Destination Math California Intervention correlated to the California Intervention 4 7 s McDougal Littell Riverdeep
STANDARDS MAPS for a Mathematics Intervention Program (Grades 4-7) The standards maps for a Mathematics Intervention program consist of two parts: Part A: Subset of standards for Number Sense (NS); Algebra and Function (AF); Measurement and Geometry (MG); and Statistics, Data Analysis, and Probability (SDAP). The standards map for Part A is organized by the six topical Volumes (I-VI) required for adoption in Appendix E (refer to the tables on pages 342-343 of the Mathematics Framework, Appendix E) and includes the required subset of standards from grades K-7. The standards map for Part A does not include standards from the Mathematical Reasoning strand. Part B: All standards in the Mathematical Reasoning (MR) strand only. The standards map for Part B includes all of the Mathematical Reasoning (MR) standards for grades K-7 (refer to the table on page 341 of the Mathematics Framework, Appendix E) and is organized by grade level. The MR standards must be systematically embedded in the teaching of the subset of standards from the content strands in Part A (NS, AF, MG, and/or SDAP). Page 1
PART A: STANDARDS MAPS for Mathematics Intervention Programs Subset of standards for Number Sense (NS); Algebra and Function (AF); Measurement and Geometry (MG); and Statistics, Data Analysis, and Probability (SDAP). VOLUME I Place Value and Basic Number Skills Grade/ GRADE 1 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 1.1 Count, read, and write whole numbers to 100. V1-3 1.2 Compare and order whole numbers to 100 by using the symbols for less than, equal to, or greater than (<, =, >). 1.3 Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions (to 20) (e.g., 8 may be represented as 4 + 4, 5 + 3, 2 + 2 + 2 + 2, 10-2, 11-3). MSC2_ 1.1.1 Counting by Grouping MSC2_ 1.1.2 Place Values: Tens and Ones V1-5 MSC2_ 1.1.5 Comparing and Ordering V1-1 V1-2 V1-8 V1-10 Page 2
Grade/ Strand/ Language Primary Citations Supporting Citations 1.4 Count and group objects in ones and tens (e.g., three groups of 10 and 4 equals 34, or 30 + 4). 2.1 Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory. V1-1, V1-2 MSC2_ 1.1.1 Counting by Grouping MSC2_ 1.1.2 Place Values: Tens and Ones V1-9 Page 3
Grade/ Strand/ Language Primary Citations Supporting Citations 2.5 Show the meaning of addition (putting together, increasing) and subtraction (taking away, comparing, finding the difference). 2.6 Solve addition and subtraction problems with one-and two-digit numbers (e.g., 5 + 58 = ). V1-7; V1-14 2.7 Find the sum of three one-digit numbers. V1-20 MSC2_ 2.1.1 Sums Less than 100 MSC2_ 2.1.3 Differences within 100 V1-12; V1-17 MSC2_ 2.1.1 Sums Less than 100 MSC2_ 2.1.3 Differences within 100 V1-15 Page 4
Grade/ GRADE 2 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 1.1 Count, read, and write whole numbers to 1,000 and identify the place value for each digit. 1.2 Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000). 1.3 Order and compare whole numbers to 1,000 by using the symbols <, =, >. 2.2 Find the sum or difference of two whole numbers up to three digits long. V1-2; V1-4 MSC2_ 1.1.2 Place Values: Tens and Ones MSC2_ 1.1.3 Place Values: Hundreds, Tens, and Ones V1-4 MSC2_ 1.1.2 Place Values: Tens and Ones MSC2_ 1.1.3 Place Values: Hundreds, Tens, and Ones MSC2_1.1.4 Expanded Form and Equivalent Representat-ions of a Number V1-5 MSC2_1.1.5 Comparing and Ordering V1-11, V1-15, V1-16 MSC2_ 2.1.1 Sums Less than 100 MSC2_2.1.2 Estimating and Finding Sums Less than 1,000 MSC2_ 2.1.3 Differences within 100 MSC2_ 2.1.4 Estimating and Finding Differences within 1,000 V1-3, V1-6 MSC2_ 1.1.1 Counting by Grouping V1-1 MSC2_ 1.1.1 Counting by Grouping Page 5
Grade/ Strand/ Language Primary Citations Supporting Citations 2.3 Use mental arithmetic to find the sum or difference of two two-digit numbers. 3.1 Use repeated addition, arrays, and counting by multiples to do multiplication. 3.3 Know the multiplication tables of 2s, 5s, and 10s (to "times 10") and commit them to memory. V1-19 V1-21, V1-22 MSC2_ 2.2.1 Repeated Addition and Arrays MSC2_ 2.2.2 Skip Counting to Show Multiplication V1-23 MSC2_ 2.2.3 Finding Products Less than 100 Page 6
Grade/ GRADE 3 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 1.3 Identify the place value for each digit in numbers to 10,000. 1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6). 2.1 Find the sum or difference of two whole numbers between 0 and 10,000. 2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10. 2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 x 3 = ). 2.6 Understand the special properties of 0 and 1 in multiplication and division. V1-4, V1-6 MSC2_ 1.2.1 Place Values: Thousands, Hundreds, Tens, and Ones V1-4 MSC2_ 1.2.1 Place Values: Thousands, Hundreds, Tens, and Ones V1-12, V1-13, V1-17, V1-18 MSC2_2.1.2 Estimating and Finding Sums Less than 1,000 MSC2_2.1.5 Estimating and Finding Differences within 9,999 MSC3_2.1.1 Whole Number Sums MSC3_2.1.2 Differences Between Large Numbers V1-23 V1-24 MSC2_2.2.3 Finding Products Less than 100 V1-31 V1-25 MSC2_1.1.4 Expanded Form and Equivalent Representations of a Number V1-15, V1-16 MSC2_ 2.1.4 Estimating and Finding Differences within 1,000 MSC3_2.3.1 Two-Digit Multipliers Page 7
