GRADE 5 CORRELATED GLES
ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies.
State Framework Grade-Level Expectations CMT Correlations District Correlations
1.1 Understand and describe 1. Represent, extend and compare 17A. Identify, describe and/or classify two- patterns and functional geometric and numeric patterns using dimensional geometric shapes and figures. relationships. words, tables, graphs and equations 19A. Identify correct information from tables, 2. Analyze patterns and data to make bar graphs, pictographs and charts. generalizations, make predictions and to identify trends. 20 A. Draw reasonable conclusions from data in tables, bar graphs, pictographs, circle graphs and charts. 22A. Identify the missing terms in a pattern, or identify rules for a given pattern using whole numbers and attributes. 22B. Extend or complete patterns and state rules for given patterns using whole numbers and attributes. 24A. Solve logic, counting and classification problems involving the organization of data. 25A. Solve extended numerical and statistical problems.
GRADE 5 | ALGEBRAIC REASONING | 1 ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies.
State Framework Grade-Level Expectations CMT Correlations District Correlations
1.2 Represent and analyze 3. Represent and describe mathematical 5 A. Identify the appropriate operation or quantitative relationships in a relationships using variables or number sentence to solve a story problem. variety of ways. symbols in expressions, equations and inequalities 5B. Write story problems from multiplication or division number sentences, using one- and two- 4. Describe how a change in one digit numbers. variable relates to a change in a second variable in context. For 9A. Solve one-step story problems involving example: If a recipe requires two whole numbers and money amounts with or cups of flour for eight servings, the without extraneous information. Use all flour must be doubled for 16 servings operations. or increased by one-half for 12 servings. 9B. Solve two-step story problems involving whole numbers and money amounts with or without extraneous information.
10A. Identify the best expression to find an estimate.
22A. Extend or complete patterns, or identify rules using numbers and attributes.
22B. Extend or complete patterns and state rules using numbers and attributes. 23 A. Solve simple one-step algebraic equations involving addition, subtraction, multiplication and fact families.
25A. Solve extended numerical and statistical problems.
GRADE 5 | ALGEBRAIC REASONING | 2 ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies.
State Framework Grade-Level Expectations CMT Correlations District Correlations
1.3 Use operations, properties and 5. Replace variables or symbols in 5 A. Identify the appropriate operation or algebraic symbols to determine algebraic expressions with given number sentence to solve a story problem. equivalence and solve problems. values and evaluate or simplify the expression, e.g., If □ =5, find the 5B. Write story problems from multiplication or value of 4 x □ +7. division number sentences, using one- and two- digit numbers. 6. Model, write and solve one-step equations by using appropriate 9A. Solve one-step story problems involving concrete materials that model whole numbers and money amounts with or equivalence, e.g., If 4 x △ = 36, then without extraneous information. Use all △ equals 9. operations. 9B. Solve two-step story problems involving whole numbers and money amounts with or without extraneous information.
10A. Identify the best expression to find an estimate.
11 A. Identify a reasonable estimate to a problem, including estimating change.
23 A. Solve simple one-step algebraic equations involving addition, subtraction, multiplication and fact families.
25A. Solve extended numerical and statistical problems.
GRADE 5 | ALGEBRAIC REASONING | 3 NUMERICAL AND PROPORTIONAL REASONING Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.
State Framework Grade-Level Expectations* CMT Correlations District Correlations
2.1 Understand that a variety of 7. Compare, order and round whole 1A. Solve problems involving 100 more/less or numerical representations can be numbers to 1,000,000 using number 1,000 more/less than a given number. used to describe quantitative patterns, number lines and diagrams. relationships. 1B. Identify alternative forms of expressing 8. Represent whole numbers up to whole numbers less than 10,000 using expanded 1,000,000 in expanded and regrouped notation. forms and use the forms to support computation. 1C. Identify alternative forms of expressing 9. Construct and use models, number whole numbers less than 10,000 using patterns and pictorial representations to regrouping. extend place value concepts and 1D. Use place value concepts to identify and patterns to decimals, e.g., 0.1 is one- tenth of one and 0.01 is one one- compare the magnitude and value of digits in hundredth of one and one-tenth of 0.1. numbers. 10. Investigate negative integers (values 2A. Relate decimals (0.01-2.99) to pictorial less than zero) using place value representations and vice versa. models, diagrams and number lines and represent negative integers in practical 2B. Relate fractions and mixed numbers to applications, e.g. temperatures, money pictures and vice versa. and locations below sea level. 2C. Identify and/or shade fractional parts of 11. Classify numbers as prime, composite regions, sets or mixed numbers in pictures. or perfect squares and identify factor pairs using rectangular arrays. 3A. Rename equivalent fractions. 12. Represent equivalent fractions, 3B. Rename equivalent mixed numbers as decimals, ratios and percents using improper fractions and vice versa. models, pictures, number patterns and 4A. Order whole numbers less than 100,000. common factors. 4B. Order mixed numbers, fractions and decimals.
GRADE 5 | NUMERICAL AND PROPORTIONAL REASONING | 4 NUMERICAL AND PROPORTIONAL REASONING Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.
