Mathematics Scope & Sequence Grade 5 Revised: August 24, 2012 Topic 19: Graphs and Data First Nine Weeks (44 ) 5.13B describe characteristics of data presented in tables and graphs including median, mode, and range. 5.13A use tables of related number pairs to make line graphs. 5.13C graph a given set of data using an appropriate graphical representation such as a picture or line graph. Interpret data tables to describe median, mode, and range. Describe the process of how to find median (given and even number and an odd number of data), mode (can be none, zero, or more than one mode), and the range of a given data set. Horizontal and vertical bar graphs and data tables Given a data table, match it to the line graph. Given a line graph, match it to the data table. Given a line graph, name all points and organize the related number pairs in a table with appropriate labels. Read points from table as (x, y) and relate the points on the graph labeled with a capital letter. Choose the appropriate graph could include, bar, line, line plot, circle Textbook Sections: 19-1, 19-2, 19-3, 19-5, 19-6 Aug.27 thru Oct. 26 Topic 1: Place Value and Numeration Topic 2: Addition and Subtraction Number Sense 5.1A use place value to read, write, compare, and order whole numbers through 999,999,999,999. 5.1B use place value to read, write, compare, and order decimals through the thousandths place. Distinguish between a digit and a number. Students need to see numbers represented in words, standard form, and expanded form. Appropriately use the word and to represent the decimal. Describe the place and the value of a digit. Compare and order whole numbers and decimals using symbols and words. Create a number smaller, in-between, or larger than given numbers Textbook Sections: 1-1, 1-2, 1-3, 1-4, 1-5 5.3A use addition and subtraction to solve problems involving whole numbers and decimals. Textbook Sections: 2-1, 2-2, 2-3, 2-4 Use addition and subtraction involving whole numbers through 999,999,999 and decimals through thousandths in problem solving. Recognize that addition and subtraction are inverse operations. Use multi-step problems. CCA Sept. 17-21 First Nine Weeks continues on next page.
Topic 3: Adding and Subtracting to Solve Problems 5.3A use addition and subtraction to solve problems involving whole numbers and decimals. Textbook Sections: 3-1, 3-2, 3-3, 3-4 Use addition and subtraction involving whole numbers through 999,999,999 and decimals through thousandths in problem solving. Recognize that addition and subtraction are inverse operations. Use multi-step problems. Topic 4: Multiplying to Solve Problems 5.3B use multiplication to solve problems involving whole numbers (no more than two-digit divisor and three-digit dividends without technology). Use array model from beginning with small numbers and as the numbers get larger, build arrays with base ten blocks to show the steps of the traditional method. Use multi-step problems. One-digit numbers should not be rounded. Extract necessary information needed to solve multi-step problems (ignore extraneous information) Textbook Sections: 4-1, 4-2, 4-3, 4-4, 4-5 Topic 5: Dividing with 1-Digit Divisors 5.3C use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends without technology), including interpreting the remainder within a given context. Understands the two meanings of division - sharing equally and forming equal groups. Interpret the remainder dependent upon the context of the problem. Example: Quotient would need to be rounded up when finding the number of buses to transport a group of students. Quotient would be dropped in a situation of sharing baseballs among a group of people. One-digit numbers should not be rounded. Textbook Sections: 5-1, 5-2, 5-3, 5-5,, 5-7 Topic 6: Dividing with 2-Digit Divisors 5.3C use division to solve problems involving whole numbers (no more than two-digit divisors and three-digit dividends without technology), including interpreting the remainder within a given context. Understands the two meanings of division - sharing equally and forming equal groups Interpret the remainder dependent upon the context of the problem. Example: Quotient would need to be rounded up when finding the number of buses to transport a group of students. Quotient would be dropped in a situation of sharing baseballs among a group of people. Emphasize estimating before solving problem situations Relate estimation answers to a range of numbers or a number less than or greater than a given value One-digit numbers should not be rounded. Oct. 22-26 Textbook Sections: 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-8
