands them a real number. Students place their number on a Venn diagram drawn on the board. Students must explain the placement of the number.
“Clothesline” ordering relay: Teacher will create several examples of numbers in the real number system (rational and irrational) and prepare cards with those examples. The number of examples is up to the teacher (1 per student, 1 per group, etc.). The teacher will also provide a “clothesline” for the activity. Each group/student will then place their number on the clothesline. Teacher designates the order (least to greatest, greatest to least). After all have been placed, the students and the teacher will check to make sure they are in order and correct as necessary. Note: The same numbers can be used as were used in the Venn diagram activity.
Square Activity using Color Tiles: Students use color tiles to build squares. A recording sheet similar to the one below is used.
# of tiles used / Make square?Yes/No / length / width / of tiles
1 / Yes / 1 / 1 / 1
2 / No
3 / No
4 / Yes / 2 / 2 / 2
Students continue building with tiles until they can predict the next perfect square and its square root. The idea is for the students to see the connection between the side of the square and its square root.
Cube Activity using Unifix Cubes/Multilinks: same activity as above except it incorporates 3-D shapes. The idea is for the students to see the connection between the edge of a cube and its cubed root.
GLE: 0806.2.2 Solve problems involving exponents and scientific notation using technology appropriately.
0806.2.4 Understand and use the laws of exponents.
0806.1.1 Use mathematical language, symbols, and definitions while developing mathematical reasoning.
0806.1.2 Apply and adapt a variety of appropriate strategies to problem-solving, including estimation, and
reasonableness of solution.
0806.1.4 Move flexibly between concrete and abstract representations of mathematical ideas in order to
solve problems, model mathematical ideas, and communicate solution strategies.
0806.1.6 Read and interpret the language of mathematics and use written/oral communication to express
mathematical ideas precisely.
0806.1.7 Recognize the historical development of mathematics, mathematics in context, and the
connections between mathematics and the real world.
0806.1.8 Use technology/manipulatives appropriately to develop understanding of mathematical algorithms, to
facilitate problem solving, and to create accurate and reliable models of mathematical concepts.
Prerequisite Skills: evaluate using exponents, use exponential notation, and simplify expressions
Essential Questions: Why do the laws of exponents, when multiplying and dividing numbers in scientific notation, make solving the
problems easier?
Why is scientific notation used in real-life problems?
Unit Vocabulary: scientific notation, standard notation, laws of exponents
Checks for Understanding / State Performance Indicators / Assessments / Instructional Resources/Strategies / Connections
0806.2.6 Simplify expressions using laws of exponents. / Quiz over laws of exponents- thatquiz.org / Exponent Rules Definitions and Practice:
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_ExponentsRules.xml
Exponent Rules Practice:
http://www.ltcconline.net/greenl/java/BasicAlgebra/ExponentRules/ExponentRules.html
PH Sect. 4.7, 4.8
0806.2.1 Recognize and use exponential, scientific, and calculator notation.
0806.2.7 Add, subtract, multiply, and divide numbers expressed in scientific notation. / 0806.2.3 Use scientific notation to compute products and quotients. / Teacher created
I Have/Who Has game
Writing World Populations in Scientific Notation (see appendix) / Operations with Scientific Notation:
tutorial and practice
http://staff.argyll.epsb.ca/jreed/math9/strand1/sci_notation_operations.htm
PH pg. 209, 221-222, Sect. 4.9 / Presenting Scientific Data- science
Populations- Social Studies
0806.2.1 Recognize and use exponential, scientific, and calculator notation.
0806.2.7 Add, subtract, multiply, and divide numbers expressed in scientific notation.
0806.1.4 Relate data concepts to relevant concepts in the earth and space, life, and physical sciences. / 0806.2.4 Solve real-world problems requiring scientific notation. / Find examples in real life of exponential and scientific / All For A Walk on the Moon- Problem Solving
http://www.beaconlearningcenter.com/documents/1669_4927.pdf
Appendix for Unit 3:
Writing World Populations in Scientific Notation: Students will use almanac to locate the population of various countries. Each population must be rounded to the place predetermined by the teacher. The rounded number is then expressed in scientific notation. All classroom data is recorded on a large chart for hall display. Note: Be careful when giving place to round to- make sure all populations can be expressed in scientific notation.
