Use with Your Students! GRADE MATHEMATICS STAAR Readiness Review and Practice NEW TEKS Readiness TEKS Lessons Over authentic STAAR practice items -step approach for efficient remediation STAAR is a registered trademark of the Texas Education Agency, which does not endorse this program or its content.
STAAR GRADE MATHEMATICS REFERENCE MATERIALS Centimeters LENGTH Customary Metric mile (mi) =, yards (yd) kilometer (km) =, meters (m) yard (yd) = feet (ft) meter (m) = centimeters (cm) foot (ft) = inches (in.) centimeter (cm) = millimeters (mm) VOLUME AND CAPACITY Customary Metric gallon (gal) = quarts (qt) liter (L) =, milliliters (ml) quart (qt) = pints (pt) pint (pt) = cups (c) cup (c) = fluid ounces (fl oz) WEIGHT AND MASS Customary Metric ton (T) =, pounds (lb) kilogram (kg) =, grams (g) pound (lb) = ounces (oz) gram (g) =, milligrams (mg)
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Unlawful to photocopy or project without permission Table of Contents Included in Welcome Letter....v How to Use This Book for STAAR Success...vi STAAR Problem-Solving Strategies: Keys to Success... x Great Griddables...xiii Student Progress Monitoring Chart... READINESS REVIEW Instruction & Practice in all Readiness TEKS Diagnostic Test Identify Your Needs.... Remediation Lesson Review and Practice Solving Problems Using Rational Numbers (.B).... Solving Problems Using Ratios, Rates, and Percents (.D)... Solving Problems Using Similar Shapes and Scale Drawings (.C)... CUMULATIVE REVIEW: Lessons... Modeling and Solving One-Variable Equations and Inequalities (.A)... Representing Rates of Change (.A)... Representing Linear Relationships (.A)... CUMULATIVE REVIEW: Lessons... Finding Circumference and Area of Circles (.B).... Finding Area of Composite Figures (.C).... Finding Volume of Prisms and Pyramids (.A).... CUMULATIVE REVIEW: Lessons... Finding Probabilities (.I)... Solving Problems Using Probabilities (.H)... Solving Problems Using Data Representations (.G)... Comparing Data with Dot Plots and Box Plots (.A)... CUMULATIVE REVIEW: Lessons... Post Test Check Your Progress.... SUPPORTING SUCCESS Practice in all Supporting TEKS REPORTING CATEGORY : Probability and Numerical Representations Classifying Numbers (.A)... Probability and Sample Spaces (.A,.C,.D,.E )... Table of Contents iii
SUPPORTING SUCCESS (continued) REPORTING CATEGORY : Computations and Algebraic Relationships Operating with Rational Numbers (.A).... Unit Rates and Proportional Relationships (.B,.C).... Solutions to Equations and Inequalities (.B,.B).... Modeling with Equations and Inequalities (.A,.C)... REPORTING CATEGORY : Geometry and Measurement Geometry and Measurement (.E,.A,.B,.D,.C)... REPORTING CATEGORY : Data Analysis and Personal Financial Literacy Data Analysis (.B,.C)... Financial Literacy (.A,.B,.C,.D,.E,.F)... Glossary of Key Terms.... Student Answer Sheets.... Reference Materials.... inside front & back cover TEKS Correlations Where to Find Them Readiness TEKS Readiness Lesson Supporting TEKS Supporting Topic.B Lesson (p. ).A Topic (p. ).A Lesson (p. ).A Topic (p. ).D Lesson (p. ).B,.C Topic (p. ).C Lesson (p. ).E,.A,.B Topic (p. ).G Lesson (p. ).A,.C,.D,.E Topic (p. ).H Lesson (p. ).D Topic (p. ).I Lesson (p. ).A Topic (p. ).A Lesson (p. ).B Topic (p. ).A Lesson (p. ).C Topic (p. ).B Lesson (p. ).B Topic (p. ).C Lesson (p. ).C Topic (p. ).A Lesson (p. ).B,.C Topic (p. ).A Lesson (p. ).A,.B,.C,.D,.E,.F Topic (p. ) Unlawful to photocopy or project without permission iv Table of Contents
Unlawful to photocopy or project without permission Dear Students, The STAAR Grade Mathematics assessment measures your knowledge of the Grade math standards (TEKS). STAAR tests are not designed to measure many important qualities of character and intelligence as this cartoon shows. But performing well on the STAAR tests is important, so you want to do all you can to succeed on them. That s where this workbook comes in! Qualities Not Measured by STAAR Tests Persistence Curiosity Enthusiasm COURAGE Leadership Creativity Civic-Minded Resourcefulness Sense of Wonder Big-Picture Thinking Compassion Reliability Motivation Humor Empathy Sense of Beauty Humility Resilience Positivity What are some other important qualities of character and intelligence missing in STAAR tests? This workbook was designed to help you prepare for the STAAR Grade Mathematics test by teaching the skills to approach and answer different STAAR test questions, and by providing practice questions that are similar to those you will answer on the actual test. But as good as this workbook is, it only helps if you use it. So, please use this workbook! Practicing Smart Is the Secret to STAAR Success There is a secret to success on the STAAR tests practice, practice, and more practice. This is good news because you are in control of how much effort you put into practicing. But not all practice is the same you need to practice smart. First, practice with test questions that are very similar to the actual STAAR test. That s easy because this workbook is full of them! Next, focus on your weaknesses spend extra time on questions you have trouble with. Think of it like this: if your basketball shot needs improvement, you don t practice dribbling. Instead, you practice shooting. Focusing on your weaknesses also means carefully analyzing each test question you get wrong. Why did you get it wrong? Why is another answer correct? You can learn more from test questions you get wrong, so don t be afraid of making mistakes. If your basketball shot is off, you identify what you are doing wrong (too far left), and correct it with your next shot (aim further right). When you practice, give each question your full attention. Do not take a break until after you answer the question. Your attention is like a muscle that you can build by using it, one practice test question at a time. Do you believe unfocused, sloppy practice of your basketball shot will help you perform during a big game? No! Your attention is your greatest power. You develop it with practice. Preparing for the STAAR test can actually be a fun challenge. And when you practice smart, you are building life skills while you prepare for the STAAR test! DyslexicKids.net Your partners in STAAR success, The Sirius Education Team Welcome Letter v
How to Use This Book for STAAR Success -Step Approach to Differentiate Instruction This interactive workbook is easily adapted for different needs and includes an optional -step approach to efficiently prioritize and individualize remediation when preparation time is limited. STEP Identify Your Needs Diagnostic Test Use the -item Diagnostic Test to identify what you know and what you need to review. Record your results in the Student Progress Monitoring Chart. Each item correlates to a lesson. Name Class Date Diagnostic Test Read each question carefully. Determine the best answer to the question from the four answer choices provided. There are players on a football team. of the players are offensive players. of the players are special teams players. The remaining players are defensive players. Each team member is either an offensive, defensive, or special teams player. The number of defensive players is A B C D A motorist drove miles in hours. At that rate, how many miles would the motorist travel in a half hour? F mi G mi H mi J mi A graphic designer is enlarging a rectangular poster. The enlargement will be similar to the original poster. The ratio of the original side lengths to the new side lengths is. If the original poster is inches wide, how many inches wide will the new poster be? A in. B in. C in. D in. Grade Mathematics STAAR Readiness Review and Practice Name Class Date Student Progress Monitoring Chart Diagnostic Mark a next to each test question that you answered correctly. Find the total. Need Review? If you did not check a question in, circle the lesson next to it. Study each circled lesson, and put a in the Practiced column when done. Post Test Mark a next to each question that you answered correctly. Find the total. Repeat or review each lesson that is unchecked in column. Question Diagnostic Need Review? Practiced Post Test TEKS Lesson Title Lesson.B Solving Problems Using Rational Numbers Lesson.D Solving Problems Using Ratios, Rates, and Percents Lesson.C Solving Problems Using Similar Shapes and Scale Drawings Lesson.A Modeling and Solving One-Variable Equations and Inequalities Lesson.A Representing Rates of Change Lesson.A Representing Linear Relationships Lesson.B Finding Circumference and Area of Circles Lesson.C Finding Area of Composite Figures Lesson.A Finding Volume of Prisms and Pyramids Lesson.I Finding Probabilities Lesson.H Solving Problems Using Probabilities Lesson.G Solving Problems Using Data Representations Lesson.A with Dot Plots.B Box Plots Solving Problems Using Rational Numbers Lesson Comparing Data and Total Correct / / Student Progress Monitoring Chart STEP Focus Intervention Lesson Instruction and STAAR Practice Use your Diagnostic Test results to focus TEKS instruction and STAAR practice on your unique needs. Readiness Lessons Lesson Finding Area of Composite Figures.C Determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles. In this lesson, you will solve problems involving areas of geometric figures. The