# Mathematics LV 5 (with QuickTables)

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2 Subtraction with multiple regrouping steps involving 3 digit numbers Subtraction with multiple regrouping steps involving 4 digit numbers Subtraction and regrouping with zeros Fact families for addition and subtraction Word problem with addition or subtraction of whole numbers Estimating Sums and Differences (2 topics) Estimating a sum of whole numbers: Problem type 1 Estimating a difference of whole numbers: Problem type 1 Understanding Multiplication (8 topics) Using equal groups to find a total Multiplying one digit numbers: Problem type 1 Multiplying one digit numbers: Problem type 2 Multiplication as repeated addition Writing addition and multiplication sentences for equal groups Using multiplication to find the number of squares Multiplying 2 digit and 1 digit numbers without regrouping Word problem with multiplication of whole numbers Understanding Division (6 topics) Division facts: Problem type 1 Division facts: Problem type 2 Relating multiplication and division facts Fact families for multiplication and division Division of whole numbers given in fractional form Word problem with division of whole numbers Introduction to Perimeter and Area (4 topics) Perimeter of a polygon Perimeter of a square or a rectangle Area of a rectangle on a grid Area of a rectangle with one digit side lengths Multiplying Whole Numbers (27 topics) Multiplication Patterns (5 topics) Multiplication by 10, 100, and 1000 Introduction to multiplication with a trailing zero Multiplication with trailing zeros: Problem type 1 Multiples: Problem type 1 Multiples: Problem type 2 Properties of Multiplication (3 topics) Using the distributive property to multiply two whole numbers Introduction to properties of multiplication Introduction to parentheses Multiplying Multi Digit Numbers (10 topics) Multiplying 2 digit and 1 digit numbers with regrouping: Problem type 1 Multiplying 2 digit and 1 digit numbers with regrouping: Problem type 2 Understanding multiplication of a one digit number with a larger number Multiplying multi digit and 1 digit numbers with regrouping Introduction to multiplication using an area model Multiplying a multi digit and a 1 digit number using an area model Introduction to multiplication of large numbers Area of a rectangle with two digit by one digit side lengths Multiplication of large numbers Multiplication with trailing zeros: Problem type 2 Estimating Products (1 topics) Estimating a product Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 2/13

3 Comparisons and Word Problems Involving Multiplication (5 topics) Multiplicative comparison involving groups of objects Word problem involving multiplicative or additive comparison Word problem with multiplication or division of whole numbers Word problem on unit rates associated with ratios of whole numbers: Whole number answers Word problem with multiplication and addition or subtraction of whole numbers Exponents and Powers of Ten (3 topics) Writing expressions using exponents Introduction to exponents Power of 10: Positive exponent Dividing Whole Numbers (21 topics) Dividing Two Digit Dividends (6 topics) Division without regrouping Division with regrouping: 1 digit divisor, 2 digit dividend Quotient with remainder: 1 digit divisor, 2 digit dividend Writing a division sentence for equal groups Writing a division sentence for equal groups and a remainder Whole number division: 2 digit by 2 digit, no remainder Division Patterns (1 topics) Division with trailing zeros: Problem type 1 Dividing Three and Four Digit Dividends (6 topics) Division with regrouping: 1 digit divisor, 3 digit or 4 digit dividend Quotient with remainder: 1 digit divisor, 3 digit or 4 digit dividend Division involving quotients with intermediate zeros: Problem type 1 Division involving quotients with intermediate zeros: Problem type 2 Division with remainder involving quotients with intermediate zeros: Problem type 1 Division with trailing zeros: Problem type 2 Dividing by Two Digit Divisors (4 topics) Whole number division: 3 digit by 2 digit, no remainder Division with no remainder and a two digit divisor: Problem type 2 Division with remainder and a two digit divisor: Problem type 1 Division with remainder and a two digit divisor: Problem type 2 Estimating Quotients (1 topics) Estimating a quotient Interpreting Remainders (3 topics) Word problem on quotient and remainder Word problem with division of whole numbers and rounding: Problem type 1 Word problem with division of whole numbers and rounding: Problem type 2 Adding and Subtracting Decimals (26 topics) Decimal Place Value (3 topics) Decimal place value: Tenths and hundredths Writing a decimal number less than 1 given its name Writing a decimal number greater than 1 given its name Relating Fractions and Decimals (6 topics) Introduction to unit fractions Introduction to non unit fractions Writing a decimal and a fraction for a shaded region Converting a fraction with a denominator of 10 or 100 to a decimal Converting a fraction with a denominator of 100 or 1000 to a decimal Converting a decimal to a proper fraction without simplifying: Basic Decimals on the Number Line (2 topics) Reading decimal position on a number line: Tenths Reading decimal position on a number line: Hundredths Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 3/13