Grade/ GRADE 4 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 1.1 Read and write whole numbers in the millions. V1-2, V1-4 V1-6 1.2 Order and compare whole numbers and decimals to two decimal places. 1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. 1.6 Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or.50; 7/4 = 1 3/4 = 1.75). 3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers. MSC3_1.1.2 Ordering and Rounding Whole Numbers V1-5 MSC3_1.1.2 Ordering and Rounding Whole Numbers MSC3_ 4.1.2 Ordering and Rounding V1-6 MSC3_1.1.2 Ordering and Rounding Whole Numbers MSC3_ 4.1.1 Tenths, Hundredths, and Thousandths V1-13; V1-18; V1-20 MSC3_ 2.1.1 Whole Number Sums MSC3_ 2.1.2 Differences Between Large Numbers MSC3_1.1.1 Whole Numbers to One Million MSC2_ 2.1.5 Estimating and Finding Differences within 9,999 Page 8
Grade/ Strand/ Language Primary Citations Supporting Citations 3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results. 4.1 Understand that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3). V1-25, V1-26, V1-27, V1-28, V1-29, V1-30 MSC3_ 2.3.1 Two-Digit Multipliers MSC3_ 2.3.2 Introduction to Long Division V1-23 MSC3_ 1.2.1 Finding Factors MSC2_ 2.3.2 Dividing by a 1-Digit Number MSC3_2.3.3 Two-Digit Divisors MSC3_ 1.2.2 Prime and Composite Numbers MSC3_ 1.2.3 Identifying Common Factors Page 9
VOLUME II Fractions and Decimals Grade/ GRADE 2 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 4.0 Students understand that fractions and decimals may refer to parts of a set and parts of a whole: 4.1 Recognize, name, and compare unit fractions from 1/12 to 1/2. 4.3 Know that when all fractional parts are included, such as four-fourths, the result is equal to the whole and to one. 5.1 Solve problems using combinations of coins and bills. 5.2 Know and use the decimal notation and the dollar and cent symbols for money. V2-4, V2-18 MSC2_ 2.3.3 Fractional Parts MSC3_ 3.1.1 Proper Fractions V2-4, V2-7 MSC2_ 2.3.3 Fractional Parts MSC3_ 3.1.1 Proper Fractions V2-6, p. 25 b MSC2_ 2.3.3 Fractional Parts MSC3_ 3.1.1 Proper Fractions V-2-30 MSC2_3.2.2 Money V2-23, V2-30 MSC2_3.2.2 Money V2-24 Page 10
Grade/ GRADE 3 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 3.1 Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g., 1/2 of a pizza is the same amount as 2/4 of another pizza that is the same size; show that 3/8 is larger than 1/4). 3.2 Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2). 3.4 Know and understand that fractions and decimals are two different representations of the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a dollar). V2-5, V2-10, V2-11 MSC2_ 2.3.3 Fractional Parts MSC3_3.1.3 Equivalent Fractions V2-11, V2-12 MSC3_ 3.2.1 Sums Involving Like Denominators V2-21 MSC3_ 4.1.1 Tenths, Hundredths, and Thousandths MSC3_ 4.1.3 Ratios, Decimals, and Percents MSC3_ 3.1.4 Ordering and Rounding Fractions MSC3_ 3.2.1 Sums Involving Like Denominators MSC3_ 3.2.2 Differences Involving Like Denominators Page 11
Grade/ GRADE 4 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions (see 4.0). 1.6 Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or.50; 7/4 = 1 3/4 = 1.75). 1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line. 1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in "owing"). 2.0 Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals: V2-4, V2-5, V2-8 MSC3_3.1.3 Equivalent Fractions MSC4_1.1.1 Recognizing a Fraction V2-4, V2-8, V2-18 MSC3_4.1.1 Tenths, Hundredths, and Thousandths V2-4, V2-22 MSC3_ 3.1.1 Proper Fractions MSC3_ 3.1.3 Equivalent Fractions MSC3_4.1.1 Tenths, Hundredths, and Thousandths V2-31 MSC3_ 1.1.3 Negative Whole Numbers V2-23 MSC3_ 4.2.1 Adding Decimals MSC3_ 4.2.2 Subtracting Decimals MSC4_ 2.2.1 Using Place Value Grids MSC4_ 2.2.2 Regrouping with Whole Numbers MSC4_ 2.2.3 Regrouping to Hundredths MSC4_1.2.2 Expressing Fractions in Lowest Terms MSC4_2.1.1 Investigating Decimal Place Values MSC3_ 4.1.3 Ratios, Decimals, and Percents MSC3_ 2.1.1 Whole Number Sums MSC3_ 2.1.2 Differences Between Large Numbers Page 12
Grade/ GRADE 5 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers. 2.0 Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals: V2-18, V2-19 V2-20, V2-22, V2-31, V2-33, V2-35 MSC3_ 1.1.3 Negative Whole Numbers MSC3_ 3.1.1 Proper Fractions MSC3_ 3.1.2 Improper Fractions MSC3_ 4.1.1 Tenths, Hundredths, and Thousandths MSC3_ 4.1.2 Ordering and Rounding V2-11, V2-12, V2-13, V2-14, V2-15, V2-16, V2-24, V2-25, V2-26, V2-27, V2-28 MSC3_ 4.3.1 Multiplying Decimals MSC3_2.2.1 Integer Sums MSC3_3.3.1 Finding Products MSC3_3.3.2 Quotients and Remainders V2-23 Page 13
Grade/ Strand/ Language Primary Citations Supporting Citations 2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results. 2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems. V2-23,V2-24, V2-26, V2-27, V2-28, V2-37 MSC3_ 4.2.1 Adding Decimals MSC3_ 4.2.2 Subtracting Decimals MSC3_ 4.3.1 Multiplying Decimals MSC3_ 4.3.2 Dividing Decimals by Whole Numbers MSC3_2.2.1 Integer Sums MSC3_2.2.2 Differences Between Integers V2-14, V2-16, V2-17 MSC3_3.3.1 Finding Products MSC3_3.3.2 Quotients and Remainders MSC4_4.1.2 Adding with Absolute Value MSC4_4.1.3 Subtracting with Absolute Value MSC4_1.3.1 Finding Products of Fractions, Whole Numbers, and Mixed Numbers MSC4_1.3.2 Using the GCF in Finding Products MSC4_1.3.3 Representing Multiplication MSC4_1.4.1 Estimating Quotients of Fractions MSC4_1.4.2 Using Multiplicative Inverses Page 14
