freehold borough public schools curriculum...

FREEHOLD BOROUGH PUBLIC SCHOOLS Curriculum Management System

Mathematics Grade 7

Board Approved: August 2007

Freehold Borough Public Schools Curriculum Management System

Grade 7 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. Audrey 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. Par 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 Committee

Andrea Berman Heidi Brache Yatta Dukuly Annette Gianatiempo Julieth Hoayeck

Mary Ann Illes Kim Lombardi Debbie Moore Bob Robinson Karen Soto

Mission


Grade 7 Mathematics


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 7 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 7 Mathematics


New Jersey Core Curriculum Content Standards for Mathematics

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

Scope and Sequence

I. Fraction operation

a. equivalent, simplest form (reduce) b. addition and subtraction c. multiplication and division

II. Ratios, proportions, rates

a. ratios b. rates c. solving proportion d. writing proportions e. Indirect measures f. scale drawing

III. Percents

a. percent conversions b. percent equations c. large and small percents d. percent of increase and decrease

IV. Probability, data analysis, statistics, graphs

a. data collections b. mean, median, mode c. graphing d. Venn diagrams e. experimental and theoretical probability f. permutations g. combinations

h. Patterns i. recognition j. description (tables, verbal, symbolic rules) k. extensions

V. Plane geometry, spatial geometry (polyhedrons) a. plane geometry, shapes b. coordinate plane, transformations c. solid figures d. formulas (perimeter, area, surface area,

circumference, volume) e. measurement (review)

VI. Integers

a. order and compare on a number line b. addition and subtraction c. multiplication and division d. order of operation

VII. Algebraic Expressions, Simple Equations, inequalities

a. Create, evaluate, and simplify algebraic expressions involving variables

b. one step, equations and inequalities c. 2 step, equations and inequalities d. multi step, equations and inequalities e. functions


Grade 7 Mathematics


Freehold Borough Curriculum Management Grade Level/Subject Grade 7 Mathematics

Topic I: Fraction operation

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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

2

A. Equivalent, simplest form (reduce)

CPI: 4.1.7B1

Compare, order and determine equivalent fractions Use models to represent fractions Write fractions in order using a given denominator then write its equivalent

write in simplest from 56/63 George Washington Carver produced 100 products from sweet potatoes and 325 products from peanuts. Write the number of sweet potato products as a fraction of the number of peanut products in simplest from.

Study island, calculator, fraction bars, circles, blocks Math Marvel Weather Math Project Book Fraction Card Game and/or Fraction Puzzle Booklet Real life career master: Property manager and/or inventory manager www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm

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B. Addition and subtraction CPI: 4.1.7B1

Add and subtract fractions and mixed numbers Apply addition and subtraction of fraction and mixed numbers to practical problems Reduce solution to simplest form

9/10+1/3 -5/8+11/12 Ms. Maple owns a restaurant. Typically 1/5 of the customers order fish, while ¼ of the customer or poultry. What fraction of her customers ordered either fish or poultry?

Study island, calculator, fraction bars, circles, blocks Math Marvel Weather Math project book: Fractional Fairy tale www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm

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C. Multiplication and division CPI: 4.1.7B1

Multiply and divide fractions and mixed numbers Apply multiplication and division knowledge to solve practical problems

4/7*5/8 13 ½ / 7 2/9 If a puppet requires ¾ yards of material, how many puppets can be made from 9 yards of materials? Anna wants to make 4 sets of

Study island, calculator, fraction bars, circles, blocks Math Marvel Weather Real life career master: baker www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics


curtains. Each set requires 5 1/8 yards of fabric. How much fabric does she need?

What is the reciprocal of523 ?

Which is the value of 312

926 ÷

If an eight-inch square cake serves nine people, how many eight-inch square cakes are needed to provide equivalent servings for forty people?


