Grade 8



Grade 8

Mathematics

Table of Contents

Unit 1: Real Numbers, Measures, and Models 1-1

Unit 2: Transformations and the Pythagorean Theorem 2-1

Unit 3: Transversals, Surface Area and Volume 3-1

Unit 4: Expressions and Equations in Algebra 4-1

Unit 5: Functions, Growth and Patterns, Part 1 5-1

Unit 6: Functions, Growth and Patterns Part 2 6-1

Unit 7: Data and Lines of Best Fit 7-1

Unit 8: Enhancing Understanding and Fluency 8-1

2012 Louisiana Transitional Comprehensive Curriculum

Course Introduction

The Louisiana Department of Education issued the first version of the Comprehensive Curriculum in 2005. The 2012 Louisiana Transitional Comprehensive Curriculum is aligned with Grade-Level Expectations (GLEs) and Common Core State Standards (CCSS) as outlined in the 2012-13 and 2013-14 Curriculum and Assessment Summaries posted at . The Louisiana Transitional Comprehensive Curriculum is designed to assist with the transition from using GLEs to full implementation of the CCSS beginning the school year 2014-15.

Organizational Structure

The curriculum is organized into coherent, time-bound units with sample activities and classroom assessments to guide teaching and learning. Unless otherwise indicated, activities in the curriculum are to be taught in 2012-13 and continued through 2013-14. Activities labeled as 2013-14 align with new CCSS content that are to be implemented in 2013-14 and may be skipped in 2012-13 without interrupting the flow or sequence of the activities within a unit. New CCSS to be implemented in 2014-15 are not included in activities in this document.

Implementation of Activities in the Classroom

Incorporation of activities into lesson plans is critical to the successful implementation of the Louisiana Transitional Comprehensive Curriculum. Lesson plans should be designed to introduce students to one or more of the activities, to provide background information and follow-up, and to prepare students for success in mastering the CCSS associated with the activities. Lesson plans should address individual needs of students and should include processes for re-teaching concepts or skills for students who need additional instruction. Appropriate accommodations must be made for students with disabilities.

Features

Content Area Literacy Strategies are an integral part of approximately one-third of the activities. Strategy names are italicized. The link (view literacy strategy descriptions) opens a document containing detailed descriptions and examples of the literacy strategies. This document can also be accessed directly at .

Underlined standard numbers on the title line of an activity indicate that the content of the standards is a focus in the activity. Other standards listed are included, but not the primary content emphasis.

A Materials List is provided for each activity and Blackline Masters (BLMs) are provided to assist in the delivery of activities or to assess student learning. A separate Blackline Master document is provided for the course.

The Access Guide to the Comprehensive Curriculum is an online database of suggested strategies, accommodations, assistive technology, and assessment options that may provide greater access to the curriculum activities. This guide is currently being updated to align with the CCSS. Click on the Access Guide icon found on the first page of each unit or access the guide directly at .

Grade 8

Mathematics

Unit 1: Real Numbers, Measures, and Models

Time Frame: Approximately four weeks

Unit Description

This unit focuses on number theory and the comparison of rational and irrational numbers. Comparing the size of these numbers to each other and zero is the focus of the contents of the unit. Writing very large and very small numbers in scientific notation is also a part of this unit.

Student Understandings

The student will determine the relative size of rational numbers, comparing fractions, integers, decimals and percents. The student will compare rational and irrational numbers and discuss the differences. Students will determine which two whole numbers that radicals are located between.

Guiding Questions

1. Can students compare rational numbers using symbolic notation as well as use position on a number line?

2. Can students recognize, interpret, and evaluate problem-solving contexts with rational numbers?

3. Can students determine approximate value of non-square radicals?

4. Can students group numbers into categories of rational and irrational numbers?

5. Can students perform operations with numbers written in scientific notation?

Unit 1 Grade-Level Expectations (GLEs) and Common Core State Standards (CCSS)

|Grade-Level Expectations |

|GLE # |GLE Text and Benchmarks |

|Number and Number Relations |

|1. |Compare rational numbers using symbols (i.e., ) and position on a number line (N-1-M) |

| |(N-2-M) |

|2. |Use whole number exponents (0-3) in problem-solving contexts (N-1-M) (N-6-M) |

|CCSS# |CCSS Text |

|8.NS.1 |Know that numbers that are not rational are called irrational, and approximate them by rational |

| |numbers. Understand informally that every number has a decimal expansion; for rational numbers show |

| |that the decimal expansion repeats eventually, and convert a decimal expansion which repeats |

| |eventually into a rational number. |

|8.NS.2 |Use rational approximations of irrational numbers to compare the size of irrational numbers, locate |

| |them approximately on a number line diagram, and estimate the value of expressions (e.g., (2). For |