Grade/ GRADE 6 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line. 2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. V2-7, V2-9, V2-34, V2-36 MSC3_3.1.1 Proper Fractions MSC3_3.1.2 Improper Fractions MSC3_3.1.4 Ordering and Rounding Fractions MSC3_4.1.1 Tenths, Hundredths, and Thousandths MSC3_4.1.2 Ordering and Rounding V2-17 explain, e.g. p. 71, #11-15 MSC3_ 3.2.1 Sums Involving Like Denominators MSC3_ 3.2.2 Differences Involving Like Denominators MSC3_ 3.2.3 Working with Unlike Denominators MSC3_3.3.1 Finding Products MSC3_3.3.2 Quotients and Remainders MSC4_2.1.2 Rounding Decimals MSC4_ 1.4.3 Solving Missing Value Problems when Dividing Fractions MSC4_ 1.5.3 Solving Missing Value Problems when Adding Fractions MSC4_ 1.6.3 Solving Missing Value Problems when Subtracting Fractions Page 15
Grade/ Strand/ Language Primary Citations Supporting Citations 2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. GRADE 7 NUMBER SENSE 1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. V2-37, V2-38, V2-39, V2-40, V2-41 MSC4_ 4.1.1 Exploring the Number Line and Absolute Value MSC4_ 4.1.2 Adding with Absolute Value MSC4_ 4.1.3 Subtracting with Absolute Value MSC4_ 4.2.1 Finding Products of Signed Numbers MSC4_ 4.2.2 Representing the Multiplication of Signed Numbers MSC4_ 4.2.3 Finding Quotients using Reciprocals V2-42, V2-43 MSC3_ 3.2.3 Working with Unlike Denominators MSC3_ 3.3.1 Finding Products MSC3_ 3.3.2 Quotients and Remainders MSC3_ 4.3.1 Multiplying Decimals MSC3_ 4.3.2 Dividing Decimals by Whole Numbers MSC4_ 4.3.1 Simplifying Expressions MSC5_ 3.1.2 Investigating Squares and Square Roots Page 16
VOLUME III Ratio, Rates, and Percents Grade/ GRADE 3 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 2.7 Determine the unit cost when given the total cost and number of units. GRADE 3 ALGEBRA AND FUNCTIONS 1.4 Express simple unit conversions in symbolic form (e.g., inches = feet x 12). 2.1 Solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit). 2.2 Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s or by multiplying the number of horses by 4). GRADE 3 MEASUREMENT AND GEOMETRY 1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes). V3-4 V3-5, V3-6 MSC2_ 4.1.1 Number Patterns and Properties V3-4, V3-9 MSC2_ 2.2.3 Finding Products Less than 100 V3-2 MSC2_ 4.1.1 Number Patterns and Properties V3-5, V3-6 Page 17
Grade/ GRADE 5 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 1.2 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. GRADE 5 STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.3 Use fractions and percentages to compare data sets of different sizes. V3-11, V3-12, V3-13 MSC3_ 4.1.3 Ratios, Decimals, and Percents MSC4_ 3.1.1 Investigating the Meaning of Percent MSC4_ 3.2.1 Finding Percents of a Whole MSC4_ 3.2.2 Expressing Ratios as Percents V3-18 MSC3_ 4.1.3 Ratios, Decimals, and Percents MSC5_ 5.1.3 Interpreting Pie Charts Page 18
Grade/ GRADE 6 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b). 1.3 Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/ 21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. 1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips. V3-3 MSC5_ 4.1.1 Defining Ratio MSC5_ 4.1.2 Expressing Ratios as Equivalent Fractions and Decimals MSC5_ 4.1.3 Forming Ratios between Unlike Quantities V3-9, V3-10 MSC5_ 4.2.1 Defining a Proportion MSC5_ 4.2.2 Solving for a Variable in a Proportion MSC5_ 4.2.3 Applying the Means/ Extremes Property MSC5_ 4.4.1 Defining Similarity MSC5_ 4.4.2 Identifying Equivalent Ratios MSC5_ 4.4.3 Setting Up and Solving Proportions in Similar Polygons V3-13, V3-15, V3-16 MSC4_ 3.2.1 Finding Percents of a Whole MSC4_ 3.3.1 Calculating Percent Increases MSC4_ 3.3.2 Calculating Percent Decreases MSC4_ 3.3.3 Calculating Simple Interest MSC5_ 4.3.1 Exploring and Solving Direct Variation Problems Page 19
Grade/ GRADE 6 Strand/ Language Primary Citations Supporting Citations ALGEBRA AND FUNCTIONS 2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches). 2.2 Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity. 2.3 Solve problems involving rates, average speed, distance, and time. GRADE 6 STATISTICS, DATA ANALYSIS, AND PROBABILITY 3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1- P is the probability of an event not occurring. V3-7 MSC4_ 2.4.1 Dividing Decimals by Whole Numbers Workout 4 MSC4_ 2.4.3 Dividing by Powers of 10 Workout 3 V3-4 V3-4 V3-20 MSC3_ 6.1.2 Looking at Chance MSC5_ 6.1.1 Defining and Expressing Probability Page 20
Grade/ GRADE 7 Strand/ Language Primary Citations Supporting Citations NUMBER SENSE 1.6 Calculate the percentage of increases and decreases of a quantity. 1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest. GRADE 7 ALGEBRA AND FUNCTIONS 4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation. V3-14 MSC4_ 3.3.1 Calculating Percent Increases MSC4_ 3.3.2 Calculating Percent Decreases V3-15, V3-16, V3-17 MSC4_ 3.3.3 Calculating Simple Interest V3-4 MSC5_ 4.3.1 Exploring and Solving Direct Variation Problems Page 21
