The student will be able to... The teacher will... SKILLS/CONCEPTS K
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1 MATHEMATCS Subject Area: Component V: MATHEMATCS WHOLE NUMBER SENSE ndiana Academic Standard 1: Number Sense and Computation Understanding the number system is the basis of mathematics. Students develop and extend their understanding of the place value system to count, read, and write whole numbers, fractions, and decimals. Through the years students will broaden their understanding of numbers through the concepts of percentages, ratios, rational and irrational numbers, scientific notation, and square roots. GOALS: The student will be able to... A. Sort/Classify physical objects B. Order physical objects according to specific attributes C. Compare sets to determine if they are/are not equivalent D. Count objects in a collection and write the corresponding number (one-to-onecorrespondence) E. Determine numbers which come before/after a given number F. dentify patterns in whole number counting G. Compare numbers identifying numbers greater/less LEGEND: = the grade at which the skill is introduced Grey-shaded area= grades at which the skill is to be developed and expanded. State standards are assessed annually, beginning the year after introduction. The student will be able to... The teacher will... SKLLS/CONCEPTS K A. Sort and Classify A1 Count, recognize, represent, name, and order a number of objects (up to 20). (K.1.6) A2 Match the ordinary numbers, (first, second, third, etc.) with an ordered set of up to 100 items. (2.1.3) A3 Convert between numbers in words and numbers in figures, for numbers up to millions and decimals to thousandths. A4 Understand and apply the basic concept of negative numbers (e.g., on a number line, in counting, in temperature, in owing ). A5 Use models to represent ratios. Diocese of Lafayette-in-ndiana Core Curriculum Guide August,
2 MATHEMATCS SKLLS/CONCEPTS K B Order Physical Objects B1 Compare/Order physical objects according to size. (K.3.1) B2 Know that larger numbers describe sets with more objects in them than sets described by smaller numbers. C Compare Sets C1 Compare sets of up to 20 objects, and identify whether one set is equal to, more than, less than another. (K.1.2) C2 Use correctly the words one/many, none/some/all, more/less, and most/least. (K.1.3) C3 Record and organize information using objects and pictures. (K.1.4, K.1.6) C4 Compare whole numbers up to 100 and arrange them in numerical order. (2.1.1) C5 Compare whole numbers up to 1000 and arrange them in numerical order. C6 Rename and rewrite whole numbers as fractions. D One on One Correspondence D1 Match sets of objects one-to-one. (K.1.1) D2 Count, read, and write whole numbers up to 100. (1.1.1, 4.1.1) D3 Match the number names first, second, third, etc. with an ordered set of up to 10 items. (1.1.3) D4 Count, read, write, compare, and plot on a number line whole numbers up to at least 10,000. (2.1.1, 3.1.1, 4.1.1) D5 Plot and label whole numbers on a number line up to 100. Estimate positions on the number line. (4.1.1) D6 Count, read, write, compare, and plot whole numbers using words, models, number lines and expanded form up to at least 1,000,000. (4.1.1) E Before and After Numbers 14 Diocese of Lafayette-in-ndiana Core Curriculum Guide August, 2009
3 MATHEMATCS SKLLS/CONCEPTS K E1 Order a set of numbers (0-99) from smallest to largest. (1.1.2) E2 Find the number that is one more or less than any whole number up to 20. (K.1.2) E3 Name the number that is one more or less than any number up to 100. (1.1.2) E4 Compare whole numbers up to 10 and arrange them in numerical order. (1.1.2) E5 dentify numbers up to 100 in various combinations of tens and ones. (1.1.4) E6 nterpret the absolute value of a number as the distance from zero on a number line, and find the absolute value of real numbers. (6.1.2) F dentify Patterns F1 Create and extend number patterns using addition. (1.2.1) F2 Count and identify by ones, twos, fives, and tens up to (2.1.2) F32 Count and identify by ones, twos, fives, and tens up to 100. F4 dentify even and odd numbers up to 100. (2.1.5) G dentifying Numbers Greater/Less G1 Compare any two 2-digit numbers to determine which is less or greater. G2 Order and compare whole numbers using symbols for less than (<), equal to (=), and greater than (>). (4.1.2) G3 Arrange in numerical order and compare whole numbers or decimals to two places by using the symbols for less than (<), equal to (=), and greater than (>). Diocese of Lafayette-in-ndiana Core Curriculum Guide August,
4 MATHEMATCS Subject Area: Component V: MATHEMATCS PLACE VALUE 16 Diocese of Lafayette-in-ndiana Core Curriculum Guide August, 2009