table shows the basic shapes you will use, along with formulas for their areas, A. h Rectangle h b A = bh Triangle b A = _ bh Area Formulas Square s s A = s s or A = s Trapezoid b h b A = (b b )h. Find the area of each figure. a. in. b. in. cm h Parallelogram b A = bh Circle r A = πr ( π». or ) Question Diagnostic STAAR Practice.C Odd Set The figure shown is composed of a right triangle and a parallelogram. m. m. m What is the area of the figure in square meters? (.B,.C,.E,.F) A. m B. m C. m D. m This diagram of a baseball field is composed of a square, a semicircle, and a quarter circle. ft ft Need Review? Practiced Post Test Lesson.D Solving Problems Using Ratios, Rates, and Pe Even Set A parallelogram and a trapezoid form the figure shown below. mm mm mm Both the trapezoid and the parallelogram have height mm. mm What is the area of the figure in square millimeters? (.B,.C,.E,.F) F mm G mm H mm J mm An ice cream shop has a sign in the shape of an ice cream cone. The sign is made using a semicircle and a triangle, as modeled below. The base of the triangle is the in. diameter of the semicircle. in. TEKS Lesson Title Monitor your progress. Focus on where you most need practice. Ample practice arranged in increasing order of difficulty Unlawful to photocopy or project without permission Interactive questions and examples c. cm A = A = d. ft in. ft in. ft Which measurement is the best estimate of the area of the field in square feet? (.A,.B,.C,.E,.F) A, ft B, ft C, ft D, ft Which is the best estimate of the area of the sign in square inches? (.A,.B,.C,.E,.F) F in. G in. H in. J in. A = A = Grade Mathematics STAAR Readiness Review and Practice Lesson Finding Area of Composite Figures STEP Monitor Your Progress Post Test Use the -item Post Test to monitor progress and to identify additional lessons for review. The Post Test uses the same TEKS in the same order as the Diagnostic Test. Name Class Date Post Test Read each question carefully. Determine the best answer to the question from the four answer choices provided. Joseph bought a box of pens for $.. The price included a $. donation to the local food drive. ina bought boxes of the same type of pens, but did NOT donate to the vi How to Use This Book for STAAR Success
Lessons with TEKS Instruction and STAAR Practice Unlawful to photocopy or project without permission Lesson TEKS Instruction Engaging Interactive Learning Concise and student-friendly instruction reviews each Readiness TEKS. Students actively participate in learning with interactive questions and scaffolded Your Turn instruction. Summary tables Lesson Interactive questions reinforce key concepts and c. provide a quick check of understanding. Finding Area of Composite Figures.C Determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles. In this lesson, you will solve problems involving areas of geometric figures. The table shows the basic shapes you will use, along with formulas for their areas, A. h Rectangle h b A = bh Triangle b A = _ bh Area Formulas Square s s A = s s or A = s Trapezoid b h b A = (b b )h. Find the area of each figure. a. in. b. in. A = A = in. in. A = A = d. cm cm ft ft ft h Parallelogram b A = bh Circle r A = πr ( π». or ) Full TEKS Sometimes you may have to subtract to find the area of a composite figure. Example Finding Area by Subtracting The figure is composed of a square inside a larger square. What is the area of the unshaded region of the figure? Unshaded area = Area of large square Area of small square = ()() ()() = = The area of the unshaded region is cm. Your Turn This figure is composed of two right triangles. Use a ruler to measure the dimensions of the figure to the nearest quarter inch. What is the area of the unshaded region of the figure? The unshaded area is equal to the area of the large small triangle minus the area of the large small triangle. Use an inch ruler to measure each dimension to the nearest quarter inch. Then find the area of each triangle. Large Triangle Small Triangle Base in. Base in. cm cm Height in. Height in. Area = bh = ( )( ) Area = bh = ( )( ) = = Unshaded area = = square inches Examples with full solutions Your Turn provides step-by-step scaffolding for students to apply what they learn in each Example. Grade Mathematics STAAR Readiness Review and Practice Grade Mathematics STAAR Readiness Review and Practice Lesson STAAR Practice Abundant and Systematic Practice STAAR practice with matching questions in a two-column format (Odd and Even Sets). Questions are arranged in increasing order of difficulty and include answer grids STAAR Practice.C Odd Set Even Set Odd Set A square and a right triangle were used to form the following figure. Even Set The figure below is composed of a right triangle inside a rectangle. Questions are in increasing order of difficulty Matching questions are minimally different to promote careful reading and thinking. The figure shown is composed of a right triangle and a parallelogram. m. m. m What is the area of the figure in square meters? (.B,.C,.E,.F) A. m B. m C. m D. m This diagram of a baseball field is composed of a square, a semicircle, and a quarter circle. ft ft Which measurement is the best estimate of the area of the field in square feet? (.A,.B,.C,.E,.F) A, ft B, ft C, ft D, ft A parallelogram and a trapezoid form the figure shown below. mm mm mm Both the trapezoid and the parallelogram have height mm. Lesson Finding Area of Composite Figures mm What is the area of the figure in square millimeters? (.B,.C,.E,.F) F mm G mm H mm J mm An ice cream shop has a sign in the shape of an ice cream cone. The sign is made using a semicircle and a triangle, as modeled below. The base of the triangle is the in. diameter of the semicircle. in. Which is the best estimate of the area of the sign in square inches? (.A,.B,.C,.E,.F) F in. G in. H in. J in. Tips alert students to key facts. cm cm cm What is the area of the unshaded region of this figure in square centimeters? (.B,.C,.E,.F) Vince used a parallelogram and a rectangle to form the figure shown. Use a ruler to measure the dimensions of the figure to the nearest half of a centimeter. How do you measure the base and height of a parallelogram? Which measurement is closest to the area of the figure in square centimeters? (.B,.C,.E,.F) A cm C cm B cm D cm Ample practice with authentic STAAR questions ft ft ft What is the area of the unshaded region of this figure in square feet? (.B,.C,.E,.F) Lesson Finding Area of Composite Figures A square and a trapezoid were used to form the following figure. Use a ruler to measure the dimensions of the figure to the nearest half of a centimeter. Which is closest to the area of the figure in square centimeters? (.B,.C,.E,.F) F cm H cm G cm J cm Includes practice filling in grids How to Use This Book for STAAR Success vii
Additional In-Book Resources for STAAR Success STAAR Test-Taking Strategies strategies with interactive practice to help students learn how to solve STAAR questions. Free Response Grids An interactive review on how to correctly complete grids and avoid careless mistakes. STAAR Problem-Solving Strategies: Keys to Success Each year, the STAAR Grade Mathematics exam tests the same concepts in similar ways. In fact, it would not be fair unless the STAAR test was consistent from one year to the next. This means the STAAR test questions are predictable. So by using this workbook, you will be well prepared for the actual STAAR test! The test is challenging, and there are no secret tricks. But using the following strategies will make a difference. So practice them as you use this workbook. Read EVERY Word Carefully and More Than Once The STAAR Grade Mathematics exam also tests your reading skills because many questions are word problems. Plan to read each question at least two times. Here are some recommended reading strategies:. First read the problem for the big picture of what is going on. To do this, you ignore details such as names and numbers. This first read prepares you for a closer second read. º To show you understand a problem, write a generalized name for the problem using the format Given, find.. Next, read the problem for supporting facts or details. Circle each piece of given information and underline what you are asked to find. º Read graphs or tables. The titles, labels, and scales include important information. º Read all answer choices. You may also want to compare and contrast the answers. Let s apply these suggestions. Read the question below carefully. Big Picture: The price was reduced. The problem name could be: x The price of a video game was reduced from $ to $. By what percentage was the price of the video game reduced? STAAR Grade Mathematics # F % G % H % J % Given the original price and the new price, find the STAAR Problem-Solving Strategies: Keys to Success that the price was reduced. Supporting Facts: Original price: $ Sale price after reduction: Read the answer choices. Use estimation to eliminate unreasonable answers. The price is reduced by $. This amount is more less than one-half of $. F and G are reasonable answers. Circle the correct choice. H is not reasonable because % is more than one-half of $. What is the correct answer? Why? Cumulative Review Comprehensive practice after every Lessons provides spaced review. Cumulative