VOLUME IV The Core Processes of Mathematics Grade/ GRADE 2 Strand/ Language Primary Citations Supporting Citations ALGEBRA AND FUNCTIONS 1.1 Use the commutative and associative rules to simplify mental calculations and to check results. GRADE 3 ALGEBRA AND FUNCTIONS 1.0 Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships: 1.5 Recognize and use the commutative and associative properties of multiplication (e.g., if 5 x 7 = 35, then what is 7 x 5? and if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?). V4-3 MSC2_ 4.1.1 Number Patterns and Properties V4-5 MSC2_ 1.1.5 Comparing and Ordering MSC2_ 4.1.1 Number Patterns and Properties V4-3 MSC2_ 4.1.1 Number Patterns and Properties MSC3_ 2.3.1 Two-Digit Multipliers V4-1 MSC3_ 1.1.2 Ordering and Rounding Whole Numbers MSC3_ 1.1.3 Negative Whole Numbers MSC3_ 2.3.1 Two-Digit Multipliers Page 22
Grade/ GRADE 4 Strand/ Language Primary Citations Supporting Citations ALGEBRA AND FUNCTIONS 1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable). 2.1 Know and understand that equals added to equals are equal. 2.2 Know and understand that equals multiplied by equals are equal. GRADE 5 ALGEBRA AND FUNCTIONS 1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution. 1.3 Know and use the distributive property in equations and expressions with variables. V4-1, V4-8 MSC3_ 2.3.1 Two-Digit Multipliers MSC3_ 2.3.2 Introduction to Long Division MSC5_ 1.1.1 Introducing Variables MSC5_ 1.1.2 Identifying Components of Algebraic Expressions MSC5_ 1.1.3 Replacing Variables in a Formula V4-6 MSC5_ 1.3.3 Solving Simple Equations V4-7 MSC5_ 1.3.3 Solving Simple Equations V4-1, V4-2 MSC5_1.4.1 Writing Equations MSC5_1.4.2 Simplifying Both Sides of an Equation MSC5_1.4.3 Checking the Solution to an Equation V4-4, V4-5 MSC5_1.2.2 Combining Like Terms Page 23
Grade/ GRADE 6 Strand/ Language Primary Citations Supporting Citations ALGEBRA AND FUNCTIONS 1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables. GRADE 7 NUMBER SENSE 1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. V4-1, V4-2 MSC5_1.4.1 Writing Equations MSC5_1.4.2 Simplifying Both Sides of an Equation MSC5_1.4.3 Checking the Solution to an Equation V4-11 MSC3_ 4.1.1 Tenths, Hundredths, and Thousandths MSC3_ 4.1.3 Ratios, Decimals, and Percents MSC4_ 2.1.1 Investigating Decimal Place Values MSC4_ 3.1.1 Investigating the Meaning of Percent Page 24
Grade/ GRADE 7 Strand/ Language Primary Citations Supporting Citations ALGEBRA AND FUNCTIONS 1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A). 1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5) 2. 1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used. 4.0 Students solve simple linear equations and inequalities over the rational numbers: V4-2, V4-8 MSC5_1.4.1 Writing Equations V4-1 MSC5_1.2.2 Combining Like Terms V4-3, V4-4, V4-5 p. 21, #23, #26 MSC4_ 4.3.1 Simplifying Expressions MSC4_ 4.3.2 Introducing the Distributive Property MSC4_ 4.3.3 Using Grouping Symbols V4-6, V4-7, V4-9 MSC5_1.4.1 Writing Equations MSC5_1.4.2 Simplifying Both Sides of an Equation MSC5_1.4.3 Checking the Solution to an Equation MSC5_ 1.3.1 Using Variables to Express Relationships MSC5_ 1.2.2 Combining Like Terms Page 25
VOLUME V Functions and Equations Grade/ K Strand/ Language Primary Citations Supporting Citations ALGEBRA AND FUNCTIONS 1.1 Identify, sort, and classify objects by attribute and identify objects that do not belong to a particular group (e.g., all these balls are green, those are red). GRADE 1 STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.1 Sort objects and data by common attributes and describe the categories. 1.2 Represent and compare data (e.g., largest, smallest, most often, least often) by using pictures, bar graphs, tally charts, and picture graphs. 2.1 Describe, extend, and explain ways to get to a next element in simple repeating patterns (e.g., rhythmic, numeric, color, and shape). GRADE 2 STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.1 Record numerical data in systematic ways, keeping track of what has been counted. 1.2 Represent the same data set in more than one way (e.g., bar graphs and charts with tallies). 2.1 Recognize, describe, and extend patterns and determine a next term in lisnear patterns (e.g., 4, 8, 12...; the number of ears on one horse, two horses, three horses, four horses). V5-1 V5-1 V5-4 V5-9 V5-2 V5-3 V5-9 MSC2_ 4.1.1 Number Patterns and Properties Page 26
Grade/ GRADE 3 Strand/ Language Primary Citations Supporting Citations ALGEBRA AND FUNCTIONS 2.1 Solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit). 2.2 Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s or by multiplying the number of horses by 4). GRADE 3 STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.3 Summarize and display the results of probability experiments in a clear and organized way (e.g., use a bar graph or a line plot). V5-11, V5-14 MSC2_ 2.2.3 Finding Products Less than 100 V5-10 MSC2_ 4.1.1 Number Patterns and Properties V5-5 MSC3_ 6.1.2 Looking at Chance V5-21, e.g. Practice, p. 88 #1, #2 Page 27
Grade/ GRADE 4 Strand/ Language Primary Citations Supporting Citations ALGEBRA AND FUNCTIONS 1.5 Understand that an equation such as y = 3 x + 5 is a prescription for determining a second number when a first number is given. GRADE 4 MEASUREMENT AND GEOMETRY 2.0 Students use two-dimensional coordinate grids to represent points and graph lines and simple figures: V5-17 V5-15, V5-16, V5-17 2.1 Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3x and connect them by using a straight line). MSC3_ 5.2.1 The Coordinate Plane V5-17, V5-19 Page 28
