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Common Core Lesson Plans and Worksheets for Grade 7

Common Core for Mathematics

In Grade 7, instructional time should focus on four critical areas

(1) developing understanding of and applying proportional relationships

(2) developing understanding of operations with rational numbers and working with expressions and linear equations

(3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume

(4) drawing inferences about populations based on samples.

### Ratios and Proportional Relationships

### The Number System

### Expressions and Equations

### Geometry

### Statistics and Probability

Common Core Lesson Plans and Worksheets for Grade 7

Common Core for Mathematics

In Grade 7, instructional time should focus on four critical areas

(1) developing understanding of and applying proportional relationships

(2) developing understanding of operations with rational numbers and working with expressions and linear equations

(3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume

(4) drawing inferences about populations based on samples.

7.RP.A.1 Compute unit rates associated with ratios of fractions,
including ratios of lengths, areas and other quantities
measured in like or different units. |

7.RP.A.2 Recognize and represent proportional relationships between quantities. 7.RP.A.2a 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.A.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. |

7.RP.A.2c Represent proportional relationships by equations. |

7.RP.A.2d Explain what a point ( |

7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. |

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

7.NS.A.1b Understand |

7.NS.A.1c Understand subtraction of rational numbers as adding the
additive inverse, |

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

7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 7.NS.A.2a 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.A.2b Understand that integers can be divided, provided that
the divisor is not zero, and every quotient of integers
(with non-zero divisor) is a rational number. If |

7.NS.A.2c Apply properties of operations as strategies to multiply and divide rational numbers. |

7.NS.A.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. |

7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers. |

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

7.EE.A.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. |

7.EE.B.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.B.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.B.4a Solve word problems leading to equations of the
form |

7.EE.B.4b Solve word problems leading to inequalities of the
form |

7.G.A.1 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. 7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. |

7.G.A.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. |

7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. |

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

7.G.B.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.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. |

7.SP.A.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. |

7.SP.B.3 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. |

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

7.SP.C.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 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. |

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

7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 7.SP.C.8a 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.C.8b 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., polling double sixes, identify the outcomes in the sample space which compose the event. |

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

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