XIV. Mathematics, Grade 8

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "XIV. Mathematics, Grade 8"

Transcription

1 XIV. Mathematics, Grade 8

2 Grade 8 Mathematics Test The spring 0 grade 8 Mathematics test was based on standards in the five domains for grade 8 in the Massachusetts Curriculum Framework for Mathematics (March 0). The grade 8 standards can be found on pages 6 69 in the Framework, and the five domains are listed below. The Number Sstem Epressions and Equations Functions Geometr Statistics and Probabilit The Curriculum Framework for Mathematics is available on the Department website at Mathematics test results are reported under five MCAS reporting categories, which are identical to the five framework domains listed above. Test Sessions The grade 8 Mathematics test included two separate test sessions. Each session included multiplechoice, short-answer, and open-response questions. Approimatel half of the common test items are shown on the following pages as the appeared in test booklets. Reference Materials and Tools Each student taking the grade 8 Mathematics test was provided with a plastic ruler and a grade 8 Mathematics Reference Sheet. A cop of the reference sheet follows the final question in this chapter. An image of the ruler is not reproduced in this publication. During session, each student had sole access to a calculator with at least four functions and a square root ke. Calculator use was not allowed during session. The use of bilingual word-to-word dictionaries was allowed for current and former English language learner students onl, during both Mathematics test sessions. No other reference tools or materials were allowed. Cross-Reference Information The tables at the conclusion of this chapter indicate each released and unreleased common item s reporting categor and the framework standard it assesses. The correct answers for released multiplechoice and short-answer questions are also displaed in the released item table. 0

3 Grade 8 Mathematics Session You ma use our reference sheet and MCAS ruler during this session. You ma not use a calculator during this session. DIRECTIONS This session contains eight multiple-choice questions, two short-answer questions, and one open-response question. Mark our answers to these questions in the spaces provided in our Student Answer Booklet. ID:877 C Common What is the value of the epression below? A. B. 6 C. 9 D. 8 ( 9) 0

4 Mathematics Session ID:767 cmh076_rotation.eps, [opt A Common Seth drew a figure on a coordinate grid and labeled one point P, as shown below. 0 P He then rotated the figure 80 clockwise around point P. Which of the following shows the figure after Seth rotated it? A. C. 0 P P 0 B. D. 0 P P 0

5 Mathematics Session ID:6070 CMH_opposite.eps [stem D Common Carmella graphed line p on the coordinate grid shown below. p 0 Which of the following lines appears to have the same slope as line p? A. C. 0 0 B. D. 0 0

6 Mathematics Session ID:967 LPW00_slope.eps [stem_0 B Common The total cost in dollars,, of a membership at each of four health clubs is represented below in terms of, the number of months of the membership. Health Club A: 60 Health Club B: 0 $ 0 $ $ $6 $8 ID:68 B Common In 00, the U.S. Mint in Denver produced Oregon state quarters. What is written in standard notation? A. 0,00,000 B. 0,000,000 C.,00,000,000 D. 0,00,000,000 Health Club C: Total Cost (in dollars) (, 70) (, 0) Number of Months Health Club D: A customer pas a one-time fee of $0 plus $0 each month for months. Which representation has the greatest rate of change? A. Health Club A B. Health Club B C. Health Club C D. Health Club D

7 Mathematics Session Question 6 is a short-answer question. Write our answer to question 6 in the bo provided in our Student Answer Booklet. Do not write our answer in this test booklet. You ma do our figuring in the test booklet. ID:68 Common 6 What is the solution of the equation below? 7

8 Mathematics Session Mark our answers to multiple-choice questions 7 and 8 in the spaces provided in our Student Answer Booklet. Do not write our answers in this test booklet. You ma do our figuring in the test booklet. ID:9679 D Common 7 Which of the following equations has infinitel man solutions? A. B. C. D. ID:696 D Common 8 Which of the following numbers is not a rational number? A. B..7 C. D. 6

9 Mathematics Session Question 9 is a short-answer question. Write our answer to question 9 in the bo provided in our Student Answer Booklet. Do not write our answer in this test booklet. You ma do our figuring in the test booklet. ID:970 LW88007_rectangle.eps Common 9 The students in a science club planted a rectangular flower garden in front of their school. The garden is 6 feet wide and has a diagonal length of 0 feet. 6 feet 0 feet What is, the length in feet of the garden? 7

10 Mathematics Session Mark our answer to multiple-choice question 0 in the space provided in our Student Answer Booklet. Do not write our answer in this test booklet. You ma do our figuring in the test booklet. ID:87 B Common 0 What is the value of the epression below? A. 6 B. C. D. 6 ( ) ( ) 8