5 MATHEMATCS ndiana Academic Standard 1: Number Sense and Computation Understanding the number system is the basis of mathematics. Students develop and extend their understanding of the place value system to count, read, and write whole numbers, fractions, and decimals. Through the years students will broaden their understanding of numbers through the concepts of percentages, ratios, rational and irrational numbers, scientific notation, and square roots. GOALS: The student will be able to... A. Use place value models to represent numbers up to a hundred thousand B. Use a ten as a unit or as a collection of ten objects C. Use a hundred as a unit, as a collection of ten tens, or as a collection of a hundred ones, or as a combination of tens and ones D. Use a thousand as a unit, as a collection of ten hundreds, or one hundred tens or a thousand ones, or as a combination of hundreds, tens and ones E. Write numbers up to a hundred thousand using numerals F. Round numbers to the nearest ten, hundred, or thousand, orally and in writing G. Demonstrate number sense H. Read/Write whole numbers, decimals and fractions. Tell the value of a digit in a number by the place it holds J. Write whole numbers/decimals/fractions in expanded form and in scientific notation LEGEND: = the grade at which the skill is introduced Grey-shaded area= grades at which the skill is to be developed and expanded. State standards are assessed annually, beginning the year after introduction. The student will be able to... The teacher will... SKLLS/CONCEPTS K A Use Place Value Models A1 Put objects into groups of tens and ones. A2 Read and write whole numbers up to 1,000. (2.1.1) A3 dentify and write whole numbers up to 1,000,000 given a place-value model. B Use Ten as a Unit B1 dentify the number of tens and ones in numbers less than 100. (1.1.4) Diocese of Lafayette-in-ndiana Core Curriculum Guide August,
6 MATHEMATCS SKLLS/CONCEPTS K B2 dentify the pattern of numbers in each group of ten, from tens through nineties. B3 Name the number that is ten more or less than any number 10 through 90. (1.1.2) C Use a Hundred as a Unit C1 dentify the number one hundred in various formats. C2 dentify/write a 3-digit number given a place value model or number of hundreds, tens, and ones. D Use a Thousand as a Unit D1 dentify and write in expanded form the numbers up to one thousand. (2.1.4) D2 dentify/write a 4-digit number, given a place value model or the number of thousands, hundreds, tens, and ones. (2.1.4) D3 dentify the nearest thousand, hundred, or ten given a 4-digit number. D4 Name the value for numbers in the thousand place. D5 dentify numbers up to 1000 in various combinations. E Write Numbers up to a Hundred Thousand E1 Read/Write any numeral less than one million. F Round Numbers Orally and in Writing F1 Round any given whole number to any specified place value. F2 Round numbers less than 1,000 to the nearest hundred. F3 Round any given whole number to the nearest ten, hundred, or thousand. F4 Round two-place decimals to tenths or to the nearest whole number. G Demonstrate Number Sense G1 dentify the numeral from millions to thousandths, and thousandths to millions 18 Diocese of Lafayette-in-ndiana Core Curriculum Guide August, 2009
7 MATHEMATCS SKLLS/CONCEPTS K given a word name for a numeral. H Read and Write Whole Numbers, Decimals, and Fractions H1 Name the place value from thousandths to millions of a particular digit given a whole number or decimal. H2 Order sequentially a set of whole numbers and decimals from millions to thousandths. (7.1.6) H3 Order a set of rational numbers sequentially. H4 Write tenths and hundredths in decimal and fraction notation. Know the fraction and decimal equivalents for halves and fourths. H5 Round whole numbers and decimals to any place value. H6 nterpret percents as part of a hundred. Find decimal and percent equivalents for common fractions and explain why they represent the same value. H7 Count, read, write, compare, and plot on a number line decimals to thousandths using words, models and expanded form. (5.1.1) Know the Value of a Digit by its Place 1 Tell the value and the place a number holds when given a word name for a numeral. J Write in Expanded Form and Scientific Notation J1 Use words, models, standard form and expanded form to represent place value and to show equivalent forms of whole numbers up to at least 10,000 (3.1.4) J2. Read, write, compare, and solve problems using whole numbers in scientific notation. (7.1.1) J3 Find the prime factorization of whole numbers and write the results using exponents. (7.1.3) J4 Read, write, compare, and solve problems using decimals in scientific notation. (8.1.1) J5 Use words, models, standard form and expanded form to represent place value of Diocese of Lafayette-in-ndiana Core Curriculum Guide August,
