NCTM Curriculum Focal Points for Grade 5. Everyday Mathematics, Grade 5

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1 NCTM Curriculum Focal Points and, Grade 5 NCTM Curriculum Focal Points for Grade 5 Number and Operations and Algebra: Developing an understanding of and fluency with division of whole numbers Students apply their understanding of models for division, place value, properties, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multidigit dividends , , , Operations and Computation Goal 2 Demonstrate automaticity with multiplication facts and proficiency with division facts and extensions. Operations and Computation Goal 7 Use repeated addition, arrays, area, and scaling to model multiplication and division; use ratios expressed as words, fractions, percents, and with colons; solve problems involving ratios of parts of a set to the whole set. Patterns, Functions, and Algebra Goal 4 Describe and apply the properties of arithmetic. Students select appropriate methods and apply them accurately to estimate quotients or calculate them mentally, depending on the context and numbers involved , , , Operations and Computation Goal 3 problems involving the multiplication of whole numbers and decimals and the division of multidigit whole numbers and decimals by whole numbers; express remainders as whole numbers or fractions as appropriate; describe the strategies used and explain how they work. Grade 5 Correlation 53 Operations and Computation Goal 6 Make reasonable estimates for whole number and decimal addition, subtraction, multiplication, and division problems and fraction and mixed number addition and subtraction problems; explain how the estimates were obtained. Reprinted with permission from Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence, copyright 2006 by the National Council of Teachers of Mathematics. All rights reserved. Please visit for more information.

2 54 and Curriculum Focal Points NCTM Curriculum Focal Points for Grade 5 Students develop fluency with efficient procedures, including the standard algorithm, for dividing whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems. Students consider the context in which a problem is situated to select the most useful form of the quotient for the solution, and they interpret it appropriately , 52 56, , , See also for Algorithms Handbook pp , and Algorithms in which contain online animations and associated print resources. Operations and Computation Goal 2 Demonstrate automaticity with multiplication facts and proficiency with division facts and fact extensions. Operations and Computation Goal 3 problems involving the multiplication of whole numbers and decimals and the division of multidigit whole numbers and decimals by whole numbers; express remainders as whole numbers or fractions as appropriate; describe the strategies used and explain how they work. Patterns, Functions, and Algebra Goal 4 Describe and apply the properties of arithmetic , , Operations and Computation Goal 3 problems involving the multiplication of whole numbers and decimals and the division of multidigit whole numbers and decimals by whole numbers; express remainders as whole numbers or fractions as appropriate; describe the strategies used and explain how they work. Number and Operations: Developing an understanding of and fluency with addition and subtraction of fractions and decimals Students apply their understandings of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators , , , , , , , , Number and Numeration Goal 2 Solve problems involving percents and discounts; describe and explain strategies used; identify the unit whole in situations involving fractions. Number and Numeration Goal 5 Use numerical expressions to find and represent equivalent names for fractions, decimals, and percents; use and explain multiplication and division rules to find equivalent fractions and fractions in simplest form; convert between fractions and mixed numbers; convert between fractions, decimals, and percents. Number and Numeration Goal 6 Compare and order rational numbers; use area models, benchmark fractions, and analyses of numerators and denominators to compare and order fractions and mixed numbers; describe strategies used to compare fractions and mixed numbers. Operations and Computation Goal 4 Use mental arithmetic, paper-and-pencil algorithms, and calculators to solve problems involving the addition and subtraction of fractions and mixed numbers; describe the strategies used and explain how they work.

3 NCTM Curriculum Focal Points for Grade 5 Students apply their understandings of decimal models, place value, and properties to add and subtract decimals. Students develop fluency with standard procedures for adding and subtracting fractions and decimals. Students make reasonable estimates of fraction and decimal sums and differences. Students add and subtract fractions and decimals to solve problems, including problems involving measurement , 91 96, Number and Numeration Goal 1 Read and write whole numbers and decimals; identify places in such numbers and the values of the digits in those places; use expanded notation to represent whole numbers and decimals , 91 96, , , , , , , See also for Algorithms Handbook pp , 34 41, and Algorithms in which contain online animations and associated print resources. Operations and Computation Goal 1 problems involving the addition and subtraction of whole numbers, decimals, and signed numbers; describe the strategies used and explain how they work. Operations and Computation Goal 4 Use mental arithmetic, paper-and-pencil algorithms, and calculators to solve problems involving the addition and subtraction of fractions and mixed numbers; describe the strategies used and explain how they work , 91 96, Operations and Computation Goal 6 Make reasonable estimates for whole number and decimal addition, subtraction, multiplication, and division problems and fraction and mixed number addition and subtraction problems; explain how the estimates were obtained , 91 96, , , , , , , , Operations and Computation Goal 1 problems involving the addition and subtraction of whole numbers, decimals, and signed numbers; describe the strategies used and explain how they work. Operations and Computation Goal 4 Use mental arithmetic, paper-and-pencil algorithms, and calculators to solve problems involving the addition and subtraction of fractions and mixed numbers; describe the strategies used and explain how they work. Grade 5 Correlation 55 Geometry and Measurement and Algebra: Describing three-dimensional shapes and analyzing their properties, including volume and surface area Students relate two-dimensional shapes to three-dimensional shapes and analyze properties of polyhedral solids, describing them by the number of edges, faces, or vertices as well as the types of faces , , , , , , , Geometry Goal 1 Identify, describe, compare, name, and draw right, acute, obtuse, straight, and reflex angles; determine angle measures in vertical and supplementary angles and by applying properties of sums of angle measures in triangles and quadrangles. Geometry Goal 2 Describe, compare, and classify plane and solid figures using appropriate geometric terms; identify congruent figures and describe their properties.