Review The figure shown is composed of a right triangle and a rectangle. ft. ft. ft What is the area of the figure in square feet? (.C Lesson ) A. ft C. ft B. ft D. ft Which statement best describes the unit rate for the data shown in the table? (.A Lesson ) x y F As x increases by, y increases by. G The ratio of y to x is to. H As x increases by, y decreases by. J The value of y changes by each time x changes by. A circle has a radius of yards. What is the approximate circumference of the circle? (.B Lesson ) A. yd C. yd B. yd D. yd A map of Palo Alto Battlefield National Historical Park uses a scale of centimeters to kilometers. There are kilometers of hiking trails shown on the map. What is the length in centimeters of the segments representing hiking trails on the map? (.C Lesson ) F cm H cm G cm J cm What is the volume of the triangular prism shown below? (.A Lesson ) cm cm cm A,. cm C. cm B, cm D cm One brand of frozen broccoli sells for $. per ounce. What is the price of a -ounce bag of broccoli? Give your answer in dollars and cents. (.D Lesson ) STAAR strategies are modelled using released test questions. Mixed review of previous lessons in a random order Great Griddables Of the STAAR Grade Mathematics test questions, require griddable answers. These are just like other questions, except that you need to find your own numerical answer (instead of selecting among answer choices). After you ve found your answer, you need to fill it in correctly on your answer document. Here s how you do it: Use the Boxes Write your answer in the top row of boxes before filling in any bubbles. The scoring machine only reads the bubbles, but using the boxes will help you fill in the bubbles correctly. Position with the Decimal Point Your answer must be positioned properly with the provided decimal point. Fill in Bubbles Fill in a bubble to match each number in the boxes above. Then check your bubbles with the boxes to avoid making a careless error! Decimals Decimals can be gridded to a maximum of two decimal places (hundredths place). So decimals like. need to be rounded to.. For decimals between and, like., you do not need to grid the before the decimal point (although you may). You cannot grid fractions, so convert them to decimals before gridding. Negative Numbers If your answer is negative, fill in the bubble containing a negative sign in the first column. If it s positive, leave the first column blank. Look at the grids below showing correct and incorrect ways to grid. CORRECT INCORRECT / The decimal is rounded The and uses negative is placed both places. The You cannot sign is immediately negative grid fractions, written to the left of sign is not only decimals. in the the decimal shaded. box and point. shaded. Your Turn Write each number in the boxes in griddable format. The first box is reserved for the sign....... _.,. Great Griddables Supporting Success Practice in all Supporting TEKS, with an emphasis on the most tested standards. Classifying Numbers SUPPORTING SUCCESS Reporting Category.A Which diagram shows the numbers placed in the correct sets? (.A.B,.E,.F) R = {rational numbers} I = {integers} Set I A. Set R Set R Set I B. Set I C. D. Set I Set R. Set R Boxes Bubbles xiii Which list contains only integers that are NOT also whole numbers? (.A.B,.F) F,,,, H,,, G,,, J,,, Set A represents all rational numbers. Set B represents all whole numbers. Which Venn diagram correctly illustrates the relationship between Set A and Set B? (.A.B,.E,.G) A B C D Set A Set B Set A Set B Set B Set A Set B Set A, because whole numbers and rational numbers have no elements in common., because some whole numbers are not rational numbers., because all whole numbers are rational numbers., because some whole numbers are not rational numbers. Practice for each Supporting TEKS Unlawful to photocopy or project without permission Grade Mathematics STAAR Readiness Review and Practice Supporting Success Classifying Numbers viii How to Use This Book for STAAR Success
Additional In-Book Resources for STAAR Success Progress Monitoring Chart Use the chart to record your preparation needs and track your progress. Reference Materials Practice using the Reference Materials included on the front & back covers of this workbook! Unlawful to photocopy or project without permission Name Class Date Student Progress Monitoring Chart Diagnostic Mark a next to each test question that you answered correctly. Find the total. Need Review? If you did not check a question in, circle the lesson next to it. Study each circled lesson, and put a in the Practiced column when done. Post Test Mark a next to each question that you answered correctly. Find the total. Repeat or review each lesson that is unchecked in column. Question Diagnostic Need Review? Practiced Post Test Lesson.B Solving Problems Using Rational Numbers Lesson.D Solving Problems Using Ratios, Rates, and Percents Lesson.C Lesson.A Solving Problems Using Similar Shapes and Scale Drawings Modeling and Solving One-Variable Equations and Inequalities Lesson.A Representing Rates of Change Lesson.A Representing Linear Relationships Lesson.B Finding Circumference and Area of Circles Lesson.C Finding Area of Composite Figures Lesson.A Finding Volume of Prisms and Pyramids Lesson.I Finding Probabilities Lesson.H Solving Problems Using Probabilities TEKS Lesson.G Solving Problems Using Data Representations Lesson.A Comparing Data with Dot Plots and Box Plots / / Total Correct Lesson Title Centimeters STAAR GRADE MATHEMATICS REFERENCE MATERIALS LENGTH STAAR GRADE MATHEMATICS Customary Metric mile (mi) =, yards (yd) kilometer (km) =, meters (m) yard (yd) = feet REFERENCE (ft) MATERIALS meter (m) = centimeters (cm) foot (ft) = inches (in.) centimeter (cm) = millimeters (mm) LINEAR EQUATIONS VOLUME AND CAPACITY Slope-intercept = form y mx b Customary Metric y Constant of proportionality k = gallon (gal) = quarts (qt) liter (L) =, milliliters (ml) x quart (qt) = pints CIRCUMFERENCE (pt) pint (pt) = cups (c) Circle C = πr or C = πd cup (c) = fluid ounces (fl oz) AREA WEIGHT AND MASS Triangle A = h b Customary Metric parall = b Rectangle or elogram A h ton (T) =, pounds (lb) kilogram (kg) =, grams (g) pound (lb) = ounces (oz) gram (g) =, milligrams (mg) (b Trapezoid A b ) = h Circle A = πr VOLUME Prism V = Bh Pyramid V Bh = ADDITIONAL INFORMATION Pi π. or π Distance d = rt Simple interest I = Prt ( = Compound interest A P r) t Inches Student Progress Monitoring Chart Glossary The essential terms that you need to know are described as they will be found on the STAAR test. Student Answer Sheets Use the provided bubble sheets for the Diagnostic, Post Test, and Cumulative Review. Glossary of Key Terms area The number of square units needed to cover a given surface. Triangle Parallelogram Trapezoid h b A = _ bh h b A = bh h b b A = _ (b b )h Circle r A = π r box plot A graph that displays summary measures, the highest and lowest quarters of data as whiskers, and the middle two quarters of the data as a box. Least value: Lower or first quartile:. Median: Upper or third quartile: circle The set of all points (in a plane) that are equidistant from the center point. radius A line segment that connects the center to a point on the circle, or the length of that segment. The radius is one-half the diameter. diameter A line segment that passes through the center and connects two points on the circle, or the length of that segment. circumference The distance around the circle. congruent figures Figures that have the same size and shape. dot plot A number line with dots that show the frequencies of data values. radius center diameter Greatest value: Birding Club circumference Number of Eagles Seen first (or lower) quartile The median of the lower half of an ordered data set. inequality A mathematical sentence that compares quantities that are not equivalent; it uses the symbols <, >,, ³, and sometimes ¹. < x ³ interquartile range The difference between the third and first quartiles of a data set. mean or average The sum of the data values divided by the number of values. Name Class Date Form Cumulative Reviews Cumulative Review A B C D F G H J A B C D F G H J A B C D F G H J A B C D Cumulative Review A B C D F G H J A B C D F G H J A B C D F G H J A B C D F G H J A B C D F G H J A B C D F G H J A B C D Cumulative Review A B C D F G H J A B C D F G H J A B C D A B C D F G H J A B C D F G H J A B C D F G H J F G H J A B C D F G H J Cumulative Review A B C D F G H J A B C D F G H J A B C D F G H J A B C D F G H J A B C D Student Answer Sheet A B C D F G H J A B C D F G H J A B C D A B C D F G H J Glossary How to Use This Book for STAAR Success ix
Name Class Date Student Progress Monitoring Chart Unlawful to photocopy or project without permission Diagnostic Mark a next to each test question that you answered correctly. Find the total. Need Review? If you did not check a question in, circle the lesson next to it. Study each circled lesson, and put a in the Practiced column when done. Post Test Mark a next to each question that you answered correctly. Find the total. Repeat or review each lesson that is unchecked in column. Question Diagnostic Need Review? Practiced Post Test TEKS Lesson.B Solving Problems Using Rational Numbers Lesson.D Solving Problems Using Ratios, Rates, and Percents Lesson.C Lesson.A Lesson Title Included in Solving Problems Using Similar Shapes and Scale Drawings Modeling and Solving One-Variable Equations and Inequalities Lesson.A Representing Rates of Change Lesson.A Representing Linear Relationships Lesson.B Finding Circumference and Area of Circles Lesson.C Finding Area of Composite Figures Lesson.A Finding Volume of Prisms and Pyramids Lesson.I Finding Probabilities Lesson.H Solving Problems Using Probabilities Lesson.G Solving Problems Using Data Representations Lesson.A Comparing Data with Dot Plots and Box Plots / / Total Correct Student Progress Monitoring Chart