8 MATHEMATCS SKLLS/CONCEPTS K decimal numbers to thousandths. (5.1.4) Subject Area: Component V: MATHEMATCS FRACTON AND DECMAL SENSE 20 Diocese of Lafayette-in-ndiana Core Curriculum Guide August, 2009
9 MATHEMATCS ndiana Academic Standard 1: Number Sense and Computation Understanding the number system is the basis of mathematics. Students develop and extend their understanding of the place value system to count, read, and write whole numbers, fractions, and decimals. Through the years students will broaden their understanding of numbers through the concepts of percentages, ratios, rational and irrational numbers, scientific notation, and square roots. GOALS: The student will be able to... A. dentify fractions/mixed numerals using physical models and illustrations for regions and sets B. nvestigate/use different physical representations for the same fractional parts of regions and sets C. nvestigate/use equivalent fractional parts of regions and sets expressed in different forms using manipulatives D. Write fractions to represent fractional parts E. Write whole numbers as fractions F. Write mixed numerals to represent improper fractions G. nvestigate/use decimals through thousandths as representing place value or fractions with appropriate manipulatives H. dentify fractional names for decimals through exploration with fractional and decimal models.. Extend number system to include negative numbers, percentages, fractions, decimals, and ratios. LEGEND: = the grade at which the skill is introduced Grey-shaded area= grades at which the skill is to be developed and expanded. State standards are assessed annually, beginning the year after introduction. The student will be able to... The teacher will... SKLLS/CONCEPTS K A Physical Models and llustrations A1 Use physical models or illustrations to represent equivalent fractions when given a fraction. (3.1.3) A2 Divide sets of ten or fewer objects into equal groups. A3 Divide shapes into equal parts. B Different Physical Representations B1 Recognize when a shape is divided into congruent (matching) parts. (2.3.2) C Using Manipulatives Diocese of Lafayette-in-ndiana Core Curriculum Guide August,
10 MATHEMATCS SKLLS/CONCEPTS K C1 dentify and use correct names for numerators and denominations. C2 Label which fraction is larger or smaller by using physical models or illustrations when given a pair of fractions. (3.1.3) D Represent Fractional Parts D1 Name/Write, when given a set of fractional models, those that represent equivalent fractions. D2 For a shape divided into 8 or fewer congruent (matching) parts, describe a shaded portion as -out of-parts and write the fraction. D3 For a set of 8 or fewer objects, describe a subset as -out of-parts and write the fraction. D4 Recognize fractions as parts of a whole or parts of a group (up to 12 parts). (3.1.3) D5 Recognize, name, and compare fractions using the symbols for less than (<), equals (=), and greater than (>). (4.1.2) D6 Compare and order fractions by using models, benchmark fractions, or common numerators or denominators. (3.1.3) D7 Find equivalent fractions and then use them to compare and order whole numbers and fractions using the symbols for less than (<), equals (=), and greater than (>). (4.1.2) E Whole Numbers as Fractions E1 Rename/Rewrite whole numbers as fractions with varying denominators. E2 Know that, when all fractional parts are included, the result is equal to the whole and to one. F Mixed Numerals F1 Name and write mixed numbers as improper fractions, using objects or pictures. G Decimals With Manipulatives 22 Diocese of Lafayette-in-ndiana Core Curriculum Guide August, 2009
11 MATHEMATCS SKLLS/CONCEPTS K G1 Name/Write, when given physical models or illustrations, a decimal to represent tenths and hundredths. G2 Name/Write, when given a decimal representing tenths as a fraction using place value models. G3 Round any decimal number to any specified place. H Fractional and Decimal Models H1 Name/Write, when given a decimal representing hundredths, a fraction using place value models H2 Solve problems involving decimals to the hundredths. nterpret and model decimals as parts of a whole, parts of a group, and points and distances on a number line. Use benchmarks to compare decimals between 0 and 1.0. Write decimals as fractions. (4.1.3) H3 Name and write mixed numbers, using objects or pictures. H4 Explain different interpretations of fractions: as part of a whole, parts of a set, and division of whole numbers by whole numbers. H5 nterpret and model decimals as parts of a whole, parts of a group and point and distances on a number line. (4.1.3) H6 Use words, models, standard form and expanded form to represent place value of decimal numbers, to hundredths. (4.1.4) H7 Compare, order and represent on a number line positive and negative integers, fractions, decimals (to hundredths), and mixed numbers. (4.1.3, 6.1.1) H8 Compare and order fractions, decimals (to thousandths), and mixed numbers by using symbols for less than (<), equal to (=), and greater than (>) (5.1.2). Extend Number System 1 dentify on a number line the relative Diocese of Lafayette-in-ndiana Core Curriculum Guide August,
