Decimals Basics. Percent decimals through the thousandths place

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1 TEKS Reasoning Mind Curriculum Alignment for 5 th Grade Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg 7623; amended to be effective August 1, 2006, 30 TexReg Introduction In this day and age of accountability, teachers and administrators need reassurance that the curriculum they are using meets state and district standards. Though this document can be used to help teachers plan their Reasoning Mind (RM) curriculum, its main purpose is to provide certainty that RM s curriculum is aligned. TEKS Objective Note: Objectives 14 through 16 of the Texas Essential Knowledge and Skills deals with underlying processes and mathematical tools. These skills are not addressed in isolation, but are incorporated throughout the entire Reasoning Mind curriculum. Explanation RM Objective TAKS Objective 1: Number, operation, and quantitative reasoning 5.1 Number, operation, and quantitative reasoning. The student uses place value to represent whole numbers and decimals. 5.1A Use place value to read, write, compare, and order whole numbers through 999,999,999,999 Whole Numbers and the Decimal System Comparing Whole Numbers Convenient Addition (Expanded Form; Adding by Place) 5.1B Use place value to read, write, compare, and order Decimals Basics. Percent decimals through the thousandths place Comparing Decimals 5.2 Number, operation, and quantitative reasoning. The student uses fractions in problem-solving situations. 5.2A Generate a fraction equivalent to a given fraction such as Mini-Lesson: Fractions 1/2 and 3/6 or 4/12 and 1/3 Fraction Basics Fractions, Division, and Ratios Comparing Fractions in Simple Cases 1

2 5.2B Generate a mixed number equivalent to a given improper Fractions, Division, and Ratios fraction or generate an improper fraction equivalent to a Mixed Numbers given mixed number Add and Subtract Mixed Numbers with Like Denominators 5.2C Compare two fractional quantities in problem-solving Mini-Lesson: Fractions situations using a variety of methods, including common Fraction Basics denominators Fractions, Division, and Ratios Comparing Fractions with Like Denominators Comparing Fractions in Simple Cases 5.2D Use models to relate decimals to fractions that name Mini-Lesson: Decimals tenths, hundredths, and thousandths Fraction Basics Decimals Basics. Percent 5.3 Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve meaningful problems. 5.3A Use addition and subtraction to solve problems involving SOC: Addition and Subtraction within 20 whole numbers and decimals Mini-Lesson: Decimals Operation of Addition Convenient Addition Column Addition Definition of Subtraction; Subtrahend, Minuend Subtraction Basics Properties of Subtraction Column Subtraction Numerical Expressions; Parentheses Solving Problems Using Numerical Expressions Algebraic Expressions Equalities and Equations Order of Operations Order of All Operations 2

3 5.3B Use multiplication to solve problems involving whole numbers (no more than 3 digits times 2 digits without technology) Distributive Property Ways to Simplify Calculations Solving Problems Using Algebraic Expressions Adding Decimals Subtracting Decimals SOC: Multiplication Table SOC: Multiplying a 2-Digit Number by a 1-Digit Number Operation of Multiplication Properties of Multiplication Multiplying by Powers of 10 and Round Numbers Column Multiplication by a One-Digit Number Column Multiplication by a Two-Digit Number Powers of Numbers Order of Operations Solving Equations with Multiplication and Division Order of All Operations Distributive Property Ways to Simplify Calculations Solving Problems Using Algebraic Expressions Formulas Basics Distance, Speed, Time Price, Amount, Cost Area of a Geometric Shape Unit Conversion Volume of a Geometric Solid GCFs and LCMs 3

4 5.3C Use division to solve problems involving whole numbers SOC: The Basic Concept of Division (no more than 2-digit divisors and 3-digit dividends SOC: Division within the Multiplication Table without technology), including interpreting the remainder Operation of Division within a given context All Properties of Division Division with a Remainder Long Division Order of Operations Solving Equations with Multiplication and Division Order of All Operations Distance, Speed, Time GCFs and LCMs Unit Conversion Fractions, Division, and Ratios 5.3D Identify common factors of a set of whole numbers GCFs and LCMs 5.3E Model situations using addition and/or subtraction Add and Subtract Fractions with Like Denominators involving fractions with like denominators using concrete objects, pictures, words, and numbers Add and Subtract Mixed Numbers with Like Denominators 5.4 Number, operation, and quantitative reasoning. The Mini-Lesson: Decimals student estimates to determine reasonable results. Rounding Natural Numbers Convenient Addition The student is expected to use strategies, including Ways to Simplify Calculations rounding and compatible numbers, to estimate solutions to Rounding Decimals addition, subtraction, multiplication, and division Estimating Sums and Differences problems. Overestimates and Underestimates Estimating Products and Quotients TAKS Objective 2: Patterns, relationships, and algebraic thinking 5.5 Patterns, relationships, and algebraic thinking. The student makes generalizations based on observed patterns and relationships. 4