4 Ordering Decimals (2 topics) Introduction to ordering decimals Ordering decimals Adding Decimals (5 topics) Addition of decimals: Vertically aligned Decimal addition with 2 numbers Decimal addition with 3 numbers Addition with money Word problem with addition of 3 or 4 decimals and whole numbers Subtracting Decimals (6 topics) Subtraction of aligned decimals Decimal subtraction: Basic Decimal subtraction: Advanced Subtraction with money Word problem with addition or subtraction of 2 decimals Word problem with subtraction of a whole number and a decimal: Regrouping with zeros Estimating Sums and Differences (2 topics) Rounding decimals Estimating a decimal sum or difference Multiplying and Dividing Decimals (16 topics) Multiplying Decimals by Powers of Ten (1 topics) Multiplication of a decimal by a power of ten Multiplying Decimals by Whole Numbers (4 topics) Multiplying a decimal less than 1 by a whole number Multiplying a decimal by a whole number Word problem with multiplication of a decimal and a whole number Word problem with multiple decimal operations: Problem type 1 Multiplying Decimals (4 topics) Multiplying decimals less than 1: Problem type 1 Decimal multiplication: Problem type 1 Multiplication of a decimal by a power of 0.1 Word problem with multiplication of two decimals Dividing Decimals by Powers of Ten (1 topics) Division of a decimal by a power of ten Dividing Decimals by Whole Numbers (3 topics) Division of a decimal by a whole number Word problem with division of a decimal and a whole number Word problem with multiple decimal operations: Problem type 2 Dividing Decimals (3 topics) Division of a decimal by a 1 digit decimal: Problem type 1 Division of a decimal by a 2 digit decimal Word problem with division of two decimals Fractions (22 topics) Prime Numbers and Factors (4 topics) Even and odd numbers Divisibility rules for 2, 5, and 10 Factors Prime numbers Equivalent Fractions (10 topics) Understanding equivalent fractions: Problem type 1 Understanding equivalent fractions: Problem type 2 Modeling and writing equivalent fractions Conversions involving division in fractional form and whole numbers Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 4/13

6 Division involving a whole number and a unit fraction Multiplying and Dividing Mixed Numbers (4 topics) Multiplying mixed numbers: Problem type 1 Multiplying mixed numbers: Problem type 2 Multiplying a mixed number and a whole number: Problem type 1 Multiplying a mixed number and a whole number: Problem type 2 Expressions and Equations (15 topics) 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 Evaluating Expressions (3 topics) Evaluating an algebraic expression: Whole number addition or subtraction Evaluating an algebraic expression: Whole number multiplication or division Evaluating an algebraic expression: Whole numbers with two operations Solving Addition and Subtraction Equations (1 topics) Additive property of equality with whole numbers Solving Multiplication and Division Equations (1 topics) Introduction to solving an equation with multiplication or division Patterns and Sequences (5 topics) Describing an increasing or decreasing pattern from a table of values Function tables with one step rules Finding the next terms of an arithmetic sequence with whole numbers Finding the next terms of a geometric sequence with whole numbers Finding patterns in shapes Ordered Pairs (2 topics) Reading a point in quadrant 1 Plotting a point in quadrant 1 Measurement (22 topics) Measuring with U.S. Customary Units (2 topics) Measuring length to the nearest inch Measuring length to the nearest quarter or half inch Converting with U.S. Customary Units of Length (3 topics) Conversion table with U.S. Customary length U.S. Customary length conversion with whole number values Conversions involving measurements in feet and inches Converting with U.S. Customary Units of Volume and Weight (6 topics) Conversion table with U.S. Customary weight Conversion table with U.S. Customary volume U.S. Customary volume conversion with whole number values U.S. Customary weight conversions with whole number values U.S. Customary unit conversion with whole number values: Two step conversion U.S. Customary unit conversion with mixed number values: One step conversion Measuring with Metric Units (3 topics) Measuring length to the nearest centimeter Word problem involving metric mass or volume: Addition or subtraction Word problem involving metric mass or volume: Multiplication or division Converting with Metric Units of Length (3 topics) Conversion table with metric distance Metric distance conversion with whole number values Metric distance conversion with decimal values Converting with Metric Units of Volume and Mass (2 topics) Conversion table with metric mass or volume Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 6/13