11 Mathematics Session Question is an open-response question. BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION. Show all our work (diagrams, tables, or computations) in our Student Answer Booklet. If ou do the work in our head, eplain in writing how ou did the work. Write our answer to question in the space provided in our Student Answer Booklet. ID:980 CMC_compan.eps Common Ton collected data on the ears of emploment and the annual salaries of the salespeople at Compan Z. He made a scatterplot and drew a trend line that approimated the line of best fit for the data, as shown below. Salaries of Salespeople at Compan Z $70,000 $60,000 (9, $,000) Salar $0,000 $0,000 $0, Years of Emploment a. Based on the trend line drawn for the data, what is the salar a salesperson with ears of emploment at Compan Z can epect to earn? Show or eplain how ou got our answer. b. What is the slope of the trend line that Ton drew? Show or eplain how ou got our answer. c. What does the slope mean in this situation? Ton epects his salar to be about $70,000 after he has been emploed as a salesperson at Compan Z for ears. d. Use the trend line and our answer from part (b) to eplain wh Ton s salar epectation is reasonable. 9

12 Grade 8 Mathematics Session You ma use our reference sheet and MCAS ruler during this session. You ma use a calculator during this session. DIRECTIONS This session contains eight multiple-choice questions, one short-answer question, and one open-response question. Mark our answers to these questions in the spaces provided in our Student Answer Booklet. ID:7 CMH070_triangles.eps A Common 6 cm A mathematical puzzle uses four triangles with the dimensions shown below. P 8 cm 6 cm 6 cm Q 8 cm 6 cm ID:998 C Common A cand is in the shape of a sphere. The cand has a radius of. centimeters. Which of the following is closest to the volume of the cand? (Use. for π.) A. cm B. 9 cm C. cm D. cm 9 cm R 9 cm cm S cm cm cm Which of the following triangles are congruent? A. P and Q B. Q and R C. R and S D. S and P 0

13 Mathematics Session ID:9897 CMC_pq.eps C Common The sstem of equations represented b lines p and q is shown on the graph below q 6 p ID:07 A Common Barb purchased a loaf of bread for $ and p pounds of sliced ham at $ per pound for a total of $.. The relationship between what she purchased and her total purchase price is represented b the equation below. p. What was the total number of pounds of ham that Barb purchased? A.. pounds B..6 pounds C..0 pounds D..6 pounds Based on the graph, what is the solution of the sstem of equations? A. (0, 0) B. (0, ) C. (, ) D. (, )

14 Mathematics Session ID:67 CMC0_triangles.eps C Common 6 Triangle EFG is similar to triangle TUV, as shown below. E 6 cm 0 0 cm G 8 8 F T 8 cm cm V U Based on the measurements of the triangles, what is the measure of angle U? A. B. 8 C. 8 D.

15 Mathematics Session Question 7 is a short-answer question. Write our answer to question 7 in the bo provided in our Student Answer Booklet. Do not write our answer in this test booklet. You ma do our figuring in the test booklet. ID:99 Common 7 A mailing tube in the shape of a clinder has a height of inches and a radius of inches. What is the volume, in cubic inches, of the mailing tube? (Use. for p.)

16 Mathematics Session Mark our answers to multiple-choice questions 8 and 9 in the spaces provided in our Student Answer Booklet. Do not write our answers in this test booklet. You ma do our figuring in the test booklet. ID:9767 CMC0_function.eps [opt_ C Common 8 Which of the following tables does not represent a function? ID:6787 CMC9_lines_mn.eps B Common 9 Amanda graphed line m and line n on a coordinate plane, as shown below. A m n B C. 0 D Which of the following statements is true? A. The slope of line m is greater than the slope of line n. B. The slope of line n is greater than the slope of line m. C. The -intercept of line m is greater than the -intercept of line n. D. The -intercept of line n is greater than the -intercept of line m.

17 Mathematics Session Question 0 is an open-response question. BE SURE TO ANSWER AND LABEL ALL PARTS OF THE QUESTION. Show all our work (diagrams, tables, or computations) in our Student Answer Booklet. If ou do the work in our head, eplain in writing how ou did the work. Write our answer to question 0 in the space provided in our Student Answer Booklet. ID:8769 Common 0 Some of the students from Eastwood School are taking a trip to a museum. In all, fewer than 60 students will go on the trip. The cost for food and admission to the museum is $8 per student. a. What is the total cost for food and admission to the museum for students? Show or eplain how ou got our answer. The students will travel on one bus to the museum. The cost of the bus is $800. b. In our Student Answer Booklet, cop and complete the table below to show the total cost for food, admission, and the bus for different numbers of students to go to the museum. Show or eplain how ou got our answers. Number of Students Student Trip to the Museum Total Cost for Food, Admission, and the Bus 0 $ $ c. Write an epression that can be used to find the total cost for food, admission, and the bus for n students from Eastwood School to go to the museum. d. A total of students go to the museum. What is the total cost, for food, admission, and the bus, per student to go to the museum? Show or eplain how ou got our answer.

