Standards with Progressions grades K-HS v. 1.3 - Kentucky ...

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Reason about and solve one-variable equations and inequalities. 6.EE.5: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.6: Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.7: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 6.EE.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Represent and analyze quantitative relationships between dependent and independent variables. 6.EE.9: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Geometry Solve real-world and mathematical problems involving area, surface area, and volume. 6.G.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. 6.G.2: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 6.G.3: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. 6.G.4: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Develop understanding of statistical variability. 6.SP.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I” is not a statistical question, but “How old are the students in my school” is a statistical question because one anticipates variability in students’ ages. 6.SP.2: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Summarize and describe distributions. 6.SP.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 6.SP.5: Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Kentucky Department of Education 44 | P a g e
Seventh Grade Overview Domains Clusters Mathematical Practices Ratios & Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. The Number System Expressions and Equations Geometry Statistics and Probability Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers Use properties of operations to generate equivalent expressions Solve real-life and mathematical problems using numerical and algebraic expressions and equations 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. Draw, construct and describe geometrical figures and describe the relationships between them Solve real-life and mathematical problems involving angle measure, area, surface and volume 5. Use appropriate tools strategically. 6. Attend to precision. Use random sampling to draw inferences about a population Draw informal comparative inferences about two populations Investigate chance processes and develop, use and evaluate probability models 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. In Grade 7, instructional time should focus on four critical areas: 1. Developing understanding of and applying proportional relationships Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships. 2. Developing understanding of operations with rational numbers and working with expressions and linear equations Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems. 3. Solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume Students continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity in Grade 8 they reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two- and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. 4. Drawing inferences about populations based on samples Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences. Kentucky Department of Education 45 | P a g e
Page 1 and 2: KCAS A Closer Look at the Mathemati
Page 3 and 4: Grades K - 2 Section Kentucky Depar
Page 6 and 7: Domain: Number and Operations in Ba
Page 8 and 9: Domain: Geometry Kindergarten Grade
Page 10 and 11: Kindergarten Standards Counting and
Page 13 and 14: Domains Clusters Mathematical Pract
Page 15: Grades 3 - 5 Section Kentucky Depar
Page 18 and 19: Number and Operations: Fractions Gr
Page 20 and 21: Measurement and Data Grade 3 Grade
Page 22 and 23: Geometry Grade 3 Grade 4 Grade 5 Re
Page 25 and 26: Geometric measurement: understand c
Page 27 and 28: Fourth Grade - Standards (2 pages)
Page 29 and 30: Fifth Grade Overview Domains Cluste
Page 31 and 32: c. Solve real world problems involv
Page 33 and 34: Progressions by Domains, Clusters a
Page 35 and 36: The Number System (continued) Grade
Page 37 and 38: Expressions and Equations (continue
Page 39 and 40: Geometry Grade 6 Grade 7 Grade 8 So
Page 41 and 42: Statistics and Probability (continu
Page 43: Sixth Grade Standards (2 pages) Rat
Page 47 and 48: Statistics and Probability Use rand
Page 49 and 50: Eighth Grade Standards (2 pages) Th
Page 51 and 52: HS Section Use this section in conj
Page 53 and 54: The Real Number System N -RN Extend
Page 55 and 56: Seeing Structure in Expressions A-S
Page 57 and 58: Clusters HS Conceptual Category: Fu
Page 59 and 60: 7. (+) Use inverse functions to sol
Page 61 and 62: Domains Congruence Similarity, Righ
Page 63 and 64: Modeling with Geometry G-MG Apply g
Page 65 and 66: Interpreting Categorical and Quanti

Standards with Progressions grades K-HS v. 1.3 - Kentucky ...

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