FREEHOLD BOROUGH PUBLIC SCHOOLS Curriculum …include.pbworks.com/f/...+_Revised+Oct2007_.pdf ·...

FREEHOLD BOROUGH PUBLIC SCHOOLS Curriculum Management System

Mathematics Grade 8

Board Approved: August 2007

Freehold Borough Public Schools Curriculum Management System

Grade 8 Mathematics

• Problem-solving (a specified cluster of the New Jersey Core Curriculum Content Standards) will be embedded throughout the curriculum (year-long) 2

Freehold Borough Board of Education

Mr. James Keelan, President Mr. Ron Reich, Vice President

Mr. Andrew DeFonzo

Mrs. Audry Evans Mr. Frank Gill

Mrs. Annette Jordan

Dr. Eileen McGough Mrs. Victoria Muller

Mr. Adam Reich

District Administration

Mrs. Elizabeth O'Connell, Superintendent

Mrs Veronica Wolf, Business Administrator Ms. Ronnie Dougherty, Director of Curriculum/Language Arts

Supervisor Mrs. Pat Rizzo, Director of Special Programs

Mr. Thomas Tramaglini, Director of Technology and Assessment

Mr. Jermaine Moore, Supervisor of Buildings & Grounds Ms. Janet Morales, Bilingual/ESL Supervisor/Community

Liaison

Curriculum Review Committee

Andrea Berman Heidi Brache Yatta Dukuly

Annette Gianatiempo Julieth Hoayeck Mary Ann Illes

Kim Lombardi Debbie Moore Bob Robinson Karen Soto


Grade 8 Mathematics


Mission

We will inspire the creativity and imagination of all students

and empower them as knowledgeable, skillful, and confident learners who flourish and contribute willingly in a changing world.

Core Beliefs

We believe that:

• All people have inherent worth. • Life-long learning is basic to the survival and advancement of society. • The primary influence on the individual's development is the family in all its forms. • Valuing diversity is essential to individual growth and the advancement of society. • All individuals have strengths and human potential has no known limits. • Democracy thrives when individuals accept responsibility for their choices. • Being trustworthy builds trust. • Creativity and imagination are essential for society to flourish. • A safe environment is essential for the well-being of the individual and for society to flourish


Grade 8 Mathematics


Philosophy

The Freehold Borough Public Schools are committed to inspiring the creativity and imagination of all students and empowering them as

knowledgeable, skillful, and confident learners who flourish and contribute willingly in a changing world. We believe that life-long learning is basic to the survival and advancement of society, as well as the notion that all individuals, especially our students, have strengths and human potential without limits.

The mathematics program at Freehold Intermediate School will embrace our district mission by providing a challenging yet exciting academic curriculum that fosters learning in all children, regardless of their learning style or ability level. Students in our classrooms will experience meaningful, collaborative lessons that connect content and skill development to attainable, real-life activities. Lessons, which are aligned with the New Jersey Core Curriculum Content Standards (NJCCCS), will target problem solving and critical thinking skills. Further, all students will be encouraged to grow via student-centered lessons, as well as take risks each day.

Goals

• To incorporate hands-on activities as a primary vehicle towards meeting the needs of all learners, regardless of learning style • To understand the process of using differentiated instruction as an approach to teaching content, process, and product; to incorporate

lessons which are differentiated in content, process and product to maximize student performance • To use technology as an integral tool for enhancing learning experiences in the classroom • To develop students’ fundamental math skills which are to be used to solve mathematical concepts in the math classroom, as well as outside

of the classroom. • To use authentic lessons and instructional strategies that connect content and activities to real life experiences • Establish successful endeavors which build student confidence and encouragement in math


Grade 8 Mathematics


New Jersey Cure Curriculum Content Standards

4.1. Number and Numerical Operations

A. Number Sense

B. Numerical Operations

C. Estimation

4.2. Geometry and Measurement

A. Geometric Properties

B. Transforming Shapes

C. Coordinate Geometry

D. Units of Measurement

E. Measuring Geometric Objects

4.3. Patterns and Algebra

A. Patterns and Relationships

B. Functions

C. Modeling

D. Procedures

4.4. Data Analysis, Probability, and Discrete Mathematics

A. Data Analysis (Statistics)

B. Probability

C. Discrete Mathematics--Systematic Listing and Counting

D. Discrete Mathematics--Vertex-Edge Graphs and Algorithms

4.5. Mathematical Processes

A. Problem Solving

B. Communication

C. Connections

D. Reasoning

E. Representations

F. Technology


Grade 8 Mathematics


Scope and Sequence

I. Number Sense and Operations a. exponents b. square & cube roots c. Order of Operations d. Scientific Notation e. Patterns f. Number Classifications (rational irrational) g. Estimation (Roots)