7 Metric mass or volume conversion with whole number values Line Plots (3 topics) Interpreting a tally table Constructing a line plot Constructing a line plot with fractional values: Fourths Geometry (9 topics) Segments, Rays, and Lines (1 topics) Identifying parallel and perpendicular lines Classifying and Measuring Angles (2 topics) Classifying angles as smaller than right, right, larger than right Acute, obtuse, and right angles Polygons (1 topics) Naming polygons Classifying Triangles (2 topics) Acute, obtuse, and right triangles Classifying scalene, isosceles, and equilateral triangles by side lengths Quadrilaterals (3 topics) Shared attributes among categories of quadrilaterals Identifying parallelograms, rectangles, and squares Properties of quadrilaterals Perimeter, Area, and Volume (12 topics) Perimeter (1 topics) Finding the missing length in a figure Area of Rectangles (2 topics) Relating the area of a rectangle to multiplying its side lengths Word problem involving the area of a rectangle: Problem type 1 Area of Composite Figures (4 topics) Finding the area of a composite figure on a grid Introduction to area of a piecewise rectangular figure Area of a piecewise rectangular figure Word problem on finding the area of a piecewise rectangular figure Volume (5 topics) Volume of a rectangular prism made of unit cubes Volume of a rectangular prism Writing equivalent expressions for the volume of a rectangular prism Volume of a piecewise rectangular prism Word problem involving the volume of a piecewise rectangular prism Other Topics Available(*) (258 additional topics) Place Value and Review of Arithmetic (10 topics) Finding the value of a collection of coins Finding the value of a collection of bills and coins Addition or subtraction with 10 or 100 Addition or subtraction with 10, 100, or 1000 Estimating a sum of whole numbers: Problem type 2 Estimating a difference of whole numbers: Problem type 2 Using addition and multiplication to count the objects on a grid Deciding if a story represents a multiplication Deciding if a story represents a division Perimeter of a rectangle on a grid Multiplying Whole Numbers (4 topics) Using an area model to represent the distributive property Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 7/13

10 Finding distances between points that share a common coordinate given their coordinates Graphing whole number functions Function tables with two step rules Graphing a line in quadrant 1 Measurement (22 topics) Choosing a measuring tool Choosing U.S. Customary measurement units Adding measurements in feet and inches U.S. Customary area unit conversion with whole number values U.S. Customary unit conversion with mixed number values: Two step conversion Choosing metric measurement units Measuring length to the nearest millimeter Metric area unit conversion with decimal values Metric conversion with decimal values: Two step problem Converting between metric and U.S. Customary unit systems Time unit conversion with whole number values Telling time: Minutes are a multiple of 5 Telling time: Minutes are not a multiple of 5 Telling time and determining AM or PM Word problem involving adding or subtracting time within the hour Introduction to adding time Adding time Word problem on elapsed time within the hour Word problem on elapsed time less than one hour Word problem on elapsed time more than one hour Word problem on elapsed times crossing AM and PM Reading a calendar Geometry (23 topics) Naming segments, rays, and lines Measuring an angle with the protractor Drawing an angle with the protractor Introduction to angle addition Finding an angle measure in a figure with a right or straight angle Classifying scalene, isosceles, and equilateral triangles by side lengths or angles Finding an angle measure of a triangle given two angles Finding an angle measure for a triangle with an extended side Interpreting a Venn diagram of 2 sets Classifying parallelograms Sum of the angle measures of a quadrilateral Identifying congruent shapes on a grid Identifying similar or congruent shapes on a grid Introduction to translations Introduction to reflections Identifying transformations Drawing lines of symmetry Finding an angle of rotation Identifying rotational symmetry and angles of rotation Constructing congruent line segments Constructing the perpendicular bisector of a line segment Constructing an angle bisector Constructing congruent angles Perimeter, Area, and Volume (33 topics) Perimeter of a piecewise rectangular figure Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 10/13

