Mathematics - LV 5 (with QuickTables)

Transcription

1 Mathematics - LV 5 (with QuickTables) Correlation of the ALEKS Course Mathematics LV 5 to the California Mathematics Content Standards for Grade 5 (1998) Number Sense: NS1.1: NS1.2: NS1.3: NS1.4: TD = Teacher Directed NS1.0: Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers: Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbers. Expanded form Rounding to tens or hundreds Rounding to thousands, ten thousands, or hundred thousands Rounding to hundreds or thousands Estimating a sum of whole numbers Estimating a difference of whole numbers Estimating a product Estimating a quotient Rounding decimals Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number. Converting a decimal to a fraction: Basic Converting a decimal to a proper fraction in simplest form: Advanced Converting a fraction with a denominator of 10, 100, or 1000 to a decimal Converting a fraction to a terminating decimal Converting a fraction to a repeating decimal Converting a decimal to a mixed number Converting a mixed number to a decimal Finding the percentage of a grid that is shaded Converting a percentage to a fraction in simplest form Converting a fraction to a percentage: Denominator of 20, 25, or 50 Writing a ratio as a percentage without a calculator Finding a percentage of a whole number without a calculator: Basic Understand and compute positive integer powers of nonnegative integers; compute examples as repeated multiplication. Introduction to exponents Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor (e.g., 24 = 2 x 2 x 2 x 3 = 2 3 x 3). ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 1/9

2 NS1.5: Prime factorization Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers. Fractional position on a number line Plotting fractions on a number line Plotting integers on a number line Plotting rational numbers on a number line NS2.0: Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals: NS2.1: NS2.2: NS2.3: Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results. Addition of aligned decimals Decimal addition with 3 numbers Subtraction of aligned decimals Multiplication of a decimal by a power of ten Multiplication of a decimal by a whole number Decimal multiplication: Problem type 1 Decimal multiplication: Problem type 2 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 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 Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors. Division without carry Division with carry Division with trailing zeros: Problem type 1 Division with trailing zeros: Problem type 2 Division involving quotients with intermediate zeros Quotient and remainder: Problem type 1 Quotient and remainder: Problem type 2 Quotient and remainder: Problem type 3 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 Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the simplest form. Addition or subtraction of fractions with the same denominator Addition or subtraction of unit fractions Introduction to addition or subtraction of fractions with different denominators Addition or subtraction of fractions with different denominators Fractional part of a circle ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 2/9

3 NS2.4: NS2.5: 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 2 Understand the concept of multiplication and division of fractions. TD Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems. Product of a unit fraction and a whole number Product of a fraction and a whole number: Problem type 1 Introduction to fraction multiplication Fraction multiplication Division involving a whole number and a fraction Fraction division Mixed number multiplication: Problem type 1 Mixed number multiplication: Problem type 2 Mixed number division Solving a fraction word problem using a linear equation of the form Ax = B Algebra and Functions AF1.1: AF1.2: AF1.3: AF1.0: Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results: Use information taken from a graph or equation to answer questions about a problem situation. Interpreting a bar graph Interpreting a double bar graph Interpreting a line graph Interpreting a circle graph or pie chart Interpreting a stem-and-leaf plot Reading a point in the coordinate plane Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution. 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 Writing a one-step expression for a real-world situation Writing a one-step variable expression for a real-world situation Translating a sentence into a one-step equation Function tables with two-step rules Know and use the distributive property in equations and expressions with variables. Understanding the distributive property ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 3/9