II. Ratios, Proportions, Percents

a. Simplifying Ratios & Rates b. Using Ratios, Rates, & Proportions to solve word problems c. Similar Figures & Scale Drawings d. Conversions Fraction-Decimal-Percent (Including Repeating Decimals) e. Ordering & Graphing Fractions, Decimals, & Percents on the number line f. Solving Percent Word Problems, percent of increase and decrease g. Estimating Percents

III. Data Analysis, Probability, & Discrete Math

a. Data Analysis i. Mean, Median, Mode ii. Making Inferences from data iii. Box-and-Whisker Plots iv. Scatterplots, Lines of best fit, interpolation v. Draw conclusions from gathered data

b. Probability i. Probability of Compound Events ii. Probability of Conditional Events iii. Experimental vs. Theoretical Probability (Simulations)

c. Discrete Math i. Systematic Listing and Counting Principle ii. Combinations iii. Permutations iv. Venn Diagrams v. Vertex-Edge Graphs & Algorithms

IV. Geometry


Grade 8 Mathematics


a. Concepts involving lines, angles, and planes i. Congruent, complementary, and supplementary angles ii. Angles being formed by parallel lines being cut by a transversal iii. Bisectors and perpendicular bisectors

b. Properties of Polygons i. Triangles ii. Quadrilaterals iii. Regular polygons iv. Interior and exterior angles of polygons

c. Transformations in the Coordinate Plane d. Pythagorean Theorem e. Classifying 3-dimensional objects f. Perimeter, Area, Surface Area, Volume (understanding and applying formulas) g. Converting units of measure

V. Integers a. Absolute Value b. Adding & Subtracting c. Multiplying & Dividing

VI. Pre-Algebra

a. Evaluating Expressions b. Translate verbal models to numeric expressions/equations c. Simplifying Expressions (Distributive Property) d. Solving One-Step Equations & Inequalities e. Solving Multi-Step Equations & Inequalities f. Writing Simple equations from Word Problems g. Graphing Linear Equations h. Recognize & Describe the difference between linear & exponential growth using the graphing calculator

VII. Fractions

a. Equivalent, simplest form (reduce) b. Comparing & Ordering c. Adding & Subtracting d. Multiplying & Dividing


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Freehold Borough Curriculum Management Grade Level/Subject Grade 8 Mathematics

Topic I: Number Sense and Operations

Concept New Jersey Core Curriculum Content Standard/Cumulative

Progress Indicator (CPI)

Specific Learning Objectives/ Essential Questions

The Students Will Be Able

To:

Assessment

Instructional Tools / Materials / Technology / Resources /

Learning Activities / Interdisciplinary Activities /

Assessment Model

1

A. Exponents CPI: 4.1.8A1

• Evaluate exponents and realize that they are a short-cut for repeated multiplication

• Make the connection between exponents and geometry

• Solve exponents with same base, add exponents and keep base the same out of 3 choices

Which of the following is equivalent to the expression below?

(25)(26)

a. 211 b. 230 c. 411 d. 430

• Calculators (and poster) to learn exponent buttons, cube model to relate to geometry

1

B. Square & Cube Roots CPI: 4.1.8A1

• Evaluate Square Roots & Cubed Roots

• Make the connection between roots and geometry

• Write and evaluate square and cubed roots

Albert is an interior designer. His client wants him to decorate a square room that has an area of 484 square feet. What is the length of each side of the room? The volume of a cube is 125 in3. Find the length of each edge.

• Calculators (and poster) to learn root buttons, cube model to relate to geometry

• Use the order of operations and distributive property

• Break down the algebraic expression by highlighting the order of what comes first, next, then last to solve a problem (first-green, next-yellow, last-blue)

Evaluate a) 34 b) 3 216

• Color code order (first, next, last)


Grade 8 Mathematics


1

C. Order of Operations CPI:4.1.8B5

• Understand & apply the standard algebraic order of operations, including appropriate use of grouping symbols

( )[ ] 2102242 −+÷+ 20 + 4 – 3 x 4 2

• Use the PEMDAS mnemonic device • List the order in what

comes first (Now-Next) formulas

• Color coded paper clips • Calculators, colored chips • Rules of order of

operations 1. ( ) 2. x 3. ÷ 4. + 5. –

4

D. Scientific Notation CPI: 4.1.8A1,4

• Use scientific notation to represent very large or very small numbers

• Discuss scientific uses for it • Compare & order numbers

in scientific notation • Calculate using scientific

notation on calculators • Write numbers in both

scientific notation and standard form

The average distance from the Earth to the sun is 9.296 X 107 miles. The distance written in standard form is?

