# Whole Numbers and Integers (44 topics, no due date)

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1 Course Name: PreAlgebra into Algebra Summer Hwk Course Code: GHMKU-KPMR9 ALEKS Course: Pre-Algebra Instructor: Ms. Rhame Course Dates: Begin: 05/30/2015 End: 12/31/2015 Course Content: 302 topics Whole Numbers and Integers (44 topics, no due date) Operations with Whole Numbers (12 topics) Addition with carry to the hundreds place Addition of large numbers Subtraction with borrowing Subtraction and regrouping with zeros Word problem with addition or subtraction of whole numbers Multiplication with carry Introduction to multiplication of large numbers Multiplication of large numbers Division with carry Quotient and remainder: Problem type 2 Quotient and remainder: Problem type 3 Word problem with multiplication or division of whole numbers Number Sense, Rounding, and Estimation (7 topics) Ordering large numbers Rounding to tens or hundreds Rounding to thousands, ten thousands, or hundred thousands Estimating a sum of whole numbers Estimating a difference of whole numbers Estimating a product Estimating a quotient Order of Operations (3 topics) Introduction to order of operations Order of operations with whole numbers Order of operations with whole numbers and grouping symbols Factors, Prime Numbers, and Divisibilty (8 topics) Factors Prime numbers Prime factorization Greatest common factor of 2 numbers Least common multiple of 2 numbers Word problem with common multiples Divisibility rules for 2, 5, and 10 Divisibility rules for 3 and 9 Measurement (5 topics) U.S. Customary unit conversion with whole number values U.S. Customary unit conversion with whole number values: Two-step conversion Metric distance conversion with whole number values Metric mass or capacity conversion with whole number values Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/7

2 Time unit conversion with whole number values Integers (9 topics) Reading the temperature from a thermometer Plotting integers on a number line Absolute value of a number Integer addition: Problem type 1 Integer addition: Problem type 2 Integer subtraction: Problem type 1 Integer subtraction: Problem type 2 Integer subtraction: Problem type 3 Integer multiplication and division Rational Numbers (56 topics, no due date) Equivalent Fractions (11 topics) Introduction to fractions Writing ratios for real-world situations Understanding equivalent fractions Equivalent fractions Simplifying a fraction Fractional position on a number line Plotting fractions on a number line Plotting rational numbers on a number line Ordering fractions with the same denominator Ordering fractions with the same numerator Using a common denominator to order fractions Operation with Fractions (12 topics) Addition or subtraction of fractions with the same denominator Addition or subtraction of fractions with different denominators Fractional part of a circle The reciprocal of a number Product of a unit fraction and a whole number Unit fraction multiplication Product of a fraction and a whole number: Problem type 1 Fraction multiplication Multi-step word problem involving fractions and multiplication Fraction division Signed fraction addition or subtraction: Advanced Signed fraction multiplication: Advanced Mixed numbers (10 topics) Writing a mixed number and an improper fraction for a shaded region Writing an improper fraction as a mixed number Writing a mixed number as an improper fraction Addition or subtraction of mixed numbers with the same denominator Addition of mixed numbers with the same denominator and carry Subtraction of mixed numbers with the same denominator and borrowing Addition or subtraction of mixed numbers with different denominators Mixed number multiplication: Problem type 1 Mixed number multiplication: Problem type 2 Mixed number division Decimal Place Value and Rounding (4 topics) Decimal place value: Hundreds to ten thousandths Rounding decimals Ordering decimals Ordering fractions and decimals Operations with Decimals (13 topics) Addition of aligned decimals Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/7