Lesson Finding Area of Composite Figures.C Determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles. In this lesson, you will solve problems involving areas of geometric figures. The table shows the basic shapes you will use, along with formulas for their areas, A. h Rectangle h b A = bh Triangle b A = _ bh Area Formulas s Square s A = s s or A = s Trapezoid h b b A = (b b )h. Find the area of each figure. a. in. b. in. cm cm h Parallelogram b A = bh Circle r A = πr ( π». or ) Unlawful to photocopy or project without permission c. A = A = d. ft in. ft in. A = A = ft Grade Mathematics STAAR Readiness Review and Practice
Geometric figures that are made up of two or more basic shapes are called composite figures. To find the area of a composite figure, first find the area of each individual shape. Then add the individual areas to find the total. Total area = I II III II I III Unlawful to photocopy or project without permission Example Finding the Area of a Composite Figure The figure is composed of an isosceles right triangle, a rectangle, and a quarter circle. Find the area of the composite figure. Area of composite figure = Area of triangle Area of rectangle Area of quarter circle Step Use the diagram to find the shapes dimensions. The base of the rectangle is cm. The radius of the quarter circle is cm. h = cm The height of the rectangle is equal to the radius, cm. The base and height of the triangle are both cm. Step Use area formulas. Area of Triangle Area of Quarter Circle A = bh A = (area of circle) = = πr =.» (.)» (.) Area of Rectangle A = bh = =». cm b = cm cm cm cm A quarter circle is one-fourth of a circle. To find its area, multiply the area of the circle by. radius h = r = cm r = = cm Step Add to find the total area. Area of figure = Area of triangle Area of rectangle Area of quarter circle»..». The area of the composite figure is about square centimeters. Lesson Finding Area of Composite Figures
Your Turn The figure is composed of a right triangle, a semicircle, and a square. Find the area of the composite figure. cm Each side of the square measures cm. The base of the triangle is = cm. The height of the triangle is The radius of the semicircle is Area of Square cm. cm. A = s s = = cm Area of Triangle A = _ bh = ( )( ) = cm Area of Semicircle A = Formula for area of a semicircle» (.)( ) Substitute π» and r =.» (.) Evaluate. = Multiply. Area of figure = Area of square Area of triangle Area of semicircle»» cm The area of the composite figure is about. Explain how to find the radius of the semicircle. Remember, the radius of a circle is equal to onehalf the diameter. A semicircle is half of a circle. square centimeters. cm Unlawful to photocopy or project without permission. List in order from least to greatest the area of the square, triangle, and semicircle in the composite figure in Your Turn. Does your list make sense? Grade Mathematics STAAR Readiness Review and Practice
To find the area of a composite figure, you may need to use congruency. If two figures are congruent, then their corresponding side and angle measures are the same. For example, if the two triangles in this figure are congruent, then: in. A Unlawful to photocopy or project without permission AB = in. CB = in. m ACB =. What must be true about the areas of congruent figures? Explain. in. in. C B in. in. The parallelograms are congruent, so their areas are equal.. A student found the area of the figure by calculating ( )() =. in.. Why does this method work? Lesson Finding Area of Composite Figures
Sometimes you may have to subtract to find the area of a composite figure. Example Finding Area by Subtracting The figure is composed of a square inside a larger square. What is the area of the unshaded region of the figure? Unshaded area = Area of large square Area of small square = ()() ()() = = The area of the unshaded region is cm. Your Turn This figure is composed of two right triangles. Use a ruler to measure the dimensions of the figure to the nearest quarter inch. What is the area of the unshaded region of the figure? The unshaded area is equal to the area of the large small triangle minus the area of the large small triangle. Use an inch ruler to measure each dimension to the nearest quarter inch. Then find the area of each triangle. Large Triangle Small Triangle Base in. Base in. cm cm Unlawful to photocopy or project without permission Height in. Height in. Area = bh = ( )( ) Area = bh = ( )( ) = = Unshaded area = = square inches Grade Mathematics STAAR Readiness Review and Practice
STAAR Practice.C Odd Set Even Set Unlawful to photocopy or project without permission The figure shown is composed of a right triangle and a parallelogram. m. m. m What is the area of the figure in square meters? (.B,.C,.E,.F) A. m B. m C. m D. m A parallelogram and a trapezoid form the figure shown below. mm mm mm Both the trapezoid and the parallelogram have height mm. mm What is the area of the figure in square millimeters? (.B,.C,.E,.F) F mm G mm H mm J mm This diagram of a baseball field is composed of a square, a semicircle, and a quarter circle. ft ft Which measurement is the best estimate of the area of the field in square feet? (.A,.B,.C,.E,.F) A, ft B, ft C, ft D, ft An ice cream shop has a sign in the shape of an ice cream cone. The sign is made using a semicircle and a triangle, as modeled below. The base of the triangle is the in. diameter of the semicircle. in. Which is the best estimate of the area of the sign in square inches? (.A,.B,.C,.E,.F) F in. G in. H in. J in. Lesson Finding Area of Composite Figures
Odd Set Even Set Jaycee created a figure by drawing a right triangle next to a rectangle. The base of the triangle is centimeters. The height of the rectangle and the height of the triangle are both centimeters. The base of the rectangle is centimeters. What is the area of the figure in square centimeters? (.B,.C,.F) A cm B cm C cm D cm A painted design on a tile is composed of a square and two right triangles. Each side of the square and the height of each triangle measure. inches. The base of each triangle measures inches. What is the total area of the painted design in square inches? (.A,.B,.C,.F) Add the areas of each shape. A figure is composed of a triangle and a rectangle. The height of the triangle and the height of the rectangle both measure inch. The base of the triangle and the base of the rectangle both measure inches. What is the area of the figure in square inches? (.B,.C,.F)t F in. G in. H in. J in. The front of a house is composed of a trapezoid and a rectangle. The height of the rectangle is feet. The base of the rectangle and one base of the trapezoid each measure feet. The height of the trapezoid is feet and its second base measures feet. What is the area of the front of the house in square feet? (.A,.B,.C,.F) Draw and label a diagram to help you solve the problem. Unlawful to photocopy or project without permission Grade Mathematics STAAR Readiness Review and Practice
Odd Set A square and a right triangle were used to form the following figure. Even Set The figure below is composed of a right triangle inside a rectangle. Unlawful to photocopy or project without permission cm cm cm What is the area of the unshaded region of this figure in square centimeters? (.B,.C,.E,.F) ft ft ft What is the area of the unshaded region of this figure in square feet? (.B,.C,.E,.F) Vince used a parallelogram and a rectangle to form the figure shown. Use a ruler to measure the dimensions of the figure to the nearest half of a centimeter. How do you measure the base and height of a parallelogram? A square and a trapezoid were used to form the following figure. Use a ruler to measure the dimensions of the figure to the nearest half of a centimeter. Which is closest to the area of the figure in square centimeters? (.B,.C,.E,.F) Which measurement is closest to the area of the figure in square centimeters? (.B,.C,.E,.F) A cm C cm B cm D cm F cm H cm G cm J cm Lesson Finding Area of Composite Figures
Odd Set Even Set This model of the side view of a speaker is composed of a square and a trapezoid. Use a ruler to measure the dimensions of the model to the nearest quarter of an inch. Which of the following is closest to the area of the figure in square inches? (.A,.B,.C,.E,.F) A in. C in. B in. D in. A rectangle and four semicircles were used to create the following figure. Use a ruler to measure the dimensions of the figure to the nearest half of a centimeter. Which is the best estimate of the area of the unshaded region of this figure in square centimeters? (.B,.C,.E,.F) A cm C cm B cm D cm This model of the front of a steel beam is composed of two rectangles and a square. Use a ruler to measure the dimensions of the model to the nearest quarter of an inch. Which measurement is closest to the area of the beam in square inches? (.A,.B,.C,.E,.F) F G in. H in. in. J in. The figure below shows three rectangles inside a parallelogram. Use a ruler to measure the dimensions of the figure to the nearest half of a centimeter. Which measurement is closest to the area of the unshaded region of this figure in square centimeters? (.B,.C,.E,.F) F cm G cm H cm J cm Can you eliminate any answer choices by estimating? Unlawful to photocopy or project without permission Grade Mathematics STAAR Readiness Review and Practice