A. 92,960 B. 9.296,000 C. 92,960,000 D. 92,960,000,000

Mr. Loya stated that the circumference of Earth at the equator is 24,902.4 miles. Which expression represents this number in scientific notation?

a. 2.49024 X 104 b. 24.9024 X 104 c. 249.024 X 104 d. 2.49024 X 104

• Use of real-life planetary data such as distances planets are from the sun, their surface area and/or mass, video clip from website

• www.studyisland.com • Calculators • Powers of 10 table


Grade 8 Mathematics


3

E. Patterns CPI:4.3.8A1

• Recognize, describe, extend, and create patterns

• Identify and describe patterns to match predictions

• Use variables of the descriptions to extend patterns beyond the numbers in the tables

Jian made some designs using equilateral triangles, as shown below. He noticed that as he added new triangles, there was a relationship between n, the number of triangles, and p, the outer perimeter of the design.

The table below lists the outer perimeters for the designs shown.

Number of

Triangles 1 2 3 4 … n

Outer Perimeter (in units)

3 4 5 6 … p

a. If the pattern is continued, what would be the outer perimeter of a design using 10 triangles? b. Write a rule for finding p, the outer perimeter for a design that uses n triangles.

• Fibonacci rabbit problem • Groundworks Algebra

Puzzles & Problems (G - 7) – Make a Table, Keep Building

• Tables • Rulers • Graph Paper


Grade 8 Mathematics


• Bo rides in the May bike marathon. To

train for the event, he rides 4 miles the first day, 8 miles the second day, and 12 miles the third day. If he continues this pattern, how many miles will Bo have ridden in all by the end of the fourth day?

5

F. Number Classifications (rational irrational)

CPI: 4.1.8A1,4,5,6,7

• Identify and distinguish between rational & irrational numbers

• Convert from decimal to fractions and vice versa (including repeating decimals)

• Classify numbers as whole, integers, rational, irrational, prime, composite, etc.

• Compare & order rational & irrational numbers

• Construct meanings for common irrational numbers such as pi

Which of the following is not a rational number?

A. -3 B. 4

C. 6

D. 253

• Students hold number cards and put themselves in order and classify themselves as different types of real numbers, measure the circumference and diameter of a circle to calculate pi (measure different size circles with string, measure on Geometer’s Sketchpad as a demonstration or check of activity

• Passport to Algebra – Geometry text

4

G. Estimation (Roots) CPI: 4.1.8C

- Estimate square & cubed roots of numbers

70 is between which two whole numbers?

A. 5 and 6 B. 6 and 7 C. 7 and 8 D. 8 and 9

• www.studyisland.com • Calculators • Manipulatives • Grid paper • www.aaamath.com • Tiles • www.PHSSchool.com


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Topic (s) II: Ratios, Proportions, Percents




The Students Will Be Able To:

Assessment



Assessment Model

1

A. Simplifying Ratios & Rates

CPI: 4.1.8A3

• Understand and use ratios & rates

• Simplify ratios & rates • Relate ratios & rates to real life

Write the quotient as a ratio in simplest form

s300min2

Find the unit rate if a student earns $33 for four hours of work.

• Bring in examples of ratios and/or rates used in everyday life (i.e. adds from grocery stores, labels cut off of food packages, record local gasoline prices)

3

B. Using Ratios, Rates, & Proportions to solve word problems

CPI: 4.1.8A3

• Use proportions to solve a variety of word problems

• Find unit rates and unit costs using proportional reasoning including word problems

Sharon played an electronic game. There were 15 questions, of which she answered 3 incorrectly. At this rate, how many questions should Sharon expect to answer incorrectly if she answers a total of 135 questions? a. 45 b. 27 c. 9 d. 5

• Students write word problems based on their data from above

• Groundworks Algebra Puzzles & Problems (G - 7)– This and That

• Passport to Algebra – Geometry practice pg. 20

• www.studyisland.com • www.aaamath.com


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C. Similar Figures & Scale Drawings

CPI: 4.1A3,B4,4.2.8A4

• Understand & apply the concept of similarity

• Use proportions to find the missing measures of similar figures

• Construct scale drawings • Use real-life objects (flagpole or

tree) and its corresponding shadow to determine height

A flagpole is casting a shadow of 15 ft. You are 5 ft tall and cast a 3 ft. shadow. What is the height of the flagpole? The picture below is Larry’s favorite picture.