State Framework Grade-Level Expectations* CMT Correlations District Correlations
13. Choose and use benchmarks to 4C. Describe magnitude of whole numbers less approximate locations, of fractions, than 100,000 and decimals. mixed numbers and decimals, on number lines and coordinate grids. 4D. Describe magnitude of mixed numbers and fractions. 14. Write division problems in fraction form and round the fraction form to 4E. Round whole numbers in context. estimate an answer to a division 14 4F. Round decimals. problem, e.g., ⁄3 = 4 ⅔ ≈ 5. 4G. Locate points (fractions, decimals and 15. Use models and pictures to identify and compare ratios and represent ratios in whole numbers) on number lines and scales equivalent fraction and decimal forms. 10A. Identify the best expression to find an 16. Solve practical problems involving 10, estimate. 100, 1,000 and 10,000 more or less than 11A. Identify a reasonable estimate to a a number. problem, including estimating change. 17. Estimate products and missing factors using multiples of 10, 100 and 1,000. 22A. Identify the missing terms in a pattern, or identify rules for a given pattern using whole 18. Develop and use strategies involving numbers and attributes. place value relationships, inverse operations and algebraic properties 22B. Extend or complete patterns and state rules (commutative, associative and for given patterns using whole numbers and distributive) to simplify addition, attributes. subtraction and multiplication problems with three-, four- and five-digit 25A. Solve extended numerical and statistical numbers and money amounts and problems. division by one-digit factors. 19. Multiply and divide decimals and money amounts by whole numbers.
Italics indicate links not evident in 2005 framework.
GRADE 5 | NUMERICAL AND PROPORTIONAL REASONING | 5 NUMERICAL AND PROPORTIONAL REASONING Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.
State Framework Grade-Level Expectations* CMT Correlations District Correlations
2.2 Use numbers and their 20. Write and solve multistep problems for 5A. Identify the appropriate operation or properties to compute flexibly all four operations involving multidigit number sentence to solve a story problem. and fluently and to reasonably whole numbers and money amounts and estimate measures and quantities. explain how answers were determined, 5B. Write story problems from multiplication or orally and in writing. division number sentences, using one- and two- digit numbers. 21. Find fractional parts of a set by using estimation, counting, grouping of 6A. Multiply and divide facts. objects, number patterns, equivalent ratios and division. 7A. Add and subtract two-, three- and four-digit whole numbers and money amounts less than 22. Add and subtract fractions, decimals $100. and mixed numbers using a variety of strategies, e.g., models, mental math, 7B. Multiply and divide multiples of 10 and 100 equivalence and substitution: ½ + ¾ by 10 and 100. can also be solved using 0.5 + 0.75. 7C. Multiply and divide two- and three-digit 23. Construct and use models and pictorial whole numbers and money amounts less than representations to multiply common $10 by one-digit numbers. fractions and mixed numbers by whole numbers. 8A. Add and subtract fractions and mixed 24. Use ratios and proportions to solve numbers with like denominators. practical problems, e.g., interpreting scale 9A. Solve one-step story problems involving drawings and maps and determining the whole numbers and money amounts with or probability of an event. without extraneous information. Use all 25. Use estimation to predict results and to operations. recognize when an answer is or is not reasonable, or will result in an 9B. Solve two-step story problems involving overestimate or underestimate and whole numbers and money amounts with or explain the reasoning used orally and in without extraneous information. writing.
GRADE 5 | NUMERICAL AND PROPORTIONAL REASONING | 6 NUMERICAL AND PROPORTIONAL REASONING Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.
State Framework Grade-Level Expectations* CMT Correlations District Correlations
10A. Identify the best expression to find an estimate. 10B. Identify whether and why a particular strategy will result in an overestimate or an underestimate. 11A. Identify a reasonable estimate to a problem, including estimating change. 19A. Identify correct information from tables, bar graphs, pictographs and charts. 23A. Solve simple one-step algebraic equations involving addition, subtraction, multiplication and fact families. 25A. Solve extended numerical and statistical problems.
GRADE 5 | NUMERICAL AND PROPORTIONAL REASONING | 7 GEOMETRY AND MEASUREMENT Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies.
State Framework Grade-Level Expectations* CMT Correlations District Correlations
3.1 Use properties and characteristics 1. Represent the surface of three- 15A. Estimate lengths and areas. of two- and three-dimensional shapes dimensional solids using two- and geometric theorems to describe dimensional nets. 16B. Measure and determine perimeters and relationships, communicate ideas and areas. solve problems. 2. Develop formulas for finding the perimeter and area of squares, rectangles 17A. Identify, describe and/or classify two- and triangles and use them to solve dimensional geometric shapes and figures. problems. 17B. Draw, describe and/or classify two- 3. Use the attributes of parallel sides, dimensional geometric shapes and figures. perpendicular sides, congruent 18A. Identify lines of symmetry. sides/angles, number and length of sides or faces and number and kinds of angles 18B. Draw lines of symmetry. (right, acute or obtuse) to describe, classify and sort polygons and solids 18C. Identify congruent figures. (cube, prism, pyramid and sphere). 18D. Locate points on grids 4. Make and test conjectures about polygons using geometric relationships 24A. Solve logic, counting and classification problems involving the organization of data.