18 Mathematics Session Mark our answer to multiple-choice question in the space provided in our Student Answer Booklet. Do not write our answer in this test booklet. You ma do our figuring in the test booklet. ID:9767 CMC0_MN.eps D Common Right triangle LMN is shown on the coordinate grid below. 8 M(, 7) 7 6 L(, ) N(, ) unit 8 unit Which of the following is the length, in units, of line segment MN? A. 8 B. 8 C. D. 6

19 Massachusetts Comprehensive Assessment Sstem Grade 8 Mathematics Reference Sheet PERIMETER FORMULAS square P s rectangle P b h OR P l w triangle P a b c AREA FORMULAS square A s rectangle A bh OR A lw parallelogram..... A bh triangle A bh trapezoid A h( b b ) VOLUME FORMULAS rectangular prism V lwh OR V Bh (B = area of a base) cube V s (s length of an edge) clinder V sphere V CIRCLE FORMULAS C C A πr OR πd πr πr h PYTHAGOREAN THEOREM πr circle A πr TOTAL SURFACE AREA FORMULAS a c rectangular prism.. SA ( lw) ( hw) ( lh) clinder SA πr πrh sphere SA πr b a b c 7

20 Grade 8 Mathematics Spring 0 Released Items: Reporting Categories, Standards, and Correct Answers* Item No. Page No. Reporting Categor Standard Correct Answer (MC/SA)* Epressions and Equations EE. C Geometr G. A Functions F. D Functions F. B Epressions and Equations EE. B 6 Epressions and Equations EE.7 = 7 6 Epressions and Equations EE.7 D 8 6 The Number Sstem NS. D 9 7 Geometr G.7 8 feet 0 8 Epressions and Equations EE. B 9 Statistics and Probabilit SP. 0 Geometr G. A 0 Geometr G.9 C Epressions and Equations EE.8 C Epressions and Equations EE.7 A 6 Geometr G. C 7 Geometr G cubic inches 8 Functions F. C 9 Epressions and Equations EE. B 0 Functions F. 6 Geometr G.8 D * Answers are provided here for multiple-choice and short-answer items onl. Sample responses and scoring guidelines for open-response items, which are indicated b the shaded cells, will be posted to the Department s website later this ear. 8

21 Grade 8 Mathematics Spring 0 Unreleased Common Items: Reporting Categories and Standards Item No. Reporting Categor Standard Geometr G.9 Statistics and Probabilit SP. Functions F. Functions F. 6 Epressions and Equations EE. 7 Epressions and Equations EE. 8 Epressions and Equations EE. 9 The Number Sstem NS. 0 Epressions and Equations EE.8 The Number Sstem NS. Functions F. Geometr G.7 Functions F. Functions F. 6 Statistics and Probabilit SP. 7 Epressions and Equations EE.8 8 Geometr G.8 9 Geometr G. 0 Functions F. Geometr G. Geometr G. 9

XIV. Mathematics, Grade 8

XIV. Mathematics, Grade 8 XIV. Mathematics, Grade 8 Grade 8 Mathematics Test The spring 0 grade 8 Mathematics test was based on learning standards in the five major content strands in the Massachusetts Mathematics Curriculum Framework

More information

XII. Mathematics, Grade 6

XII. Mathematics, Grade 6 XII. Mathematics, Grade 6 Grade 6 Mathematics Test The spring 2013 grade 6 Mathematics test was based on standards in the five domains for grade 6 in the Massachusetts Curriculum Framework for Mathematics

More information

XII. Mathematics, Grade 6

XII. Mathematics, Grade 6 XII. Mathematics, Grade 6 Grade 6 Mathematics Test The spring 04 grade 6 Mathematics test was based on standards in the five domains for grade 6 in the Massachusetts Curriculum Framework for Mathematics

More information

XV. Mathematics, Grade 10

XV. Mathematics, Grade 10 V. Mathematics, Grade 10 Grade 10 Mathematics Test The spring 014 grade 10 Mathematics test was based on standards in the 011 Massachusetts Curriculum Framework for Mathematics that match content in the

More information

XII. Mathematics, Grade 6

XII. Mathematics, Grade 6 XII. Mathematics, Grade 6 Grade 6 Mathematics Test The spring 2011 grade 6 MCAS Mathematics test was based on learning standards in the Massachusetts Mathematics Curriculum Framework (2000). The Framework