Larry had a reduced copy of the picture made as a gift for his father. If the reduced picture was similar to the original and the height of the reduced picture was 7 inches, what was its width?

a. 13 in. b. 5.60 in. c. 8.75 in. d. 10 in.

In the diagram below, ABCΔ and

• In small groups, students measure the classroom and construct scale drawings of it.

• Measuring tools • Real-life objects • Indirect measure • Students construct similar

triangles • Grid paper


Grade 8 Mathematics


DEFΔ are similar triangles with the dimensions below, in units.

What is the length, in units, of EF

3

D. Conversions Fraction-Decimal-Percent(Including Repeating Decimals)

CPI:4.1.8A5,6

• Convert from fractions to decimals to percents and vice versa (including repeating decimals)

Convert 2/3 into a decimal and a percent.

• Calculators (and poster) to learn fraction to decimal & decimal to fraction button

• D2P Rule: Decimals to percents

3

E. Ordering & Graphing Fractions, Decimals,& Percents on the number line

CPI: 4.1A1,3,4,5

• Use whole numbers, fractions, decimals, and percents to represent equivalent forms of the same number (Include %’s greater than 100 and less than 1 as well as %’s with decimals & fractions in them

• Order & graph fractions, decimals, & percents on the number line

Write 4/9, 45%, .445, 7/18, and .045 in ascending order. Explain how you compared the numbers.

• Calculators (and poster) to learn fraction to decimal & decimal to fraction button Students hold number cards and put themselves in order and classify themselves as different types of real numbers.

• Number line


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F. Solving Percent Word Problems, percent of increase and decrease

CPI: 4.1.8B4

• Solve real-life problems involving percents (including percent increase & decrease and consecutive discounts

• Use the information in a table to create a circle graph

You paid $36.96, which is 80% of the full price for a new computer software game. What is the full price? In 1990, the total population of the United States was 250 million people. Nine million people were Native Americans. What percent is this? Origin of Foreign Students in U.S. College

Of the 500,000 foreign students who attended college in the U.S., how many were from Europe OR Asia?

a. 330,000 b. 270,000 c. 210,000 d. 60,000

• Analyze and construct circle graphs

• Tables • www.studyisland.com

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G. Estimating Percents CPI: 4.1.8C2

• Use equivalent representations of numbers such as fractions, decimals, and percents to facilitate estimation

You are shopping at the store and do not have a calculator on you. Your purchases total $63.45. The cashier tells you that if you open a charge card you will get 23% off. You want to estimate how much off that will be to see if you want to open the card. Which of the following is the closest

• Students convert percents to easy-to-work-with fractions in order to estimate a percent of a number

• Red, blue, white fraction chips, markers

• Fraction-decimal equivalence models


Grade 8 Mathematics


estimate that can easily be done using mental math?

a. 20% of 60 b. 20% of 70 c. 25% of 64 d. 25% of 65


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Topic (s) III: Data Analysis, Probability, & Discrete Math





Assessment



Assessment Model 2

1 4

A. Data Analysis 1. Mean, Median, Mode

CPI:4.4.8A1

2. Box-and-Whisker Plots CPI:4.4.8A1

3. Scatter plots, Lines of best fit, interpolation, and make inferences from data

CPI:4.4.8A1,2,3

• Calculate mean, median, mode

• Determine new data needed to raise the mean to a new predetermined mean

• Decide which measure of central tendency best fits a set of data

-Organize data with a box-and-whisker plot -Interpret real-life data from a box-and whisker plot -Construct a scatter plot -Recognize positive, negative or no correlation -Estimate lines of best fit -Interpolate & Extrapolate to estimate points not given

The number of patients treated at Dr. Merrell’s dentist office each day was recorded for 8 days.

• Find the mean, median, and mode of the data.

17,12,11,18, 12,11,17,18, 11, 19

Ms. Alison drew this box-and-whisker plot to represent her students’ scores on a mid-term assessment.

If Julie earned a 68 on the test, what percent of the students scored above her? Use the data below showing the age of a tree (in years) and its diameter (in inches). (5, 1), (8, 2), (10, 3), (16, 5), (25, 5), (30, 6), (35, 7), (40, 8)

• Students measure each other’s heights, find the mean, median, and mode, and determine which best describes their heights

-Students measure forearm length and foot length and plot them on a scatter plot; determine if there is a correlation


Grade 8 Mathematics


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4. Draw conclusions from gathered data

CPI:4.4.8A4

-Conduct a survey -Construct a double-bar graph, pictograph, circle graph and computer graphs based on surveyed data

a. Draw a scatter plot that relates the age of the tree with its diameter (on graph paper). b. Does the scatter plot show a positive correlation, a negative correlation, or no correlation? c. Based on the scatter plot, about how large would you expect the diameter of a 50-year old tree to be?