Odd Set Even Set Paige used three congruent triangles and a semicircle to design the tulip logo shown. A flower garden is composed of four congruent semicircles and one square, as shown below. Unlawful to photocopy or project without permission cm cm Which is the best estimate of the area of the logo in square centimeters? (.A,.B,.C,.E,.F) A cm B cm C cm D cm How can you find the diameter of the semicircle? m Which measurement is closest to the area of the figure in square meters? (.A,.B,.C,.E,.F) F m G m H m J m Two congruent semicircles form one circle. A parking lot has six sections, as modeled below. Two sections are congruent right triangles and four sections are congruent parallelograms.. ft A traffic sign is constructed from a rectangle and two congruent triangles, as modeled below.. m m ft. ft Which is the best estimate of the area of the parking lot in square feet? (.A,.B,.C,.E,.F) A ft B ft C ft D ft. m. m. m m Which is the best estimate of the area of the sign in square meters? (.A,.B,.C,.E,.F) F m G m H m J m The triangles have the same base and height. Lesson Finding Area of Composite Figures
Cumulative Review The figure shown is composed of a right triangle and a rectangle.. ft ft. ft What is the area of the figure in square feet? (.C Lesson ) A. ft C. ft B. ft D. ft Which statement best describes the unit rate for the data shown in the table? (.A Lesson ) F x y As x increases by, y increases by. G The ratio of y to x is to. H As x increases by, y decreases by. J The value of y changes by each time x changes by. A circle has a radius of yards. What is the approximate circumference of the circle? (.B Lesson ) A. yd B. yd C. yd D. yd A map of Palo Alto Battlefield National Historical Park uses a scale of centimeters to kilometers. There are kilometers of hiking trails shown on the map. What is the length in centimeters of the segments representing hiking trails on the map? (.C Lesson ) F cm H cm G cm J cm What is the volume of the triangular prism shown below? (.A Lesson ) cm cm cm A,. cm C. cm B, cm D cm One brand of frozen broccoli sells for $. per ounce. What is the price of a -ounce bag of broccoli? Give your answer in dollars and cents. (.D Lesson ) Unlawful to photocopy or project without permission Grade Mathematics STAAR Readiness Review and Practice
Unlawful to photocopy or project without permission A hula hoop is in the shape of a circle with a diameter of. inches. Which measurement is closest to the circumference of the hula hoop? (.B Lesson ) A in. B in. C in. D in. What is the solution to the inequality? (.A Lesson ) F x ³ G x H x J x ³ x ³ x Which equation best represents the relationship between x and y in the graph? (.A Lesson ) F y = x G y = x H y = x J y = x y x A brick is in the shape of a rectangular prism. The dimensions of the brick are shown in the diagram. This diagram of a park is composed of a square, a semicircle, and a quarter circle. yd. in. in. in. What is the volume of the brick in cubic inches? (.A Lesson ) A. in. B. in. C. in. D. in. yd Which measurement is the best estimate of the area of the park in square yards? (.C Lesson ) A, yd B yd C, yd D, yd Lessons Cumulative Review
The cost of cupcakes at Barry s Bakery, including $. sales tax, is $.. What is the cost of one cupcake, not including sales tax? (.B Lesson ) F $. H $. G $. J $. The base of a rectangular pyramid has dimensions meters by meters. The height of the pyramid is meters. What is the volume of the rectangular pyramid in cubic meters? (.A Lesson ) Hopping at a constant rate, it takes seconds for a goliath frog to hop yards. Let y represent distance and x represent time. Which equation represents the unit hopping rate of the goliath frog? (.A Lesson ) F y = x G y = x H y = x J y = x This model of the side view of a house is composed of a square and a trapezoid. Use a ruler to measure the dimensions of the model to the nearest quarter of an inch. Which of the following is closest to the area of the figure in square inches? (.C Lesson ) A in. C in. B in. D in. What value of x makes the equation modeled below true? (.A Lesson ) x x x F x = G x = H x = J x = Unlawful to photocopy or project without permission Grade Mathematics STAAR Readiness Review and Practice
Teacher s Edition Using This Teacher s Edition The Sirius Grade Mathematics STAAR Readiness Review and Practice workbook provides comprehensive and systematic coverage of the Readiness TEKS that make up % of the STAAR Grade Mathematics test. The Lesson STAAR Practice includes over test items with unique problem types. STAAR Practice Resources for Teachers Two sets of paired questions for use in class and at home, or in groups and individually. Assignment Guide shows exercises are arranged in increasing order of difficulty (Easy, Medium, Hard). Margin notes include: Test-Taking Strategy Error Prevention Teaching Tip English Language Learners Full solutions next to each question. ASSIGNMENT GUIDE Easy Medium Hard D Find the area of each shape. Then add to find the total. Parallelogram: A = bh = ()(.) =. m Triangle: A = _ bh = _ (.)(.) =. m Total:.. =. m C Add the areas of the shapes that make up the field. Square: A = bh = ()() =, ft Semicircle: A = π r = π () =,π ft Quarter circle: A = π r = π () =,π ft Total: A =,,π,π»,,(.),(.) =,,,. =,. ft Answer C is the best estimate for the area of the field. TEST-TAKING STRATEGY Point out that the answer choices are not close in value, so students may be able to identify the correct answer by estimating. For example, students can simplify calculations by using π» in the formula for area of a circle. Each pair of questions includes a sample problem name. STAAR Practice.C Odd Set Even Set The figure shown is composed of a right A parallelogram and a trapezoid form the triangle and a parallelogram. figure shown below. mm m mm mm mm. m. m Both the trapezoid and the parallelogram have What is the area of the figure in square height mm. meters? (.B,.C,.E,.F) A. m What is the area of the figure in square B. m millimeters? (.B,.C,.E,.F) C. m F mm D. m G mm H mm J mm Given Diagram of Composite Figure, Find Area This diagram of a baseball field is An ice cream shop has a sign in the shape composed of a square, a semicircle, and a of an ice cream cone. The sign is made quarter circle. using a semicircle and a triangle, as modeled below. The base of the triangle is the in. diameter of the semicircle. ft in. ft Which measurement is the best estimate of the area of the field in square feet? Which is the best estimate of the area (.A,.B,.C,.E,.F) of the sign in square inches? (.A,.B, A, ft.c,.e,.f) B, ft F in. C, ft G in. D, ft H in. J in. Given Diagram of Real-World Composite Figure, Find (Estimate of) Area Lesson Finding Area of Composite Figures G Find the area of each shape. Then add to find the total. Parallelogram: A = bh = ()() = mm Trapezoid: A = _ (b b )h = _ ( )() = _ ()() = mm Total: = mm Red boxes on mini student pages show correct answers. J Add the areas of the shapes that make up the sign. Triangle: A = _ bh = _ ()() = in. Semicircle: A = π r = π ().() =. in. Total: A». =. in. Answer J is the best estimate for the area of the sign. TEACHING TIP Be sure students understand that a semicircle is onehalf of a circle. The area of a circle is A = π r, so the area of a semicircle is A = π r. Students can use this formula to find the area of a semicircle, or they can find the area of a circle and then divide the result by. Show that both methods give the same answer. Naming Problems Helps Students Read for Understanding Writing a problem name gives students a concrete task to do that helps them read and re-read the problem for understanding. A problem name has two elements: what is given and what is asked for. Its format is: Given, Find Naming can help students see a problem s larger structure and give them confidence to name something is to know it. After naming, students often recognize that the problem is familiar and they can see how to move forward and solve it. Suggested problem name STAAR Practice.C Odd Set A painted design on a tile is composed of a square and two right triangles. Each side of the square and the height of each triangle measure. inches. The base of each triangle measures inches. What is the total area of the painted design in square inches? (.A,.B,.C,.F) Even Set The front of a house is composed of a trapezoid and a rectangle. The height of the rectangle is feet. The base of the rectangle and one base of the trapezoid each measure feet. The height of the trapezoid is feet and its second base measures feet. What is the area of the front of the house in square feet? (.A,.B,.C,.F) Naming easy math problems prepares students for naming complex problems. Draw and label a diagram to help you solve the problem. How is this story problem similar to Given Description of Real-World Composite Figure, Find above? Area Using This Teacher s Guide T