More information

XII. Mathematics, Grade 6

XII. Mathematics, Grade 6 XII. Mathematics, Grade 6 Grade 6 Mathematics Test The spring 01 grade 6 Mathematics test was based on learning standards in the five major content strands in the Massachusetts Mathematics Curriculum Framework

More information

XI. Mathematics, Grade 5

XI. Mathematics, Grade 5 XI. Mathematics, Grade 5 Grade 5 Mathematics Test The spring 2012 grade 5 Mathematics test was based on learning standards in the five major content strands of the Massachusetts Mathematics Curriculum

More information

XI. Mathematics, Grade 5

XI. Mathematics, Grade 5 XI. Mathematics, Grade 5 Grade 5 Mathematics Test The spring 2013 grade 5 Mathematics test was based on standards in the five major domains for grade 5 in the Massachusetts Curriculum Framework for Mathematics

More information

XV. Mathematics, Grade 10

XV. Mathematics, Grade 10 XV. Mathematics, Grade 10 Grade 10 Mathematics Test The spring 2011 grade 10 MCAS Mathematics test was based on learning standards in the Massachusetts Mathematics Curriculum Framework (2000). The Framework

More information

XV. Mathematics, Grade 10

XV. Mathematics, Grade 10 XV. Mathematics, Grade 10 Grade 10 Mathematics Test The spring 013 grade 10 Mathematics test was based on standards in the 011 Massachusetts Curriculum Framework for Mathematics that match content in the

More information

Algebra II. Administered May 2013 RELEASED

Algebra II. Administered May 2013 RELEASED STAAR State of Teas Assessments of Academic Readiness Algebra II Administered Ma 0 RELEASED Copright 0, Teas Education Agenc. All rights reserved. Reproduction of all or portions of this work is prohibited

More information

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Tuesday, January 24, 2012 9:15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Tuesday, January 24, 2012 9:15 a.m. to 12:15 p.m. INTEGRATED ALGEBRA The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Tuesda, Januar 4, 01 9:15 a.m. to 1:15 p.m., onl Student Name: School Name: Print our name and

More information

X. Mathematics, Grade 4

X. Mathematics, Grade 4 . Mathematics, Grade 4 Grade 4 Mathematics Test The spring 2014 grade 4 Mathematics test was based on standards in the five domains for grade 4 in the Massachusetts Curriculum Framework for Mathematics

More information

X. Mathematics, Grade 4

X. Mathematics, Grade 4 X. Mathematics, Grade 4 Grade 4 Mathematics Test The spring 2013 grade 4 Mathematics test was based on standards in the five domains for grade 4 in the Massachusetts Curriculum Framework for Mathematics

More information

2014 2015 Geometry B Exam Review

2014 2015 Geometry B Exam Review Semester Eam Review 014 015 Geometr B Eam Review Notes to the student: This review prepares ou for the semester B Geometr Eam. The eam will cover units 3, 4, and 5 of the Geometr curriculum. The eam consists

More information

ALGEBRA I (Common Core) Tuesday, June 3, 2014 9:15 a.m. to 12:15 p.m., only

ALGEBRA I (Common Core) Tuesday, June 3, 2014 9:15 a.m. to 12:15 p.m., only ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Tuesday, June 3, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The

More information

MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60

MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60 MATH REVIEW SHEETS BEGINNING ALGEBRA MATH 60 A Summar of Concepts Needed to be Successful in Mathematics The following sheets list the ke concepts which are taught in the specified math course. The sheets

More information

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

*1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

More information

Geometry Notes PERIMETER AND AREA

Geometry Notes PERIMETER AND AREA Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

More information

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks MATHCOUNTS TOOLBOX Facts, Formulas and Tricks MATHCOUNTS Coaching Kit 40 I. PRIME NUMBERS from 1 through 100 (1 is not prime!) 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 II.

More information

ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only

ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The

More information

In Problems #1 - #4, find the surface area and volume of each prism.