Graph survey project

4 3 4

B. Probability

1. Experimental vs. Theoretical Probability (Simulations)

CPI: 4.4.8B1,4,5

2. Probability of Compound Events

CPI: 4.48B1,2,4

3. Probability of Conditional Events

CPI:4.48B1,2,3

• Compare & contrast theoretical probability, odds, and experimental probability

• Interpret probabilities as ratios, percents, and decimals

• Estimate probabilities & make predictions based on experimental & theoretical probabilities

• Discover compound probability

by playing & analyzing probability-based games

• Discuss the concepts of fairness and expected value

• Understand how compound probability is calculated by making systematic lists and identifying winning possibilities

• Explore the probabilities of

conditional events • Determine how probability is

effected depending on whether the first item is replaced or not

• A pin is dropped onto the rectangle below. If the point of the pin lands in one of the small square regions, what is the probability that the point lands inside a shaded region.

• A coin is tossed 50 times. Tails

comes up 28 times. What is the experimental probability tossing tails?

• A coin is tossed and a die is rolled.

What is the probability that the coin shows heads and the die shows a one?

You have 2 blue marbles, 4 green marbles, and 6 pink marbles. If you pick a marble and do not replace it, what is the probability of picking a green and then a pink?

• Penny toss for comparing theoretical & experimental, cup toss for experimental and making predictions

Fair Dice games: Assigning #’s for single die, assigning #’s for 2 dice, placing pennies on #’s that they think will come up. Clear jar with different colored unifix cubes for demonstration & understanding


Grade 8 Mathematics


2 4 2 5

C. Discrete Math 1. Systematic Listing and

Counting Principle CPI:4.48C3

2. Combinations & Permutations

CPI:4.4.8C1,3

3. Venn Diagrams CPI:4.4.8C2

4. Vertex – Edge Graphs & Algorithms

CPI:4.4.8D1

• Make systematic lists & construct tree diagrams to do menu-type problems

• Apply the multiplication counting principle

-Distinguish between combinations & permutations -Use factorial notation to calculate combinations & permutations -Discover & use Pascal’s triangle to solve combination problems -Explore counting problems involving Venn Diagrams with 2 and 3 attributes -Use Vertex-edged graphs & algorithmic thinking to represent and find solutions to practical problems -Connect Vertex-edged graphs, combination factorials, and Pascal’s Triangle

Yumi Yogurt offers sundaes made from a choice of four different flavors of yogurt, a choice of three different toppings and a choice of a small, medium, or large cup. How many different yogurt sundaes are possible? There are 10 batters on a softball team. How many ways can the coach pick the first 4 batters? Midtown Music Store has 20 different CDs on a sale table. These CDs are priced 3 for $30. How many combinations of 3 CDs can be purchased? There are 30 people in the band and 15 in chorus. Of these 5 are in both. a. Make a Venn Diagram. b. How many students are only in band? c. How many are only in chorus? d. If the band and chorus go on a trip together, how many students will be going? Five classmates greet each other with a handshake so that each person shakes

• Open-ended menu problems and samples of student responses to score using a rubric

• Tower problem with unifix

cubes to practice systematic listings and to discover Pascal’s triangle, Calculator (and Poster) and GEPA reference sheet to introduce and use new formulas, Problems from NJDOE website

• Student Survey to construct Venn Diagram, Select problems that will also review number sets

-Handshake problem, Problems from NJDOE website • www.studyisland.com • www.aaamath.com


Grade 8 Mathematics


the hand of every other person once and only once. Graph the network of handshakes using the vertices of the graph to represent each person, and the edges to represent the handshakes. How many distinct handshakes were made?


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Topic (s) IV: Geometry





Assessment



Assessment Model

7

A. Concepts involving lines; angles; planes

-Congruent, complementary & supplementary angles -Parallel, skew, intersecting, and perpendicular lines -Angles formed by parallel lines being cut by a transversal -Bisectors & perpendicular bisectors CPI: 4.2.8A1

• Understand & apply concepts involving lines, angles, and planes

• Determine angle measures of angles formed by parallel lines cut by a transversal given one angle

• Compare & Contrast parallel, skew, intersecting, and perpendicular lines

• Construct bisectors & perpendicular bisectors

What is the measure of ∠ X in the diagram below?