Grade/ GRADE 5 Strand/ Language Primary Citations Supporting Citations ALGEBRA AND FUNCTIONS 1.5 Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid. GRADE 5 STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.4 Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph. 1.5 Know how to write ordered pairs correctly; for example, ( x, y ). GRADE 6 NUMBER SENSE 1.3 Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/ 21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. V5-21 V5-15, V5-21 MSC5_ 5.1.1 Exploring Line Graphs V5-14 MSC3_ 5.2.1 The Coordinate Plane V5-11, V5-12, V5-13 MSC5_ 4.2.1 Defining a Proportion MSC5_ 4.2.2 Solving for a Variable in a Proportion MSC5_ 4.2.3 Applying the Means/ Extremes Property MSC5_ 4.4.1 Defining Similarity MSC5_ 4.4.2 Identifying Equivalent Ratios MSC5_ 4.4.3 Setting Up and Solving Proportions in Similar Polygons MSC3_ 6.1.1 Displaying and Analyzing Data MSC5_ 4.3.1 Exploring and Solving Direct Variation Problems Page 29
Grade/ GRADE 6 Strand/ Language Primary Citations Supporting Citations ALGEBRA AND FUNCTIONS 2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches). GRADE 7 ALGEBRA AND FUNCTIONS 3.0 Students graph and interpret linear and some nonlinear functions: 3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. 3.3 Graph linear functions, noting that the vertical change (change in y- value) per unit of horizontal change (change in x- value) is always the same and know that the ratio ("rise over run") is called the slope of a graph. 3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities. V5-6, V5-7, V5-8 V5-20, V5-22 V5-22 V5-18 V5-20 V5-19 Page 30
VOLUME VI Measurement Grade/ GRADE 2 Strand/ Language Primary Citations Supporting Citations MEASUREMENT AND GEOMETRY 1.3 Measure the length of an object to the nearest inch and/or centimeter. GRADE 3 ALGEBRA AND FUNCTIONS 1.4 Express simple unit conversions in symbolic form (e.g., inches = feet x 12). V6-1 V6-26 V6-27 GRADE 3 MEASUREMENT AND GEOMETRY 1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them. 1.3 Find the perimeter of a polygon with integer sides. 1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes). MSC2_ 4.1.1 Number Patterns and Properties V6-10 V6-11 MSC2_3.1.1 Area MSC2_3.1.2 Volume V6-2 MSC3_5.1.2 Rectangles and Squares V6-26 V6-27 MSC3_5.1.3 Triangles Page 31
Grade/ GRADE 4 Strand/ Language Primary Citations Supporting Citations MEASUREMENT AND GEOMETRY 1.1 Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm 2 ), square meter (m 2 ), square kilometer (km 2 ), square inch (in 2 ), square yard (yd 2 ), or square mile (mi 2 ). 2.2 Understand that the length of a horizontal line segment equals the difference of the x- coordinates. 2.3 Understand that the length of a vertical line segment equals the difference of the y- coordinates. GRADE 5 MEASUREMENT AND GEOMETRY 1.1 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). 1.2 Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area for these objects. 1.3 Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic centimeter [cm 3 ], cubic meter [m 3 ], cubic inch [in 3 ], cubic yard [yd 3 ]) to compute the volume of rectangular solids. V6-3 MSC3_5.1.2 Rectangles and Squares V6-1, V6-2 MSC3_ 5.2.1 The Coordinate Plane V6-1, V6-2 MSC3_ 5.2.1 The Coordinate Plane V6-4, V6-5 MSC3_ 5.1.4 Parallelograms and Trapezoids MSC5_ 2.2.2 Exploring the Area of a Triangle V6-9 V6-11 MSC5_ 2.3.1 Calculating the Volume of a Right Triangular Prism MSC4_ 2.3.3 Finding the Volume of a Prism Page 32
Grade/ Strand/ Language Primary Citations Supporting Citations 2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software). 2.2 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. GRADE 6 ALGEBRA AND FUNCTIONS 2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches). GRADE 6 MEASUREMENT AND GEOMETRY 1.2 Know common estimates of p (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements. 1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base x height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid. V6-3, V6-14, V6-15, V6-17, V6-23, MSC3_ 5.1.1 Lines, Angles, and Circles MSC3_ 5.1.2 Rectangles and Squares MSC5_ 2.1.1 Naming and Measuring Angles V6-19 MSC3_ 5.1.3 Triangles MSC5_ 2.2.3 Classifying Triangles by Angles V6-28 V6-7, V6-8 MSC5_2.3.3 Calculating the Volume and Surface Area of a Right Cylinder V6-12, V6-13 MSC5_ 2.3.1 Calculating the Volume of a Right Triangular Prism MSC5_ 2.3.3 Calculating the Volume and Surface Area of a Right Cylinder Page 33
Grade/ Strand/ Language Primary Citations Supporting Citations 2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. GRADE 7 MEASUREMENT AND GEOMETRY 1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). 1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer. 3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement. 3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures. V6-16, V6-19 MSC5_ 2.1.2 Defining Complement-ary and Supplementary Angles MSC5_ 2.2.3 Classifying Triangles by Angles V6-28 V6-31, p. 121 V6-33 V6-21, V6-22 MSC5_ 3.1.1 Exploring the Pythagorean Theorem MSC5_ 3.1.2 Investigating Squares and Square Roots MSC5_ 3.1.3 Defining Irrational Numbers V6-7, V6-24 MSC5_ 4.4.3 Setting Up and Solving Proportions in Similar Polygons Page 34