4 AF1.4: AF1.5: Identify and graph ordered pairs in the four quadrants of the coordinate plane. Reading a point in the coordinate plane Plotting a point in the coordinate plane Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid. Function tables with two-step rules Finding a solution to a linear equation in two variables Graphing a line in quadrant 1 Measurement and Geometry MG1.1: MG1.2: MG1.3: Understand the concept of volume and use the appropriate units in common measuring systems (i.e., MG1.4: MG1.0: Students understand and compute the volumes and areas of simple objects: Derive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectangle of the same area by cutting and pasting a right triangle on the parallelogram). Area of a triangle Area of a parallelogram Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area for these objects. Surface area of a cube or a rectangular prism Nets of solids cubic centimeter [cm 3 ], cubic meter [m 3 ], cubic inch [in 3 ], cubic yard [yd 3 ]) to compute the volume of rectangular solids. Volume of a rectangular prism made of unit cubes Volume of a rectangular prism Differentiate between, and use appropriate units of measures for, two-and three-dimensional objects (i.e., find the perimeter, area, volume). Area of a triangle Perimeter of a square or a rectangle Perimeter of a polygon Area of a square or a rectangle Distinguishing between the area and perimeter of a rectangle Area of a piecewise rectangular figure Area of a parallelogram Volume of a rectangular prism made of unit cubes Volume of a rectangular prism MG2.0: Students identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures: MG2.1: Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 4/9

5 MG2.2: using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software). Measuring an angle with the protractor Drawing an angle with the protractor Constructing congruent angles Identifying parallel and perpendicular lines Know that the sum of the angles of any triangle is 180 and the sum of the angles of any quadrilateral is 360 and use this information to solve problems. Finding an angle measure of a triangle given two angles Finding an angle measure for a triangle with an extended side Sum of the angle measures of a quadrilateral MG2.3: Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids. Side views of a solid made of cubes Statistics, Data Analysis, and Probability SP1.1: SP1.2: SP1.3: SP1.4: SP1.5: SP1.0: Students display, analyze, compare, and interpret different data sets, including data sets of different sizes: Know the concepts of mean, median, and mode; compute and compare simple examples to show that they may differ. Mode of a data set Finding the mode and range of a data set How changing a value affects the mean and median Organize and display single-variable data in appropriate graphs and representations (e.g., histogram, circle graphs) and explain which types of graphs are appropriate for various data sets. Constructing a histogram for numerical data Constructing a bar graph for non-numerical data Constructing a line plot Use fractions and percentages to compare data sets of different sizes. Interpreting a circle graph or pie chart Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph. Interpreting a line graph Reading a point in the coordinate plane Know how to write ordered pairs correctly; for example, (x, y). Reading a point in quadrant 1 Reading a point in the coordinate plane Mathematical Reasoning: ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 5/9

6 MR1.1: MR1.0: Students make decisions about how to approach problems: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. Finding the next terms of a sequence with whole numbers Word problem with multiple decimal operations: Problem type 1 Acute, obtuse, and right triangles Scalene, isosceles, and equilateral triangles Area of a triangle Identifying parallelograms, rectangles, and squares Classifying quadrilaterals Sides of polygons having the same perimeter Finding the side length of a rectangle given its perimeter or area Identifying congruent shapes on a grid Identifying transformations Interpreting a double bar graph Interpreting a tree diagram Introduction to the counting principle Interpreting a Venn diagram of 2 sets MR1.2: Determine when and how to break a problem into simpler parts. Order of operations with whole numbers Order of operations with whole numbers and grouping symbols Word problem with multiple decimal operations: Problem type 1 Area of a piecewise rectangular figure Surface area of a piecewise rectangular prism made of unit cubes U.S. Customary unit conversion with whole number values: Two-step conversion Adding time Introduction to elapsed time Elapsed time MR2.0: Students use strategies, skills, and concepts in finding solutions: MR2.1: Use estimation to verify the reasonableness of calculated results. Word problem with division of whole numbers and rounding Estimating a sum of whole numbers Estimating a difference of whole numbers Estimating a product Estimating a quotient MR2.2: Apply strategies and results from simpler problems to more complex problems. Addition or subtraction of fractions with different denominators Introduction to fraction multiplication Fraction multiplication Division involving a whole number and a fraction Fraction division Addition or subtraction of mixed numbers with different denominators Mixed number multiplication: Problem type 1 ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 6/9

