7.MP: Mathematical Practices

(Framing Text): Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes.

7.MP.1: Make sense of problems and persevere in solving them.

7.MP.1.a: Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, “Does this make sense?” Consider analogous problems, make connections between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers to problems using a different method.

 Biconditional Statements
 Estimating Population Size
 Improper Fractions and Mixed Numbers
 Linear Inequalities in Two Variables
 Modeling One-Step Equations
 Multiplying with Decimals
 Pattern Finder
 Solving Equations on the Number Line
 Using Algebraic Equations
 Using Algebraic Expressions

7.MP.3: Construct viable arguments and critique the reasoning of others.

7.MP.3.a: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.

 Biconditional Statements

7.MP.4: Model with mathematics.

7.MP.4.a: Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to construct a mathematical model. Routinely interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

 Estimating Population Size

7.MP.7: Look for and make use of structure.

7.MP.7.a: Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.

 Arithmetic Sequences
 Finding Patterns
 Function Machines 2 (Functions, Tables, and Graphs)
 Geometric Sequences
 Pattern Finder

7.MP.8: Look for and express regularity in repeated reasoning.

7.MP.8.a: Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences

7.RP: Ratios and Proportional Relationships

(Framing Text): Analyze proportional relationships and use them to solve real-world and mathematical problems.

7.RP.2: Recognize and represent proportional relationships between quantities.

7.RP.2.a: 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.

 Direct and Inverse Variation
 Proportions and Common Multipliers

7.RP.2.b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

 Beam to Moon (Ratios and Proportions)
 Dilations
 Perimeters and Areas of Similar Figures
 Similar Figures

7.RP.2.c: Represent proportional relationships by equations.

 Beam to Moon (Ratios and Proportions)
 Estimating Population Size
 Geometric Probability
 Polling: Neighborhood
 Theoretical and Experimental Probability

7.RP.2.d: 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.

 Direct and Inverse Variation

7.RP.3: Use proportional relationships to solve multi-step ratio and percent problems.

 Beam to Moon (Ratios and Proportions)
 Part-to-part and Part-to-whole Ratios
 Percent of Change
 Percents and Proportions
 Percents, Fractions, and Decimals
 Proportions and Common Multipliers

7.NS: The Number System

(Framing Text): Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

7.NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.1.a: Describe situations in which opposite quantities combine to make 0.

 Adding and Subtracting Integers
 Adding and Subtracting Integers with Chips
 Integers, Opposites, and Absolute Values

7.NS.1.b: Understand 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. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

 Adding and Subtracting Integers
 Adding on the Number Line
 Improper Fractions and Mixed Numbers
 Integers, Opposites, and Absolute Values
 Rational Numbers, Opposites, and Absolute Values
 Simplifying Algebraic Expressions I
 Solving Algebraic Equations I
 Sums and Differences with Decimals

7.NS.1.c: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). 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.

 Adding and Subtracting Integers
 Adding on the Number Line
 Simplifying Algebraic Expressions I
 Sums and Differences with Decimals

7.NS.1.d: Apply properties of operations as strategies to add and subtract rational numbers.

 Adding and Subtracting Integers with Chips

7.NS.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

7.NS.2.b: Understand that integers can be divided, provided the divisor is not zero, and that every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

 Dividing Mixed Numbers

7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.

 Adding Fractions (Fraction Tiles)
 Adding and Subtracting Integers
 Adding on the Number Line
 Dividing Fractions
 Dividing Mixed Numbers
 Estimating Population Size
 Estimating Sums and Differences
 Fractions Greater than One (Fraction Tiles)
 Improper Fractions and Mixed Numbers
 Multiplying Fractions
 Multiplying Mixed Numbers
 Multiplying with Decimals
 Sums and Differences with Decimals

7.EE: Expressions and Equations

(Framing Text): Use properties of operations to generate equivalent expressions.

7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

 Equivalent Algebraic Expressions I
 Equivalent Algebraic Expressions II
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II
 Solving Algebraic Equations I
 Solving Algebraic Equations II

7.EE.2: 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.

 Exponents and Power Rules
 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c

(Framing Text): Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

7.EE.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. 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.

 Adding Fractions (Fraction Tiles)
 Adding and Subtracting Integers
 Adding on the Number Line
 Dividing Fractions
 Dividing Mixed Numbers
 Estimating Sums and Differences
 Fraction Garden (Comparing Fractions)
 Fractions Greater than One (Fraction Tiles)
 Fractions with Unlike Denominators
 Improper Fractions and Mixed Numbers
 Multiplying Fractions
 Multiplying Mixed Numbers
 Multiplying with Decimals
 Part-to-part and Part-to-whole Ratios
 Percents, Fractions, and Decimals
 Rational Numbers, Opposites, and Absolute Values
 Sums and Differences with Decimals

7.EE.4: 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.a: 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.

 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II
 Solving Equations on the Number Line
 Solving Two-Step Equations

7.EE.4.b: 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 interpret it in the context of the problem.

 Absolute Value Equations and Inequalities
 Rational Numbers, Opposites, and Absolute Values
 Solving Linear Inequalities in One Variable

7.G: Geometry

(Framing Text): Draw, construct, and describe geometrical figures, and describe the relationships between them.

7.G.1: Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

 Dilations
 Similar Figures

(Framing Text): Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

7.G.4: Know the formulas for the area and circumference of a circle, and solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

 Circumference and Area of Circles

7.G.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write, and use them to solve simple equations for an unknown angle in a figure.

 Investigating Angle Theorems
 Triangle Angle Sum

7.G.6: 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.

 Area of Parallelograms
 Balancing Blocks (Volume)
 Perimeter and Area of Rectangles
 Prisms and Cylinders
 Pyramids and Cones
 Surface and Lateral Areas of Pyramids and Cones

7.SP: Statistics and Probability

(Framing Text): Use random sampling to draw inferences about a population.

7.SP.1: Understand that statistics can be used to gain information about a population by examining a sample of the population, and that generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling is more likely to produce representative samples and support valid inferences.

 Polling: City
 Polling: Neighborhood
 Populations and Samples

7.SP.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

 Estimating Population Size
 Polling: City
 Polling: Neighborhood
 Populations and Samples

(Framing Text): Draw informal comparative inferences about two populations.

7.SP.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, estimating the difference between the centers by expressing it as a multiple of a measure of variability.

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Mean, Median, and Mode
 Movie Reviewer (Mean and Median)
 Reaction Time 1 (Graphs and Statistics)
 Reaction Time 2 (Graphs and Statistics)
 Real-Time Histogram

7.SP.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

 Box-and-Whisker Plots
 Reaction Time 1 (Graphs and Statistics)
 Real-Time Histogram

(Framing Text): Investigate chance processes and develop, use, and evaluate probability models.

7.SP.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

 Geometric Probability
 Probability Simulations
 Spin the Big Wheel! (Probability)
 Theoretical and Experimental Probability

7.SP.6: 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.

 Probability Simulations
 Theoretical and Experimental Probability

7.SP.7: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

7.SP.7.a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

 Independent and Dependent Events
 Probability Simulations

7.SP.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

7.SP.8.a: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

 Independent and Dependent Events

7.SP.8.b: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

 Independent and Dependent Events
 Permutations and Combinations

7.SP.8.c: Design and use a simulation to generate frequencies for compound events.

 Independent and Dependent Events

Correlation last revised: 4/4/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.