GLE: 0806.4.1 Derive the Pythagorean Theorem and understand its applications.
0806.1.1 Use mathematical language, symbols, and definitions while developing mathematical reasoning.
0806.1.2 Apply and adapt a variety of appropriate strategies to problem-solving, including estimation, and
reasonableness of solution.
0806.1.4 Move flexibly between concrete and abstract representations of mathematical ideas in order to
solve problems, model mathematical ideas, and communicate solution strategies.
0806.1.7 Recognize the historical development of mathematics, mathematics in context, and the
connections between mathematics and the real world.
0806.1.8 Use technology/manipulatives appropriately to develop understanding of mathematical
algorithms, to facilitate problem solving, and to create accurate and reliable models of
mathematical concepts.
Prerequisite Skills: solve 1-step equations, evaluate expressions, square roots
Essential Question: How does the Pythagorean Theorem apply in real-life situations?
How can the Pythagorean Theorem be used to classify triangles?
Unit Vocabulary: Pythagorean Theorem, hypotenuse, legs of a triangle
Checks for Understanding / State Performance Indicators / Assessments / Instructional Resources/Strategies / Connections
0806.1.5 Use age appropriate books, stories, and videos to convey ideas in mathematics.
0806.4.1 Model the Pythagorean Theorem.
0806.4.2 Use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle. / 0806.4.1 Use the Pythagorean Theorem to solve contextual problems. / Performance Task: Applying Pythagorean Theorem (see appendix)
“Fine Feathered Friend?” (see appendix) / Real Life Application for Pythagorean Theorem:
http://middle-school-curriculum.suite101.com/article.cfm/the_pythagorean_theorem
http://www.learnnc.org/lp/pages/3650
Source of Additional Resources:
http://mathforum.org/dr.math/faq/faq.pythagorean.html
PH Sect. 11.2, 11.5 / What’s Your Angle, Pythagoras? by Julie Ellis
“Matt’s Metaphor Rebuttal”
(see appendix)
0806.1.3 Research the contributions of Pythagoras to mathematics. / 0806.4.2 Apply the Pythagorean Theorem to find distances between points in the coordinate plane to measure lengths and analyze polygons and polyhedra. / Several Pgs. of Pythagorean Practice:
http://www.bigideasmath.com/protected/content/ipe_na/grade%208/06/g8_06_05.pdf
9 Weeks Assessment: all skills from Units 1 – 4 / Corner to Corner Problem:
http://illuminations.nctm.org/LessonDetail.aspx?ID=L684
PH Sect. 11.3 / History of Pythagoras:
http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm
Appendix for Unit 4:
Performance Task: Applying Pythagorean Theorem: Students will take a trip outside and use various items to experiment with the Pythagorean Theorem and its converse. Ex: meter stick/shadow- find hypotenuse; locate triangles and prove if they are right triangles or not. After the activity, the students will create their own problem relating to their outside experiments and have another student complete that problem. The pair will discuss their findings.
Matt’s Metaphor Rebuttal-
This activity comes from Real-Life Math Problem Solving by Mark Illingworth published by Scholastic. This book is out of print but can be found on various sites such as amazon.com and half.com.
Here is the bottom-line:
A square peg can fit into a round hole. Students must find the diameter of the smallest hole that a square peg could fit through. Teacher determines the base of the square peg (square prism).
Fine Feathered Friend-
This activity comes from Real-Life Math Problem Solving by Mark Illingworth published by Scholastic. This book is out of print but can be found on various sites such as amazon.com and half.com.
Here is the bottom-line:
It is based on the expression “as the crow flies”. A bird and a person are racing to the sandwich shop. The bird flies and the person walks via the street. Students will use the Pythagorean Theorem to determine the winner of the race.
7