Teacher s Edition Lesson Finding Area of Composite Figures.C Determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles. In this lesson, you will solve problems involving areas of geometric figures. The table shows the basic shapes you will use, along with formulas for their areas, A. Area Formulas Rectangle Square Parallelogram h s h b A = bh s b A = s s or A = s A = bh Triangle Trapezoid Circle b h h r b A = _ bh b A = (b b )h ( A = πr π». or ). Find the area of each figure. a. in. b. in. cm cm in. cm A = A = c. d. ft in. ft in. ft in.² ft A = A = Grade Mathematics STAAR Readiness Review and Practice Geometric figures that are made up of two or more basic shapes are called composite figures. To find the area of a composite figure, first find the area of each individual shape. Then add the individual areas to find the total. I Total area = I II III II III Example Finding the Area of a Composite Figure The figure is composed of an isosceles right triangle, a rectangle, and a quarter circle. Find the area of the composite figure. cm cm Area of composite figure = Area of triangle Area of rectangle Area of quarter circle Step Use the diagram to find the shapes dimensions. The base of the rectangle is cm. The radius of the quarter circle is cm. The height of the rectangle is equal to the radius, cm. The base and height of the triangle are both cm. h = cm cm cm h = r = cm Step Use area formulas. Area of Triangle Area of Quarter Circle A = bh A = (area of circle) = = πr =.» (.)» (.)». b = cm r = = cm A quarter circle is one-fourth of a circle. To find its area, multiply the area of the circle by. radius Area of Rectangle A = bh = = Step Add to find the total area. Area of figure = Area of triangle Area of rectangle Area of quarter circle»..». The area of the composite figure is about square centimeters. Lesson Finding Area of Composite Figures Lesson Finding Area of Composite Figures
Teacher s Edition Your Turn The figure is composed of a right triangle, a semicircle, and a square. Find the area of the composite figure. Each side of the square measures cm. The base of the triangle is = cm. The height of the triangle is cm. The radius of the semicircle is cm. Remember, the radius of a circle is equal to onehalf the diameter. cm cm Area of Square A = s s = = cm Area of Triangle A = _ bh = ( )( ) = cm A semicircle is Area of Semicircle half of a circle. A = πr Formula for area of a semicircle» (.)( ) Substitute π». and r =.» (.) Evaluate.. = Multiply. Area of figure = Area of square Area of triangle Area of semicircle.»» cm. The area of the composite figure is about square centimeters. The diameter is the same as the side length of the square, cm. So the radius is = cm.. Explain how to find the radius of the semicircle.. List in order from least to greatest the area of the square, triangle, and semicircle in the composite figure in Your Turn. Does your list semicircle < triangle < square; Yes, the square is largest, the triangle is slightly larger than half the square (because one side is longer than the side length of the square), and the semicircle is smallest at less than half the square. make sense? Grade Mathematics STAAR Readiness Review and Practice To find the area of a composite figure, you may need to use congruency. If two figures are congruent, then their corresponding side and angle measures are the same. For example, if the two triangles in this figure are congruent, then: in. A AB = in. CB = in. m ACB = B C in.. What must be true about the areas of congruent figures? Explain. The areas are the same; Sample answer: Congruent figures have the same dimensions, so you perform the same calculation to find their areas. in. in. in.. A student found the area of the figure by calculating ( )() =. in.. Why does this method work? The figure is a trapezoid with bases in. and in. and height in. The calculation uses the formula for the area of a trapezoid. Lesson Finding Area of Composite Figures Grade Mathematics STAAR Readiness Review and Practice
Teacher s Edition Sometimes you may have to subtract to find the area of a composite figure. Example Finding Area by Subtracting The figure is composed of a square inside a larger square. What is the area of the unshaded region of the figure? cm cm Unshaded area = Area of large square Area of small square = ()() ()() = = The area of the unshaded region is cm. Your Turn This figure is composed of two right triangles. Use a ruler to measure the dimensions of the figure to the nearest quarter inch. What is the area of the unshaded region of the figure? The unshaded area is equal to the area of the large small triangle minus the area of the large small triangle. Use an inch ruler to measure each dimension to the nearest quarter inch. Then find the area of each triangle. Large Triangle Small Triangle Base in. Base in. Height in. Height in. Area = bh = ( )( ) Area = bh = ( )( ) = _ = Unshaded area = = square inches _ Grade Mathematics STAAR Readiness Review and Practice Notes Lesson Finding Area of Composite Figures
Teacher s Edition ASSIGNMENT GUIDE Easy Medium Hard D Find the area of each shape. Then add to find the total. Parallelogram: A = bh = ()(.) =. m Triangle: A = _ bh = _ (.)(.) =. m Total:.. =. m C Add the areas of the shapes that make up the field. Square: A = bh = ()() =, ft Semicircle: A = π r = π () Quarter circle: A = π r Total: = π () =,π ft =,π ft A =,,π,π»,,(.),(.) =,,,. =,. ft Answer C is the best estimate for the area of the field. TEST-TAKING STRATEGY Point out that the answer choices are not close in value, so students may be able to identify the correct answer by estimating. For example, students can simplify calculations by using π» in the formula for area of a circle. STAAR Practice.C Odd Set Even Set The figure shown is composed of a right triangle and a parallelogram. A parallelogram and a trapezoid form the figure shown below. mm m mm. m. m What is the area of the figure in square meters? (.B,.C,.E,.F) mm mm Both the trapezoid and the parallelogram have height mm. A. m B. m What is the area of the figure in square millimeters? (.B,.C,.E,.F) C. m F mm D. m G mm H mm J mm Given Diagram of Composite Figure, Find Area This diagram of a baseball field is composed of a square, a semicircle, and a quarter circle. ft An ice cream shop has a sign in the shape of an ice cream cone. The sign is made using a semicircle and a triangle, as modeled below. in. The base of the triangle is the diameter of the semicircle. ft in. Which measurement is the best estimate of the area of the field in square feet? (.A,.B,.C,.E,.F) A, ft Which is the best estimate of the area of the sign in square inches? (.A,.B,.C,.E,.F) B, ft F in. C, ft G in. D, ft H in. J in. Given Diagram of Real-World Composite Figure, Find (Estimate of) Area Lesson Finding Area of Composite Figures G Find the area of each shape. Then add to find the total. Parallelogram: A = bh = ()() = mm Trapezoid: A = _ (b b )h = _ ( )() = _ ()() = mm Total: = mm J Add the areas of the shapes that make up the sign. Triangle: A = _ bh = _ Semicircle: A = π r ()() = in. = π ().() =. in. Total: A». =. in. Answer J is the best estimate for the area of the sign. TEACHING TIP Be sure students understand that a semicircle is onehalf of a circle. The area of a circle is A = π r, so the area of a semicircle is A = π r. Students can use this formula to find the area of a semicircle, or they can find the area of a circle and then divide the result by. Show that both methods give the same answer. Grade Mathematics STAAR Readiness Review and Practice
Teacher s Edition A Find the area of each shape. Then add to find the total. Rectangle: A = bh = ()() = cm Triangle: A = _ bh = _ ()() = cm Total: = cm TEST-TAKING STRATEGY Point out that once students have found the area of the rectangle, they can eliminate answers B, C, and D because the total area must be greater than cm.. Add the area of the square to the combined areas of the triangles. The triangles have the same base and height, so they have equal areas. Square: A = bh = (.)(.) =. in. Each triangle: A = bh = ()(.) =. in. Painted design: A =... =. in. TEACHING TIP Encourage students to sketch each figure before trying to find the answer. Odd Set Even Set Jaycee created a figure by drawing a right triangle next to a rectangle. The base of the triangle is centimeters. The height of the rectangle and the height of the triangle are both centimeters. The base of the rectangle is centimeters. A figure is composed of a triangle and a rectangle. The height of the triangle and the height of the rectangle both measure inch. The base of the triangle and the base of the rectangle both What is the area of the figure in square centimeters? (.B,.C,.F) A cm B cm C cm D cm Add the areas of each shape. measure inches. What is the area of the figure in square inches? (.B,.C,.F)t F in. G in. H in. J in. Given Description of Composite Figure, Find Area A painted design on a tile is composed of a square and two right triangles. Each side of the square and the height of each triangle measure. inches. The base of each triangle measures inches. What is the total area of the painted design in square inches? (.A,.B,.C,.F) The front of a house is composed of a trapezoid and a rectangle. The height of the rectangle is feet. The base of the rectangle and one base of the trapezoid each measure feet. The height of the trapezoid is feet and its second base measures feet. What is the area of the front of the house in square feet? (.A,.B,.C,.F) Given Description of Real-World Composite Figure, Find Area Draw and label a diagram to help you solve the problem. Grade Mathematics STAAR Readiness Review and Practice H Find the area of each shape. Then add to find the total. Rectangle: A = bh = ( _ ) ( _ ) = ( ) ( _ ) = _ in. Triangle: A = _ = ( _ bh = _ ) ( ( _ ) ( _ ) ) ( _ ) = _ in. Total: = in. TEST-TAKING STRATEGY Estimate by rounding mixed numbers to the nearest whole number. For example, round _ to. Then the rectangle s area is about _ = _ and the triangle s area is about _ = _ ;» =. Add the area of the trapezoid to the area of the rectangle. Trapezoid: A = _ (b b )h = _ ( )() = ft Rectangle: A = bh = ()() = ft Front of the house: A = = ft Lesson Finding Area of Composite Figures