Grade 7 Mathematics



Topic (s)II: Ratios, proportions, and rates

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Curriculum Content Standard/Cumulative



Essential Questions




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A. Ratios CPI: 4.1.7A3

Express ratios as a fraction in lowest terms and write ratios three different ways Decide whether two ratios are equivalent Work in small group to compile a list of how ratios are used in their daily lives

During baseball season, a stadium can seat 1000 people. During football season, the stadium can seat 1500 people. What is the ratio of baseball seating to football season?

Study island, calculator, compare sport records, Math Marvels Transportation of the future Math project book : Ratio of age to height www.aaamath.com http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm http://nlvm.usu.edu/en/nav/vlibrary.html

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B. Rates CPI: 4.1.7A3

Determine and apply unit rate Convert rates into ratios Use rates to solve practical problems Create a table using common unit rates to solve everyday situations

A 10-ounce box of cereal costs $2.98, and a 20- ounce box of the same cereal costs $5.49. Which of these statements will help a shopper decide which box is the better buy? a. The 10-ounce box is the better buy because it is less expensive per ounce of cereal.

b. The 10-ounce box is the better buy because $2.98 is about $3. and $3 goes into $5.49 about 3 times. c. The 20-ounce box is the better buy because it is more expensive

Study island, calculator, use store ads to find unit rate Math Marvels Transportation of the future Math project book: comparing prices and ingredients of cereal Real life career master: Store owner www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics


per ounce of cereal. d. The 20-ounce box is the

better buy because two of the 10-ounce boxes cost more than one 20-ounce box.

What is the rate as a fraction in simplest form 56 to 16? What ratio is NOT equivalent to 8:12?

a. 2:3 b. 16:24 c. 12:14 d. 4:6

Convert the rate into a ratio.

ftyd

51

ozlb

74

3

C. Solving proportion CPI: 4.1.7A3

Solve proportions to find the missing term Determine if a given pair of ratios forms a proportion Use cross products to solve proportion

Solve the proportion

1. N is to 9 as 10 is to 18 2. 35 is to 25 as z is to 5

m/6=9/54 You are hiring counselors for summer camp. You need 2 counselors for every 15 campers. There are 180 campers. How many counselors are needed?

Study island, calculator, cross country trip Math Marvels Transportation of the future Math Project book: Drawing Proportional figures Real life career master: Photo Developer and/ or builder www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics


4

D. Writing Proportion CPI: 4.1.7A3

Write proportions that represent equivalent relationship between to sets Solve practical problems that involve proportions

The exchange rate for money in Kenya us 52 shilling to $1.00. How many shillings can you get for $5.50 A person who weighs 120 lbs on Earth would weigh only 20lbs on the moon. How much would a person who weighs 150 lbs o Earth weigh on the moon?

Study island, make a model Math Marvels Transportation of the future Math Stories: The Fabulous Rappozis and/or Sylvester James Lee and/or Burger Battle www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm

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E. Indirect measures CPI: 4.2.7A2

Write proportions to express relationship between the length of corresponding sides of similar figures Use proportions to find the missing measure Apply proportional reasoning to enlarge and shrink figures using visual aids and models

XYZΔ is similar to RSTΔ . What

is the length of ST

a. 5 cm b. 7.5 cm c. 9 cm d. 10 cm

Study island, calculator, photo project on pg 304 www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm

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F. Scale drawing CPI: 4.2.7A2

Apply proportions to solve practical problems involving scale drawing Interpret a scale drawing

The scale on a map is ½ inch = 65 miles. How far apart are two cities that are 6 ½ inches apart on the map? Explain your answer and approach.

Study island, calculator, make a class model, read blue prints Math Project book: plan a bike trip, and/or design the perfect classroom Read; Cut down to size at high noon www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics



Grade 7 Mathematics



Topic III: Percents

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Content Standard/Cumulative



Essential Questions




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A. Percent conversions CPI: 4.1.7A5

Represent a number in fraction, decimal and percent form Use percent conversations to solve practical problems

Turn the following items into % .465

503

Study island, calculator, interrupt survey results Math Stories: The Exaggerated news www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm

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B. Percent equations CPI: 4.1.7A3

Use proportions to solve percent equations for practical problems Find the percent of a number Find the base of a percent Find the missing number in a percent equations

Bradley answered 80% of the questions on his science test correctly. There were 30 questions on the test, and all of the questions had equal value. How many questions did Bradley NOT answer correctly on his test?

a. 6 b. 18 c. 24 d. 20

Of the 850 students at Brown Middle School, 38% are in the school band. How many students are in the school band?