11 Word problem on finding the perimeter of a rectangle Finding an unknown side length of a polygon given the perimeter Sides of polygons having the same perimeter Word problem involving the area of a rectangle: Problem type 2 Finding side lengths of rectangles given one dimension and an area or a perimeter Finding side lengths of squares given an area and a perimeter Estimates and exact answers Area between two rectangles Areas of rectangles with the same perimeter Distinguishing between the area and perimeter of a rectangle Word problem on optimizing an area or perimeter Finding the area of a right triangle on a grid Finding the area of a right triangle or its corresponding rectangle Area of a triangle Area of a parallelogram Finding the area of a trapezoid on a grid by using triangles and rectangles Area of a trapezoid Introduction to a circle: Diameter, radius, and chord Circumference of a circle Area of a circle Classifying solids Vertices, edges, and faces of a solid Identifying geometric shapes that model real world objects Nets of solids Counting the cubes in a solid made of cubes Side views of a solid made of cubes Word problem involving the volume of a rectangular prism Volume of a triangular prism Surface area of a rectangular prism made of unit cubes Surface area of a cube or a rectangular prism Surface area of a piecewise rectangular prism made of unit cubes Surface area of a triangular prism Data, Ratios, and Probability (65 topics) Introduction to interpreting a pictograph Interpreting a pictograph table Constructing a bar graph for non numerical data Interpreting a bar graph Interpreting a double bar graph Constructing a histogram for numerical data Interpreting a line graph Mode of a data set Finding the mode and range of a data set Finding the mode and range from a line plot Average of two numbers Mean of a data set Finding the value for a new score that will yield a given mean Mean and median of a data set How changing a value affects the mean and median Finding outliers in a data set Interpreting a stem and leaf plot Finding if a question can be answered by the data Writing ratios using different notations Writing ratios for real world situations Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 11/13

12 Simplifying a ratio of whole numbers: Problem type 1 Finding a unit price Using tables to compare ratios Computing unit prices to find the better buy Word problem on unit rates associated with ratios of whole numbers: Decimal answers Solving a word problem on proportions using a unit rate Solving a proportion of the form x/a=b/c: Basic Solving a proportion of the form x/a = b/c Word problem on proportions: Problem type 1 Similar polygons Word problem with powers of ten Interpreting a Venn diagram of 3 sets Interpreting a tree diagram Introduction to the counting principle Determining a sample space and outcomes for a simple event Classifying likelihood Introduction to the probability of an event Probability of an event Understanding likelihood Outcomes and event probability Converting a fraction with a denominator of 100 to a percentage Converting a percentage to a fraction with a denominator of 100 Finding the percentage of a grid that is shaded Representing benchmark percentages on a grid Introduction to converting a percentage to a decimal Introduction to converting a decimal to a percentage Converting between percentages and decimals Converting between percentages and decimals in a real world situation Converting a percentage to a fraction in simplest form Converting a fraction to a percentage: Denominator of 4, 5, or 10 Finding benchmark fractions and percentages for a figure Converting a fraction to a percentage: Denominator of 20, 25, or 50 Converting a fraction to a percentage in a real world situation Finding a percentage of a whole number Finding a percentage of a whole number without a calculator: Basic Finding a percentage of a whole number without a calculator: Advanced Finding a percentage of a total amount: Real world situations Finding a percentage of a total amount without a calculator: Sales tax, commission, discount Interpreting a circle graph or pie chart Finding a percentage of a total amount in a circle graph Writing a ratio as a percentage without a calculator Finding the sale price given the original price and percent discount Finding the sale price without a calculator given the original price and percent discount Finding the total cost including tax or markup Finding simple interest without a calculator Other Topics Available By default, these topics are NOT included in the course, but can be added using the content editor in the Teacher Module. Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 12/13

13 QuickTables ALEKS QuickTables is a research based, math fact mastery program for multiplication, division, addition, and subtraction for grades 3 and up. The online program offers ongoing assessment, learning, review, and visual tracking of student progress. Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 13/13

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