12 MATHEMATCS SKLLS/CONCEPTS K position of simple positive fractions, positive mixed numbers and positive decimals. (3.1.3) 2 Recognize decimal equivalents for commonly used fractions without the use of a calculator. (6.1.4) 24 Diocese of Lafayette-in-ndiana Core Curriculum Guide August, 2009
13 MATHEMATCS Subject Area: Component X: MATHEMATCS PROPERTES OF NUMBERS ndiana Academic Standard 1: Number Sense and Computation Understanding the number system is the basis of mathematics. Students develop and extend their understanding of the place value system to count, read, and write whole numbers, fractions, and decimals. Through the years students will broaden their understanding of numbers through the concepts of percentages, ratios, rational and irrational numbers, scientific notation, and square roots. GOALS: The student will be able to... A. dentify/apply the commutative, associative, and distributive properties of rational numbers B. Apply the multiplicative and additive properties of zero, as well as additive and multiplicative inverses C. Develop/Apply an algorithm to approximate a square root D. Discuss that all measures are imprecise and estimate the error involved E. Compute the sum, difference, product, or quotient of a problem involving two or more rational numbers LEGEND: = the grade at which the skill is introduced Grey-shaded area= grades at which the skill is to be developed and expanded. State standards are assessed annually, beginning the year after introduction. The student will be able to... The teacher will... SKLLS/CONCEPTS K A Apply Properties A1 Demonstrate the commutative property of rational numbers. (2.2.3,4.2.3) A2 Demonstrate the associative property of rational numbers. (2.2.3,4.2.3) A3 Demonstrate the distributive property of rational numbers. (4.2.4) A4 Apply the commutative and associative properties of multiplication to expressions with numbers up to 10,000. (3.2.3) A5 Solve problems using the identity principle of multiplication within the set of rational numbers. (3.2.3) Diocese of Lafayette-in-ndiana Core Curriculum Guide August,
14 MATHEMATCS SKLLS/CONCEPTS K A6 Solve a problem within the set of rational numbers. (8.1.6) A7 Compute the sum, difference, product, or quotient of a problem involving two or more rational numbers. A8 Understand and use the inverse relationship between addition and subtraction facts (such as = 6, 6 2 =4, etc.) to solve simple problems. (1.1.6) B Apply Properties of Zero B1 Demonstrate the multiplication property of zero. (3.1.6) B2 Demonstrate that division by zero is impossible. (3.1.7) B3 Demonstrate the additive/multiplicative inverse of the property of zero. B4 Solve a problem within the set of rational numbers. B5 Understand the role of zero in addition and subtraction. C Develop an Algorithm for Square Root C1 Calculate and find approximations of square roots. (8.1.5) D Estimate Error D1 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. D2 Use estimation to decide whether answers are reasonable in problems involving fractions and decimals. E. Compute With Two or More Rational Numbers E1 Recognize and apply the relationships between addition and multiplication, between subtraction and division, and the inverse relationship between multiplication and division to solve problems. E2 Know, select, and apply appropriate methods of estimating results of rationalnumber computations. E3 Select and apply appropriate methods for 26 Diocese of Lafayette-in-ndiana Core Curriculum Guide August, 2009
15 MATHEMATCS SKLLS/CONCEPTS K estimating results of rational-number computations. E4 Solve addition, subtraction, multiplication, and division problems that use integers, fractions, decimals, and combinations of the four operations. (7.1.6) E5 Use mental arithmetic to compute with simple fractions, decimals, powers, and percents. E6 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) in multi-step problems. E7 Use estimation techniques to decide whether answers to computation on a calculator are reasonable. E8 Solve problems involving addition, subtraction, multiplication, and division of integers and represent computation with integers on a number line. Describe the effect of operations with numbers less than zero. (6.1.5) Diocese of Lafayette-in-ndiana Core Curriculum Guide August,
16 MATHEMATCS 28 Diocese of Lafayette-in-ndiana Core Curriculum Guide August, 2009
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