A. 45° B. 55° C. 125° D. 180°

In the diagram below, the lines are parallel.

What is the relationship between ∠ 1 and ∠ 2?

• Protractors, Geometer’s Sketchpad and packet on parallel lines, straight edge & protractor and/or Geometer’s Sketchpad to construct bisectors

• Lines on internet website


Grade 8 Mathematics


a. complementary b. corresponding c. supplementary d. vertical

9

B. Properties of polygons -Triangles -Quadrilaterals -Regular Polygons -Interior & exterior angles of polygons CPI: 4.2.8.A3

-Use logic & reasoning to make and support conjectures about polygons -Classify Triangles by angles & by sides -Classify Quadrilaterals including trapezoids, kites, parallelograms, rectangles, rhombi, and squares -Calculate the sum of the measures of interior angles of a polygon and each interior & exterior angle measurement of a regular polygon -Determine which polygons can be used alone to generate a tessellation

In ABCΔ , a median is drawn from point A

to point D. AD is ______

A. the bisector of BC B. The angle bisector of A C. Perpendicular to BC D. All of the above

I am a quadrilateral with opposite side’s parallel – who could I be?

A. Square B. Rectangle C. Rhombus D. All of the above

• Classify triangle MNO as equilateral, isosceles or scalene

• Polygon Packet, Geometer’s Sketchpad and Quadrilateral activity packet, Book – A Cloak for the Dreamer (for understanding tessellations)


Grade 8 Mathematics


Use the following formula to calculate the measure of each interior angle of a regular pentagon. (n – 2)(180)

n

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C. Transformations in the coordinate plane

CPI: 4.2B1

• Translate figures in the coordinate plane

• Reflect figures in the coordinate plane

• Determine lines of symmetry • Rotate figures in the

coordinate plane • Determine Rotational & Point

Symmetry • Dilate figures in the

coordinate plane

PRYΔ is reflected across the y-axis. Which of the following shows this transformation?

• Students perform transformations on graph paper, using folding for reflections, use overhead transparencies to develop pattern for rotations,

• Transparencies • Geoboards • Geobands • Internet website • Online Geometer’s Sketchpad • Grid map


Grade 8 Mathematics


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D. Classifying 3-dimensional objects

CPI: 4.2.8A7

-Classify polyhedrons as prisms or pyramids and name them according to their bases -Create 2-dimensional representations such as nets, projective views, and cross sections •

Melody made a solid figure by stacking cubes. The solid figure is shown below.

Which drawing best represents a front view of this solid?

3-dimensional solid figures, unifix cubes for demonstration • Unifix cubes • Pattern worksheets • Pattern blocks • Graph paper • Geosolids •


Grade 8 Mathematics


10

E. Perimeter, area, surface area, volume (understanding and applying formulas)

CPI: 4.2.8E1,2,3,4, 4.3.8B2,C1

-Calculate perimeter & area of irregular figures -Develop & apply strategies and formulas for finding the surface area of prisms & pyramids -Develop & apply strategies and formulas for finding the surface area of cylinders -Develop & apply strategies and formulas for finding the volume of prisms & cylinders -Recognize that the volume of a pyramid or cone is one-third of the volume of the prism or cylinder with the same base and height -Develop & apply strategies & formulas for finding the volume of pyramids & cones -Use formulas to find the volume and surface area of a sphere -Analyze functional relationships to explain how a change in one quantity (side length) can result

Mrs. Diaz told her math class that a particular rectangle has a perimeter of 36 units and an area of 65 square units. Which of the following could be the dimensions of the rectangle?

b. 2.5 units by 26 units c. 4 units by 9 units d. 5 units by 13 units e. 6.5 units by 11.5 units

Deb has a rectangular storage box with a height of 18 inches, as shown below.

-3-dimensional solids, cereal or shoe box & ruler to demonstrate volume & surface area of a rectangular prism, can with label to demonstrate how to find surface area of a cylinder, 3-dimensional plastic figures to pour water or rice into in order to compare volumes of prisms & cylinders to pyramids & cones, graphing calculators, view screen with overhead and poster, dimensions worksheet • Formulas for:

i. Area ii. Perimeter iii. Surface area iv. Volume

• Geoboards • Geobands • Grid paper • Make sure to distribute


Grade 8 Mathematics


in a change in another (perimeter, area, volume) using equations, charts, & graphs -Recognize and describe the difference between linear and exponential growth by determining how the change in one dimension affects perimeter, area, surface area, and volume (*Needs to be done before the GEPA and revisited more thoroughly later) • Create quadrilaterals • Square, rectangle, rhombus

using Geoboards

If Deb cuts off a 2-inch strip around the top of the box, what will be the new volume of the box in cubic inches?

a. 1,600 in.3 b. 1,440 in.3 c. 1,024 in.3 d. 1,800 in.3

Mary wants to cover the bottom and outside of a can with material to make a pencil holder. She needs to know the area of the outside of the can shown below.

