Greenwich Public Schools Mathematics Curriculum Objectives. Grade 5

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1 Mathematics Curriculum Objectives Grade 5 June 30, 2006

2 Content Strand 1: Number Sense Enduring Understandings: Students understand that a variety of numerical representations can be used to describe quantitive relationships. Student should use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities. Essential Question: How are quantitive relationships represented by numbers? Cluster: Place Value 5.01 Read and identify, in writing and orally, the place value of decimals through thousandths and whole numbers through million Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers 5.03 Round whole numbers, fractions and decimals in a context. (CMT) 5.04 Identify alternative forms of expressing whole numbers less than 100,000 using expanded and exponential notation. (CMT 5.05 Compare and order decimals, fractions, and whole numbers using <, >, or =. (CMT) 5.06 Relate decimals and fractions to percents whose equivalent fraction denominator is a factor of Compare ratios using fraction and decimal equivalents. (CFW) Cluster: Whole Number Computation 5.08 Use and describe a variety of estimation, mental computation, place value, number patterns and calculator strategies to add, subtract, multiply and divide by 1-digit with 2-, 3- and 4-digit numbers. (CFW) 5.09 Estimate and multiply or divide 2 and3- digit whole numbers, and decimals by 1- digit and 10 or 100. (CMT) 5.10 Estimate and multiply whole numbers, fractions by fractions, and mixed numbers (expressing answers in simplest form). (CMT) 5.11 Write numeric expressions in equivalent forms using the commutative, associative, and distributive properties. Cluster: Fractions and Decimals 5.12 Find the GCF and LCM of a given set of numbers Explain divisibility rules and interpret patterns with remainders. (CFW) 5.14 Write a rational number in its equivalent fraction, decimal, ratio and percent forms. (CFW) 5.15 Add and subtract fractions, decimals and mixed numbers with like and unlike denominators. (CFW) 5.16 Rename equivalent fractions and mixed numbers to improper fractions and vice versa. (CMT) 1

3 5.17 Use ratios and proportions to solve problems such as interpreting maps and scale drawings or identifying probability. (CFW) 5.18 Estimate and solve addition and subtraction word problems with whole numbers, decimals, fractions and mixed numbers, (with like and unlike denominators, expressing answers in simplest form). (CMT) 5.19 Write a rational number in its equivalent fraction, decimal, ratio and percent forms. (CFW) 5.20 Identify numbers less than zero by extending the number line and use practical applications to introduce the concept of integers. (CFW) Content Strand 2: Measurement Enduring Understanding: Students develop and apply units, systems formulas and appropriate tools to estimate and measure. Essential Question: How can accurate measurements help us to solve problems and make sense of our world? Cluster: Time 5.21 Solve problems involving the conversion of measures of time and elapsed time (days, hours, minutes and seconds). (CMT) Cluster: Units of Measure 5.22 Identify appropriate units of measures (customary and metric) for a given situation (length, area, capacity and perimeter). (CMT) 5.23 Estimate and solve problems involving conversion of units of measure (customary and metric) including time. (CMT) 5.24 Measure and determine length, perimeter and area. (CMT) Cluster: Money 5.25 Add/subtract money amounts less than $10.00 and multiply/divide money amounts less than $10.00 by a 1-digit multiplier/divisor. (CMT) 5.26 Solve problems involving real world situations of buying and selling, using simple percents (e.g. 10%, 15%, 50%) to find discounts. 2

4 Content Strand 3: Geometry Enduring Understanding: Students develop and apply units, systems, formulas and appropriate tools to estimate and measure. Students use spatial reasoning, location and geometric relationships to solve problems. Students use properties and characteristics of two-and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. Essential Question: How do geometric relationships help us to solve problems and make sense of our world? Cluster: Area, Perimeter and Volume 5.27 Develop and apply formulas to find the perimeter and area of squares, rectangles and triangles. (CMT) 5.28 Understand the concept of volume and develop and apply formulas to determine the surface area and volume of rectangular solids, and cylinders. (CFW) 5.29 Construct polygons and estimate and measure lengths, angles, perimeter and area. (CFW) 5.30 Develop and apply formulas to find the circumference and area of a circle. Cluster: Shapes and their Properties 5.31 Identify, construct, draw and classify polygons and solids using geometric terms (parallel, perpendicular and congruent) to describe the attributes of sets and subsets of shapes. (CFW) 5.32 Identify and draw lines of symmetry, rotational symmetry and transformations in 2- and 3- D shapes. (CMT) Cluster: Angles 5.33 Use a protractor to construct acute, right and obtuse angles Estimate and then use a protractor to measure an angle within 2 degrees. Cluster: Coordinate Grids 5.35 Identify and graph points on a coordinate grid. (CMT) 3

5 Content Strand 4: Data Enduring Understandings: Students collect, organize and display data using appropriate statistical and graphical methods. Students understand and apply basic concepts of probability. Essential Question: How can collecting, organizing and displaying data help us analyze information and make reasonable predictions and informed decision? Cluster: Tables, Charts and Graphs 5.36 Design surveys to collect data that represents a general population. (CFW) 5.37 Construct a variety of bar graphs, line graphs, histograms, circle graphs, Venn Diagrams, stem and leaf plots, tables, and pictographs given a set of data and using an appropriate scale Interpret data from a variety of graphs: bar graphs, line graphs, histograms, circle graphs, Venn Diagrams, stem and leaf plots, tables, and charts. Cluster: Statistics and Probability 5.39 From various tables and graphs, describe the shape and features of a set of data Calculate and determine range, mode, median, or mean of a group of numbers representing data from a given context. (CMT) 5.41 Predict outcomes and solve problems involving elementary notions of probability and fairness including justification of answers. (CMT) 5.42 Recognize patterns and trends, make predictions, and justify conclusions based on data from tables, graphs, and charts Conclude and explain why a claim is/is not reasonable based on data. (CMT) 4

6 Content Strand 5: Algebra Enduring Understanding: Students understand and describe patterns and functional relationships. Essential Question: How do patterns and functions help us describe data and physical phenomena and solve a verity of problems? Cluster: Patterns and Functions 5.44 Analyze the structure of numerical and geometrical patterns (how they grow or change). (CMT) 5.45 Create and solve multi-step problems and explore the order of operations in the context of practical situations. (CFW) 5.45 Evaluate expressions and solve simple one step algebraic equations. (CMT) 5.47 Write the rule for a (one step) function table. 5

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