GRADE ATHEMATICS CURRICULUM UIDE - Loudoun County Public Schools

Why would you count by tens and ones? What strategies are used to represent the value of a two digit number? 1.04 – Demonstrate and explain magnitude in place value. (ten times larger) 1.1 b Essential Understandings Associate oral number names with the correct numeral and set of objects. 1.2 Essential Questions Understand that 1 and 10 are special units of numbers (e.g., 10 is 10 ones, but it is also 1 ten). Understand the ten-to-one relationship of ones and tens (10 ones equals 1 ten). Understand that numbers are written to show how many tens and how many ones are in the number. Understand that groups of tens and ones can be used to tell how many. 1.2 Essential Understandings Understand that collections of objects can be grouped and skip counting can be used to count the collection. Describe patterns in counting by ones (both forward and backward) and skip counting and use those patterns to predict the next number in the counting sequence. 5 days Enrichment, Assessment, and Remediation each digit in a two-digit numeral (e.g., The place value of the 2 in the number 23 is tens. The value of the 2 in the number 23 is 20). Group a collection of objects into sets of tens and ones. Write the numeral that corresponds to the total number of objects in a given collection of objects that have been grouped into sets of tens and ones. SOL 1.2 The student will count forward by ones, twos, fives, and tens to 100 and backward by ones from 30. 1.2 Essential Knowledge and Skills Count by ones, twos, fives, and tens to 100, using concrete objects, such as counters, connecting cubes, pennies, nickels, and dimes. Demonstrate a one-to-one correspondence when counting by ones with concrete objects or representations. Skip count orally by twos, fives and tens to 100 starting at various multiples of 2, 5, or 10. Count backward by ones from 30. A Collection of Math Lessons From Grades 1-3 by Marilyn Burns and Bonnie Tank; Chapter 7: A Place-Value Menu, page 71

Summary: First grade is important for its focus on counting, which is how students develop understanding of our number system and problem-solving. In the first quarter, students will be provided with repeated opportunities to work with calendar and experience working with data as they count, compare, and combine items and information. Students explore pattern by describing sequences and predicting what comes next. This quarter helps establish the mathematical communication within the classroom by sharing and explaining strategies, as well as using pictures, numbers, and words to justify their thinking. Vocabulary Numbers, numeral, one-to-one correspondence, tally, data, vote, survey, picture graphs or pictographs, object graphs, more, less, greater than, less than, fewer, equal to, key, category Skip counting, grouping, patterns, hundreds chart, classify sort, arrange, organize size, shapes, thick, thin, pattern, growing patters, repeating pattern, geometric patterns, rotation, reflection

Grade 1 Quarter 2 School Year 2011-2012 Daily Classroom Routines are built on life skills and should be used all year. The content identified to be taught during the first 20 days of school is either a review or an extension of previous knowledge and should be addressed in scaffolded assessments throughout the year. Teachers are encouraged to use the first twenty days of school to introduce calendar concepts, time on a clock, temperature, and data as part of daily routines. Include life skill questions like: It is nine o’clock now; we have art in an hour. What time will it be then? Yesterday was Tuesday. What day is today? What day will it be tomorrow? How many days are in this month? If this month ends on Wednesday, on which day is the first of the next month? Number of Days Topics, Essential Questions, and Essential Understandings (Students should be able to answer essential questions.) REQUIRED Critical Thinking Lessons Standard(s) of Learning Essential Knowledge and Skills Additional Instructional Resources Building Numbers and Place Value 5 days 1.4 Essential Questions Understand that the last number said tells the number of objects counted. Know the decade words and recite them. Say the number name sequence forward or backward beginning from a given number instead of always beginning with one. Example: Count by tens beginning with the number 17. Why would you count by tens and ones? What strategies are used to represent the value of a two digit number? 1.04 – Demonstrate and explain magnitude in place value. (ten times larger) 1.4 Essential Understandings Magnitude refers to the size of a set. Exploring ways to estimate the number of objects in a set, based on appearance, (e.g., clustering, grouping, comparing) enhances the development of number sense. To estimate means to find a number that is INV: Building Number Sense: Investigation 2: Building Numbers in Different Ways: Sessions 1 – 9 (Sessions 6, 7, 8 Towers of Ten- place value) SOL1.4 The student, given a familiar problem situation involving magnitude, will a) select a reasonable order of magnitude from three given quantities: a one-digit numeral, a two-digit numeral, and a threedigit numeral (e.g., 5, 50, 500); and b) explain the reasonableness of the choice. INV. Building Number Sense: Investigation 1: Visualizing Numbers: Sessions 1– 9 Teaching StudentCentered Mathematics Grades K-3 by John A. Van de Walle and LouAnn H. Lovin Chapter 5: Base-Ten Concepts and Place 1.4 Essential Knowledge and Skills Select a reasonable order of magnitude Value, page 122 A Collection of Math for a given set from three given quantities: a one-digit numeral, a two- Lessons From Grades 1-3 by Marilyn Burns digit numeral, and a three-digit and Bonnie Tank; numeral (e.g., 5, 50, and 500 jelly Chapter 7: A Placebeans in jars) in a familiar problem Value Menu, page 71 situation. Given a familiar problem situation involving magnitude, explain why a particular estimate was chosen as the most reasonable from three given quantities: a one-digit numeral, a

