Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (4.NF.2) 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 C-NF Build fractions from unit fractions by applying and extending previous understanding of operations on whole numbers. Understand a fraction a / b with a > 1 as a sum of fractions 1 / b. (4.NF.3) Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. (4.NF.3a)
Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x 1/4, recording the conclusion by the equation 5/4 = 5 x 1/4 . (4.NF.4a) 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 Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.) (4.NF.4b) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? (4.NF.4c) C-NF
example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/ bd .) (5.NF.1) 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 involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. (5.NF.2) 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 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.7) 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. (6.EE.8) 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 C-EE Represent and analyze quantitative relationships between dependent and independent variables. 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.
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 Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. (5.MD.5c) 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 Statistics and Probability C-SP Develop understanding of statistical variability. 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.1)
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.2) 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. (6.SP.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 C-SP Summarize and describe distributions. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (6.SP.4) [Also see S.ID.1]