In Problems #1 - #4, find the surface area and volume of each prism. Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1 - #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR

More information

X. Mathematics, Grade 4

X. Mathematics, Grade 4 X. Mathematics, Grade 4 Grade 4 Mathematics Test The spring 2011 grade 4 MCAS Mathematics test was based on learning standards in the Massachusetts Mathematics Curriculum Framework (2000). The Framework

More information

ALGEBRA I (Common Core) Wednesday, August 13, 2014 8:30 to 11:30 a.m., only

ALGEBRA I (Common Core) Wednesday, August 13, 2014 8:30 to 11:30 a.m., only ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Wednesday, August 13, 2014 8:30 to 11:30 a.m., only Student Name: School Name: The

More information

North Carolina Community College System Diagnostic and Placement Test Sample Questions

North Carolina Community College System Diagnostic and Placement Test Sample Questions North Carolina Communit College Sstem Diagnostic and Placement Test Sample Questions 0 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College

More information

1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft

1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft 2 MODULE 6. GEOMETRY AND UNIT CONVERSION 6a Applications The most common units of length in the American system are inch, foot, yard, and mile. Converting from one unit of length to another is a requisite

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Thursday, August 16, 2012 8:30 to 11:30 a.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Thursday, August 16, 2012 8:30 to 11:30 a.m. INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Thursday, August 16, 2012 8:30 to 11:30 a.m., only Student Name: School Name: Print your name

More information

RELEASED. North Carolina READY End-of-Grade Assessment Mathematics. Grade 8. Student Booklet

RELEASED. North Carolina READY End-of-Grade Assessment Mathematics. Grade 8. Student Booklet REVISED 7/4/205 Released Form North Carolina READY End-of-Grade Assessment Mathematics Grade 8 Student Booklet Academic Services and Instructional Support Division of Accountabilit Services Copright 203

More information

Perfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through

Perfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through Perfume Packaging Gina would like to package her newest fragrance, Persuasive, in an eyecatching yet cost-efficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters

More information

Grade 8 Mathematics Practice Test

Grade 8 Mathematics Practice Test Grade 8 Mathematics Practice Test 3 4 For further information, contact: Louisiana Department of Education s Help Desk -877-453-7 Ask LDOE? http://www.louisianabelieves.com/resources/contact-us This public

More information

Geometry Unit 6 Areas and Perimeters

Geometry Unit 6 Areas and Perimeters Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose

More information

PARCC Grade 08 Mathematics Practice Test Released April, 2014 http://practice.parcc.testnav.com/#

PARCC Grade 08 Mathematics Practice Test Released April, 2014 http://practice.parcc.testnav.com/# Non-Calculator Part 1. Solve for. Enter your answer in the space provided. Enter only your solution. ( ) ( ) 2. Which decimal is equivalent to? Select your answer. A. B. C. D. 3. Two lines are graphed

More information

Released Assessment Questions, Answering Multiple-Choice Questions

Released Assessment Questions, Answering Multiple-Choice Questions Released Assessment Questions, 2015 Junior Division 16300 Grade 6 Mathematics Assessment of Reading, Writing and Mathematics INSTRUCTIONS Answering Multiple-Choice Questions Like this: Not like this: Use

More information

Geometry and Measurement

Geometry and Measurement The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for

More information

Incoming Frederick Douglass HS Geometry Students

Incoming Frederick Douglass HS Geometry Students Incoming Frederick Douglass HS Geometry Students 2016-2017 Dear FDHS Student, To better prepare you for the upcoming school year, it is the expectation is that all students bring the completed assignment

More information

Name: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd: Name: Date: Geometry Honors 2013-2014 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-6 HW: Pgs: 7-10 DAY 2: SWBAT: Calculate the Volume

More information

Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.

Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min. Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles

More information

Grade 6 FCAT 2.0 Mathematics Sample Questions

Grade 6 FCAT 2.0 Mathematics Sample Questions Grade FCAT. Mathematics Sample Questions The intent of these sample test materials is to orient teachers and students to the types of questions on FCAT. tests. By using these materials, students will become

More information

Geometry Notes VOLUME AND SURFACE AREA

Geometry Notes VOLUME AND SURFACE AREA Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications

More information

SURFACE AREA AND VOLUME

SURFACE AREA AND VOLUME SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has

More information

Grade 8 FCAT 2.0 Mathematics Sample Questions

Grade 8 FCAT 2.0 Mathematics Sample Questions Grade FCAT. Mathematics Sample Questions The intent of these sample test materials is to orient teachers and students to the types of questions on FCAT. tests. By using these materials, students will become

More information

S.A. = L.A. + 2B = ph + 2B

S.A. = L.A. + 2B = ph + 2B Page 1 of 5 View Tutorial 5c Objective: Find the lateral area, total surface area, and volume of rectangular prisms. A prism is a polyhedron with two congruent & parallel bases. The other faces are the

More information

GAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book

GAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book GAP CLOSING Volume and Surface Area Intermediate / Senior Student Book Volume and Surface Area Diagnostic...3 Volumes of Prisms...6 Volumes of Cylinders...13 Surface Areas of Prisms and Cylinders...18

More information

GEOMETRY (Common Core)

GEOMETRY (Common Core) GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Wednesday, August 12, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The