Study island, calculator, use store ads to create equations Math project book: Budgeting www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics


a. 32 b. 527 c. 323 d. 812

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C. Large and small percents CPI: 4.1.7A3

Model large and small percents Solve practical problems involving large and small percents

Write the percent as a decimal & fraction. 170% .875%

Study island, calculator, growth project pg 339 www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm

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D. Percent of increase and decrease

CPI: 4.1.7A3

Determine the percent of increase/decrease for practical problem Calculate the percents of increase/decrease

A store’s profit went from $278,350 in 1999 to $247,500 in 2000. To the nearest percent, what was the store’s percent of decrease in profit from 1999 to 2000 a. 11% b. 12% C. 13% d. 24%

Study island, calculator, use store ads to determine the increase for decrease Real life career master: Securities researcher www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics



Topic IV: Probability, data analysis, statistics, graphs

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Specific Learning Objectives/ Essential Questions


Assessment

Instructional Tools / Materials /

Technology / Resources /

Learning Activities / Interdisciplinary

Activities / Assessment Model

10

A. Data collections CPI: 4.4.7A1

Collect, analyze, display and interprets data The table shows several countries and the portion of their population that is under age 15.

Country Portion of Population

Under Age 15 Chad 47.8%

United States

51

Uganda

21

Benin

5023

Ethiopia 47.3%

Which of the following lists the countries in order from least to greatest portion of the population under age 15?

a. United States, Ethiopia, Benin, Chad, Uganda

Study island, create and conduct a survey Math project book: Collecting data and/or comparing grass growth vs. price and/or producing a math survey www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics


b. Uganda, United States, Benin, Ethiopia, Chad

c. United States, Benin, Ethiopia, Chad, Uganda

d. Uganda, Chad, Ethiopia, Benin, United States

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B. Mean, median, mode CPI: 4.4.7A1

Describe the three measures of central tendency ( mean, median, mode)and situations in which each would best represent the data Identify the mean, median, and mode in a set of data Find one measure of central tendency at a time using practice problems requiring median, mean and mode

Find the mean of the data 36,23,19,16,14,30,22,38 Find the median of the data 6,29,32,5,42,0,27,19,30 Find the mode of the data 12,18,14,15,18,14,12,15,14,13 Luis watches TV everyday. He watches 30 minutes on Monday and Tuesday, 90 minutes on Wednesday and Thursday, and 45 minutes on Friday and Saturday.

The average amount of time that Luis watches TV every day is 50 minutes.

Study island, calculator, nature project pg 223 Real life career master: Clinical Research Statistician Real life career master: Restaurant manger www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics


How much time does Luis watch TV on Sunday?

a. 20 minutes b. 30 minutes c. 45 minutes d. 50 minutes

The following data represent morning temperatures for the month of July in Washington, D.C. What are the mean and median of the data?

July Temperatures (°F) Sun Mon Tue Wed Thu. Fri Sat 89 87 85 88 93 93 93 89 90 91 90 89 88 89 87 90 91 92 92 92 90 89 87 85 86 84 84 83 85 86 88

A. mean 84.3, median 91 B. mean 82.9, median 90 C. mean 88.5, median 89 D. mean 83.9, median 88

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C. Graphing CPI: 4.4.7A1

Select, create and use appropriate graphical representation if data

A pet storeowner surveys 20 customers to determine what types of pets they own. The survey results are shown in the table below.

Study island, create graph based on your survey Math project book: analyzing graphs Read: Tiger math www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics


Which circle graph represents the data in the table?

a b.

c. d. The pictograph below records Vista Sunglasses sales for 2004.


