SEVENTH MATH GRADE BY UNITS
In September Students will take math pretest that test students on how well they have mastered six grade skills, and the MAP test. This information is used to see what math skills they have or have not mastered to better tailor instruction. It is also used to assign IXL's to practice the skills that they have not mastered. They are assigned o the average of 13 IXL's per month. Students must score 85% to get the 3 points given for each IXL. Then IXL's are given to review and practice topics taught in class. These are due at the end of each month.
Materials:
Big Ideas Math Website and App www.bigideasmath.com
Khan Academy https://www.khanacademy.org/math/cc-seventh-grade-math
Progressive Math Initiative: Class Handouts and activities
Other resources: See Math Websites Tab or Math Class Links Tab
UNIT 1 Approximately 3 weeks:September
Operations with Integers: This unit includes in this order:
What are integers: whole positive and negative numbers and zero.
Absolute Value of Integers: the distance from zero on the number line
Rules for adding, subtracting, multiplying and dividing with integers
Link for Khan Academy Video's and practice on the above skills: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract#cc-7th-absolute-value
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide
UNIT 2 Approximately 3 weeks: September/October
Operations with Rational Numbers: This unit includes in this order:
What are Rational Numbers: Whole numbers- positive and negative, zero, fractions- positive and negative, and decimals- positive and negative.
Rules for adding, subtracting, multiplying and dividing with rational numbers. These lessons review rules for positive and negative numbers.
NOTE: Many students in seventh grade still struggle with fractions and decimals.
Rules for adding, subtracting, multiplying and dividing fractions and decimals are reviewed. IXL's are given to students to practice these skills. Your child will still struggle if they do not master fractions and decimals as they are essential in seventh grade.
Link for Khan Academy Video's and practice on the above skills:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract#cc-7th-add-sub-neg-fractions
UNIT 3 Approximately 3 weeks: October/November
Expressions and Equations
Algebraic Expressions: Simplifying expressions by combining like terms
Adding and Subtracting linear expressions: using rules for positive and negative numbers and combining like terms.
Factoring Expressions: The opposite of the distributing. Factoring out a common factor or number.
Solving Equations using Addition and Subtraction: Learn how to write and solve equations. Reviews rules for positive and negative numbers. Using inverse (opposite operations) to solve equations.
Solving Equations using Multiplication and Division: Learn how to write and solve equations. Reviews rules for positive and negative numbers. Using inverse (opposite operations) to solve equations.
Solving Two-Step Equations: Learn how to write and solve equations with two steps. This includes addition or subtraction and multiplication or division Reviews rules for positive and negative numbers. Using inverse (opposite operations) to solve equations. This lesson relies on the students knowledge of Order of Operations or better known as PEMDAS: Please excuse my dear aunt Sally. This refers to the order that students should complete the steps. When solving equations the order is backwards.
Link for Khan Academy Video's and practice on the above skills:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-expressions
UNIT 4 Approximately 3 weeks: November/December
Inequalities
Writing and Graphing Inequalities: Understanding inequality symbols less than <, greater than >, greater than or equal to ≥ , less than or equal to ≤. Students will learn how to graph them on a number line and when to use an open or closed dot.
Solving Inequalities Using Addition and Subtraction: Students will reviews rules for positive and negative numbers. Using inverse (opposite operations) to solve inequalities. Graphing the solution on a number line.
Solving Inequalities Using Multiplication or Division: Students will review rules for positive and negative numbers. Using inverse (opposite operations) to solve inequalities. Graphing the solution on a number line. Students learn that multiplying or dividing an inequality by a negative requires them to reverse the inequality symbol.
Solving Two-Step Inequalities: Learn how to write and solve inequalities with two steps. This includes addition or subtraction and multiplication or division Reviews rules for positive and negative numbers. Using inverse (opposite operations) to solve inequalities. This lesson relies on the students knowledge of Order of Operations or better known as PEMDAS: Please excuse my dear aunt Sally. This refers to the order that students should complete the steps. When solving inequalities the order is backwards.
Link for Khan Academy Video's and practice on the above skills:
UNIT 5 Approximately 4 weeks: January
Ratios and Proportions
Ratios and Rates: Finding ratios and rates and writing them in three ways. Identifying Unit rate where there is a one in the denominator. Finding rates from a ratio table and a graph. Solving ratios problems.
Proportions: Determining whether two ratios form a proportion (equivalent). Determining when two quantities are proportional. Identifying proportional relationships using different methods. Students learn how to use cross products and equivalent numbers.
Graphing Proportional Relationships: Looking at graphs to see if they pass through the origin (0,0) and are a straight line, then they are proportional. Interpreting what the graph means and what we can learn from it.
Writing Proportions: Setting up a proportion using tables and units of measure.
Solving Proportions: Solving them using cross products, equivalent numbers and mental math.
Slope: Slope is the steepness of a line on a graph. Students learn about slope and learn to find the slope by using two points on a line. They also learn what the slope means in terms of the quantities it's describing.
Direct Variation: Direct variation means that the quantities are proportional. Identifying the constant of proportionality or K of a line and knowing that this number is the slope of a proportional line.
Link for Khan Academy Video's and practice on the above skills:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion
UNIT 6: Approximately 5 1/2 weeks: February/Early March
Percents
Percents and Decimals: Writing decimals as percents and percents as decimals. Students should understand percent means out of 100 and that converting means moving the decimal two places to the right (decimal to percent) or left (percent to decimal).
