1.1: Proportional reasoning involves comparisons and multiplicative relationships among ratios
1.1.a: Students can: Analyze proportional relationships and use them to solve real-world and mathematical problems.
1.1.b: Students can: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
1.1.c: Students can: Identify and represent proportional relationships between quantities.
1.1.c.i: Determine whether two quantities are in a proportional relationship.
1.1.c.ii: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
1.1.c.iii: Represent proportional relationships by equations.
1.1.c.iv: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
1.1.d: Students can: Use proportional relationships to solve multistep ratio and percent problems.
1.1.d.i: Estimate and compute unit cost of consumables (to include unit conversions if necessary) sold in quantity to make purchase decisions based on cost and practicality.
1.1.d.ii: Solve problems involving percent of a number, discounts, taxes, simple interest, percent increase, and percent decrease.
1.2: Formulate, represent, and use algorithms with rational numbers flexibly, accurately, and efficiently
1.2.a: Students can: Apply understandings of addition and subtraction to add and subtract rational numbers including integers.
1.2.a.i: Represent addition and subtraction on a horizontal or vertical number line diagram.
1.2.a.ii: Describe situations in which opposite quantities combine to make 0.
1.2.a.iii: Demonstrate p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative.
1.2.a.iv: Show that a number and its opposite have a sum of 0 (are additive inverses).
1.2.a.v: Interpret sums of rational numbers by describing real-world contexts.
1.2.a.vi: Demonstrate subtraction of rational numbers as adding the additive inverse, p – q = p + (–q).
1.2.a.vii: Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
1.2.a.viii: Apply properties of operations as strategies to add and subtract rational numbers.
1.2.b: Students can: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers including integers.
1.2.b.i: Apply properties of operations to multiplication of rational numbers.
1.2.b.ii: Interpret products of rational numbers by describing real-world contexts.
1.2.b.iv: Apply properties of operations as strategies to multiply and divide rational numbers.
1.2.b.v: Convert a rational number to a decimal using long division.
1.2.c: Students can: Solve real-world and mathematical problems involving the four operations with rational numbers.
2.1: Properties of arithmetic can be used to generate equivalent expressions
2.1.a: Students can: Use properties of operations to generate equivalent expressions.
2.1.a.i: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
2.1.a.ii: Demonstrate 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.
2.2: Equations and expressions model quantitative relationships and phenomena
2.2.a: Students can: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form, using tools strategically.
2.2.b: Students can: Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies.
2.2.c: Students can: 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.
2.2.c.i: Fluently 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.
2.2.c.ii: Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
2.2.c.iv: Graph the solution set of the inequality and interpret it in the context of the problem.
3.1: Statistics can be used to gain information about populations by examining samples
3.1.a: Students can: Use random sampling to draw inferences about a population.
3.1.a.i: Explain that generalizations about a population from a sample are valid only if the sample is representative of that population.
3.1.a.ii: Explain that random sampling tends to produce representative samples and support valid inferences.
3.1.a.iii: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.
3.1.a.iv: Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
3.1.b: Students can: Draw informal comparative inferences about two populations.
3.1.b.i: 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.
3.1.b.ii: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
3.2: Mathematical models are used to determine probability
3.2.a: Students can: Explain that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.
3.2.b: Students can: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.
3.2.c: Students can: Develop a probability model and use it to find probabilities of events.
3.2.c.i: Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
3.2.c.ii: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
3.2.c.iii: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
3.2.d: Students can: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
3.2.d.i: Explain that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
3.2.d.ii: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams.
3.2.d.iv: Design and use a simulation to generate frequencies for compound events.
4.1: Modeling geometric figures and relationships leads to informal spatial reasoning and proof
4.1.a: Students can: Draw, construct, and describe geometrical figures and describe the relationships between them.
4.1.a.i: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
4.1.a.iii: Construct triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
4.2: Linear measure, angle measure, area, and volume are fundamentally different and require different units of measure
4.2.a: Students can: State the formulas for the area and circumference of a circle and use them to solve problems.
4.2.b: Students can: Give an informal derivation of the relationship between the circumference and area of a circle.
4.2.c: Students can: Use properties of supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
4.2.d: Students can: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Correlation last revised: 1/22/2020