| |example, by truncating the decimal expansion of [pic], show that [pic]is between 1.4 and 1.5, and |

| |explain how to continue to get better approximations. |

|8.EE.1 |Know and apply the properties of integer exponents to generate equivalent numerical expressions. For|

| |example, 32 x 3-5 = [pic] |

|8.EE.2 |Use square root and cube root symbols to represent solutions to equations of the form x2 = p, where p|

| |is a positive rational number. Evaluate square roots of small perfect squares and cube roots of |

| |small perfect cubes. Know that [pic]is irrational. |

|8.EE.3 |Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very |

| |large or very small quantities, and to express how many times as much one is than the other. |

|8.EE.4 |Perform operations with numbers expressed in scientific notation, including problems where both |

| |decimal and scientific notation are used. Use scientific notation and choose units of appropriate |

| |size for measurements of very large or very small quantities (e.g., use millimeters per year for |

| |seafloor spreading). Interpret scientific notation that has been generated by technology. |

Sample Activities

Activity 1: Compare and Order (GLE: 1 , 2)

Materials List: Rational Number Line Cards - student 1 BLM, Rational Number Line Cards - student 2 BLM, Rational Number BLM, Compare and Order Word Grid BLM, calculators, paper, pencil

Have students work in pairs. Provide a number line showing only the integers –1, 0, and 1. Give each student a deck of cards containing rational numbers including some negative rational numbers. Use the Rational Number Line Cards - Student 1 BLM and the Rational Number Line Cards – Student 2 BLM to make both sets of cards for each pair of students. Student 1 should get a deck of rational numbers in fraction form, made by using Rational Number Line Cards - Student 1 BLM, and Student 2 should get a deck of rational numbers in decimal form, made using Rational Number Line Cards - Student 2 BLM. Have each student select a card from his/her deck and compare the cards. The comparison can be done using a calculator, mental math, or paper/pencil. Ask students to correctly place both rational numbers on the number line and then write a correct comparison statement using symbols. For example, if the two rational numbers were[pic] and[pic], they would place a mark at the[pic] point and the [pic] point on their number line; then they would write a correct statement like “0.05 2.5 or < 2.5(it is less than 2.5 because 5 is closer to 4 than it is to 9).

Distribute cards with real numbers, Real Number Cards BLM, to groups of four students. Explain to the students that they will work to put the numbers in order from least to greatest. If a group of students is “stuck,” guide them to look at their square root list that was prepared at the beginning of the lesson.

After the students have had time to put the numbers in order, distribute number line BLM and have students place the numbers from the cards in correct position along the number line. Have students indicate which numbers on the number line are irrational numbers and have someone explain again the definition of an irrational number. Discuss results as a class.

Challenge the students by asking the question: What do you think [pic]symbolizes? This may be the first time the students have seen the cube root symbol. Have the students use a “factor tree” to find the prime factorization of 27 so that they will get the exponential representation of 33. This gives a hint without telling the students that it represents something with a cube. At this time, tell the students that when a number is a perfect cube, the result of finding the cube root will be a whole number, as was done with the square roots. Have the students make a list of the first five perfect cube numbers. (1, 8, 27, 64, 125) Tell the students to write equations to show the cube root of each of these perfect cubes. ([pic])

Activity 6: Radically! More or Less (CCSS: 8.NS.2)

Materials: Paper, pencils

Students should write the following radical numbers on their paper: [pic]. Have the students work in groups of four to determine the two consecutive whole numbers that are on either side of the numbers and which of these whole numbers is closest to the radical number. Students should be able to justify their answers. Give the class time to complete the assignment.

Explain to the class that professor know-it-all (view literacy strategy descriptions) is a method of reviewing content. One group of four students will be in the front of the room and answer questions about determining the approximate value of radical numbers that are not square numbers. The group at the front will be the “experts,” and the class members can ask questions they have about approximating the value of radical numbers. The group at the front will “huddle” after a question is asked so that they can agree upon an answer. Since this is the first time they have used this strategy this year, it might help to have a list of questions prepared and distributed so that the students have an idea as to what type of questions will be beneficial for review. Questions such as 1) How do you determine where to start? 2) How do you decide if the radical is closer to one whole number or the other? 3) Is it possible to have a radical number that is halfway between two whole numbers?

Activity 7: Computing Using Scientific Notation (CCSS:8.EE.3)

Materials List: paper, pencil, Scientific Notation BLM, calculators

Have the students write one hundred twenty-three billion (123,000,000,000). Lead a discussion about how numbers this large become cumbersome and not easy to record accurately. This is why scientific notation is used. This same number can be written as:

1.23 x 1011

The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10.

The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 1011, the number 11 is referred to as the exponent or power of ten.

To write a number in scientific notation, place the decimal point in the original number so that a number >1 and 1 and ................
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