24B. Sort or classify objects, and draw logical conclusions from data including Venn diagrams and transitive reasoning questions.
25A. Solve extended numerical and statistical problems.
GRADE 5 | GEOMETRY AND MEASUREMENT | 8 GEOMETRY AND MEASUREMENT Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies.
State Framework Grade-Level Expectations* CMT Correlations District Correlations
3.2 Use spatial reasoning, location and 5. Use an x, y coordinate system to plot 18D. Locate points on grids geometric relationships to solve points, to estimate the distance between problems. points and to determine the horizontal or vertical distance between two points.
6. Analyze and describe the effect that changing the dimensions (perimeter) of a polygon has on its area and vice versa.
3.3 Develop and apply units, systems, 7. Use calendars and clocks to plan and 14A. Solve problems involving elapsed time formulas and appropriate tools to sequence events and to solve problems (a.m. and p.m.). estimate and measure. involving the conversion of measures of time and elapsed time using days, hours, 14B. Solve problems involving conversions minutes and seconds. of measures of time (minutes, hours and days).
25A. Solve extended numerical and statistical problems.
GRADE 5 | GEOMETRY AND MEASUREMENT | 9 GEOMETRY AND MEASUREMENT Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies.
State Framework Grade-Level Expectations* CMT Correlations District Correlations
8. Estimate and measure to solve a variety 15A. Estimate lengths and areas. of problems that involve angles, length, area, weight, mass, temperature, capacity 16A. Measure lengths to the nearest quarter- and volume in either metric or customary inch or half-centimeter. units explain the reasoning used orally 16C. Identify appropriate customary or and in writing. metric units of measure (length, capacity and 9. Use cubic inch or cubic centimeter mass) for a given situation. models to find the volume of rectangular 16D. Solve problems involving conversions solids. of measures of length. 10. Solve length problems involving 25A. Solve extended numerical and conversions of measure within the statistical problems. customary (inches, feet, yards and miles) or metric systems (millimeters, centimeters, meters and kilometers).
*Italics indicate links not evident in 2005 framework
GRADE 5 | GEOMETRY AND MEASUREMENT | 10 WORKING WITH DATA: PROBABILITY AND STATISTICS Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies.
State Framework Grade-Level Expectations* CMT Correlations District Correlations
4.1 Collect, organize and display 1. Represent sets of data using line plots, bar 19A. Identify correct information from data using appropriate graphs, double bar graphs, pictographs, simple tables, bar graphs, pictographs and charts. statistical and graphical circle graphs, stem and leaf plots and scatter methods. plots. 19B. Create bar graphs and pictographs from data in tables and charts. 2. Compare different representations of the same data set and evaluate how well each kind of 20A. Draw reasonable conclusions from display represents the features of the data. data in tables, bar graphs, pictographs, circle graphs and charts. 20B. State a conclusion and explain why a claim is or is not reasonable, based on the data. 24B. Sort or classify objects, and draw logical conclusions from data including Venn diagrams and transitive reasoning questions. 25A. Solve extended numerical and statistical problems.
GRADE 5 | WORKING WITH DATA | 11 WORKING WITH DATA: PROBABILITY AND STATISTICS Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies.
State Framework Grade-Level Expectations* CMT Correlations District Correlations
4.2 Analyze data sets to form 3. Design and conduct surveys of a representative 19A. Identify correct information from hypotheses and make sample of a population and use the data collected tables, bar graphs, pictographs and charts. predictions. to begin to make inferences about the general population. 20A. Draw reasonable conclusions from data in tables, bar graphs, pictographs, circle 4. Determine the mean, mode and median of a data graphs and charts. set and explain in writing, how they are affected by a change in the data set. 20B. State a conclusion and explain why a claim is or is not reasonable, based on the data. 24A. Solve logic, counting and classification problems involving the organization of data. 24B. Sort or classify objects, and draw logical conclusions from data including Venn diagrams and transitive reasoning questions. 25A. Solve extended numerical and statistical problems.
4.3 Understand and apply basic 5. Design and conduct probability experiments and 21A. Identify correct solutions to problems concepts of probability. simple games of chance to test predictions about involving elementary notions of probability. outcomes and fairness. 21 B. Solve problems involving elementary 6. Determine and describe possible outcomes and notions of probability and fairness, including express the likelihood of events as a fraction. justifying solutions 7. Determine and describe possible outcomes using 24A. Solve logic, counting and classification permutations, where order does matter, e.g., when problems involving the organization of data. there is a choice of vanilla (V), chocolate (C) or strawberry (S) ice cream for a three-scoop cone, 25A. Solve extended numerical and there are two possible ways to have the chocolate statistical problems. scoop on top CVS or CSV.
*Italics indicate links not evident in 2005 framework
GRADE 5 | WORKING WITH DATA | 12