5 5.5A Describe the relationship between sets of data in graphic organizers such as lists, tables, charts, and diagrams 5.5B Identify prime and composite numbers using concrete objects, pictorial models, and patterns in factor pairs 5.6 Patterns, relationships, and algebraic thinking. The student describes relationships mathematically. The student is expected to select from and use diagrams and equations such as y = to represent meaningful problem situations. Mini-Lesson: Patterns and Sequence GCFs and LCMs Working with Tables, Graphs, and Charts Mini-Lesson: Primes GCFs and LCMs Algebraic Expressions Equalities and Equations Solving Equations with Multiplication and Division Solving Problems Using Algebraic Expressions Formulas Basics Distance, Speed, Time Price, Amount, Cost Related Objectives: Numerical Expressions; Parentheses Solving Problems Using Numerical Expressions TAKS Objective 3: Geometry and spatial reasoning 5.7 Geometry and spatial reasoning. The student generates Mini-Lesson: Geometry geometric definitions using critical attributes. Lines, Segments, Rays Polygons Basics The student is expected to identify essential attributes Angles including parallel, perpendicular, and congruent parts of 2- Types of Triangles and Quadrilaterals and 3-dimensional geometric figures. The Circle and the Disk Simple Transformations; Congruence and Symmetry Polyhedrons 5.8 Geometry and spatial reasoning. The student models transformations. 5.8A Sketch the results of translations, rotations, and reflections Mini-Lesson: Geometry on a Quadrant I coordinate grid Simple Transformations; Congruence and Symmetry 5

6 5.8B Identify the transformation that generates one figure from the other when given 2 congruent figures on a Quadrant I coordinate grid 5.9 Geometry and spatial reasoning. The student recognizes the connection between ordered pairs of numbers and locations of points on a plane. Mini-Lesson: Geometry Simple Transformations; Congruence and Symmetry Mini-Lesson: Graphs The Plane and the Coordinate Grid Related Objective: Lines, Rays, Segments (Number Ray) The student is expected to locate and name points on a coordinate grid using ordered pairs of whole numbers. TAKS Objective 4: Measurement 5.10 Measurement. The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems. 5.10A Perform simple conversions within the same measurement system (SI (metric) or customary) 5.10B Connect models for perimeter, area, and volume with their respective formulas 5.10C Select and use appropriate units and formulas to measure length, perimeter, area, and volume Unit Conversion Mini-Lesson: Volume Rectangular Prism Polygons Basics (The Perimeter of a Polygon) Area of a Geometric Shape Volume of a Geometric Solid SOC: Measuring Length Basics SOC: Measuring Capacity Basics Mini-Lesson: Volume Rectangular Prism Lines, Segments, Rays Polygons Basics (The Perimeter of a Polygon) Formulas Basics Area of a Geometric Shape Volume of a Geometric Solid Related Objective: Angles (Measuring Angles) 6

7 5.11 Measurement. The student applies measurement concepts. The student measures time and temperature (in degrees Fahrenheit and Celsius). 5.11A Solve problems involving changes in temperature SOC: Measuring Temperature Basics 5.11B Solve problems involving elapsed time SOC: Measuring Time basics TAKS Objective 5: Probability and Statistics 5.12 Probability and statistics. The student describes and predicts the results of a probability experiment. 5.12A Use fractions to describe the results of an experiment Mini-Lesson: Fractions Mini-Lesson: Probability and Statistics Experiments and Random Events Equally Likely Simple Events; Probability 5.12B Use experimental results to make predictions Mini-Lesson: Probability and Statistics Equally Likely Simple Events; Probability 5.12C List all possible outcomes of a probability experiment such Mini-Lesson: Probability and Statistics as tossing a coin Tree Diagrams; Combinations Experiments and Random Events Equally Likely Simple Events; Probability 5.13 Probability and statistics. The student solves problems by collection, organizing, displaying, and interpreting sets of data. 5.13A Use tables of related number pairs to make line graphs Working with Tables, Graphs, and Charts 5.13B Describe characteristics of data presented in tables and Mini-Lesson: Graphs graphs including median, mode, and range Mini-Lesson: Median, Mode, Range Working with Tables, Graphs, and Charts 5.13C Graph a given set of data using an appropriate graphical representation such as a picture or line graph. Statistical Data: Range, Median, and Mode Mini-Lesson: Graphs Working with Tables, Graphs, and Charts 7

