Math 7This year, we will be studying the following units. I've included how this aligns with what students learned in previous years as well as future years. I've also listed the what students should understand at the end of each unit.
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Unit 1:
IntegersAlignment:In 5th grade students use all four operations when working with positive integers.
In 6th grade students use positive and negative numbers to represent real world contexts; students place positive and negative numbers on a number line understanding that absolute value is a number's distance from zero; students reason with one variable expressions and inequalities.
In 8th grade students explore expressions and equations with radicals and integer exponents; students locate irrational numbers on a number line.
In Math I students use integers to solve equations, inequalities and functions.Essential Understanding(s):Students will understand that…
Unit 2: Operations with Rational NumbersAlignment:In 5th grade students multiply and divide with whole numbers and fractions using modeling; students add and subtract fractions and mixed numbers with like and unlike denominators; students add, subtract, multiply and divide decimals; students plot rational numbers on a number line.
In 6th grade students multiply and divide fractions by fractions and mixed numbers by fractions using an algorithm; students add, subtract, multiply and divide multi-digit decimals using standard algorithm; students review fraction, decimal, percent conversions.
In 8th grade students approximate and plot irrational numbers to the closest rational number.
In Math I students rewrite expressions involving radicals and rational exponents.Essential Understanding(s):Students will understand that…
Unit 3: EquationsAlignment:In 5th grade students write simple numerical expressions without evaluating them.
In 6th grade students write and solve one-step equations using all nonnegative rational numbers; students understand that a variable represents an unknown quantity.
In 8th grade students solve linear equations with one and two variables with rational coefficients; students solve pairs of linear equations.
In Math I students determine the number of solutions of an equation.Essential Understanding(s):Students will understand that…
Unit 4:InequalitiesAlignment:In 4th grade students use < and >; symbols to compare multi-digit whole numbers.
In 5th grade students use < and >; symbols to compare decimal place value.
In 6th grade students write inequalities and graph them on a number line.
In 8th grade students compare rational approximations of irrational numbers
In Math I students write, solve and graph systems of inequalities; students graph and interpret the solutions of linear inequalities.Essential Understanding(s):Students will understand that…
Unit 5:Proportional ReasoningAlignment:In 5th grade students apply understandings of unit fractions; students create equivalent fractions.
In 6th grade students explore the concept of a ratio, make tables of equivalent ratios, and solve unit rate problems; students find percent as a rate per 100 and use ratio reasoning to convert measurement units.
In 8th grade students extend understandings of constant of proportionality into slope.
In Math I students graph and create equations of lines in the form of y=mx+b.Essential Understanding(s):Students will understand that…
Unit 6:PercentsAlignment:In 4th grade students learn place value to the 100th.
In 6th grade students convert between fractions, decimals and percents; students find percent as a rate per 100.
In Math I students estimate and interpret rate of change in linear functions; students recognize situations in which a quantity grows or decays by a constant percent rate per unit.Essential Understanding(s):Students will understand that …
Unit 7:ProbabilityAlignment:In elementary school, students learn that a rational number can be written as a fraction, decimal and a percent.
In 6th Grade in this course, students learn how to write ratios and how to solve proportions.
In elementary school and 6th grade, students learn how to find the area of two-dimensional shapes such as rectangles, squares, triangles and circles.
In CCMII students model with probability including, the fundamental counting principal, permutations and combinations, experimental vs theoretical probability, independent vs dependent probability, and conditional probability.Essential Understanding(s):Students will understand that…
Unit 8:
Data Collection & AnalysisAlignment:In 4th and 5th grades students construct a line plot to display a data set of measurements in fractions of a unit.
In 6th grade students recognize statistical questions and understand that data collected from a statistical question has a distribution, which can be described by center, spread, and overall shape; students recognize that a measure of center summarizes all its values with a single number and variation describes how the values vary with a single number; students display numerical data and summarize data sets in relation to their context on a number line, dot plots, histograms, and box plots.
In 8th grade students construct and interpret scatter plots for bivariate measurement data.