Calculate the surface area, in square

mathematics reference sheet for quarterly assessments


Grade 8 Mathematics


centimeters, of the outside of Mary’s pencil holder. Round your answer to the nearest tenths.

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F. Converting units of measure

• CPI: 4.2.8.D1,2

• Calculating with units of measurement within a measurement system

• Calculating between standard & metric using approximate equivalents

Tracy’s dog eats 8 ounces of dog food every day. How many pounds of dog food will her dog eat in 40 days? Show your work. Answer _______ pounds

• Bring in examples of measurements such as meter stick & yard stick, liter of soda & gallon of milk, etc.

• Conversions reference sheet • www.studyisland.com


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Topic (s) V: Integers

Concept New Jersey Core

Curriculum Content Standard/Cumulative


Specific Learning Objectives/

Essential Questions


Assessment Instructional Tools / Materials / Technology /

Resources / Learning Activities / Interdisciplinary Activities / Assessment Model

1

A. Absolute Value CPI: 4.1B1,4.3D1

• Calculate absolute value and understand its meaning

• Compare and order integers to find absolute values

Find the value of each expression. - 8− - 4 =

Compare 6− and 2− using <, =, >

• Compare distances of opposites on number line to develop meaning for absolute value

• Number line

2

B. Adding and subtracting

CPI: 4.1A1,B1

• Add & Subtract integers using addition & subtraction rules and by using logic (money)

• Write & solve addition and subtraction problems from real-life word problems involving integers

• Add and subtract integers to solve problems using a number line

The Chess Club at Mason Middle School is holding a tournament in which each player earns +1 point for a win, -1 point for a loss, and 0 for a draw. The scoreboard below shows the final standings of five players. Player Wins Losses

Neva 6 0 Kaitlin 4 2 Antoine 2 4 Trenna 3 3 Sarah 0 6

a. Determine each player’s total points

• Colored counters or unifix cubes, flash cards, www.mathgoodies.com/lessons/vol5/challenge_vol5.html

• Number line • Colored chips • Highlighters to illustrate negative and positive

movement • www.studyisland.com


Grade 8 Mathematics


b. Graph the total scores on a number line. Let the first letter of each player’s name be the letter for each coordinate. In 1997, NASA established websites to allow the public to follow the Pathfinder Mission to Mars. The internal temperature of the Rover fluctuated between 40 degrees C and -22 degrees C. Find the difference between the two temperatures.

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C. Multiplying and dividing

CPI: 4.1A1,B1

• Multiply & Divide integers

• Use multiplication & division to solve integer word problems

Solve x = (-3) (-2) (-5) Evaluate the expression: -32/b, if a = -8, b = 4

• Number line example, Flash cards • Algebra tiles • Rules for multiplying and dividing integers reference

sheet


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Topic (s) VI: Pre-Algebra

Concept New Jersey Core Curriculum

Content Standard/Cumulative


Specific Learning Objectives/

Essential Questions


Assessment

Instructional Tools / Materials / Technology /

Resources / Learning Activities / Interdisciplinary

Activities / Assessment Model

1

A. Evaluating expressions

CPI: 4.3.8D4

• Evaluate expressions that contain variables

• Use Formulas to model and solve word problems

If 2=x and 4=y , what is the value of the following expression?

yx 5−

a. -18 b. -12 c. 12 d. 18

• Use numerical expressions to review various operations and symbols

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B. Translate verbal models to numeric expressions/equations

CPI: 4.3.8D4

• Translate verbal phrases into algebraic expressions & vice versa

• Model real-life situations with algebraic expressions

Write an algebraic expression that represents 5 less than twice a number.

• I HAVE/WHO HAS translation game

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C. Simplifying expressions (distributive property)

CPI: 4.3.8D4

• Use the distributive property to simplify expressions

• Use the distributive property to factor expressions

Which of the following is equivalent to the expression below?

)86(21 x−−

a. x43+− b. x43+ c. x83−−

• Algebra Tiles


Grade 8 Mathematics


d. x83− Simplify the expression below.

baba 22 63 + a. ba 29 b. ba 49 c. ba 218 d. 2418 ba

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D. Solving one-step equations and inequalities

CPI: 4.3.8D2,3,5

• Understand & apply the properties of operations, numbers, equations, and inequalities

• Solve simple equations and inequalities mentally or by guess & check

• Solve simple equations and inequalities by using formal algebraic methods

What is the solution to the equation below?