PART B: STANDARDS MAPS for a Mathematics Intervention Programs All standards in the Mathematical Reasoning (MR) strand only. Part B includes all of the MR standards for grades K-7. The MR standards must be systematically embedded in the teaching of the subset of standards from the content strands in Part A (NS, AF, MG, and/or SDAP). Citations for the MR standards must reference the standards from the content strands in Part A (NS, AF, MG, and/or SDAP) and the program Volume(s) (I-VI) where the MR standards are addressed. Kindergarten (Volume V) Citations to reference all Volumes listed for the grade level MATHEMATICAL REASONING 1.0 Students make decisions about how to set up a problem: 1.1 Determine the approach, materials, and strategies to be used. 1.2 Use tools and strategies, such as manipulatives or sketches, to model problems. 2.0 Students solve problems in reasonable ways and justify their reasoning: 2.1 Explain the reasoning used with concrete objects and/or pictorial representations. 2.2 Make precise calculations and check the validity of the results in the context of the problem. (V5 Gr. K, AF 1.1) V5-1, p.5, #9 (V5 Gr. K, AF 1.1) V5-1, pp. 2, 3 Example 1, Try This, #1; p. 4, Practice, #1-3 (V5 Gr. 1, SDAP 2.1) V5-9, pp. 40, 41, #1, #3, #4, #14 (V5 Gr. 1, SDAP 2.1) V5-9, p. 41, #11,12,13 (V5 Gr. 1, SDAP 2.1) V5-9, p. 38, Try This, #1,2; p. 41, Did You Get It?, #14 (V5 Gr. 1, SDAP 2.1) V5-9, p. 39, Try This, #5 Page 35
Grade 1 (Volumes I and V) Citations to reference all Volumes listed for the grade level MATHEMATICAL REASONING 1.0 Students make decisions about how to set up a problem: (V1 Gr. 1, NS 1.1) V1-3, Did You Get It? p. 11, #15 (V1 Gr. 1, NS 2.5) V1-7, p.27, Make It a Game!; Practice #1, 2 (V1, NS 1.3) V1-8, p. 28, #1, #2; p. 29, # 3, 4, 5 1.1 Determine the approach, materials, and strategies to be used. (VI, Gr. 1, NS 1.1, 1.4) MSC2_ 1.1.1 Counting by Grouping (VI, Gr. 1, NS 1.1) MSC2_ 1.1.2 Place Values: Tens and Ones (V1, Gr.1, NS 1.3) V1-8, p. 29, Try This #5; p. 31 #7, 8 and Did You Get It?, #10, 11 (V1, NS 1.3) V1-8, p. 29, #5; p. 31, #7, 8, 11 Page 36
1.2 Use tools, such as manipulatives or sketches, to model problems. (V1, Gr. 1, NS 2.1) p. 35, # 15 (V1, Gr.1, NS 1.1) V1-3, pp. 8, 9, 10 (V1, Gr. 1, NS 2.5) V1-14, p. 55, #12 (V5, Gr. 1, SDAP 1.2) V 5-4, p. 17, Did You Get It, #11 2.0 Students solve problems and justify their reasoning: (V I, Gr. 1, NS 1.1, 1.4) MSC2_ 1.1.1 Counting by Grouping (V I, Gr. 1, NS 1.1) MSC2_ 1.1.2 Place Values: Tens and Ones (V 1 Gr. 1, NS 1.1) V1-3, p.11, #10, 11, 12, 14 (V 1 Gr. 1, NS 2.6) V1-17, p. 67, #13 (V I, Gr. 1, NS 2.5, 2.6) MSC2_ 2.1.1 Sums Less than 100 (V I, Gr. 1, NS 2.5, 2.6) MSC2_ 2.1.3 Differences within 100 Page 37
2.1 Defend the reasoning used and justify the procedures selected. (V1, Gr.1, NS 2.1) V-1-9, p. 35 Did You Get It?, #18 (V5, Gr. 1, SDAP 2.1) V 5-9, p.41, Did You Get It?, #15 2.2 Make precise calculations and check the validity of the results in the context of the problem. 3.0 Students note connections between one problem and another. (V I, Gr. 1, NS 2.5, 2.6) MSC2_ 2.1.1 Sums Less than 100 (V I, Gr. 1, NS 2.5, 2.6) MSC2_ 2.1.3 Differences within 100 (V1, Gr.1, NS 2.6) V1-17, p. 67, # 7, 8 and #13 (V I, Gr. 1, NS 2.5, 2.6) MSC2_ 2.1.1 Sums Less than 100 (V I, Gr. 1, NS 2.5, 2.6) MSC2_ 2.1.3 Differences within 100 (V1, Gr.1, NS1.1, 1.4) V1-2, p. 7, # 21 (V1, Gr. 1, NS 2.5) V1-14, p. 53, Example 3; p. 55, #12 Page 38
Grade 2 (Volumes I, II, IV, V, and VI) Citations to reference all Volumes listed for the grade level MATHEMATICAL REASONING 1.0 Students make decisions about how to set up a problem: (V4 Gr. 2 AF 1.1) V4-3, Did You Get It? p. 13, #23 (V2, Gr. 2, NS 4.0, 4.1) V2-4, p. 19, #28-30 (V IV, Gr. 2, AF 1.1, V V, Gr.2, SDAP 2.1) MSC2_4.1.1 Number Patterns and Properties (V I, Gr. 2, NS 2.2) MSC2_ 2.1.2 Estimating and Finding Sums Less than 1,000 1.1 Determine the approach, materials, and strategies to be used. (V I, Gr. 2, NS 3.1) MSC2_2.2.1 Repeated Addition and Arrays (V2, Gr. 2 NS 4.1) V2-7, p. 31, #28, #30 (V IV, Gr. 2, AF 1.1, V V, Gr.2, SDAP 2.1) MSC2_4.1.1 Number Patterns and Properties Page 39
1.2 Use tools, such as manipulatives or sketches, to model problems. (V1, Gr. 2, NS 1.2) V1-1, p. 2 (V2, Gr.2, NS 4.1) V2-7, p. 31, Did You Get It? #32. (V4, Gr. 2, NS 2.2) V1-11, Did You Get It? p. 43, # 21 (V5, Gr.2, SDAP 1.2) V5-3, p. 10, Try This, #1 and page 12, Practice, #1-5 (V I, Gr. 2, NS 2.2) MSC2_ 2.1.2 Estimating and Finding Sums Less than 1,000 2.0 Students solve problems and justify their reasoning: (V I, Gr. 2, NS 3.1) MSC2_2.2.1 Repeated Addition and Arrays (V II, Gr. 2, NS 4.0, 4.1, 4.3) MSC2_2.3.3 Fractional Parts (V1, Gr. 2, NS 1.3) V1-5, p. 19, Did You Get It? #31 and #32 (V2, Gr. 2, NS 4.1) V2 Mixed Practice p. 41, #40, #41 (V2, Gr. 2, NS 4.0) V2-18, p. 77, #37, # 40 (V I, Gr. 2, NS 2.2) MSC2_ 2.1.2 Estimating and Finding Sums Less than 1,000 (V I, Gr. 2, NS 2.2) MSC2_2.1.4 Estimating and Finding Differences within 1,000 Page 40