7 MR2.3: MR2.4: MR2.5: Mixed number division Perimeter of a piecewise rectangular figure Areas of rectangles with the same perimeter Area of a piecewise rectangular figure Conversions involving measurements in feet and inches Finding the value for a new score that will yield a given mean Using two steps to solve an equation with whole numbers Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. Understanding equivalent fractions Equivalent fractions Constructing an angle bisector Nets of solids Vertices, edges, and faces of a solid Drawing lines of symmetry Introduction to the probability of an event Writing a one-step expression for a real-world situation Writing a one-step variable expression for a real-world situation Translating a sentence into a one-step equation Function tables with one-step rules Function tables with two-step rules Graphing whole number functions Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work. Expanded form Prime factorization Using a common denominator to order fractions The reciprocal of a number Rounding decimals Converting a fraction to a terminating decimal Converting a fraction to a repeating decimal Converting between percentages and decimals Writing a ratio as a percentage without a calculator Measuring an angle with the protractor Naming segments, rays, and lines Perimeter of a square or a rectangle Area of a square or a rectangle Distinguishing between the area and perimeter of a rectangle Volume of a rectangular prism Writing a one-step expression for a real-world situation Writing a one-step variable expression for a real-world situation Translating a sentence into a one-step equation Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 7/9

8 MR2.6: Word problem with division of whole numbers and rounding Estimating a sum of whole numbers Estimating a difference of whole numbers Estimating a product Estimating a quotient Make precise calculations and check the validity of the results from the context of the problem. Solving a word problem on proportions using a unit rate Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Word problem with multiple decimal operations: Problem type 1 Word problem with multiple decimal operations: Problem type 2 Sides of polygons having the same perimeter Finding the side length of a rectangle given its perimeter or area Areas of rectangles with the same perimeter U.S. Customary unit conversion with whole number values: Two-step conversion Metric mass or capacity conversion with whole number values Metric distance conversion with decimal values Finding the value for a new score that will yield a given mean MR3.0: Students move beyond a particular problem by generalizing to other situations: MR3.1: Evaluate the reasonableness of the solution in the context of the original situation. MR3.2: Solving a word problem on proportions using a unit rate Word problem with one decimal operation: Problem type 1 Word problem with one decimal operation: Problem type 2 Word problem with multiple decimal operations: Problem type 1 Word problem with multiple decimal operations: Problem type 2 Sides of polygons having the same perimeter Finding the side length of a rectangle given its perimeter or area Areas of rectangles with the same perimeter U.S. Customary unit conversion with whole number values: Two-step conversion Metric mass or capacity conversion with whole number values Metric distance conversion with decimal values Finding the value for a new score that will yield a given mean Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems. Factors Prime factorization Finding the next terms of a sequence with whole numbers Equivalent fractions Addition or subtraction of fractions with different denominators Introduction to fraction multiplication Fraction multiplication ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 8/9

9 MR3.3: Addition or subtraction of mixed numbers with different denominators Mixed number multiplication: Problem type 1 Writing a ratio as a percentage without a calculator Finding a percentage of a whole number without a calculator: Basic Finding an angle measure of a triangle given two angles Area of a square or a rectangle Area of a piecewise rectangular figure Introduction to the probability of an event Probability of an event Integer addition: Problem type 1 Integer subtraction: Problem type 1 Integer subtraction: Problem type 2 Integer subtraction: Problem type 3 Additive property of equality with integers Multiplicative property of equality with whole numbers Using two steps to solve an equation with whole numbers Develop generalizations of the results obtained and apply them in other circumstances. Least common multiple of 2 numbers Word problem with common multiples Finding the next terms of a sequence with whole numbers Writing ratios for real-world situations Solving a word problem on proportions using a unit rate Introduction to ordering decimals Ordering decimals Ordering fractions and decimals Finding a percentage of a whole number without a calculator: Basic Finding an angle measure of a triangle given two angles Finding an angle measure for a triangle with an extended side Finding the value for a new score that will yield a given mean Interpreting a tree diagram Introduction to the counting principle ALEKS - Copyright 2014 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. P. 9/9