Grade 1 Quarter 2 School Year 2011-2012 close to the exact amount. When asking for an estimate, teachers might ask, “about how much?” or “about how many?” or “Is this about 10 or about 50?” Students should be provided opportunities to estimate a quantity, given a benchmark of 10 and/or 100 objects. two-digit numeral, and a three-digit numeral.

Grade 1 Quarter 2 School Year 2011-2012 Number of Days Topics, Essential Questions, and Essential Understandings (Students should be able to answer essential questions.) Combining and Separating Situations 1.5 Essential Questions What is a sum? What is a difference? Explain and justify how addition and subtraction are related. Illustrate and explain a set of related facts. Compare and contrast strategies for combining and separating situations in real life scenarios. Create, explain, and justify the sum and/or difference for a real life scenario. Model and explain addition and subtraction with an unknown change. 10 days 1.5 Essential Understandings Understand that picture graphs use pictures to represent and compare data while object graphs use concrete objects to represent and compare data. Understand that data can be analyzed and interpreted, using the terms more, less, fewer, greater than, less than, and equal to. Understand the following properties but it is not necessary to use the mathematical terms: that the order of two addends does not change the sum (commutative); when adding zero a number, it remains the same (additive identity); when adding three numbers, it does not matter which of the two are added REQUIRED Critical Thinking Lessons INV Building Number Sense, Investigation 4: Addition and Subtraction, Sessions 1-10 Standard(s) of Learning Essential Knowledge and Skills SOL 1.5 The student will interpret information displayed in a picture or object graph, using the vocabulary more, less, fewer, greater than, less than, and equal to. 1.5 Essential Knowledge and Skills Compare one category to another in a graph, indicating which has more or which has less, or which is equal to. Interpret information displayed in object graphs and picture graphs, using the words more, less, fewer, greater than, less than, and equal to. Find answers to questions, using graphs (e.g., “Which category has more?”, “How many more?”, and “How many in all?”). Additional Instructional Resources Teaching StudentCentered Mathematics Grades K-3 by John A. Van de Walle and LouAnn H. Lovin Chapter 6: Strategies for Whole-Number Computation Chapter 4: Helping Children Master the Basic Facts