Comparing and Ordering Fractions, Decimals, and Percents: Students must be able to convert from fractions to decimals (divide the numerator by the denominator) and percents and decide which is smaller or bigger.
The Percent Proportion: Students will use proportions to solve percent problems. They will find the percent, part or whole using a proportion. Where a is the part, w is the whole and p is the percent.
a = p
w 100
The Percent Equation: Students will use equations to solve percent problems. They will find the percent, part or whole using an equation. a = p x w
Percent Change: Percent increase, percent decrease and percent error. Students will learn the equation used to find these amounts and determine when it's and increase or a decrease.
Discount and Markups: Find discount prices and marked up prices when given two of the following: percent, whole or part, using the percent proportion or the percent equation.
Simple Interest: Calculate simple interest using the formula I=prt. Where I is interest, p is principal, r is rate (decimal), and t is time in years. Students should be able to solve for any one of those four amounts, if given the other three.
Link for Khan Academy Video's and practice on the above skills:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals
UNIT 7: Approximately 3 weeks: March
Construction and Scale Drawings
Adjacent and Vertical Angles: Students should be able to classify angles as acute, right, obtuse, and straight and measure angles using a protractor. Students should also know what are the properties of vertical, adjacent and congruent angles and use this information to determine the angle measure.
Complementary and Supplementary Angles: Complementary angles add up to 90 degrees. Supplementary Angles add up to 180 e. Students should be able to use this information to classify, measure and find the measure of angles.
Triangles: Students should be able to classify triangles by their angles- acute, obtuse, right and equilangular and by their sides- scalene, isosceles and equilateral. They should be able to draw a triangle with given angle and side measurements and use technology to construct a triangle.
Angle Measures of a Triangle: Students will understand that three angles in a triangle always add up to 180 degrees. They should be able to solve for a missing angle using that information.
Quadrilaterals: Students should be able to classify quadrilaterals(four sided polygons), by knowing their properties. Students should also know that the four angles of a quadrilateral add up to 360 degrees and be able to use that information to solve for missing angle measures.
Scale Drawings and Models: Students should know that drawings are two-dimensional and models are three dimensional. Students will use proportions to find scale measurements and scale factors. Students work with perimeter and area.
Link for Khan Academy Video's and practice on the above skills:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry#cc-7th-angles
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry#cc-7th-scale-drawings
UNIT 8:Approximately 3 weeks: April
Circles and Areas
Circles and Circumference: Radius is half way across the circle, diameter is the whole way across the circle (through the middle), circumference is the distance around the circle. Students should be able the formula c=πr or πd to find either value when one is given, where c is circumference, d is diameter and r is radius.
Perimeters of Composite Figures: Students will learn how to get the perimeter of shapes that are put together to form a different shape, using the perimeter of the shapes they know.
Area of Circles: Find the area of circles or semicircles using the formula A=πr2.
Area of Composite Figures: Students will learn how to get the area of shapes that are put together to form a different shape, using the area of the shapes they know.
Link for Khan Academy Video's and practice on the above skills:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry
UNIT 9: Approximately 3 weeks: April to May
Surface Areas and Volumes
Surface area of Prisms: A prism is a three dimensional box. The Surface area of a rectangular prism is the area of its six sides. A triangular prism has triangular bases. The surface area is the area of its six sides. A cube is a three dimensional box with all equal sides. The surface area is the area of its six sides. Students will learn how to find the area using reasoning and a formula.
Surface Area of Pyramids: A pyramid is a three dimensional shape that comes to a point. The surface area of a pyramid is the area of its sides, plus the area of its base.
Surface Area of Cylinders:A cylinder is two circular bases connected by a rectangular face. Students will find the surface area by adding the area of the two bases, plus the area of its face. The formula is 2πr2 + 2πrh.
Volumes of Prisms: Volume is how much a three dimensional object can hold. The formula for volume of a prism is the area of the base times the height. Students should know that the bases can be different and remember the area of the shape of different bases and multiply that by its height. A=Bh
Volumes of Pyramids: The volume of a pyramid is 1/3 the volume of a prism of the same shape and size. Therefore the formula is 1/3 times the area of the base times the height.
A=1/3Bh
Cross Sections of Three Dimensional Figures: Students will learn how to recognize the shape of the cross section (slice) of different three dimensional shapes.
Link for Khan Academy Video's and practice on the above skills:
Unit 10: Approximately 5 1/2 weeks: May to June
Probabilities and Statistics
Outcomes and Events: students will learn about outcomes(results of an experiment) and events (number of outcomes) and identify the possible outcomes and number of favorable outcomes in a situation.
Probability: The probability of an event is the number of favorable outcomes over the number of possible outcomes. Students will find the probability of events. They will write these as fractions,decimals or percents.
Experimental and Theoretical Probability:Students will find probability of an experiment and will find the probability in theory, meaning what should happen.
Compound Events:Students will learn how to find the probability of two or more things happening together using sample spaces or tree diagrams and the fundamental counting principle (multiplying each single event together).
Independent and Dependent Events: Students will learn the difference between independent (do not affect each other) and dependent (affect each other) events and how it changes the way you find probability.
Samples and Populations: Students will learn about biased and unbiased samples and how that affects whether your decisions and predictions are valid.
Comparing Populations:Students will compare populations using measures of center (mean, median, mode and range) and analyzing box and whisper plots and other types of data displays. They will learn when to use Mean and Mean Average Deviation and when to use Interquartile range and median to describe data.
Link for Khan Academy Video's and practice on the above skills:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-probability-statistics