4 56 and Curriculum Focal Points NCTM Curriculum Focal Points for Grade 5 Students recognize volume as an attribute of three-dimensional space. Students understand that they can quantify volume by finding the total number of same-sized units of volume that they need to fill the space without gaps or overlaps. Students understand that a cube that is 1 unit on an edge is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating or measuring volume. Students decompose three-dimensional shapes and find surface areas and volumes of prisms. As students work with surface area, they find and justify relationships among the formulas for the areas of different polygons. They measure necessary attributes of shapes to use area formulas to solve problems , , , , , , , , , , , , , , , , , , , Algebra NCTM Connections to the Focal Points for Grade 5 Students use patterns, models, and relationships as contexts for writing and solving simple equations and inequalities., , , , , , , , , , , , Patterns, Functions, and Algebra Goal 1 Extend, describe, and create numeric patterns, describe rules for patterns and use them to solve problems; write rules for functions involving the four basic arithmetic operations; represent functions using words, symbols, tables, and graphs and use those representations to solve problems.

5 NCTM Connections to the Focal Points for Grade 5 Students use patterns, models, and relationships as contexts for writing and solving simple equations and inequalities , , , , , , , , , , , Patterns, Functions, and Algebra Goal 2 Determine whether number sentences are true or false; solve open number sentences and explain the solutions; use a letter variable to write an open sentence to model a number story; use a pan-balance model to solve linear equations with one unknown. Students create graphs of simple equations , , Patterns, Functions, and Algebra Goal 1 Extend, describe, and create numeric patterns, describe rules for patterns and use them to solve problems; write rules for functions involving the four basic arithmetic operations; represent functions using words, symbols, tables, and graphs and use those representations to solve problems. Students explore prime and composite numbers and discover concepts related to the addition and subtraction of fractions as they use factors and multiples, including applications of common factors and common multiples. They develop an understanding of the order of operations and use it for all operations , 57 61, 6 10, , , , , Number and Numeration Goal 3 Identify prime and composite numbers; factor numbers; find prime factorizations. Measurement Students experiences connect their work with solids and volume to their earlier work with capacity and weight or mass , , , , Students solve problems that require attention to both approximation and precision of measurement , , , , , , , , , Measurement and Reference Frames Goal 1 Estimate length with and without tools; measure length with tools to the nearest 1_ inch and millimeter; estimate the measure of angles with and without 8 tools; use tools to draw angles with given measures. Grade 5 Correlation 57 Data Analysis Students apply their understanding of whole numbers, fractions, and decimals as they construct and analyze double-bar and line graphs and use ordered pairs on coordinate grids , , , , , , , , , , Data and Chance Goal 1 Collect and organize data or use given data to create bar, line, and circle graphs with reasonable titles, keys, and intervals. Measurement and Reference Frames Goal 4 Use ordered pairs of numbers to name, locate, and plot points in all four quadrants of a coordinate grid.

6 58 and Curriculum Focal Points NCTM Connections to the Focal Points for Grade 5 Number and Operations Building on their work in grade 4, students extend their understanding of place value to numbers through millions and millionths in various contexts. They apply what they know about multiplication of whole numbers to larger numbers. Students also explore contexts that they can describe with negative numbers (e.g., situations of owing money or measuring elevations above and below sea level) , , , , , , , 80 84, , , , Number and Numeration Goal 1 Read and write whole numbers and decimals; identify places in such numbers and the values of the digits in those places; use expanded notation to represent whole numbers and decimals. Number and Numeration Goal 1 Read and write whole numbers and decimals; identify places in such numbers and the values of the digits in those places; use expanded notation to represent whole numbers and decimals. Number and Numeration Goal 4 Use numerical expressions involving one or more of the basic four arithmetic operations, grouping symbols, and exponents to give equivalent names for whole numbers; convert between base-10, exponential, and repeated-factor notations. Operations and Computation Goal 2 Demonstrate automaticity with multiplication facts and proficiency with division facts and extensions.

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