1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand Blooms DOK 6 Sample Activity Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7on a number line oriented from left to right. (6.NS.7a) Write, interpret, and explain statements of order for rational numbers in contexts. For example, write –3º C > –7º C to express the fact that – 3º C is warmer than –7º C. (6.NS.7b) Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30|=30 to describe the size of the debt in dollars. (6.NS.7c) world
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand Blooms DOK 6 Sample Activity Apply properties of operations as strategies to add and subtract rational numbers. (7.NS.1d) Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. (7.NS.2) Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1 )( –1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. (7.NS.2a)
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand Blooms DOK 6 Sample Activity D-NS Know that there are numbers that are not rational, and approximate them by rational numbers. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. (8.NS.2) D-NS Understand ratio concepts and use ratio reasoning to solve problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. (6.RP.3)
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand Blooms DOK 6 Sample Activity D-NS Analyze proportional relationships and use them to solve real-world and mathematical problems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2) / (1/4) miles per hour, equivalently 2 miles per hour. (7.RP.1) Recognize and represent proportional relationships between quantities. (7.RP.2) Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. (7.RP.2a)
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand Blooms DOK 6 Sample Activity Expressions and Equations D-EE Use properties of operations to generate equivalent expressions. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. (7.EE.1) Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” (7.EE.2) [Also see A.SSE.2, A.SSE.3, A.SSE.3a, A.CED.4] 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand Blooms DOK 6 Sample Activity D-EE
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. (7.EE.4) [Also see A.CED.1 and A.REI.3] Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? (7.EE.4a) [Also see A.CED.1 and A.REI.3] 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand Blooms DOK 6 Sample Activity Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand Blooms DOK 6 Sample Activity D-SP Draw informal comparative inferences about two populations. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. (7.SP.3) Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in one chapter of a science book are generally longer or shorter than the words in another chapter of a lower level science book. (7.SP.4) [Also see S.ID.3]