Grade 7 Mathematics


Which color of lens had sales three times greater than one of the other color lens?

a. brown b. yellow c. green d. gray

If the circle graph represents the city of Metropolis, which has 42,000 homes, how many homes are NOT heated by natural gas? How We Heat Our Homes

5

D. Venn Diagrams CPI: 4.4.7C2

Use Venn diagrams to represent sets of data Use Venn diagrams to solve practical problems Conduct a survey in class and using the collected data to make the Venn diagram

Seven girls in Ms. Bauman’s class participate in at least one school activity. Mary and Shelly play basketball only; Shawna and Layla sing only; and Trina, Stephanie, and Kim play basketball and sing. Which Venn diagram correctly represents the data?

Study island, calculator, create a pet survey and use the data to create the Venn diagram www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.


Grade 7 Mathematics


a.

b.

c.

d.

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E. Experimental and theoretical probability

CPI: 4.4.7B3

Determine theoretical/experimental probability of an event Demonstrate probability by using manipulative Predict the results of a simulation

How many times is the spinner likely to land on a space for 2 in 20 spins?

Study island, calculator, spinners, dice, cards, coins, marbles Math project book: Probability and predictions


Grade 7 Mathematics


A. 2 times B. 5 times C. 10 times D. 40 times

A spinner is divided into five equal sections numbered 1 through 5. Predict how many times out of 240 spins the spinner is most likely to stop on an odd number.

a. 80 b. 96 c. 144 d. 192

www.aaamath.com Real life career master: Actuary http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm

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F. Permutations CPI: 4.4.7C1

Find the number of permutations of n objects Use permutation to solve probability Use calculators to find factorials

April, Brittany, Christina, and Dawn are competing in a race. If there are no ties, in how many different ways can they finish the race?

a. 6 b. 12 c. 24 d. 36

Study island, calculator, determine the possible batting order for your favorite base ball team Math Stories: Sha Ling and the Three Wishes and/or Crystal bean pot lottery www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7


Grade 7 Mathematics


math.htm

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G. Combinations CPI: 4.4.7C3

List and count the number of combinations Use combinations to solve probability problems Express probability as a fraction, decimal and/or percent

Mrs. Sheldon made lunch for her family. She made tuna sandwiches and chicken sandwiches. She made coconut cookies and oatmeal cookies. Which list shows all possible outcomes if a person picked one sandwich at random and one cookie at random?

A. (Tuna,coconut),(chicken,oatmeal)

B. (Tuna,coconut)(chicken, coconut),(tuna,oatmeal),(chicken ,oatmeal)

C. (Tuna,chicken),(tuna,coconut),(tuna,oatmeal),(chicken, tuna),chicken, coconut),(chicken,oatmeal)

D. (Tuna,oatmeal,(chicken,oatmeal),(tuna,chicken,(coconut,oatmeal)

Study island, calculator, activity on pg 539 www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm

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H. Patterns CPI: 4.3.7A1

Analyze situations to discover a variety of patterns Analyze numeric and geometric sequences to discover a variety of patterns

What number is missing? 56,44,34,26,_____,16, 14

A. 18 B. 20 C. 22 D. 24

Study island, have students create their own, explore the Fibonacci sequence in nature, tessellations www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.


Grade 7 Mathematics


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I. Recognition CPI: 4.3.7A1

Recognize and explain numerical and geometric patterns What is the rule for this numerical pattern?

1, 4, 16, 64, 256

A. Add 4 to the previous term. B. Multiply the previous term by 4. C. Add the two previous terms

together. D. Multiply the two previous terms

together.

Study island, origami www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm

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J. Description (tables, verbal, symbolic rules)

CPI: 4.3.7C1

Represent a variety of patterns using tables, words, and rules

Which rule can be used to find the value of any term in the sequence below where n represents the position of the term?