Second Nine Weeks (43 ) Topic 7: Fractions and Decimals 5.2B...generate a mixed number equivalent to a given improper fraction or generate an improper fraction equivalent to a given mixed number. 5.2D use models to relate decimals to fractions that name tenths, hundredths, and thousandths. Analyze fractional quantities using a variety of methods (concrete, pictorial, verbal or abstract). Demonstrate using concrete and pictorial objects that the same improper fraction and mixed number are equivalent. Analyze the difference between proper and improper fractions. Relate fractions to decimals and decimals to fractions. (Ex. = = 0.25 and 0.25 = = ). Generalize equivalence relationship using base ten models. (Ex. = = 0.3). Oct. 29 thru Jan.17 Textbook Sections: 7-1, 7-2, 7-3, 7-4, 7-5, 7-7 5.2A generate a fraction equivalent to a given fraction such as ½ and 3/6 or 4/12 and 1/3. Demonstrate an understanding of equivalence by analyzing a concrete model, pictorial model, or a fraction to generate an equivalent fraction. Topic 8: Equivalent Fractions 5.3D identify common factors of a set of whole numbers. 5.5B identify prime and composite numbers using [concrete objects,] pictorial models, and patterns in factor pairs. Generate an equivalent fraction, given a specific numerator or a specific denominator. Demonstrate and explain methods or strategies for finding common factors of the set such as a Venn diagram. Describe the definition of prime number (recognize that 1 is not prime) Describe the definition of a composite number (recognize that 2 is the only even prime number) Identify and classify numbers as prime or composite using concrete or pictorial models. Use a variety of strategies to represent factors. Recognize prime and composite numbers in a set of numbers. Emphasize not all odd numbers are prime. Topic 9: Comparing and Ordering Fractions and Mixed Numbers Textbook Sections: 8-1, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7, 8-8, 8-9 5.2C compare two fractional quantities in problem-solving situations using a variety of methods, including common denominators. Textbook Sections: 9-1, 9-2, 9-3, 9-4, 9-5, 9-6 Second Nine Weeks continues on next page. Analyze fractional quantities using a variety of methods (concrete, pictorial, verbal or abstract). Analyze unit fractions. Compare two fractional quantities including less than 1 whole, equal to 1 whole and greater than 1 whole. Renaming fractions using common denominators. Order fractional quantities in problem-solving situations using a variety of methods. CCA Nov. 26-30
5.12B use experimental results to make predictions. Conduct experiments or evaluate a table of results and determine the probability of an event occurring. Topic 20: Probability 5.12A use fractions to describe the results of an experiment. 5.12C list all possible outcomes of a probability experiment such as tossing a coin. Describe the result (outcomes) of an experiment. Use a fraction to represent the probability of an event (including equivalent fractions). Evaluate results to predict the probability of a future event occurring. Use results to predict which even is more likely, less likely, certain, or not possible to occur. Use hands-on experiences to develop strategies to find all possible outcomes in a problem situation. Demonstrate various methods of organizing all possible outcomes (input/output, tables, lists, tree diagrams - vertical and horizontal. Topic 10: Adding and Subtracting Fractions with Like Denominators Textbook Sections: 20-1, 20-2, 20-3, 20-4 5.3E model situations using addition and/or subtraction involving fractions with like denominators using [concrete objects,] pictures, words, and numbers. Extract necessary information needed to solve the problem (ignoring extraneous information). Use various problem solving situations including: o Had 12 candies and ate 5. What fraction of the set remains? o Measuring cup - recipe o Ruler o Scales - fractions of a pound o Circle fractions to represent pizza or pie Textbook Sections: 10-1, 10-2, 10-3, 10-4, 10-5, 10-6 Topic 11: Patterns, Expressions and Equations Topic 12: Shapes and Solids 5.5A describe the relationship between sets of data in graphic organizers such as lists, tables, charts, and diagrams. 5.6A select from and use diagrams and equations such as y = 5 + 3 to represent meaningful problem situations. Evaluate multiple representations of data: lists, tables, charts, Venn diagrams and other types of graphic organizers. Represent lists, charts, tables of data in both vertical and horizontal formats. Evaluate relationships between sets of related data. Justify the rule of patterns and relationships. Generate, select from, and use equations (single and multiple step) to represent meaningful problem situations. Equations may include variable representation such as letter for unknown value. Ex. x + 5 = 8 7 Textbook Sections: 11-1, 11-2, 11-3, 11-4, 11-5 5.7A identify essential attributes including parallel, perpendicular, and congruent parts of two- and threedimensional geometric figures. Define two- and three-dimensional geometric figures using essential attributes. Identify, classify, and describe attributes of two- and threedimensional figures when given a variety of models and everyday objects. Compare and contrast both two- and three- dimensional figures according to attributes using formal geometric vocabulary Distinguish between regular and irregular polygons. Textbook Sections: 12-1, 12-2, 12-3, 12-4, 12-9, 12-5, 12-6, 12-7 Identify critical attributes of geometric figures such as perpendicular lines, parallel lines, and congruent lines as part of a whole shape or within many figures. Jan. 14-17