8 TAKS Objective 6: Underlying processes and mathematical tools 5.14 Underlying processes and mathematical tools. The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school. 5.14A Identify the mathematics in everyday situations Included in all objectives 5.14B Solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness 5.14C Select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem 5.14D Use tools such as real objects, manipulatives, and technology to solve problems 5.15 Underlying processes and mathematical tools. The student communicates about Grade 5 mathematics using informal language. 5.15A Explain and record observations using objects, words, pictures, numbers, and technology Included in all objectives 5.15B Relate informal language to mathematical language and symbols 5.16 Underlying processes and mathematical tools. The student uses logical reasoning. 5.16A Make generalizations from patterns or sets of examples and non-examples Included in all objectives 5.16B Justify why an answer is reasonable and explain the solution process. 8

9 TEKS Reasoning Mind Curriculum Alignment for 6 th Grade (ordered by TEKS objective) Source: The provisions of this adopted to be effective September 1, 1998, 22 TexReg 7623; amended to be effective August 1, 2006, 30 TexReg Introduction In this day and age of accountability, teachers and administrators need reassurance that the curriculum they are using meets state and district standards. Though this document can be used to help teachers plan their Reasoning Mind (RM) curriculum, its main purpose is to provide certainty that RM s curriculum is aligned. Note: Objectives 11 through 13 of the Texas Essential Knowledge and Skills deals with underlying processes and mathematical tools. These skills are not addressed in isolation, but are incorporated throughout the entire Reasoning Mind curriculum. TEKS Objective Explanation RM Objective TAKS Objective 1: Number, operation, and quantitative reasoning 6.1 Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. 6.1A Compare and order non-negative rational numbers SOC: Comparing Fractions with Like Denominators SOC: Comparing Fractions in Simple Cases SOC: Comparing Decimals Mini-Lesson: Decimals Review: Comparing Decimals Review: Compare, Add, Subtract Fractions with Like Denom s Comparing Fractions with Different Denominators Positive and Negative Integers Number Line Comparing Integers; Inequalities 9

10 6.1B Generate equivalent forms of rational numbers including whole numbers, fractions, and decimals SOC: Fractions Basics (Some Special Fractions; Percent) SOC: Fractions, Division, and Ratios SOC: Mixed Numbers SOC: Comparing Fractions in Simple Cases (Equivalent Fractions) SOC: Decimals Basics. Percent SOC: Comparing Decimals (Equivalent Decimals) Mini-Lesson: Decimals Mini-Lesson: Fractions Mini-Lesson: Percentage Review: Decimals Basics Review: Fraction Basics Review: Mixed Numbers Equivalent Fractions; Reducing Fractions Bringing Fractions to a Common Denominator Add and Subtract Fractions with Unlike Denom s Add and Subtract Mixed Numbers with Unlike Denom s Fractions and Mixed Numbers Multiplication Finding Fraction of a Number Dividing Fractions and Mixed Numbers Finding the Number Given a Fraction of it Fractional Expressions Basics Ratios Basics 6.1C Use integers to represent real-life situations Positive and Negative Integers Increase and Decrease of a Value 10