Position Value of Term

1 6 2 10 3 14 4 18 5 22 n

a. 42 +n b. 24 +n c. 33 +n d. 28 +n

Study island, calculator, determine the winner in sports series that requires limitation www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics


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K. Extensions CPI: 4.3.7A1

Apply functions rules and geometric patterns to extend a given pattern

What is the next number in this pattern: 18.5, 18.3, 18.1, 17.9,…?

a. 17.7 b. 17.5 c. 17.3 d. 17.1

Study island, calculator, pattern blocks, number cubes, tessellations www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics



Topic V: Plane Geometry, spatial geometry (polyhedrons)

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Essential Questions




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A. Plane geometry CPI: 4.2.7A1

Identify and name points, segments, rays, planes, parallel lines, perpendicular lines and polygons Identify acute, right, obtuse, complementary and supplementary angles Classify types of triangles and polygons according to their properties

A triangle with two congruent sides and an angle of 104° is-

a. isosceles and right b. isosceles and obtuse c. isosceles and acute d. scalene and obtuse

Study island, map reading, tile design project Math project book: Geometry dictionary and/ or Who am I? Read: A cloak for the dreamer www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html

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B. Coordinate plane, transformations

CPI: 4.2.7C2

Identify and label the axes and quadrants Identify the quadrant I which a point is positioned by examining the ordered pair Graph ordered pairs Identify the coordinates of an image that has been translated, rotated and/or reflected Sketch the image of a figure

Which of the following best represents the coordinates of the vertices of KLMΔ ?

Study island, play chess or checkers, make a pin wheel Math project book: Coordinate puzzle and/or Dancing geometric shapes Math Stories: The dog finder Real life career master: Computer game artist and/or animator Read: The fly on the ceiling a math myth www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics


that has been translated, rotated, and/or reflected Identify quadrants on maps to find location on towns, streets etc.

a. (-2,5), (1,1), -3, 1) b. (-2,5), (1,1), (1, -3) c. (5, -2), (1,1), (1, -3) d. (5, -2), (1,1), (-3, 1)

If the letter N is reflected over the y-axis, which of the following represents the image?

a. b.

c. d.


Grade 7 Mathematics


Triangle LMN is shifted 3 right and 3 down. The new vertex M’, is in which quadrant?

a. I b. II c. III d. IV

2

C. Solid figures CPI: 4.2.7A2

Identify the attributes of solid figures including edges, vertices and faces Construct a simple three dimensional design given the top, side and front view Write the dimensions of each design then determine the area of each of its surfaces

Arrange the three solid shapes in order of the number of vertices they contain, from LEAST to GREATEST.

e. pyramid, cube,

prism f. cube, prism,

pyramid g. pyramid, prism,

cube h. prism, pyramid,

cube

Study island, wooden solid figures, nets, find solid in your neighborhood www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics


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D. Formulas (perimeter, area, surface area, circumference, volume)

CPI: 4.2.7E1

Analyze a situation and determine which formula will best solve the practical problem Use formula to solve a practical problem

Sally’s swimming pool is 12 feet long, 8 feet wide, and 6 feet deep. She will fill it to the top. How much water will be in the pool?

a. 576 square feet b. 576 cubic feet c. 576 yards d. 576 square yards

What is the area of the rectangle drawn on the coordinate plane shown below?

a. 21 square units b. 24 square units c. 28 square units d. 32 square units Marilou needs to cut a piece of glass for her table. The table is in the shape of a regular hexagon. The glass should measure 1 ½ feet on each side. What is the perimeter of the piece of glass?

F. 12 ft G. 9 ft H. 18 ft H. 7.5 ft

Study island, calculator, Pi day, Garden project Math project book: Playground Game Design and/or Building a dog area, and/or Geometric rockets and/or Lunch box volume, and/or Making a “finding the shape” house Math Stories: The Circles and/or Lost on nowhere, and/or Ghengis in love Real life career master: interior designer and/or property developer Read: Sir cumference series www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics


What was the area in square feet that was sprayed?

t

A. 19,280 ft B. 20,000 ft C. 37,680 ft D. 17,680 ft

Peter wants to find the perimeter of the isosceles trapezoid shown below.