2.1 Defend the reasoning used and justify the procedures selected. (V1, Gr. 2, NS 2.2) V1-11, pg. 43, Did you Get It?, #20 and V1-16, p. 63, #13. (V 4, Gr. 2, AF 1.2) V4-3, Did You Get It? p. 13, # 24 2.2 Make precise calculations and check the validity of the results in the context of the problem. (V I, Gr. 2, NS 2.2) MSC2_ 2.1.2 Estimating and Finding Sums Less than 1,000 (V I, Gr. 2, NS 2.2) MSC2_2.1.4 Estimating and Finding Differences within 1,000 (V1, Gr. 2, NS 1.1) Mixed Review, p. 25, #34 (V1, Gr.2, NS 3.1) V1-22, p. 87 #32 (V6, Gr.2 NS 1.3) V6-1, p. 5, #9, #13 3.0 Students note connections between one problem and another. (V I, Gr. 2, NS 1.3) MSC2_1.2.2 Comparing and Ordering (V I, Gr. 2, NS 2.2) MSC2_2.1.4 Estimating and Finding Differences within 1,000 (V1, Gr.2, NS 2.3) V1-19, p. 75, #19 (V4, Gr.2, AF 1.1) V4-3, p. 12, Practice, #5, 9, 16, 17 Page 41
Grade 3 (Volumes I, II, III, IV, V, and VI) Citations to reference all Volumes listed for the grade level MATHEMATICAL REASONING 1.0 Students make decisions about how to approach problems: Numerous, e.g. (V1, Gr. 3, NS 2.1) V1-13, p. 51, #19-22) (V2 Gr. 3 NS 3.1) V2-5, p. 23, #17-19 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.2 Estimating and Finding Sums Less than 1,000 Page 42
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. Numerous, e.g. Relationships: (V6, Gr.3, AF 1.4) V6-26, p. 104, #1-18 Relevant info: (V2, Gr. 3, NS 3.1) V 2, Mixed Practice, p. 73, #22 Sequencing (V1, Gr. 3, NS 2.4) V1-24, p. 95, #15 (V2, Gr. 3, NS 3.1) V 2, Mixed Practice, p. 73, #39, 40 Patterns: (V3, Gr.3, AF 2.2) V3-2 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.2 Estimating and Finding Sums Less than 1,000 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.5 Estimating and Finding Differences within 9,999 Page 43
1.2 Determine when and how to break a problem into simpler parts. Numerous, e.g. (V1, Gr. 3, NS 2.1) V1-18, pgs. 68, 69 (V1, Gr. 3, NS 2.4) V1-24, p. 95, #15 (V1, Gr. 3, NS 2.4) V2, Mixed Practice, p. 137, # 55, 56 2.0 Students use strategies, skills, and concepts in finding solutions: (V I, Gr. 3, NS 2.4, V III, Gr. 3 AF 2.1, V V, Gr. 3 AF 2.1) MSC2_ 2.2.3 Finding Products Less than 100 Numerous, e.g. (V2, Gr. 3, NS 3.2) V-2-12, p. 51, #21-25 (V4, Gr.3, AF 1.5) V4-3, p. 10 Example 1, and p. 13, # 21, 24 (V I, Gr. 3, NS 1.3, 1.5) MSC2_ 1.2.1 Place Values: Thousands, Hundreds, Tens, and Ones (V I, Gr. 3, NS 2.1) MSC2_ 2.1.2 Estimating and Finding Sums Less than 1,000 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.4 Estimating and Finding Differences within 1,000 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.5 Estimating and Finding Differences within 9,999 (V I, Gr. 3, NS 2.4, V III, Gr. 3 AF 2.1, V V, Gr. 3 AF 2.1) MSC2_ 2.2.3 Finding Products Less than 100 Page 44
2.1 Use estimation to verify the reasonableness of calculated results. (V1, Gr. 3, NS 2.4) V1-24, p. 92-93, p. 94 # 1-10, p. 95 #11, 12 (V6, Gr. 3, MG 1.3) V6-2, p. 30, #3 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.5 Estimating and Finding Differences within 9,999 2.2 Apply strategies and results from simpler problems to more complex problems. (V I, Gr. 3, NS 2.1) MSC2_ 2.1.2 Estimating and Finding Sums Less than 1,000 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.4 Estimating and Finding Differences within 1,000 (V1 Gr. 3, NS 2.2) V1-23, p. 91, #24 (V1, Gr.3, NS 2.6) V1-31, Did You Get It?, p. 123, #26 (V6, Gr. 3, MG 1.3) V6-2, p9, #10 (V I, Gr. 3, NS 2.4, V III, Gr. 3 AF 2.1, V V, Gr. 3 AF 2.1) MSC2_ 2.2.3 Finding Products Less than 100 Page 45
2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. (V1 Gr. 3, NS 2.4) V1-24, Did You Get It? p. 95, #16 (V1, Gr.3, NS 2.6) V1-31, Did You Get It? p. 123, #27 (V2 Gr. 3 NS 3.1) V2-5, p. 23, #21; Activity 2-10, p. 42, p. 43 (V5, Gr. 3, SDAP 1.2 and 1.3) V5-5, p. 21, #6, #7, #10 (V I, Gr. 3, NS 1.3, 1.5) MSC2_ 1.2.1 Place Values: Thousands, Hundreds, Tens, and Ones (V I, Gr. 3, NS 2.4, V III, Gr. 3 AF 2.1, V V, Gr. 3 AF 2.1) MSC2_ 2.2.3 Finding Products Less than 100 (V II, Gr. 3, NS 3.1) MSC2_ 2.3.3 Fractional Parts Page 46
2.4 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. (V4, Gr. 3, AF 1.5) V4-3, p. 12 #2, #8, #15, #18, p. 13 #21, #24 (V5, Gr. 3, SDAP 1.2 and 1.3) V5, Mixed Practice, p. 23, # 15 2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. 2.6 Make precise calculations and check the validity of the results from the context of the problem. (V IV, Gr. 3, AF 1.0) MSC2_1.2.2 Comparing and Ordering (V I, Gr. 3, NS 2.1) MSC2_ 2.1.4 Estimating and Finding Differences within 1,000 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.5 Estimating and Finding Differences within 9,999 (V VI, Gr. 3, MG 1.2) MSC2_3.1.1 Area (V6, Gr. 3, AF 1.4 and MG 1.4) V6-27, p. 106, 107, 108 #5-16, p. 109 #22 (V1, Gr. 3, NS 1.3) V 1-4, Mixed Practice p. 25, #35 (V1, Gr. 3, NS 2.4) V1-24, Did You Get It? p. 95, #17 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.2 Estimating and Finding Sums Less than 1,000 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.4 Estimating and Finding Differences within 1,000 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.5 Estimating and Finding Differences within 9,999 (V VI, Gr. 3, MG 1.2) MSC2_3.1.1 Area Page 47