In CCMI students construct and interpret scatter plots, look at correlation, and calculate line of best fit; students interpret the spread of two or more different data sets using standard deviation.Essential Understanding(s):Students will understand that…
Unit 9: Geometric PropertiesAlignment:In 4th grade students measure angles in whole-number degrees using a protractor; students work with complementary and supplementary angles and solve for unknown angles.
In 5th grade students learn the properties of two-dimensional figures; students classify two-dimensional figures in a hierarchy based on properties.
In 6th grade students find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.
In 8th grade students use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal and the angle-angle criterion for the similarity of triangles.
In CCMI students prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.Essential Understanding(s):Students will understand that…
Unit 10:
Two-Dimensional GeometryAlignment:In 5th grade students classify two-dimensional figures in a hierarchy based on properties.
In 6th grade students find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes.
In 8th grade students learn that a two-dimensional figure is congruent or similar to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; students describe the effects of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
In CCMI students use coordinates to find the perimeter and area of triangles and rectangles using the distance formula.Essential Understanding(s):Students will understand that…
Unit 11:
Three-Dimensional GeometryAlignment:In 5th grade students understand that volume is an attribute of solid figures and the concept of volume measurement; students find the volume of right rectangular prisms with whole -number side lengths by packing it with unit cubes; students apply the formula for the volume of right rectangular prisms with whole-number edge lengths
In 6th grade students find the volume of right rectangular prisms with fractional edge lengths; students represent three-dimensional figures using nets.
In 8th grade students find the relationship between the volume of a cone and the volume of a cylinder; students find the volume of spheres.
In CCMI students apply the volume of cylinders, pyramids, cones and spheres to the real world.Essential Understanding(s):Students will understand that…
IntegersAlignment:In 5th grade students use all four operations when working with positive integers.
In 6th grade students use positive and negative numbers to represent real world contexts; students place positive and negative numbers on a number line understanding that absolute value is a number's distance from zero; students reason with one variable expressions and inequalities.
In 8th grade students explore expressions and equations with radicals and integer exponents; students locate irrational numbers on a number line.
In Math I students use integers to solve equations, inequalities and functions.Essential Understanding(s):Students will understand that…
- there are 8 mathematical practice standards that guide students in problem solving.
- to simplify an expression following the order of operations is key (including combining like terms and the distributive property).
- absolute value represents the distance from zero.
- modeling integers is useful to represent a number in a multitude of ways.
- subtraction of integers is equivalent to adding the opposite (inverse) of a value.
- there is an algorithm to aid in the process of solving integer problems.
- rewriting an expression in different forms can show how the quantities in it are related
- verbal expressions can be converted into algebraic expressions
Unit 2: Operations with Rational NumbersAlignment:In 5th grade students multiply and divide with whole numbers and fractions using modeling; students add and subtract fractions and mixed numbers with like and unlike denominators; students add, subtract, multiply and divide decimals; students plot rational numbers on a number line.
In 6th grade students multiply and divide fractions by fractions and mixed numbers by fractions using an algorithm; students add, subtract, multiply and divide multi-digit decimals using standard algorithm; students review fraction, decimal, percent conversions.
In 8th grade students approximate and plot irrational numbers to the closest rational number.
In Math I students rewrite expressions involving radicals and rational exponents.Essential Understanding(s):Students will understand that…
- all fractions have an equivalent repeating or terminating decimal representation
- all rational decimals can be written as a fraction
- there is an algorithm used to add, subtract, multiply and divide positive and negative decimals
- computing with negative fractions and decimals is similar to computing with negative integers
- you can use a variety of tools to solve real world mathematical problems with positive and negative rational numbers in any form.
Unit 3: EquationsAlignment:In 5th grade students write simple numerical expressions without evaluating them.
In 6th grade students write and solve one-step equations using all nonnegative rational numbers; students understand that a variable represents an unknown quantity.
In 8th grade students solve linear equations with one and two variables with rational coefficients; students solve pairs of linear equations.
In Math I students determine the number of solutions of an equation.Essential Understanding(s):Students will understand that…
- a model can be used to set up an equation with variables on both sides of the equal sign.