Which equation could Peter use to find P, the perimeter of the trapezoid? a. 5148 +⋅=P b. )52(148 ⋅++=P c. 24)148( ÷⋅+=P d. 41458 +++=P


Grade 7 Mathematics


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E. Measurement (review) CPI: 4.2.7D1

Determine the appropriate metric/customary units of length, weight, and liquid measures Make conversions with in the metric/customary units Use metric/customary measurement in applications to solve practical situations

How many pounds is 24 ounces?

1 pound = 16 ounces

i. 1 j. 1.5 k. 2 l. 2.5

Study island, calculator, rulers, scales, measuring cups and other common object found in a home Math project book: Conduct a metric Olympics www.aaamath.com http://nlvm.usu.edu/en/nav/vlibrary.html http://www.blackgold.ab.ca/ict/Divison3/gr7math.htm


Grade 7 Mathematics



Topic VI: Integers

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Essential Questions




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A. Order and compare on a number line

CPI: 4.1.7A4

Graph integers on a number line Order integers Use inequalities symbols to compare integers Use manipulative, number line and models to order integers

Place these integers on the number line below

212 , -3, 0, 4

<,>,=

2___2− 4___3 −

5___8 Order from least to greatest. 6, 4, -4, -5, -2

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5

B. Addition and subtraction CPI: 4.1.7B1

Formulate rules for adding and subtracting integers Solve practical problems involving addition and subtractions with integers Create a table to assist with rules for adding and

Your sister owes you $5. She pays $3 of it back to you. How much does your sister still owe you? In Death Valley National Park, the highest point is Telescope Park (11,049 ft) and the lowest point is Badwaters (-282 ft). What is the difference in elevation between

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Grade 7 Mathematics


subtracting integers these two points? DeAndre bought 15 party hats priced at 3 for $0.65 and 56 noisemakers priced at 7 for $1.25. What was the total cost of the hats and noisemakers, not including the tax?

a. $9.75 b. $8.75 c. $10.70 d. $13.25

4

C. Multiplication and division CPI: 4.1.7B1

Formulate rules for multiplying and dividing integers Solve practical problems involving multiplication and division Develop and apply strategies like draw and picture, look for patterns, guess and check, make a table, do a simpler problem etc to solve problems

)8(376 −÷

252 ÷

97 −×− (6) x (-74) Which word best completes the sentence? If the product of two integers is negative, then both integers are….

e. even f. odd g. different h. negative

Leon brought a dozen daisies for $3.75. Which is closest to the amount Leon paid for each daisy?

a. $0.25 b. $0.29

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Grade 7 Mathematics


c. $0.31 d. $0.38

Ed is reading the math problem shown below.

2.36.1

Which is a correct way to read this problem?

a. One and six tenths divided by three and two tenths.

b. Three and two tenths divided by one and six tenths

c. Three and two hundredths divided by one and six hundredths

d. One and six hundredths divided by three and two hundredths

On Friday, Extreme View Helicopter Tours flew 34 times. They flew the same number of times on Saturday as they did on Sunday. The total number of times they flew for the three days was 118. How many times did Extreme View Helicopter Tours fly on Saturday?

a. 34 b. 42


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c. 59 d. 84

The 8th grade party committee has decided to give an equal number of pieces of candy to each participant. There are 256 pieces to give away, which of these could not be the number of pieces of candy given away to each person under this plan?

a. 128 b. 36 c. 16 d. 8

5

D. Order of operations CPI: 4.1.7B3

Simplify expressions by using order of operation in a demonstrated step by step approach Find the value of numerical expressions Highlight parts of an expression in different colors to help them understand what to do first, next, and last or to help them understand the steps of order of operations

What is the value of the expression below?

28710 2 ÷⋅+ What is the missing number? 33 + (56 ÷ 7) x 4 = Simplify the expression below.