11 6.1D Write prime factorizations using exponents Mini-Lesson: Primes 6.1E Identify factors of a positive integer, common factors, and the greatest common factor of a set of positive integers 6.1F Identify multiples of a positive integer and common multiples and the LCM of a set of positive integers Related Objectives (prime factorization without exponents): Review: Factors, Prime and Composite Numbers, GCFs Finding GCF and LCM by Prime Factorization Review: Factors, Prime and Composite Numbers, GCFs Divisibility by 2, 5, and 10 Divisibility by 3 and 9 Divisibility by 4 and 25 Finding GCF and LCM by Prime Factorization Review: Multiples and LCMs Finding GCF and LCM by Prime Factorization 6.2 Number, operation, and quantitative reasoning. The student adds, subtracts, multiplies, and divides to solve problems and justify solutions. 6.2A Model addition and subtraction situations involving fractions with objects, pictures, words, and numbers SOC: Add and Subtract Fractions with Like Denominators SOC: Add and Subtract Mixed Numbers with Like Denominators Mini-Lesson: Fractions Review: Fraction Basics Review: Mixed Numbers Review: Compare, Add, Subtract Fractions with Like Denom s Review: Add and Subtract Mixed Numbers with Like Denom s 11

12 6.2B Use addition and subtraction to solve problems involving fractions and decimals 6.2C Use multiplication and division of whole numbers to solve problems including situations involving equivalent ratios and rates SOC: Add and Subtract Fractions with Like Denominators SOC: Add and Subtract Mixed Numbers with Like Denominators SOC: Adding Decimals SOC: Subtracting Decimals Mini-Lesson: Fractions Review: Adding and Subtracting Decimals Review: Compare, Add, Subtract Fractions with Like Denom s Add and Subtract Fractions with Unlike Denom s Review: Add and Subtract Mixed Numbers with Like Denom s Add and Subtract Mixed Numbers with Unlike Denom s SOC: Unit Conversion Mini-Lesson: Ratios Ratios Basics Ratios of Amounts which have Different Units Rates Rates of Speed; Movement Formulas Proportions Basics The Main Property of Proportions Solving Proportions Direct Proportionality Proportional Division of a Quantity Solving Percent Problems Using Proportions Conversion of Metric Units Using Proportions Conversion of Customary Units Using Proportions 12

13 6.2D Estimate and round to approximate reasonable results and to solve problems where exact answers are not required 6.2E Use order of operations to simplify whole number expressions (without exponents) in problem solving situations Scale The Mean SOC: Rounding Natural Numbers SOC: Estimating Sums and Differences SOC: Overestimates and Underestimates SOC: Estimating Products and Quotients Review: Rounding Decimals SOC: Order of Operations SOC: Order of All Operations Related objective: Offline lesson 1: Distributive Property to Simplify Calculations Offline lesson 2: Distributive Property to Simplify Expressions Offline lesson 3: Distributive Property to Simplify Equations TAKS Objective 2: Patterns, relationships, and algebraic thinking 6.3 Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships. 6.3A Use ratios to describe proportional situations SOC: Fractions Basics (Some Special Fractions; 6.3B Represent ratios and percents with concrete models, Percent) fractions, and decimals SOC: Decimals Basics. Percent 6.3C Use ratios to make predictions in proportional situations Mini-Lesson: Ratios Mini-Lesson: Percentage Ratios Basics Proportions Basics The Main Property of Proportions Solving Proportions 13

14 Direct Proportionality Proportional Division of a Quantity Solving Percent Problems Using Proportions Conversion of Metric Units Using Proportions Conversion of Customary Units Using Proportions Scale 6.4 Patterns, relationships, and algebraic thinking. The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. 6.4A Use tables and symbols to represent and describe Direct Proportionality proportional and other relationships such as those Solving Percent Problems using Proportions involving conversions, arithmetic sequences (with a Conversion of Metric Units using Proportions constant rate of change), perimeter and area Conversion of Customary Units using Proportions Mini-Lesson: Patterns and Sequence 6.4B Use tables of data to generate formulas representing We will provide supplemental materials relationships involving perimeter, area, volume of a rectangular prism, etc. 6.5 Patterns, relationships, and algebraic thinking. The SOC: Algebraic Expressions student uses letters to represent an unknown in an SOC: Equalities and Equations equation. SOC: Formulas Basics SOC: Distance, Speed, Time The student is expected to formulate equations from SOC: Price, Amount, Cost problem situations described by linear relationships. Finding the Number Given a Fraction of it Direct Proportionality Proportional Division of a Quantity Solving Percent Problems Using Proportions Conversion of Metric Units Using Proportions Conversion of Customary Units Using Proportions Scale 14

