Connecticut State Standards for Mathematics: Grade 5

CT.1. Algebraic Reasoning: Patterns and Functions: Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies.

1.1. Understand and describe patterns and functional relationships.

1.1.1. Represent, extend and compare geometric and numeric patterns using words, tables, graphs and equations

1.1.2. Analyze patterns and data to make generalizations, make predictions and to identify trends.

1.2. Represent and analyze quantitative relationships in a variety of ways.

1.2.3. Represent and describe mathematical relationships using variables or symbols in expressions, equations and inequalities

1.2.4. Describe how a change in one variable relates to a change in a second variable in context. For example: If a recipe requires two cups of flour for eight servings, the flour must be doubled for 16 servings or increased by one-half for 12 servings.

1.3. Use operations, properties and algebraic symbols to determine equivalence and solve problems.

1.3.5. Replace variables or symbols in algebraic expressions with given values and evaluate or simplify the expression, e.g., If __ =5, find the value of 4 x __ +7.

1.3.6. Model, write and solve one-step equations by using appropriate concrete materials that model equivalence, e.g., If 4 x __ = 36, then __ equals 9.

CT.2. 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.

2.1. Understand that a variety of numerical representations can be used to describe quantitative relationships.

2.1.1. Compare, order and round whole numbers to 1,000,000 using number patterns, number lines and diagrams.

2.1.2. Represent whole numbers up to 1,000,000 in expanded and regrouped forms and use the forms to support computation.

2.1.3. Construct and use models, number patterns and pictorial representations to extend place value concepts and patterns to decimals, e.g., 0.1 is one-tenth of one and 0.01 is one one-hundredth of one and one-tenth of 0.1.

2.1.4. Investigate negative integers (values less than zero) using place value models, diagrams and number lines and represent negative integers in practical applications, e.g. temperatures, money and locations below sea level.

2.1.5. Classify numbers as prime, composite or perfect squares and identify factor pairs using rectangular arrays.

2.1.6. Represent equivalent fractions, decimals, ratios and percents using models, pictures, number patterns and common factors.

2.1.7. Choose and use benchmarks to approximate locations, of fractions, mixed numbers and decimals, on number lines and coordinate grids.

2.1.8. Write division problems in fraction form and round the fraction form to estimate an answer to a division problem, e.g., 14/3 = 4 2/3 is approximately equal to 5.

2.1.9. Use models and pictures to identify and compare ratios and represent ratios in equivalent fraction and decimal forms.

2.2. Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.

2.2.10. Solve practical problems involving 10, 100, 1,000 and 10,000 more or less than a number.

2.2.11. Estimate products and missing factors using multiples of 10, 100 and 1,000.

2.2.12. Develop and use strategies involving place value relationships, inverse operations and algebraic properties (commutative, associative and distributive) to simplify addition, subtraction and multiplication problems with three-, four- and five-digit numbers and money amounts and division by one-digit factors.

2.2.13. Multiply and divide decimals and money amounts by whole numbers.

2.2.14. Write and solve multistep problems for all four operations involving multidigit whole numbers and money amounts and explain how answers were determined, orally and in writing.

2.2.15. Find fractional parts of a set by using estimation, counting, grouping of objects, number patterns, equivalent ratios and division.

2.2.16. Add and subtract fractions, decimals and mixed numbers using a variety of strategies, e.g., models, mental math, equivalence and substitution: 1/2 + 3/4 can also be solved using 0.5 + 0.75.

2.2.17. Construct and use models and pictorial representations to multiply common fractions and mixed numbers by whole numbers.

2.2.18. Use ratios and proportions to solve practical problems, e.g., interpreting scale drawings and maps and determining the probability of an event.

2.2.19. Use estimation to predict results and to recognize when an answer is or is not reasonable, or will result in an overestimate or underestimate and explain the reasoning used orally and in writing.

CT.3. Geometry and Measurement: Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies.

3.1. Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems.

3.1.1. Represent the surface of three-dimensional solids using two-dimensional nets.

3.1.2. Develop formulas for finding the perimeter and area of squares, rectangles and triangles and use them to solve problems.

3.1.3. Use the attributes of parallel sides, perpendicular sides, congruent sides/angles, number and length of sides or faces and number and kinds of angles (right, acute or obtuse) to describe, classify and sort polygons and solids (cube, prism, pyramid and sphere).

3.1.4. Make and test conjectures about polygons using geometric relationships

3.2. Use spatial reasoning, location and geometric relationships to solve problems.

3.2.5. Use an x, y coordinate system to plot points, to estimate the distance between points and to determine the horizontal or vertical distance between two points.

3.2.6. 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, formulas and appropriate tools to estimate and measure.

3.3.7. Use calendars and clocks to plan and sequence events and to solve problems involving the conversion of measures of time and elapsed time using days, hours, minutes and seconds.

3.3.8. Estimate and measure to solve a variety of problems that involve angles, length, area, weight, mass, temperature, capacity and volume in either metric or customary units explain the reasoning used orally and in writing.

3.3.9. Use cubic inch or cubic centimeter models to find the volume of rectangular solids.

3.3.10. Solve length problems involving conversions of measure within the customary (inches, feet, yards and miles) or metric systems (millimeters, centimeters, meters and kilometers).

CT.4. Working with Data: Probability and Statistics: Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies.

4.1. Collect, organize and display data using appropriate statistical and graphical methods.

4.1.1. Represent sets of data using line plots, bar graphs, double bar graphs, pictographs, simple circle graphs, stem and leaf plots and scatter plots.

4.1.2. Compare different representations of the same data set and evaluate how well each kind of display represents the features of the data.

4.2. Analyze data sets to form hypotheses and make predictions.

4.2.3. Design and conduct surveys of a representative sample of a population and use the data collected to begin to make inferences about the general population.

4.2.4. Determine the mean, mode and median of a data set and explain in writing, how they are affected by a change in the data set.

4.3. Understand and apply basic concepts of probability.

4.3.5. Design and conduct probability experiments and simple games of chance to test predictions about outcomes and fairness.

4.3.6. Determine and describe possible outcomes and express the likelihood of events as a fraction.

4.3.7. Determine and describe possible outcomes using permutations, where order does matter, e.g., when there is a choice of vanilla (V), chocolate (C) or strawberry (S) ice cream for a three-scoop cone, there are two possible ways to have the chocolate scoop on top CVS or CSV.