Grade 1 Quarter 2 School Year 2011-2012 together first (associative property of addition). 1.6 Essential Questions 1.6 Essential Understandings Understand the same set of objects can be sorted and classified in different ways. SOL 1.6 The student will sort and classify concrete objects according to one or more attributes, including color, size, shape, and thickness. 1.6 Essential Knowledge and Skills Sort and classify objects into appropriate subsets (categories) based on one or two attributes, such as size, shape, color, or thickness. Characteristics of Plane Figures 1.12 Essential Questions Compare and contrast characteristics of plane geometric figures. Illustrate and explain objects in the environments as geometric shapes. What is the core of a pattern? (quilts) Demonstrate and explain a variety of ways of replicating a pattern. (quilts) 14 days 1.12 Essential Understandings Develop strategies to sort and/or group plane geometric figures and refine the vocabulary used to explain their strategies. INV Quilt Square and SOL 1.12 The student will identify and trace, Block Towns, Investigation describe, and sort plane geometric figures 1: 2-D Shapes and (triangle, square, rectangle, and circle) Patterns, Sessions 1-15 according to number of sides, vertices, and Books: A Cloak for the right angles. Dreamer by Aileen Friedman/Eight Hands 2009: 1.12, 1.13, 1.17 Understand that shapes Round: A Patchwork of can be seen as having parts, sides, angles, and Alphabet by Anne that shapes can be put together to compose Whitford Paul/Shapes, other shapes. Shapes, Shapes by Tana Distinguish between defining attributes (e.g., Hoban/Sam Johnson and triangles have 3 sides) versus non-defining the Blue Ribbon Quilt by attributes (e.g., color, orientation, or overall Lisa Campbell Ernst size) 1.12 Essential Knowledge and Skills Describe a circle. Trace triangles, squares, rectangles, and circles. Describe triangles, squares, and rectangles by the number of sides, vertices, and right angles.

Grade 1 Quarter 2 School Year 2011-2012 Sort plane geometric figures into appropriate subsets (categories) based on characteristics (number of sides, vertices, angles, curved, etc.). Identify the name of the geometric figure when given information about the number of sides, vertices, and right angles. 1.13 Essential Questions 1.13 Essential Understandings Understand that geometric figures are integral parts of the environment. Use familiarity with the figure, structure, and location to develop spatial reasoning. 1.17 Essential Questions 1.17 Essential Understandings Understand that patterns are a way to recognize order, to organize their world, and to predict what comes next in an arrangement. Recognize and state the core of a pattern. Analyze how both repeating and growing patterns are generated. SOL 1.13 The student will construct, model, and describe objects in the environment as geometric shapes (triangle, rectangle, square, and circle) and explain the reasonableness of each choice. 1.13 Essential Knowledge and Skills Construct plane geometric figures. Identify models of representations of circles, squares, rectangles, and triangles in the environment at school and home and tell why they represent those figures. Describe representations of circles, squares, rectangles, and triangles in the environment and explain the reasonableness of the choice. SOL 1.17 The student will recognize, describe, extend, and create a wide variety of growing and repeating patterns. 1.17 Essential Knowledge and Skills Recognize the pattern in a given rhythmic, color, geometric figure, or numerical sequence. Describe the pattern in a given rhythmic, color, geometric figure, or numerical

Grade 1 Quarter 2 School Year 2011-2012 sequence in terms of the core (the part of the sequence that repeats). Extend a pattern, using manipulatives, geometric figures, numbers, or calculators. Transfer a pattern from one form to another. Create a repeating or growing pattern, using manipulatives, geometric figures, numbers, or calculators (e.g., the growing patterns 2, 3, 2, 4, 2, 5, 2, 6, 2, ).

Grade 1 Quarter 2 School Year 2011-2012 Number of Days Topics, Essential Questions, and Essential Understandings (Students should be able to answer the essential questions.) Graphic Representations 1.14 Essential Questions What is data? Explain and justify how to collect data. Explain why data must be represented accurately. What are different ways data can be represented accurately? Explain and interpret displayed data. Compare and contrast the displayed data. (e.g., more, less, fewer, greater than, equal to using lunch count or attendance over time) 6 days 1.14 Essential Understandings Understand how data can be collected and presented in an organized manner. Understand that data gathered and analyzed from observations and surveys can have an impact on our everyday lives. 1.15 Essential Questions Explain and interpret displayed data. Compare and contrast the displayed data. (e.g., more, less, fewer, greater than, equal to using lunch count or attendance over time) 1.15 Essential Understandings Understand that picture graphs use pictures to represent and compare data while object graphs use concrete objects to represent and REQUIRED Critical Thinking Lessons Standard(s) of Learning Essential Knowledge and Skills Additional Instructional Resources INV: Survey Questions & Secret Rules, SOL 1.14 The student will investigate, Investigation 2: Sessions identify, and describe various forms of data 1-6 collection (e.g., recording daily temperature, AIMS activities lunch count, attendance, favorite ice cream), Graphing Questions: using tables, picture graphs, and object graphs. Favorite fruit, pet, season of the year, number of sisters or brothers, 1.14 Essential Knowledge and Skills Investigate various forms of data collection, birthday month or day, letters in a name, including counting and tallying, informal surveys, observations, and voting. Identify and describe various forms of data collection in practical situations (e.g., recording daily temperature, lunch count, attendance, and favorite ice cream.) SOL 1.15 The student will interpret information displayed in a picture or object graph, using the vocabulary more, less, fewer, greater than, less than, and equal to. 1.15 Essential Understandings Compare one category to another in a graph, indicating which has more or which has less, or which is equal to. Interpret information displayed in object