3.0 Students move beyond a particular problem by generalizing to other situations: (V1, Gr. 3, NS 2.1) V1-12, Did You Get It? p. 47, #21 (V1, Gr. 3, NS 2.1) V 1-13, Did You Get It? p. 51, #21, #22 (V1, Gr. 3, NS 2.1) V1-18, Did You Get It? p. 71, #16 (V6, Gr. 3, MG 1.3) V6-2, p. 9, #11 3.1 Evaluate the reasonableness of the solution in the context of the original situation. (V I, Gr. 3, NS 2.1) MSC2_ 2.1.5 Estimating and Finding Differences within 9,999 (V2, Gr.3, NS 3.1) V2-11, Did You Get It? p. 47, #35 (V3, Gr.3, AF2.1), V3-8, p. 35, #16, #19 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.2 Estimating and Finding Sums Less than 1,000 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.4 Estimating and Finding Differences within 1,000 (V I, Gr. 3, NS 2.1) MSC2_ 2.1.5 Estimating and Finding Differences within 9,999 Page 48
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems. (V2, Gr.3, NS 3.1) V2-11, Did You Get It? p. 47, #32-34 (V5, Gr. 3, AF 1.4 and MG 1.4) V 5-6, p. 27, #19-21 and V-7, p. 31, #17-19. 3.3 Develop generalizations of the results obtained and apply them in other circumstances. (V I, Gr. 3, NS 2.1) MSC2_ 2.1.5 Estimating and Finding Differences within 9,999 (V4, Gr.3 AF 1.5) V4-3, Did You Get It? p. 13, #23 and 24 (V5, Gr. 3 AF 2.2) V 5-10, p. 45, #7-11 and #13 (V I, Gr. 3, NS 2.4, V III, Gr. 3 AF 2.1, V V, Gr. 3 AF 2.1) MSC2_ 2.2.3 Finding Products Less than 100 Page 49
Grade 4 (Volumes I, II, IV, V, and VI) Citations to reference all Volumes listed for the grade level MATHEMATICAL REASONING 1.0 Students make decisions about how to approach problems: (V1, Gr. 4, NS 3.1) V1-13, Did You Get It? p. 51, #21 and #22 (V1, Gr.4, NS 4.1) V1-23, p. 91, Did You Get It? #31 (V2, Gr.4, NS 1.5 and 1.7) V2-4, p. 19, #28-30 (V2, Gr.4, NS 1.5) p. 23, #17-19 (V I, Gr. 4, NS 3.1) MSC3_ 2.1.1 Whole Number Sums (V I, Gr. 4, NS 3.2, V IV, Gr. 4, AF 1.1) MSC3_ 2.3.2 Introduction to Long Division Page 50
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. Relationships (V1, Gr. 4, NS 4.1) V1-23, p. 91, #29-30 (V1, Gr.4, NS 3.2) V1-29, p. 115, Did You Get It? #22 Irrelevant info (V1, Gr.4, NS 3.1) V1, Mixed Practice, p. 81, #45 (V2, Gr.4, NS 2.0) V2, Mixed Practice, #37 Sequencing (V2, Gr.4 NS 1.8) V2-31, p.131. #17-20 Patterns (V1, Gr. 4, NS 3.1) V1-25, p. 98, #4-15 (V I, Gr. 4, NS 1.1) MSC3_ 1.1.1 Whole Numbers to One Million (V I, Gr. 4, NS 3.1) MSC3_ 2.1.1 Whole Number Sums (V I, Gr. 4 NS 3.1) MSC3_ 2.1.2 Differences Between Large Numbers (V I, Gr. 4, NS 3.2, V IV, Gr. 4, AF 1.1) MSC3_ 2.3.2 Introduction to Long Division (V I, Gr. 4 NS 1.6, V II, Gr. 4 NS 1.6, 1.7) MSC3_ 4.1.1 Tenths, Hundredths, and Thousandths Page 51
1.2 Determine when and how to break a problem into simpler parts. 2.0 Students use strategies, skills, and concepts in finding solutions: (V1, Gr.4, NS 1.2) V1-29, p. 115, #18, 19 (V1, Gr.4, NS 3.2) V 1, Mixed Practice, p. 137 #55-57 (V I, Gr. 4, NS 3.1) MSC3_ 2.1.1 Whole Number Sums (V I, Gr. 4, NS 3.2, V IV, Gr. 4, AF 1.1) MSC3_ 2.3.2 Introduction to Long Division (V2, Gr.4 NS 1.8) V2-31, p. 131, Did You Get It? #23 (V5, Gr.4, MG 2.1)V5-17, p. 73, # 10-12 (V6, Gr.4, MG 1.1) V6-3, p. 12, #1-13 (V I, Gr. 4 NS 1.1, 1.2, 1.3, V IV, Gr. 4 AF 1.0) MSC3_ 1.1.2 Ordering and Rounding Whole Numbers (V II, Gr. 4 NS 2.0) MSC3_ 4.2.1 Adding Decimals (V II, Gr. 4 NS 1.7) MSC3_ 4.1.3 Ratios, Decimals, and Percents Page 52
2.1 Use estimation to verify the reasonableness of calculated results. (V1, Gr.4, NS 3.2) V1-26, p. 100, Example 1; p. 101, Example 2; p. 102, #13-14; p.103 Did You Get It? #21 (V1, Gr.4, NS 3.2) V1-27, p. 107, #21, 22 (V2, Gr.4 NS 2.0,2.1) V2-29 2.2 Apply strategies and results from simpler problems to more complex problems. (V I, Gr. 4, NS 3.1) MSC3_ 2.1.1 Whole Number Sums (V II, Gr. 4 NS 2.0) MSC3_ 4.2.1 Adding Decimals (V II, Gr. 4 NS 2.0) MSC3_ 4.2.2 Subtracting Decimals (V1, Gr.4, NS 3.2) V1-26, p.103 Did You Get It? #23; V1-27, p. 107 #23 (V2, Gr.4 NS 2.0) V2, Mixed Review, p. 149, #26 (V6, Gr.4, MG 2.2) V6-1, p. 26-17, #5-6 (V I, Gr. 4, NS 1.1) MSC3_ 1.1.1 Whole Numbers to One Million (V I, Gr. 4 NS 1.1, 1.2, 1.3, V IV, Gr. 4 AF 1.0) MSC3_ 1.1.2 Ordering and Rounding Whole Numbers (V I, Gr. 4, NS 3.1) MSC3_ 2.1.1 Whole Number Sums (V I, Gr. 4 NS 3.1) MSC3_ 2.1.2 Differences Between Large Numbers Page 53
2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. (V1, Gr.4, NS 1.3) V1-6, p. 21 Example 2 (V1, Gr.4, NS 3.2) V1-29, p. 115, Did You Get It? #21 (V2, Gr.4, NS 1.5 and 1.7) V2-4, p. 18, #16-27 (V V, Gr. 4 MG 2.0) MSC3_5.2.1 The Coordinate Plane (V4, Gr.4, NS 1.1) V4-1, p. 5, Did You Get It? #24, #25 (V I, Gr. 4 NS 1.6, V II, Gr. 4 NS 1.6, 1.7) MSC3_ 4.1.1 Tenths, Hundredths, and Thousandths (V I, Gr. 4 NS 1.2) MSC3_ 4.1.2 Ordering and Rounding 2.4 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. (V II, Gr. 4 NS 1.7) MSC3_ 4.1.3 Ratios, Decimals, and Percents (V2, Gr.4, NS 1.6) V2-8, p. 35, #26-28 (V5, Gr.4, MG 2.0, 2.1) V5-15, p. 67, #20-23 (V VI, Gr. 4 MG 1.1) MSC3_ 5.1.2 Rectangles and Squares Page 54
2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. (V1, Gr. 4, NS 1.3) V1-5, p. 23, #26-29, #31 (V1, Gr.4, NS 3.2) V1-26, p. 100, Example 1 (V1, Gr.4, NS 3.2) V1, Mixed Practice, p. 137, #55-57 (V2, Gr.4, NS 2.3) V2-19, p. 81, #27-29 2.6 Make precise calculations and check the validity of the results from the context of the problem. (V6, Gr.4, MG 2.2) V6-1, p. 5, #9, #13 (V1, Gr. 4, NS 3.1) V1-20, p. 79, Did You Get It? #20 (V2, Gr.4, NS 2.1) V2-29, p. 121, #24-26 (V I, Gr. 4, NS 3.1) MSC3_ 2.1.1 Whole Number Sums (V I, Gr. 4 NS 3.1) MSC3_ 2.1.2 Differences Between Large Numbers Page 55