- each side of an equation maintains the same value.
- inverse operations are used to isolate the variable.
- equations can be constructed to represent real-world problems.
Unit 4:InequalitiesAlignment:In 4th grade students use < and >; symbols to compare multi-digit whole numbers.
In 5th grade students use < and >; symbols to compare decimal place value.
In 6th grade students write inequalities and graph them on a number line.
In 8th grade students compare rational approximations of irrational numbers
In Math I students write, solve and graph systems of inequalities; students graph and interpret the solutions of linear inequalities.Essential Understanding(s):Students will understand that…
- inequalities can be represented verbally, algebraically and graphically.
- inequalities have an infinite number of solutions.
- multiplying or dividing by a negative value will reverse the inequality symbol.
- solving inequalities follows the same algorithm as solving equations.
Unit 5:Proportional ReasoningAlignment:In 5th grade students apply understandings of unit fractions; students create equivalent fractions.
In 6th grade students explore the concept of a ratio, make tables of equivalent ratios, and solve unit rate problems; students find percent as a rate per 100 and use ratio reasoning to convert measurement units.
In 8th grade students extend understandings of constant of proportionality into slope.
In Math I students graph and create equations of lines in the form of y=mx+b.Essential Understanding(s):Students will understand that…
- Unit rates can be derived from any ratio
- There are multiple methods to model equivalent ratios
- The terms unit rate and constant of proportionality are interchangeable
- The constant of proportionality can be identified in a table or on a graph
- Proportions can be used to solve for a missing value in a ratio
- Similar figures have congruent angles and proportional side lengths
- It is possible to find actual measurements when given a scale drawing or scale model
Unit 6:PercentsAlignment:In 4th grade students learn place value to the 100th.
In 6th grade students convert between fractions, decimals and percents; students find percent as a rate per 100.
In Math I students estimate and interpret rate of change in linear functions; students recognize situations in which a quantity grows or decays by a constant percent rate per unit.Essential Understanding(s):Students will understand that …
- Percent problems can be solved using double number lines, tape diagrams, equations and proportions
- Tax, tip and markup are added to the original amount, whereas discount is subtracted
- There is a difference between principle, interest and balance and be able to find these appropriately
- There are algorithms for calculating the percent of change and percent error
Unit 7:ProbabilityAlignment:In elementary school, students learn that a rational number can be written as a fraction, decimal and a percent.
In 6th Grade in this course, students learn how to write ratios and how to solve proportions.
In elementary school and 6th grade, students learn how to find the area of two-dimensional shapes such as rectangles, squares, triangles and circles.
In CCMII students model with probability including, the fundamental counting principal, permutations and combinations, experimental vs theoretical probability, independent vs dependent probability, and conditional probability.Essential Understanding(s):Students will understand that…
- probability is the ratio of the number of ways an event can occur out of all possible outcomes
- probability is written as a fraction, decimal or percent ranging from 0 - 1
- theoretical probability is based on what "could" happen while experimental probability (relative frequency) is based on what "did" happen
- you can set up proportions to predict outcomes using theoretical or experimental probability
- the ratio of shaded area to total area is the probability of hitting a target on a geometric model
- the fundamental counting principle can be used to determine the total number of possible outcomes
- tree diagrams, organized lists, and area models (Punnett squares) can show all possible outcomes
- when outcomes do not affect future outcomes you have independent events
- when outcomes affect future outcomes (not replacing drawn items) you have dependent events
- you can simulate situations with multiple outcomes using spinners, dice, etc.
Unit 8:
Data Collection & AnalysisAlignment:In 4th and 5th grades students construct a line plot to display a data set of measurements in fractions of a unit.
In 6th grade students recognize statistical questions and understand that data collected from a statistical question has a distribution, which can be described by center, spread, and overall shape; students recognize that a measure of center summarizes all its values with a single number and variation describes how the values vary with a single number; students display numerical data and summarize data sets in relation to their context on a number line, dot plots, histograms, and box plots.
In 8th grade students construct and interpret scatter plots for bivariate measurement data.
