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Connecticut Math Standards - 5th Grade

MathScore aligns to the Connecticut Math Standards for 5th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.

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View the Connecticut Math Standards at other levels.

Patterns and Functions

1.1 Understand and describe patterns and functional relationships.
   1. Represent, extend and compare geometric and numeric patterns using words, tables, graphs and equations (Patterns: Numbers , Function Tables , Function Tables 2 )
   2. Analyze patterns and data to make generalizations, make predictions and to identify trends. (Line Graphs )

1.2 Represent and analyze quantitative relationships in a variety of ways.
   3. Represent and describe mathematical relationships using variables or symbols in expressions, equations and inequalities (Phrases to Algebraic Expressions , Algebraic Word Problems , Algebraic Sentences 2 , Algebraic Sentences )
   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. (Independent and Dependent Variables , Function Tables , Function Tables 2 )

1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems.
   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. (Variable Substitution )
   6. Model, write and solve one-step equations by using appropriate concrete materials that model equivalence, e.g., If 4 x Δ = 36, then Δ equals 9. (Missing Factor , Missing Term , Single Variable Equations )

Numerical and Proportional Reasoning

2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships.
   1. Compare, order and round whole numbers to 1,000,000 using number patterns, number lines and diagrams. (Number Comparison , Order Numbers , Rounding Large Numbers )
   2. Represent whole numbers up to 1,000,000 in expanded and regrouped forms and use the forms to support computation.
   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. (Decimal Place Value , Compare Decimals )
   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. (Compare Integers )
   5. Classify numbers as prime, composite or perfect squares and identify factor pairs using rectangular arrays. (Prime Numbers , Factoring , Perfect Squares )
   6. Represent equivalent fractions, decimals, ratios and percents using models, pictures, number patterns and common factors. (Greatest Common Factor , Basic Fraction Simplification , Fraction Simplification , Fraction Pictures , Fractions to Decimals , Decimals To Fractions , Compare Mixed Values , Positive Number Line , Percentages , Percentage Pictures )
   7. Choose and use benchmarks to approximate locations, of fractions, mixed numbers and decimals, on number lines and coordinate grids. (Positive Number Line )
   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 ≈ 5.
   9. Use models and pictures to identify and compare ratios and represent ratios in equivalent fraction and decimal forms. (Proportions 1 , Ratios )

2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.
   10. Solve practical problems involving 10, 100, 1,000 and 10,000 more or less than a number. (Mental Addition and Subtraction to 100 , Mental Addition and Subtraction )
   11. Estimate products and missing factors using multiples of 10, 100 and 1,000. (Multiply By Multiples Of 10 , Estimated Multiplication , Estimated Division , Estimated Multiply Divide Word Problems )
   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. (Long Addition , Long Subtraction , Long Multiplication , Long Division By One Digit , Division with Remainders )
   13. Multiply and divide decimals and money amounts by whole numbers. (Money Multiplication , Money Division , Unit Cost )
   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. (Using Parentheses , Arithmetic Word Problems , Basic Word Problems 2 )
   15. Find fractional parts of a set by using estimation, counting, grouping of objects, number patterns, equivalent ratios and division.
   16. Add and subtract fractions, decimals and mixed numbers using a variety of strategies, e.g., models, mental math, equivalence and substitution: ½ + ¾ can also be solved using 0.5 + 0.75. (Making Change , Fraction Addition , Fraction Subtraction , Fraction Word Problems , Decimal Addition , Decimal Subtraction )
   17. Construct and use models and pictorial representations to multiply common fractions and mixed numbers by whole numbers.
   18. Use ratios and proportions to solve practical problems, e.g., interpreting scale drawings and maps and determining the probability of an event. (Distance, Rate, and Time , Probability )
   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.

Geometry and Measurement

3.1 Use properties and characteristics of two- and three- dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems.
   1. Represent the surface of three-dimensional solids using two-dimensional nets.
   2. Develop formulas for finding the perimeter and area of squares, rectangles and triangles and use them to solve problems. (Triangle Area , Triangle Area 2 , Compare Rectangle Area and Perimeter )
   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). (Triangle Types , Quadrilateral Types , Polygon Names , Parallel and Perpendicular Lines )
   4. Make and test conjectures about polygons using geometric relationships

3.2 Use spatial reasoning, location and geometric relationships to solve problems.
   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. (Line Segments )
   6. Analyze and describe the effect that changing the dimensions (perimeter) of a polygon has on its area and vice versa. (Compare Rectangle Area and Perimeter , Area And Volume Proportions )

3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure.
   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. (Time Intervals , Time Conversion )
   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.
   9. Use cubic inch or cubic centimeter models to find the volume of rectangular solids. (Rectangular Solids )
   10. Solve length problems involving conversions of measure within the customary (inches, feet, yards and miles) or metric systems (millimeters, centimeters, meters and kilometers). (Distance Conversion )

Probability and Statistics

4.1 Collect, organize and display data using appropriate statistical and graphical methods.
   1. Represent sets of data using line plots, bar graphs, double bar graphs, pictographs, simple circle graphs, stem and leaf plots and scatter plots. (Stem And Leaf Plots , Tally and Pictographs , Bar Graphs )
   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.
   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. 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. (Mean, Median, Mode )

4.3 Understand and apply basic concepts of probability.
   5. Design and conduct probability experiments and simple games of chance to test predictions about outcomes and fairness.
   6. Determine and describe possible outcomes and express the likelihood of events as a fraction. (Probability )
   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.

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