Topic 13: Ordered Pairs and the Plane 5.9A locate and name points on a coordinate grid using ordered pairs of whole numbers. 5.13A use tables of related number pairs to make line graphs. Textbook Sections: 13-1, 13-2, 13-4 Third Nine Weeks (42 ) Demonstrate an understanding of the Quadrant I coordinate grid including origin, x-axis, y-axis, determining the increment or scale, and ordered pairs. Determine the ordered pair that represents a point on a grid and determine the point on a grid when given an ordered pair. Plot points from ordered pairs and from data tables. Name all specific points given on a line graph and organize the related number pairs in a table with appropriate labels. Jan. 22 thru Mar. 27 Topic 14: Transformations and Congruence 5.8A sketch the results of translations, rotations, and reflections on a Quadrant I coordinate grid. 5.8B identify the transformation that generates one figure from the other when given two congruent figures on a Quadrant I coordinate grid. Model, sketch, and identify different types of transformations on a Quadrant I coordinate grid (translations, rotations, reflections) Explain the change caused by transformation of an original figure. For example: In the translation the figure moved 2 units left and 4 units down. Identify examples and non-examples of translations, rotations, reflections when given two congruent figures on a Quadrant I coordinate grid. Topic 15: Length, Perimeter, and Area Textbook Sections: 14-1, 14-2, 14-3, 14-4, 14-5 5.10C select and use appropriate units and formulas to measure length, perimeter, area, and volume. 5.10B connect models for perimeter, area, and volume with their respective formulas. Explore measuring with different tools and real life objects to develop concepts of perimeter and area. Differentiate between concepts in real world problems such as fencing for perimeter and painting a wall for area. Explain the connection of measurements to formulas. Textbook Sections: 15-1, 15-2, 15-3, 15-4, 15-7 STAAR BA Feb. 4-8 Topic 16: Volume, Capacity, Weight, and Mass 5.10C select and use appropriate units and formulas to measure length, perimeter, area, and volume. 5.10A.perform simple conversions within the same measurement system. 5.10B connect models for perimeter, area, and volume with their respective formulas. Textbook Sections: 16-1, 16-2, 16-3, 16-4, 16-5 Estimate solutions prior to conversions. Introduce the idea of conversions with hands-on applications. Perform simple conversion between different units in problem solving such as: o What fractional part of a foot is 6 inches? o How many centimeters are in four meters? o 10 tons would be how many pounds? Explore measuring with different tools and real life objects to develop concepts of volume. Derive the formula for volume by looking and building a variety of examples. Third Nine Weeks continues on next page.
Topic 17: Converting Measurements 5.10A.perform simple conversions within the same measurement system. Understand the relationships of customary and metric units. Perform simple conversion between different units in problem solving such as: o What fractional part of a foot is 6 inches? o How many centimeters are in four meters? o 10 tons would be how many pounds? Topic 18: Time and Temperature Textbook Sections: 17-1, 17-2, 17-3, 17-4, 17-5, 17-6, 17-7 5.11A solve problems involving changes in temperature. 5.11B solve problems involving elapsed time. Textbook Sections: 18-1, 18-2, 18-3, 18-4 Associate thermometers with a number line and understand that the increments (1, 2, 5, or 10) may vary on different thermometers. Describe the change in temperature (increased by, decreased by, dropped by, or rose by). Determine the elapsed time between two given clocks. Determine the start time given the ending time and the activity time. Move from concrete (clock) to pictorial (drawing a clock) to linear, to explaining the process to abstract calculations. Recognize that time is not a base 10 system. March 18-22 STAAR Review STAAR Review 7-8
Fourth Nine Weeks (48 ) STAAR TEST 5 th Grade STAAR Test (First Administration) April 2, 2012 April 1 June 6 April 2 Extension Lessons Topic 5: Dividing with 1-Digit Divisors Lesson 5-4 Connecting Models and Symbols Topic 6: Dividing with 2-Digit Divisors Lesson 6-7 Estimating and Dividing with Greater Numbers Extension Lessons Topic 7: Fractions and Decimals Lesson 7-6 Fractions and Decimals on the Number Line Topic 12: Shapes and Solids Lesson 12-8 Views of Solids Topic 13: Ordered Pairs and the Plane Lesson 13-3 Graphing Equations Topic 15: Length, Perimeter, and Area Lesson 15-5 Area of Parallelograms Lesson 1 Area of Triangles Topic 19: Graphs and Data Lesson 19-4 Finding the Mean Review for EOY Review for End of Year Test Administer EOY May 28-31 Step Up to Grade 6 Lessons Begin Step-up to Grade 6 Lessons Lessons 1-20 (found at the end of Topic 20) End of 4 th Nine Weeks