Gizmos for Utah - Mathematics: 7th Grade (UT--Core Standards adopted 2016)

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

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.

7.MP.2: : Reason abstractly and quantitatively.

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.

7.MP.4: : Model with mathematics.

7.MP.5: : Use appropriate tools strategically.

7.MP.5.a: : Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. Identify relevant external mathematical resources and use them to pose or solve problems. Use tools to explore and deepen their understanding of concepts.

7.MP.6: : Attend to precision.

7.MP.6.a: : Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. Specify units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

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.

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.

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.

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

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

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.

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

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.

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.

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.

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

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.

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.

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.

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.

(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.

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.

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.

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.

(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.

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.

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.

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.

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.

(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.

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.

(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.

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.

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.

7.SP.7.b: : Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

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.

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.

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

Correlation last revised: 9/16/2020

Utah - Mathematics: 7th Grade

UT--Core Standards | Adopted: 2016