In CCMI students construct and interpret scatter plots, look at correlation, and calculate line of best fit; students interpret the spread of two or more different data sets using standard deviation.Essential Understanding(s):Students will understand that…
- data collected from random samples can be used to make inferences about the population as a whole.
- generalizations about a population from a sample are valid only if the sample is representative of that population
- different measures of variability can be used to make decisions about a data set.
- two or more sets of data can be compared using histograms, dot plots or boxplots with the same scale
- variability is responsible for the overlap of two data sets and an increase in variability can increase the overlap
- a set of data has a distribution, which can be described by its center, spread, and overall shape
Unit 9: Geometric PropertiesAlignment:In 4th grade students measure angles in whole-number degrees using a protractor; students work with complementary and supplementary angles and solve for unknown angles.
In 5th grade students learn the properties of two-dimensional figures; students classify two-dimensional figures in a hierarchy based on properties.
In 6th grade students find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.
In 8th grade students use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal and the angle-angle criterion for the similarity of triangles.
In CCMI students prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.Essential Understanding(s):Students will understand that…
- angles and sides can be used to classify triangles
- angle relationships can be used to find measures of missing angles
- the geometric properties of interior and exterior angles of a triangle help to find missing angle measures
- writing multi-step equations is one way to solve for missing angles
- some angle names describe a single angle, while other angle names describe a relationship between two or more angles
- vertical angles are never adjacent and are created by the intersection of two lines
- supplementary angles together form a straight angle, while complimentary angles form a right angle
- the interior angles of a triangle add up to 180
- the exterior angle of a triangle is congruent to the sum of the two remote interior angles
Unit 10:
Two-Dimensional GeometryAlignment:In 5th grade students classify two-dimensional figures in a hierarchy based on properties.
In 6th grade students find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes.
In 8th grade students learn that a two-dimensional figure is congruent or similar to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; students describe the effects of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
In CCMI students use coordinates to find the perimeter and area of triangles and rectangles using the distance formula.Essential Understanding(s):Students will understand that…
- formulas are used to solve area problems involving polygons and circles.
- you can find perimeter and area even if dimensions are variables with unknown values.
- you can find perimeter and area of rectangles, squares, triangles, and trapezoids.
- a relationship exists between the circumference and area of a circle.
- formulas can be used to find the area and circumference of a circle.
- "knowing the formula" does not mean memorization of the formula. To "know" means to have an understanding of why the formula works and how the formula relates to the measure and the figure.
- there is an impact on area when changing the dimensions of a two dimensional figure.
- you can find the area of inscribed figures and composite shapes by understanding these figures are made up of basic shapes.
- there is a proportionate relationship between scale drawings and actual lengths of a figure.
Unit 11:
Three-Dimensional GeometryAlignment:In 5th grade students understand that volume is an attribute of solid figures and the concept of volume measurement; students find the volume of right rectangular prisms with whole -number side lengths by packing it with unit cubes; students apply the formula for the volume of right rectangular prisms with whole-number edge lengths
In 6th grade students find the volume of right rectangular prisms with fractional edge lengths; students represent three-dimensional figures using nets.
In 8th grade students find the relationship between the volume of a cone and the volume of a cylinder; students find the volume of spheres.
In CCMI students apply the volume of cylinders, pyramids, cones and spheres to the real world.Essential Understanding(s):Students will understand that…
- 3-dimensional shapes can have faces, edges, and/or vertices
- cross-sections of 3-dimensional shapes can vary depending on the angle and placement of the cut
- finding the area of each face of a three-dimensional figure and adding the areas will give the surface area (rectangular prisms, triangular prisms, pyramids, and cylinders). Using nets will aid in this process.
- prisms and pyramids include the base shape in their name
- all volume formulas derive from area of Base shape times height (rectangular and triangular prisms, right square pyramids)
- pyramids have a volume that is a fraction of their dimensionally equivalent prism (cones and spheres are in 8th grade)
- putting dimensions into improper fractional equivalents can help to find the amount of fractional cubes that compose the volume formulas can be rearranged to solve for missing dimensions