Teacher s Edition. Subtract the area of the square from the area of the triangle. Triangle: A = _ bh = _ ()() =. cm Square: A = bh = ()() = cm Unshaded region: A =. =. cm ERROR PREVENTION Students who answered used b = for the base of the triangle. Tell students that they may need to perform calculations with the measures in a diagram before using a formula. Show that the base of the triangle is =. B Measure and find the area of each shape. Then add to find the total. Rectangle: To the nearest half of a centimeter, the base is. cm and the height is cm. A = bh = (.)() = cm Parallelogram: To the nearest half of a centimeter, the base is. cm and the height is cm. A = bh = (.)() = cm Total: A = = cm Odd Set Even Set A square and a right triangle were used to form the following figure. The figure below is composed of a right triangle inside a rectangle. cm ft ft ft cm cm What is the area of the unshaded region of this figure in square centimeters? (.B,.C,.E,.F) Vince used a parallelogram and a rectangle to form the figure shown. Use a ruler to measure the dimensions of the figure to the nearest half of a centimeter. What is the area of the unshaded region of this figure in square feet? (.B,.C,.E,.F) Given Diagram of (Nested) Composite Figure, Find Area A square and a trapezoid were used to form the following figure. Use a ruler to measure the dimensions of the figure to the nearest half of a centimeter. How do you measure the base and height of a parallelogram? Which is closest to the area of the figure in square centimeters? (.B,.C,.E,.F) Which measurement is closest to the area of the figure in square centimeters? (.B,.C,.E,.F) A cm C cm F cm H cm B cm D cm G cm J cm Given Composite Figure, Measure and Find Area Lesson Finding Area of Composite Figures Subtract the areas of the two shaded triangles from the area of the rectangle. Rectangle: A = bh = () = ft Each shaded triangle: ()() = ft A = bh = Unshaded region: A = = ft ENGLISH LANGUAGE LEARNERS Explain that unshaded region refers to the portion of the figure that is white. Point out that the unshaded region is the larger white right triangle, while the shaded region is made up of two smaller right triangles. G Measure and find the area of each shape. Then add to find the total. Square: To the nearest half of a centimeter, the side length is. cm. A = bh = (.)(.) =. cm Trapezoid: To the nearest half of a centimeter, the bases are. cm and. cm, and the height is cm. A = _ (b b )h = _ (..)() =. cm Total: A =.. =. cm Answer G is closest to the area. Grade Mathematics STAAR Readiness Review and Practice
Teacher s Edition A Measure and find the area of each shape. Then add to find the total. Square: To the nearest quarter of an inch, the side length is _ in. A = bh = _ ( ) ( _ ) = in. Trapezoid: To the nearest quarter of an inch, the bases are _ in. and _ in., and the height is _ in. A = _ (b b )h = _ ( ) ( _ ) = in. Total: A = = = in. TEST-TAKING STRATEGY Once students have found the area of the square, they can eliminate answer C. Further, the area of the trapezoid is greater than the area of the square, so the total area must be greater than the area of two squares, or ( ) = = ; this eliminates answer B. D Subtract the areas of the four semicircles from the area of the rectangle. To the nearest half of a centimeter, the rectangle s base is. cm and its height is. cm. The radius of each semicircle is about cm. Unshaded region: A = A rectangle A semicircle = bh ( π r ) = (.)(.) π( )».. =. cm Answer D is the best estimate of the area. Odd Set Even Set This model of the side view of a speaker is composed of a square and a trapezoid. Use a ruler to measure the dimensions of the model to the nearest quarter of an inch. This model of the front of a steel beam is composed of two rectangles and a square. Use a ruler to measure the dimensions of the model to the nearest quarter of an inch. Which of the following is closest to the area of the figure in square inches? (.A,.B,.C,.E,.F) Which measurement is closest to the area of the beam in square inches? (.A,.B,.C,.E,.F) F in. H in. A in. C in. G in. J in. B in. D in. Given Real-World Composite Figure, Measure and Find Area Can you eliminate any answer choices by estimating? A rectangle and four semicircles were used to create the following figure. Use a ruler to measure the dimensions of the figure to the nearest half of a centimeter. The figure below shows three rectangles inside a parallelogram. Use a ruler to measure the dimensions of the figure to the nearest half of a centimeter. Which measurement is closest to the area of the unshaded region of this figure in square centimeters? (.B,.C,.E,.F) Which is the best estimate of the area of the unshaded region of this figure in square centimeters? (.B,.C,.E,.F) F cm G cm H cm A cm C cm J cm B cm D cm Given (Nested) Composite Figure, Measure and Find Area Grade Mathematics STAAR Readiness Review and Practice J Measure and find the area of each shape. Then add to find the total. The two rectangles have the same dimensions. To the nearest quarter of an inch, the bases are _ heights are _ in. Each rectangle: in.and the A = bh = ( _ ) ( _ ) = _ ( ) ( ) _ = in. Square: To the nearest quarter of an inch, the side length is in. A = bh = ( ) ( ) = in. Total: A = _ = = _ in. Answer J is closest to the area. F Subtract the areas of the three rectangles from the area of the parallelogram. To the nearest half of a centimeter, the base of each rectangle is cm and the height is cm. The parallelogram s base is. cm and its height is. cm. Unshaded region: A = A parallelogram A rectangle = bh (bh) = (.)(.) ()() =. =. cm Answer F is closest to the area. ERROR PREVENTION Point out that the measurements in the answer choices are close together, and stress the importance of measuring carefully and accurately. Lesson Finding Area of Composite Figures
Teacher s Edition A Find the area of each shape. Then add to find the total. Each triangle: A = _ bh = _ Semicircle: A = π r = π (.) ()() = cm».(.)» cm Total: A» = cm Answer A is the best estimate of the area. TEACHING TIP Not all dimensions are labeled on the diagram. Guide students to use the information about congruent triangles to determine the diameter of the semicircle. B The parking lot is a rectangle. Its base is ()().» = ft. Round the height from. ft to ft. A = bh» ()() = ft Answer B is the best estimate of the area. TEACHING TIP As a class, discuss other ways to estimate the area. For example, students could estimate and add the areas of the triangles and parallelograms. Odd Set Even Set Paige used three congruent triangles and a semicircle to design the tulip logo shown. A flower garden is composed of four congruent semicircles and one square, as shown below. cm cm How can you find the diameter of the semicircle? m Two congruent semicircles form one circle. Which is the best estimate of the area of the logo in square centimeters? (.A,.B,.C,.E,.F) A cm Which measurement is closest to the area of the figure in square meters? (.A,.B,.C,.E,.F) B cm F m C cm G m D cm H m J m Given Diagram of Composite Figure (and Congruency Information), Find Area A parking lot has six sections, as modeled below. Two sections are congruent right triangles and four sections are congruent parallelograms. A traffic sign is constructed from a rectangle and two congruent triangles, as modeled below.. ft. m m. ft. m ft Which is the best estimate of the area of the parking lot in square feet? (.A,.B,.C,.E,.F) A ft B ft. m The triangles have the same base and height.. m m Which is the best estimate of the area of the sign in square meters? (.A,.B,.C,.E,.F) F m C ft G m D ft H m J m Given Diagram of Real-World Composite Figure (and Congruency Information), Find (Estimate of) Area Lesson Finding Area of Composite Figures H Find the area of each shape. Then add to find the total. Square: A = bh = ()() = m The four congruent semicircles combine to form two circles. So, multiply the formula for area of a circle by. Semicircles: A = π r = π () = π» (.) =. m Total: A». =. m Answer H is closest to the area. ENGLISH LANGUAGE LEARNERS Remind students that congruent figures have the same size and shape. Each semicircle has the same diameter, m, and the same area. G Find the area of each shape. Then add to find the total. Each large triangle: The base of each triangle is ()() = m. The height of each triangle is.. A =» bh» =. m. ()(.) =. m Rectangle: The height is (.)() = m. Round the base from. m to m. A = bh» ()() = m Total: A».. = m Answer G is the best estimate of the area. Grade Mathematics STAAR Readiness Review and Practice