15 TAKS Objective 3: Geometry and spatial reasoning 6.6 Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. 6.6A Use angle measurements to classify angles as acute, SOC: Angles obtuse, or right SOC: Types of Triangles and Quadrilaterals Mini-Lesson: Geometry Review: Angles Types of Triangles 6.6B Identify relationships involving angles in triangles and SOC: Polygons Basics quadrilaterals SOC: Types of Triangles and Quadrilaterals Mini-Lesson: Geometry Review: Polygons Basics Regular Polygons Sum of the Angles of a Triangle and Quadrilateral Types of Triangles Trapezoids and Parallelograms 6.6C Describe the relationship between radius, diameter, and SOC: The Circle and the Disk circumference of a circle Mini-Lesson: Geometry Review: Circle and Disk Circumference of a Circle; Area of a Disk 6.7 Geometry and spatial reasoning. The student uses coordinate geometry to identify location in two dimensions. SOC: The Plane and the Coordinate Grid Coordinate Plane The student is expected to locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers. TAKS Objective 4: Measurement 6.8 Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. 15

16 6.8A Estimate measurements (including circumference) and SOC: Measuring Time Basics evaluate reasonableness of results SOC: Measuring Temperature Basics SOC: Measuring Length Basics SOC: Measuring Mass and Weight Basics SOC: Measuring Capacity Basics SOC: Area of a Geometric Shape Review: Area Area of Triangle and Trapezoid Circumference of a Circle; Area of a Disk 6.8B Select and use appropriate units, tools, or formulas to All of the above, and also the following: measure and to solve problems involving length SOC: Polygons Basics (The Perimeter of a Polygon) (including perimeter), area, time, temperature, volume, SOC: Formulas Basics and weight SOC: Volume of a Geometric Solid 6.8C Measure angles Review: Angles 6.8D Convert measures within the same measurement system SOC: Unit Conversion (customary and metric) based on relationships between Conversion of Metric Units Using Proportions units Conversion of Customary Units Using Proportions TAKS Objective 5: Probability and Statistics 6.9 Probability and Statistics. The student uses experimental and theoretical probability to make predictions. 6.9A Construct sample spaces using lists and tree diagrams SOC: Tree Diagrams; Combinations SOC: Experiments and Random Events SOC: Equally Likely Simple Events; Probability Review: Tree Diagrams; Combinations Review: Experiments and Random Events Review: Equally Likely Outcomes, Probability Sample Spaces and Complement Events 6.9B Find the probabilities of a simple event and its Review: Equally Likely Outcomes, Probability complement and describe the relationship between the two Sample Spaces and Complement Events 16

17 6.10 Probability and statistics. The student uses statistical representations to analyze data. 6.10A Select and use an appropriate representation for SOC: Working with Tables, Graphs, and Charts presenting and displaying different graphical Mini-Lesson: Graphs representations of the same data including line plot, line Graphs on Coordinate Plane graph, bar graph, and stem and leaf plot Line Plots; Stem and Leaf Plots 6.10B Identify mean (using concrete objects and pictorial SOC: Statistical Data: Range, Median, and Mode models), median, mode, and range of a set of data Review: Range, Median, and Mode The Mean 6.10C Sketch circle graphs to display data Mini-Lesson: Graphs 6.10D Solve problems by collecting, organizing, displaying, SOC: Experiments and Random Events and interpreting data SOC: Equally Likely Simple Events; Probability SOC: Statistical Data: Range, Median, and Mode Graphs on Coordinate Plane Review: Range, Median, and Mode The Mean Line Plots; Stem and Leaf Plots Review: Tree Diagrams; Combinations Review: Experiments and Random Events Sample Spaces and Complement Events TAKS Objective 6: Underlying processes and mathematical tools 6.11 Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. 6.11A Identify and apply mathematics to everyday experiences, Included in all objectives. to activities in and outside of school, with other disciplines, and with other mathematical topics 6.11B Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness 17

18 6.11C Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem 6.11D Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems 6.12 Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. 6.12A Communicate mathematical ideas using language, Included in all objectives. efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models 6.12B Evaluate the effectiveness of different representations to communicate ideas 6.13 Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. 6.13A Make conjectures from patterns or sets of examples and Included in all objectives. non-examples 6.13B Validate his/her conclusions using mathematical properties and relationships 18