3 Subtraction of aligned decimals Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Signed decimal addition and subtraction with 3 numbers Multiplication of a decimal by a power of ten Multiplication of a decimal by a whole number Decimal multiplication: Problem type 1 Word problem with powers of ten Word problem with multiple decimal operations: Problem type 1 Division of a decimal by a power of ten Division of a decimal by a whole number Division of a decimal by a 2-digit decimal Conversion and Measurement (6 topics) Converting a decimal to a proper fraction in simplest form: Advanced Converting a fraction to a terminating decimal Converting a fraction to a repeating decimal Converting a mixed number to a decimal Metric distance conversion with decimal values Metric conversion with decimal values: Two-step problem Proportion, Percent, Data and Probability (51 topics, no due date) Proportion (8 topics) Word problem on unit rates associated with ratios of whole numbers: Decimal answers Solving a word problem involving rates and time conversion Solving a proportion of the form x/a = b/c Solving a word problem on proportions using a unit rate Word problem on proportions: Problem type 1 Converting between metric and U.S. Customary unit systems Converting between compound units: Basic Converting between compound units: Advanced Percent (11 topics) Finding the percentage of a grid that is shaded Converting between percentages and decimals Converting a percentage to a fraction in simplest form Converting a fraction to a percentage: Denominator of 20, 25, or 50 Finding a percentage of a whole number without a calculator: Basic Writing a ratio as a percentage without a calculator Finding the sale price without a calculator given the original price and percent discount Finding the original price given the sale price and percent discount Finding the percentage increase or decrease: Advanced Finding simple interest without a calculator Computing a percentage from a table of values Data Analysis (18 topics) Constructing a line plot Constructing a histogram for numerical data Constructing a bar graph for non-numerical data Interpreting a bar graph Interpreting a double bar graph Interpreting a line graph Interpreting a circle graph or pie chart Mode of a data set Mean and median of a data set Finding the value for a new score that will yield a given mean How changing a value affects the mean and median Choosing the best measure to describe data Interpreting a stem-and-leaf plot Using back-to-back stem-and-leaf plots to compare data sets Constructing a box-and-whisker plot Scatter plots and correlation Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 3/7

4 Sketching the line of best fit Interpreting a Venn diagram of 3 sets Probability (14 topics) Interpreting a tree diagram Introduction to the counting principle Counting principle Word problem involving permutations Word problem involving combinations Odds of an event Outcomes and event probability Introduction to the probability of an event Probability of an event Probability of independent events Probability of dependent events Probabilities involving two dice Experimental and theoretical probability Introduction to expectation Variable Expressions and Equations (38 topics, no due date) Real Numbers and Variable Expressions (13 topics) Introduction to properties of addition Introduction to properties of multiplication Understanding the distributive property Distributive property: Whole number coefficients Distributive property: Integer coefficients Combining like terms: Integer coefficients Combining like terms: Advanced Identifying numbers as integers or non-integers Identifying numbers as rational or irrational Evaluating an algebraic expression: Whole numbers with two operations Evaluating a linear expression: Integer multiplication with addition or subtraction Evaluating a quadratic expression: Integers Writing a one-step variable expression for a real-world situation Equations (13 topics) Additive property of equality with whole numbers Additive property of equality with decimals Additive property of equality with fractions and mixed numbers Additive property of equality with integers Additive property of equality with a negative coefficient Multiplicative property of equality with whole numbers Multiplicative property of equality with signed fractions Solving a two-step equation with integers Solving a two-step equation with signed fractions Solving an equation to find the value of an expression Solving a linear equation with several occurrences of the variable: Variables on the same side and distribution Solving a linear equation with several occurrences of the variable: Variables on both sides and distribution Solving a linear equation with several occurrences of the variable: Variables on both sides and two distributions Applications (7 topics) Translating a sentence into a one-step equation Solving a fraction word problem using a linear equation of the form Ax = B Solving a word problem with two unknowns using a linear equation Solving a decimal word problem using a linear equation with the variable on both sides Solving a decimal word problem using a linear equation of the form Ax + B = C Solving a fraction word problem using a linear equation with the variable on both sides Introduction to algebraic symbol manipulation Inequalities (5 topics) Translating a sentence by using an inequality symbol Solving a linear inequality: Problem type 1 Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 4/7