More information

Section 2.1 Rectangular Coordinate Systems

Section 2.1 Rectangular Coordinate Systems P a g e 1 Section 2.1 Rectangular Coordinate Systems 1. Pythagorean Theorem In a right triangle, the lengths of the sides are related by the equation where a and b are the lengths of the legs and c is

More information

Pre-Algebra Curriculum Crawford Central School District

Pre-Algebra Curriculum Crawford Central School District Concept Competency Resources Larson Pre- Algebra Resource Vocabulary Strategy PA Core Eligible Content PA Core Standards PA Core Standards Scope and Sequence Number System identify numbers as either rational

More information

Answer Key For The California Mathematics Standards Grade 7

Answer Key For The California Mathematics Standards Grade 7 Introduction: Summary of Goals GRADE SEVEN By the end of grade seven, students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use

More information

Area of Parallelograms (pages 546 549)

Area of Parallelograms (pages 546 549) A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular

More information

Archdiocese of Washington Catholic Schools Academic Standards Mathematics

Archdiocese of Washington Catholic Schools Academic Standards Mathematics 5 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,

More information

Finding Volume of Rectangular Prisms

Finding Volume of Rectangular Prisms MA.FL.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2 Use formulas to find surface areas and volume of three-dimensional composite shapes.

More information

Area, Perimeter, Volume and Pythagorean Theorem Assessment

Area, Perimeter, Volume and Pythagorean Theorem Assessment Area, Perimeter, Volume and Pythagorean Theorem Assessment Name: 1. Find the perimeter of a right triangle with legs measuring 10 inches and 24 inches a. 34 inches b. 60 inches c. 120 inches d. 240 inches

More information

ENTRY LEVEL MATHEMATICS TEST

ENTRY LEVEL MATHEMATICS TEST ENTRY LEVEL MATHEMATICS TEST Copyright 0 by the Trustees of the California State University. All rights reserved. C Geometry Reference Formulas Rectangle w Area = w Perimeter = + w l Triangle h Area =

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only. GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your

More information

Year 9 mathematics test

Year 9 mathematics test Ma KEY STAGE 3 Year 9 mathematics test Tier 6 8 Paper 1 Calculator not allowed First name Last name Class Date Please read this page, but do not open your booklet until your teacher tells you to start.

More information

MATH 100 PRACTICE FINAL EXAM

MATH 100 PRACTICE FINAL EXAM MATH 100 PRACTICE FINAL EXAM Lecture Version Name: ID Number: Instructor: Section: Do not open this booklet until told to do so! On the separate answer sheet, fill in your name and identification number

More information

Math 113 Sample Exam III: Systems of Linear Equations & Geometry = 2.) 4.) 6.) 8.) 10.)

Math 113 Sample Exam III: Systems of Linear Equations & Geometry = 2.) 4.) 6.) 8.) 10.) 1 Math 11 Sample Eam III: Sstems of Linear Equations & Geometr Section I Sstem of Linear Equations Solve each sstem of linear equations using substitution 1.) 9 1.) 1.) 5 0 s r s r.) 1 Solve each sstem

More information

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry. Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know

More information

A = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height

A = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height Formula Key b 1 base height rea b or (b 1 / b for a trapezoid) h b Perimeter diagonal P d (d 1 / d for a kite) d 1 d Perpendicular two lines form a angle. Perimeter P = total of all sides (side + side

More information

YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!

YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR! DETAILED SOLUTIONS AND CONCEPTS - SIMPLE GEOMETRIC FIGURES Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST

More information

Applied. Grade 9 Assessment of Mathematics LARGE PRINT RELEASED ASSESSMENT QUESTIONS

Applied. Grade 9 Assessment of Mathematics LARGE PRINT RELEASED ASSESSMENT QUESTIONS Applied Grade 9 Assessment of Mathematics 2014 RELEASED ASSESSMENT QUESTIONS Record your answers to multiple-choice questions on the Student Answer Sheet (2014, Applied). LARGE PRINT Please note: The format

More information

Solids. Objective A: Volume of a Solids

Solids. Objective A: Volume of a Solids Solids Math00 Objective A: Volume of a Solids Geometric solids are figures in space. Five common geometric solids are the rectangular solid, the sphere, the cylinder, the cone and the pyramid. A rectangular

More information

How does one make and support a reasonable conclusion regarding a problem? How does what I measure influence how I measure?