217=

−y

a. 3−=y b. 3=y c. 147=y d. 147−=y

• Groundworks Algebra Puzzles & Problems (G-7)– Balance It, Place It Right, Unknown Weights, Solve It, Puzzle Grid, Tag Sale

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E. Solving multi-step equations and inequalities

CPI: 4.3.8D2,3,5

• Understand & apply the properties of operations, numbers, equations, and inequalities

• Solve multi-step equations and inequalities by using formal algebraic methods

Solve. 5x + 4 = 19 Which of the following numbers is a solution for the inequality shown below?

49)32(7 >−x a. 10 b. 5 c. 0 d. -6

• Groundworks Algebra Puzzles & Problems (G-7)– Balance It, Place It Right, Unknown Weights, Solve It, Puzzle Grid, Tag Sale


Grade 8 Mathematics


4

F. Writing simple equations from word problems

CPI: 4.3.8C2

- Write & solve simple equations from word problems

Noel is a computer repairman. To fix a computer, he charges a customer $40 per hour, plus a fixed fee of $15 for the service call, as represented by the equation below.

1540 += xy In the equation, what is represented by the variable x? A. The number of hours Noel worked B. The amount Noel charged per hour C. The fixed fee for the service call D. The total cost of the repair job

• Techniques: verbal models, basis of comparison, generalizing a number pattern

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G. Graphing linear equations

CPI: 4.3.8B1,2,D2

-Graph linear equations by using substitution to make an x-y chart -Recognize and describe the difference between linear and exponential growth using the calculator

Make a table of values for the line y = 2x + 8 using x-values of 1,2,3,4 and 5. Graph the line. Graph y = -x+2

• Salary Problem (Would you rather a $100,000 salary for a month’s work, or start with $1000 and increase by $50 a day for a month, or start with a penny and double amount you have each day for a month?)

• Groundworks Algebra Puzzles & Problems (G-7)–Functions & Graphs

• Graph paper • Calculators • Online graphing

calculators • Tables


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Topic #VII: Fractions





Assessment



Assessment Model

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A. Equivalent, simplest form (reduce)

CPI: 4.1.8A5

• Make equivalent fractions • Understand the role the identity

property plays in producing equivalent fractions

• Write fractions in simplest form (lowest terms)

Pedro wanted to find the number of minutes in 5/6 of an hour, so he changed the fraction to an equivalent fraction with a denominator of 60. The numerator is the number of minutes. How many minutes are in 5/6 hour?

• Paper folding mini-activity, Teacher-made fraction circles

• Students make fraction bars from construction paper & tape together to compare & determine equivalent fractions

• Fraction-Decimal Equivalence Model I (PL)

• Model sets of equivalent fractions using fraction strips/bars, then reduce to simplest form

• Fraction strips/bars • Multiplication table

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B. Comparing and Ordering CPI: 4.1.8A4,5

• Compare and Order fractions by making equivalent fractions with common denominators

• Compare & Order fractions by converting to decimals

• Compare & Order fractions using proportions

Barbara and Michelle earn the same salary. Barbara saves 1/6 of her salary, while Michelle saves 1/7 of her salary. Who saves more, Barbara or Michelle?

• Students hold number cards and put themselves in order


• Calculator • www.studyisland.com • Fraction strip/bars


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C. Adding and subtracting CPI: 4.1.8B1

• Add & Subtract fractions with and without the use of manipulatives

Linda studies for 2 3/5 hours in the morning and 1 3/10 hour in the afternoon. How long did she study altogether? Jill spent 3 ¾ hours on her project and Mike spent 2 ½ hours on his project. How much more time did Jill spend on her project?

• Teacher-made fraction circles, Student sets of fraction circles


• Fraction bars • Number line • <, > symbols

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D. Multiplying and dividing CPI: 4.1.8B1

• Multiply & Divide fractions • Multiply and divide fractions

using paper to fold fractional parts

In the last local election in Mike’s town, 200 people voted. 7/8 of the voters were women. How many voters were women? Ricardo is having a party. He says that for every person, he needs 5/6 box of pasta. How many people are coming if Ricardo uses 10 boxes of pasta?

• Teacher-made fraction circles • Fraction bars • Calculator • Paper folding activity

FREEHOLD BOROUGH PUBLIC SCHOOLS Curriculum …include.pbworks.com/f/...+_Revised+Oct2007_.pdf ·...

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