5 Solving a linear inequality: Problem type 2 Solving a linear inequality: Problem type 3 Graphing a linear inequality on the number line Functions and Graphs (29 topics, no due date) Functions and Sequences (9 topics) Function tables with two-step rules Table for a linear function Writing a function rule given a table of ordered pairs: One-step rules Writing a function rule given a table of ordered pairs: Two-step rules Reading a point in the coordinate plane Plotting a point in the coordinate plane Vertical line test Interpreting the graphs of two functions Finding the next terms of a sequence with whole numbers Graphs of Linear Equations (5 topics) Graphing a line given its x- and y-intercepts Graphing a line given its equation in slope-intercept form Graphing a line given its equation in standard form Graphing a line through a given point with a given slope Graphing a vertical or horizontal line Properties of Lines (11 topics) Finding a solution to a linear equation in two variables Determining whether given points lie on one, both, or neither of 2 lines given equations Finding x- and y-intercepts of a line given the equation: Advanced Finding slope given the graph of a line on a grid Finding slope given two points on the line Finding the slope of a line given its equation Writing an equation of a line given the y-intercept and another point Writing the equation of a line given the slope and a point on the line Writing the equation of the line through two given points Writing an equation and drawing its graph to model a real-world situation: Advanced Graphically solving a system of linear equations Graphs of Inequalities and Nonlinear Equations (4 topics) Graphing a linear inequality in the plane: Vertical or horizontal line Graphing a linear inequality in the plane: Slope-intercept form Graphing a parabola of the form y = ax 2 Graphing a cubic function of the form y = ax 3 Exponents and Polynomials (17 topics, no due date) Exponents (12 topics) Introduction to exponents Evaluating expressions with exponents: Problem type 1 Order of operations with integers and exponents Evaluating an expression with a negative exponent: Positive fraction base Evaluating an expression with a negative exponent: Negative integer base Ordering numbers with positive exponents Scientific notation with positive exponent Scientific notation with negative exponent Introduction to the product rule of exponents Product rule with positive exponents: Multivariate Quotient of expressions involving exponents Power rules with positive exponents Square Roots (2 topics) Square root of a perfect square Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/7

6 Estimating a square root Polynomials (3 topics) Simplifying a sum or difference of three univariate polynomials Multiplying binomials with leading coefficients of 1 Squaring a binomial: Univariate Geometry (67 topics, no due date) Lines and Angles (12 topics) Naming segments, rays, and lines Measuring an angle with the protractor Drawing an angle with the protractor Acute, obtuse, and right angles Finding supplementary and complementary angles Identifying corresponding and alternate angles Identifying supplementary and vertical angles Solving equations involving vertical angles Solving equations involving angles and a pair of parallel lines Constructing congruent angles Constructing an angle bisector Constructing the perpendicular bisector of a line segment Triangles and Trigonometry (6 topics) Acute, obtuse, and right triangles Scalene, isosceles, and equilateral triangles Area of a triangle Finding an angle measure of a triangle given two angles Finding an angle measure for a triangle with an extended side Pythagorean Theorem Quadrilaterals and Other Polygons (16 topics) Classifying quadrilaterals Perimeter of a square or a rectangle Perimeter of a polygon Finding a side length given the perimeter and side lengths with variables Sides of polygons having the same perimeter Finding the side length of a rectangle given its perimeter or area Distinguishing between the area and perimeter of a rectangle Areas of rectangles with the same perimeter Perimeter of a piecewise rectangular figure Area of a square or a rectangle Area of a piecewise rectangular figure Area of a parallelogram Area of a trapezoid Word problem involving the area between two rectangles Area involving rectangles and triangles Finding the perimeter or area of a rectangle given one of these values Circles (7 topics) Introduction to a circle: Diameter, radius, and chord Circumference of a circle Circumference and area of a circle Finding the radius or the diameter of a circle given its circumference Word problem involving the area between two concentric circles Area involving rectangles and circles Area involving inscribed figures Volume and Surface Areas (16 topics) Volume of a rectangular prism Volume of a piecewise rectangular prism Volume of a triangular prism Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/7

7 Volume of a pyramid Volume of a cylinder Word problem involving the rate of filling or emptying a cylinder Volume of a cone: Exact answers in terms of pi Vertices, edges, and faces of a solid Side views of a solid made of cubes Counting the cubes in a solid made of cubes Nets of solids Surface area of a piecewise rectangular prism made of unit cubes Surface area of a cube or a rectangular prism Surface area of a triangular prism Surface area of a cylinder: Exact answers in terms of pi Surface area involving prisms or cylinders Similarity and Transformations (10 topics) Similar polygons Indirect measurement Identifying transformations Translating a polygon Using a translated point to find coordinates of other translated points Reflecting a polygon over a vertical or horizontal line Finding the coordinates of three points reflected over an axis Drawing lines of symmetry Rotating a figure about the origin Dilating a figure Copyright 2015 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 7/7

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