Teacher s Edition C Find the area of each shape. Then add to find the total. Rectangle: A = bh = ()(.) =. ft Triangle: A = _ bh = _ (.)(.) =. ft Total:.. =. ft TEACHING TIP Point out that the height of the triangle, which is not labeled on the diagram, can be determined because the problem states that the figure on the left is a rectangle. Since opposite sides of a rectangle are congruent, the length of the side the triangle shares with the rectangle is. ft. H Determine the ratio of y to x for each corresponding x- and y-value. y_ x : = = = The ratio of y to x is to. The unit rate is described by H. B The radius is given, so use the circumference formula C = πr: C = πr» (.)()». Cumulative Review The figure shown is composed of a right triangle and a rectangle.. ft ft A map of Palo Alto Battlefield National Historical Park uses a scale of centimeters to kilometers. There are kilometers of hiking trails shown on the map. What is the length in centimeters of the segments representing hiking trails on the map? (.C Lesson ) F cm H cm G cm J cm. ft What is the area of the figure in square feet? (.C Lesson ) A. ft C. ft What is the volume of the triangular prism shown below? (.A Lesson ) B. ft D. ft Which statement best describes the unit rate for the data shown in the table? (.A Lesson ) x y cm cm cm A,. cm C. cm B, cm D cm F As x increases by, y increases by. G The ratio of y to x is to. H As x increases by, y decreases by. J The value of y changes by each time x changes by. One brand of frozen broccoli sells for $. per ounce. What is the price of a -ounce bag of broccoli? Give your answer in dollars and cents. (.D Lesson ) A circle has a radius of yards. What is the approximate circumference of the circle? (.B Lesson ) A. yd C. yd B. yd D. yd Grade Mathematics STAAR Readiness Review and Practice J Use the given map scale and the actual known length to set up a proportion. Let x represent the length of hiking trails shown. cm km = x cm km ()() = x = x cm = x The lines representing hiking trails have a total length of centimeters. A The volume is V = Bh, where B is the area of the triangular base and h is the height of the prism. First, find B. B = _ bh B = _ ()() = cm Then substitute B and h in the volume formula. V = Bh = () ( ) =,. cm. Multiply the unit price by the mass of the bag. oz $. oz = $. The price of a -oz bag of broccoli is $.. TEACHING TIP Remind students that one cent is equal to $., so $. per ounce can be read as cents per ounce. Multiplying by. gives the answer as a decimal in which the whole-number part represents dollars and the number of hundredths represents cents. Lessons Cumulative Review
Teacher s Edition B The diameter is given, so use the circumference formula C = πd: C = πd».(.)». Answer B is closest to. inches. TEST-TAKING STRATEGY Since no two of the answer choices are close in value, the correct choice can be found by estimating. () =, which is closest to answer B. F Solve the two-step inequality using inverse operations. x ³ x x x ³ x x ³ x or x ³ B The brick is a rectangular prism, so its volume is V = Bh, where B is the area of the base and h is the height of the prism. First, find B. B = bh = ()() = in. Then substitute B and h in the volume formula. V = Bh = ()(.) =. in. A hula hoop is in the shape of a circle with a diameter of. inches. Which measurement is closest to the circumference of the hula hoop? (.B Lesson ) A in. B in. C in. D in. What is the solution to the inequality? (.A Lesson ) x ³ x F x ³ G x H x J x ³ A brick is in the shape of a rectangular prism. The dimensions of the brick are shown in the diagram.. in. in. in. What is the volume of the brick in cubic inches? (.A Lesson ) A. in. B. in. C. in. D. in. Which equation best represents the relationship between x and y in the graph? (.A Lesson ) y x F y = x G y = x H y = x J y = x This diagram of a park is composed of a square, a semicircle, and a quarter circle. yd yd Which measurement is the best estimate of the area of the park in square yards? (.C Lesson ) A, yd B yd C, yd D, yd Lessons Cumulative Review H Since the graph is a line, use the slope-intercept form of a linear equation, y = mx b. First, find b. The line crosses the y-axis at (, ), so b =. Next, use the graph to find m. Choose two points on the line. You could use (, ) and (, ). Starting from (, ) and moving to (, ), the change in y (rise) is units and the change in x (run) is units, so m = rise run = _. In slope-intercept form, the equation of the line is y = _ x, answer H. TEACHING TIP Point out that although any two points on the line can be used to find the slope, choosing points with integer coordinates will make an accurate calculation possible. Students could use any pair of the points (, ), (, ), (, ), (, ), and (, ). D Add the areas of the shapes that make up the park. Square: A = bh = ()() = yd Semicircle: A = π r = π() Quarter circle: A = π r π() = Total: =.π yd = π yd A =.π π».() () =. =,. yd Answer D is the best estimate for the area of the park. Grade Mathematics STAAR Readiness Review and Practice
Teacher s Edition F Use subtraction and division to find the cost of one cupcake. First, subtract to find the cost of cupcakes without sales tax. $.. = $. Then, divide this cost by to find the cost of one cupcake. $. $. The cost of one cupcake is $.. The volume of a pyramid Bh, where B is the area of is V = _ the base and h is the height of the pyramid. First, find B. B = bh ()() = m Then substitute B and h in the volume formula. V = _ Bh = _ ()() = ()() = m F Use d = rt to find the rate. = r = r = r The goliath frog s rate is _ yards per second. Since y represents distance and x represents time, equation F represents the hopping rate. The cost of cupcakes at Barry s Bakery, including $. sales tax, is $.. What is the cost of one cupcake, not including sales tax? (.B Lesson ) F $. H $. This model of the side view of a house is composed of a square and a trapezoid. Use a ruler to measure the dimensions of the model to the nearest quarter of an inch. G $. J $. The base of a rectangular pyramid has dimensions meters by meters. The height of the pyramid is meters. What is the volume of the rectangular pyramid in cubic meters? (.A Lesson ) Which of the following is closest to the area of the figure in square inches? (.C Lesson ) A B in. C in. D in. in. What value of x makes the equation modeled below true? (.A Lesson ) Hopping at a constant rate, it takes seconds for a goliath frog to hop yards. Let y represent distance and x represent time. Which equation represents the unit hopping rate of the goliath frog? (.A Lesson ) x x x F y = x G y = x F x = G x = H x = H y = x J x = J y = x Grade Mathematics STAAR Readiness Review and Practice D Measure the dimensions of each shape and then compute the areas. Square: The sides measure _ in. A = bh = _ ( ) ( _ ) = in. Trapezoid: The measures are: short base _ in., long base _ in., height _ in. A = _ (b b )h = _ ( ) ( _ ) = in. Add the areas of each shape in square inches to find the area of the model. A = = = in. The area in D is the closest measure. F For the scale to be balanced, the value of the expression on the left side has to have the same value as the expression on the right side. Remove x-piece and unit block from each side of the scale. This leaves unit blocks on the left side and x-piece on the right. So, each x-piece must have a value of. TEACHING TIP Remind students that they can check their answers by writing the value of x above each x-piece in the model and adding to find the total value on each side of the scale. The total should be the same on both sides of the scale. Lessons Cumulative Review
STAAR GRADE MATHEMATICS REFERENCE MATERIALS LINEAR EQUATIONS Slope-intercept form y = mx b Inches Constant of proportionality k = y x CIRCUMFERENCE Circle C = πr or C = πd AREA Triangle A = h b Rectangle or parallelogram A = bh Trapezoid A = (b b h ) Circle A = π r VOLUME Prism V = Bh Pyramid V = Bh ADDITIONAL INFORMATION Pi π. or π Distance d = rt Simple interest I = P rt Compound interest A = P ( r) t
GRADE MATHEMATICS CONTENTS Visit SiriusEducationSolutions.com for additional STAAR EOC resources. Solving Problems Using Rational Numbers Solving Problems Using Ratios, Rates, and Percents Solving Problems Using Similar Shapes and Scale Drawings CUMULATIVE REVIEW Modeling and Solving One-Variable Equations and Inequalities Representing Rates of Change Representing Linear Relationships CUMULATIVE REVIEW Finding Area and Circumference of Circles Finding Area of Composite Figures Finding Volume of Prisms and Pyramids CUMULATIVE REVIEW Finding Probabilities Solving Problems Using Probabilities Solving Problems Using Data Representations Comparing Data with Dot Plots and Box Plots CUMULATIVE REVIEW Supporting Success Use with your class for free! Printed in Texas on recycled paper.