16)26( 42 ⋅−

a. 16 b. 64 c. 80 d. 108

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Grade 7 Mathematics


Simplify the expression below.

23 23 −

a. 1 b. 5 c. 23 d. 25


Grade 7 Mathematics



Topic VII: Algebraic Expressions, Simple equations; inequalities

Sugg

este

d D

ays

of

Inst

ruct

ion

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

5

A. Create, evaluate, simplify algebraic expressions involving variables

CPI: 4.3.7D3

Apply the following algebraic terms appropriately to equation, inequality, and expression Identify examples of equations, inequalities and expressions Write/ translate verbal expressions as equations, inequalities and expressions

Which situation is best represented by the equation 164 =−x ?

a. Miranda picked 16 apples

and ate 41

of them. What is

x, the number f apples she had?

b. Felipe ran for 16 minutes and walked for 4 minutes. What is x, the difference between the time he spent running and the time he spent walking?

c. Jordan spent $4 of his allowance and had $16 left. What is the x, the total of Jordan’s allowance?

d. Cecelia has hit 4 of the last 16 balls pitched. What is x, the total number of balls pitched?

Anna works as a painter. She charges $130 for paint supplies and $25 for each hour, h , she works.

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Grade 7 Mathematics


Which expression represents the total amount of money Anna charges? a. h)25130( + b. h25130 + c. 25130 +h d. )25(130 h++ Graciella is one year less than twice as old as her youngest brother. Which expression could be used to show her age? a. b21− b. 12 −b c. b2 d. 12 +b A newspaper gains and loses subscribers daily, as some people subscribe and other people cancel their subscriptions. The table below shows the subscriptions and cancellations for a newspaper during the firs two months of the year.

Subscriptions

Month New

Subscrip tions

Cancellations

January 100 30 February 450 120

If the newspaper started the year with s subscriptions, which expression can be used to find how many subscriptions the newspaper


Grade 7 Mathematics


had at the end of the two-month period?

a. s+100+(-30)+450+(-120) b. s+100+30+450+120 c. s+100+450 d. s+(-30)+(-120)

)32(5 +n

5

B. One-step, equations and inequalities

CPI: 4.3.7C1

Translate one step word problems and practical problems into equation/inequalities and solve them Solve for a given variable

42 >−x

47 <+ b The sum of x and 49 is 165

1005 =y

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C. Two-step, equations and inequalities

CPI: 4.3.7C1

Demonstrate a step by step approach for solving two step equations and inequalities Solve for the given variable Solve equation/inequalities with variables on both sides

Within the set of integers, which of the following represents the solution of the inequality?

813 <+x a. {…,-3, -2, -1, 0, 1, 2} b. {…,-3, -2, -1,0,1,2,3} c. {…,-3, -2, -1, 0, 1,2,3,4,5,6,7} d. {…,-3, -2, -1, 0, 1, 2, 2 1/3} Erin shops at two stores for a new sweater. The sweater at the first store costs $15 less than three times the cost, c, of the sweater at the second store. The sweater at the first store costs $90. The equation below can be used to determine the cost of the sweater at the second store.

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Grade 7 Mathematics


90153 =−c

Solve the equation to find the cost of the sweater at the second store. Show your work

2242 =−− r Eight times a number, plus 12 is 100

10

D. Multi-step, equations and inequalities

CPI: 4.3.7C1

Demonstrate a step by step approach for solving for multi step equations and inequalities Solve for a given variable Solve equation/inequalities with variables on both sides

0)246(3 =+− pp

965 −≥+a

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E. Functions CPI: 4.3.7B1

Represent a variety of function rules using tables and graphs

A function is described by the equation y = x + 2.. Complete the table by finding the value of y when x is 10.

x 1 2 3 … 10 y 3 4 5 … ?

The following graphs represent Andy riding his bike. Which graph shows Andy accelerating, traveling at a constant speed, and then quickly stopping?

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Grade 7 Mathematics


I. II.

III. IV. a. I b. II c. III d. IV

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