How does one make and support a reasonable conclusion regarding a problem? How does what I measure influence how I measure? Middletown Public Schools Mathematics Unit Planning Organizer Subject Mathematics Grade/Course Grade 7 Unit 3 Two and Three Dimensional Geometry Duration 23 instructional days (+4 days reteaching/enrichment)

More information

GEOMETRY (Common Core)

GEOMETRY (Common Core) GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Tuesday, June 2, 2015 1:15 to 4:15 p.m., only Student Name: School Name: The possession

More information

10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres. 10.4 Day 1 Warm-up

10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres. 10.4 Day 1 Warm-up 10.4 Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres 10.4 Day 1 Warm-up 1. Which identifies the figure? A rectangular pyramid B rectangular prism C cube D square pyramid 3. A polyhedron

More information

Perimeter is the length of the boundary of a two dimensional figure.

Perimeter is the length of the boundary of a two dimensional figure. Section 2.2: Perimeter and Area Perimeter is the length of the boundary of a two dimensional figure. The perimeter of a circle is called the circumference. The perimeter of any two dimensional figure whose

More information

INVESTIGATIONS AND FUNCTIONS 1.1.1 1.1.4. Example 1

INVESTIGATIONS AND FUNCTIONS 1.1.1 1.1.4. Example 1 Chapter 1 INVESTIGATIONS AND FUNCTIONS 1.1.1 1.1.4 This opening section introduces the students to man of the big ideas of Algebra 2, as well as different was of thinking and various problem solving strategies.

More information

The GED math test gives you a page of math formulas that

The GED math test gives you a page of math formulas that Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding

More information

Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)

Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes) Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.

More information

Characteristics of the Four Main Geometrical Figures

Characteristics of the Four Main Geometrical Figures Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.

More information

Assessment For The California Mathematics Standards Grade 3

Assessment For The California Mathematics Standards Grade 3 Introduction: Summary of Goals GRADE THREE By the end of grade three, students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication,

More information

MENSURATION. Definition

MENSURATION. Definition MENSURATION Definition 1. Mensuration : It is a branch of mathematics which deals with the lengths of lines, areas of surfaces and volumes of solids. 2. Plane Mensuration : It deals with the sides, perimeters

More information

Students will understand 1. use numerical bases and the laws of exponents

Students will understand 1. use numerical bases and the laws of exponents Grade 8 Expressions and Equations Essential Questions: 1. How do you use patterns to understand mathematics and model situations? 2. What is algebra? 3. How are the horizontal and vertical axes related?

More information

GEOMETRY (Common Core)

GEOMETRY (Common Core) GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Thursday, January 28, 2016 9:15 a.m. to 12:15 p.m., only Student Name: School Name:

More information

Grade 8 Unit 2 Pythagorean Theorem Applications. Assessment Plan

Grade 8 Unit 2 Pythagorean Theorem Applications. Assessment Plan Grade 8 Unit 2 Pythagorean Theorem Applications Work with radicals and integer exponents Assessment Plan 8. EE.2 Use square root and cube root symbols to represent solutions to equations. Evaluate square

More information

Middle Grades Mathematics 5 9

Middle Grades Mathematics 5 9 Middle Grades Mathematics 5 9 Section 25 1 Knowledge of mathematics through problem solving 1. Identify appropriate mathematical problems from real-world situations. 2. Apply problem-solving strategies

More information

Common Core State Standard I Can Statements 8 th Grade Mathematics. The Number System (NS)

Common Core State Standard I Can Statements 8 th Grade Mathematics. The Number System (NS) CCSS Key: The Number System (NS) Expressions & Equations (EE) Functions (F) Geometry (G) Statistics & Probability (SP) Common Core State Standard I Can Statements 8 th Grade Mathematics 8.NS.1. Understand

More information

Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object.

Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object. Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object. Surface area is the sum of areas of all the faces or sides of a three-dimensional

More information

Surface Area and Volume

Surface Area and Volume 1 Area Surface Area and Volume 8 th Grade 10 days by Jackie Gerwitz-Dunn and Linda Kelly 2 What do you want the students to understand at the end of this lesson? The students should be able to distinguish

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE I. Thursday, August 16, 2001 8:30 to 11:30 a.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE I. Thursday, August 16, 2001 8:30 to 11:30 a.m. The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE I Thursda, August 16, 2001 8:30 to 11:30 a.m., onl Notice... Scientific calculators

More information

Mathematics Common Core Cluster. Mathematics Common Core Standard. Domain

Mathematics Common Core Cluster. Mathematics Common Core Standard. Domain Mathematics Common Core Domain Mathematics Common Core Cluster Mathematics Common Core Standard Number System Know that there are numbers that are not rational, and approximate them by rational numbers.