Grade 1 Quarter 2 School Year 2011-2012 compare data. Understand that data can be analyzed and interpreted, using the terms more, less, fewer, greater than, less than, and equal to. Organize, represent, and interpret data with several categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than another. 5 days Assessment, Enrichment, and Remediation graphs and picture graphs, using the words more, less, fewer, greater than, less than, and equal to. Find answers to questions, using graphs (e.g., “Which category has more?”, “How many more?”, and “How many in all?”).

Grade 1 Quarter 3 School Year 2011-2012 Daily Classroom Routines are built on life skills and should be used all year. The content identified to be taught during the first 20 days of school is either a review or an extension of previous knowledge and should be addressed in scaffolded assessments throughout the year. Teachers are encouraged to use the first twenty days of school to introduce calendar concepts, time on a clock, temperature, and data as part of daily routines. Include life skill questions like: It is nine o’clock now; we have art in an hour. What time will it be then? Yesterday was Tuesday. What day is today? What day will it be tomorrow? How many days are in this month? If this month ends on Wednesday, on which day is the first of the next month? Topics, Essential Questions, and REQUIRED Number Essential Understandings Standard(s) of Learning Additional Instructional Critical Thinking of Days (Students should be able to answer Essential Knowledge and Skills Resources Lessons essential questions.) Teaching Student-Centered Sets and Regional Parts SOL 1.3 Mathematics Grades K-3 by 1.3 Essential Questions 1.3 Essential Knowledge and Skills John A. Van de Walle and What is a fair share? LouAnn H. Lovin Decompose circles and rectangles into two, 10 days Create a real life scenario using fractions. three, and four equal parts. Describe the parts Chapter 9: Early Fraction Create, explain, and justify a fair share using a Concepts using the words halves, thirds, fourths, and region model. quarters, and using the phrases half of, third of, Touchmath: Fractions kit Explain how someone could get more pieces but fourth of, quarter of. Describe the whole as two ESS: end up with a fair share. of, three of, or four of the parts. Ben Franklin’s Kite Understand that decomposing into more equal Apple Fractions 1.3 Essential Understandings shares creates smaller parts. All About the Fraction Train Books: Eating Fractions A Fair Bear Share 10 days Time SOL 1.8 1.8 Essential Questions Explain and justify how many minutes are in one hour. Compare and contrast the hands of a clock on the hour and the half hour. 1.8 Essential Knowledge and Skills 1.8 Essential Understandings 1.8, K.8, K.9 Identify the parts of an analog clock. Demonstrate a time given to the hour and half hour on an analog clock. Match a written time to the time on a digital and analog clock to the half hour. Touchmath: Time kit ESS: It’s About Time

Topics, Essential Questions, and Number Essential Understandings of Days (Students should be able to answer essential questions.) Place Value and Whole Number Operations 1.1 b Essential Question Explain and justify the pattern of counting by 2’s, 5’s and 10’s to 100. Demonstrate counting backwards from 30 to 0. 25 days 1,1 b Essential Understandings Understand that 1 and 10 are special units of numbers (e.g., 10 is 10 ones, but it is also 1 ten). Understand the ten-to-one relationship of ones and tens (10 ones equals 1 ten). Understand that numbers are written to show how many tens and how many ones are in the number. Understand that groups of tens and ones can be used to tell how many. 1.2 Essential Questions 1.2 Essential Understandings Understand that collections of objects can be grouped and skip counting can be used to count th

1.1 a Essential Question Explain and justify a group of objects that represent a numeral. 1.1 a Essential Understanding Associate oral number names with the correct numeral and set of objects. 1.11 Essential Questions How does a calendar measure time? Identify the months of the year and the seven days in a week. 1.11 Essential .