Math 7 PlusThis 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.
This course covers all material from the 7th grade curriculum and half of the 8th grade curriculum. While the EOG at the end of the year will only cover 7th grade material, students are expected to show mastery on the 8th grade material in preparation for the EOG at the end of 8th grade. |
Unit 1:
Integers
Alignment: 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 Numbers
Alignment: 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:
Equations
Alignment: 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:
Inequalities
Alignment: 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 Reasoning & Slope
Alignment: 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:
Probability
Alignment: 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 7:
Data Collection and Analysis
Alignment: 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 8:
Geometric Properties
Alignment: 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 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 9:
Transformations
Alignment: In 6th grade students graphed points on the coordinate plane; students graphed two-dimensional figures on the coordinate plane; students reflect points across the x- and y- axis.
In 6th and 7th grade students draw shapes with given conditions.
In 7th grade student solving 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.
In CCMI students find vertical and horizontal translations of linear, quadratic, and exponential functions.Essential Understanding(s):Students will understand that…
Unit 10:
Two- and Three-Dimensional Geometry
Alignment: In 5th grade students classify two-dimensional figures in a hierarchy based on properties; students understand that volume is an attribute of solid figures and understand 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 area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; students find the volume of right rectangular prisms with fractional edge lengths; students represent three-dimensional figures using nets.
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; students apply the volume of cylinders, pyramids, cones and spheres.Essential Understanding(s):Students will understand that…
Unit 11:
Exponents and Scientific Notation
Alignment: In 6th grade students write and evaluate numerical expressions with whole number exponents.
Later in this course and in CCMI students solve equations that contain exponents.
In CCMI students add, subtract, multiply, and factor polynomials.Essential Understanding(s):Students will understand that…
Integers
Alignment: 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 Numbers
Alignment: 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:
Equations
Alignment: 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.
- there is an algorithm for converting a repeating decimal to a fraction.
- perfect squares and cubes can be used to estimate irrational numbers.
- the inverse operation of a square is a square root and the inverse operation of a cube is a cube root.
Unit 4:
Inequalities
Alignment: 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 Reasoning & Slope
Alignment: 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…
- Similar figures have congruent angles and proportional side lengths
- It is possible to find actual measurements when given a scale drawing or model
- 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 triangles can be used to identify the constant of proportionality or the slope of a line
- There are positive, negative, undefined, and zero slopes
- The form y=mx+b can be used to model any linear function
Unit 6:
Probability
Alignment: 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 7:
Data Collection and Analysis
Alignment: 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 8:
Geometric Properties
Alignment: 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 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 complementary 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
- parallel lines cut by a transversal create sets of corresponding angles, which are all either congruent or supplementary
Unit 9:
Transformations
Alignment: In 6th grade students graphed points on the coordinate plane; students graphed two-dimensional figures on the coordinate plane; students reflect points across the x- and y- axis.
In 6th and 7th grade students draw shapes with given conditions.
In 7th grade student solving 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.
In CCMI students find vertical and horizontal translations of linear, quadratic, and exponential functions.Essential Understanding(s):Students will understand that…
- transformations on a coordinate plane include translations, rotations, reflections, and dilations.
- rigid transformations preserve size and shape of the pre-image.
- a dilation is a non-rigid transformation that creates similar figures.
- a sequence of transformations can be performed on a given pre-image.
Unit 10:
Two- and Three-Dimensional Geometry
Alignment: In 5th grade students classify two-dimensional figures in a hierarchy based on properties; students understand that volume is an attribute of solid figures and understand 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 area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; students find the volume of right rectangular prisms with fractional edge lengths; students represent three-dimensional figures using nets.
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; students apply the volume of cylinders, pyramids, cones and spheres.Essential Understanding(s):Students will understand that…
- 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.
- you can find the area of inscribed figures and composite shapes by understanding these figures are made up of basic shapes.
- 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.
- that 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)
- cones, spheres and pyramids have a volume that is a fraction of their dimensionally equivalent cylinder or prism.
- 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.
- there is an impact of changing dimensions on the area of a two dimensional figure
Unit 11:
Exponents and Scientific Notation
Alignment: In 6th grade students write and evaluate numerical expressions with whole number exponents.
Later in this course and in CCMI students solve equations that contain exponents.
In CCMI students add, subtract, multiply, and factor polynomials.Essential Understanding(s):Students will understand that…
- exponents are repeated multiplication.
- anything raised to the 0 power is 1.
- an expression with a negative exponent is not simplified and there is a property to simplify these expressions.
- when multiplying expressions with the same base you add the exponents.
- when raising a power to a power you multiply exponents.
- when dividing expressions with the same base you subtract the exponents.
- you convert numbers into and out of scientific notation using powers of 10.
- you can use the power of 10 to compare the size of numbers written in scientific notation.
- exponent rules still apply when performing operations in scientific notation.
- scientific notation is an efficient way to express very large and very small numbers in the real world.
- it is important to choose the appropriate measurement to fit the magnitude of the number.