More information

with functions, expressions and equations which follow in units 3 and 4.

with functions, expressions and equations which follow in units 3 and 4. Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model

More information

Think About This Situation

Think About This Situation Think About This Situation A popular game held at fairs or parties is the jelly bean guessing contest. Someone fills a jar or other large transparent container with a known quantity of jelly beans and

More information

Platonic Solids. Some solids have curved surfaces or a mix of curved and flat surfaces (so they aren't polyhedra). Examples:

Platonic Solids. Some solids have curved surfaces or a mix of curved and flat surfaces (so they aren't polyhedra). Examples: Solid Geometry Solid Geometry is the geometry of three-dimensional space, the kind of space we live in. Three Dimensions It is called three-dimensional or 3D because there are three dimensions: width,

More information

MATH STUDENT BOOK. 7th Grade Unit 9

MATH STUDENT BOOK. 7th Grade Unit 9 MATH STUDENT BOOK 7th Grade Unit 9 Unit 9 Measurement and Area Math 709 Measurement and Area Introduction 3 1. Perimeter 5 Perimeter 5 Circumference 11 Composite Figures 16 Self Test 1: Perimeter 24 2.

More information

Topic: Integers. Addition Subtraction Multiplication Division Same signs: Add & keep sign = = - 10.

Topic: Integers. Addition Subtraction Multiplication Division Same signs: Add & keep sign = = - 10. Topic: Integers Examples: Addition Subtraction Multiplication Division Same signs: Add & keep sign + 6 + + 5 = + 11-8 + - 2 = - 10 Different signs: Subtract & take sign of larger value + 9 + - 5 = + 4-6

More information

GAP CLOSING. 2D Measurement GAP CLOSING. Intermeditate / Senior Facilitator s Guide. 2D Measurement

GAP CLOSING. 2D Measurement GAP CLOSING. Intermeditate / Senior Facilitator s Guide. 2D Measurement GAP CLOSING 2D Measurement GAP CLOSING 2D Measurement Intermeditate / Senior Facilitator s Guide 2-D Measurement Diagnostic...4 Administer the diagnostic...4 Using diagnostic results to personalize interventions...4

More information

A. Areas of Parallelograms 1. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh.

A. Areas of Parallelograms 1. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh. Geometry - Areas of Parallelograms A. Areas of Parallelograms. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh. A B Ex: See how VDFA V CGB so rectangle

More information

Grade 7 Math Course Lesson Plan: 34 weeks

Grade 7 Math Course Lesson Plan: 34 weeks Grade 7 Math Course Lesson Plan: 34 weeks Welcome to Thinkwell s 7th Grade Math! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson plan is meant to be a guide

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Wednesday, June 12, 2013 1:15 to 4:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Wednesday, June 12, 2013 1:15 to 4:15 p.m. INTEGRATED ALGEBRA The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA Wednesday, June 12, 2013 1:15 to 4:15 p.m., only Student Name: School Name: The possession

More information

Covering and Surrounding: Homework Examples from ACE

Covering and Surrounding: Homework Examples from ACE Covering and Surrounding: Homework Examples from ACE Investigation 1: Extending and Building on Area and Perimeter, ACE #4, #6, #17 Investigation 2: Measuring Triangles, ACE #4, #9, #12 Investigation 3:

More information

17.2 Surface Area of Prisms and Cylinders

17.2 Surface Area of Prisms and Cylinders Name Class Date 17. Surface Area of Prisms and Cylinders Essential Question: How can you find the surface area of a prism or cylinder? Explore G.11.C Apply the formulas for the total and lateral surface

More information

ALGEBRA I (Common Core) Thursday, June 16, 2016 9:15 a.m. to 12:15 p.m., only

ALGEBRA I (Common Core) Thursday, June 16, 2016 9:15 a.m. to 12:15 p.m., only ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Thursday, June 16, 2016 9:15 a.m. to 12:15 p.m., only Student Name: School Name:

More information

12 Surface Area and Volume

12 Surface Area and Volume 12 Surface Area and Volume 12.1 Three-Dimensional Figures 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders 12.5 Volumes of Pyramids

More information

Pennsylvania System of School Assessment

Pennsylvania System of School Assessment Pennsylvania System of School Assessment The Assessment Anchors, as defined by the Eligible Content, are organized into cohesive blueprints, each structured with a common labeling system that can be read

More information

GAP CLOSING. 2D Measurement. Intermediate / Senior Student Book

GAP CLOSING. 2D Measurement. Intermediate / Senior Student Book GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2-D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas

More information

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

More information

VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:

More information

DOUBLE, DOUBLE: LOOKING AT THE EFFECT OF CHANGE

DOUBLE, DOUBLE: LOOKING AT THE EFFECT OF CHANGE DOUBLE, DOUBLE: LOOKING AT THE EFFECT OF CHANGE ON PERIMETER, AREA AND VOLUME Outcome (lesson objective) Students will demonstrate how changes in the dimensions of squares, rectangles, and circles affect

More information