Franklin County Community School Corporation - Brookville, Indiana s12

Franklin County Community School Corporation - Brookville, Indiana Curriculum Map Course Title: 3rd Grade Math Quarter: 1 Academic Year: 2011-2012 Essential Questions for this Quarter: 1. How do I add and subtract numbers up to 1,000 and check my answers for reasonableness? 2. How can I extend my understanding of place value to numbers in various contexts? 3. Why is understanding time and money important? 4. What steps can students take to be better problem solvers?

Unit/Time Frame Standards Content Skills Assessment Resources

Operations and Homework Math Text Algebraic Thinking Quizzes iPad apps 1st quarter-4weeks 3.2.1a Add numbers up to 1,000 without Add and subtract regrouping Tests Math games for numbers up to 1,000 the computer with and without 3.2.1b Subtract numbers up to 1,000 without Acuity regrouping, checking it regrouping Base-ten blocks for reasonableness Skills Tutor with estimation, front 3.2.1c Add numbers up to 1,000 with Play Money end estimation, and regrouping Informal compatible numbers. assessments Number lines 3.2.1d Subtract numbers up to 1,000 with (dry-erase board regrouping work) Number charts

3.2.1e Use inverse operations to check Pretest/Posttest addition and subtraction

3.2.7a Determine whether answers are reasonable in addition and subtraction problems using rounding, front-end estimation and convenient (compatible) numbers Franklin County Community School Corporation - Brookville, Indiana Curriculum Map Course Title: 3rd Grade Math Quarter: 1 Academic Year: 2011-2012 Essential Questions for this Quarter: 1. How do I add and subtract numbers up to 1,000 and check my answers for reasonableness? 2. How can I extend my understanding of place value to numbers in various contexts? 3. Why is understanding time and money important? 4. What steps can students take to be better problem solvers?

Number and 3.1.1a Write a number up to 1,000 in Text Text Book Operations in Base Ten standard form when hearing the oral Assessments form of the number. Teacher Resource 4-5 Weeks Acuity Books

Use number and 3.1.1b Write a number up to 1,000 when Skills Tutor Place Value operations in base ten shown a model of the number. Blocks such as place value, Homework comparing, classifying, 3.1.1c Write a number up to 1,000 when Number Cards and rounding to given the word form of the number. Informal understand numbers Assessment Place Value up to 1,000. 3.1.1d Read orally a number up to 1,000 (activities) Charts when given the standard form of the number. Rounding Roller Coaster 3.1.1e Read orally a number up to 1,000 when given the word form of the Number Line number. Trade Books 3.1.1f Count by 100s to 1,000. Math Charts 3.1.1g Name a series of numbers that follow a given a number less than 1,000. Skills Tutor

3.1.2a Name the digit located in the ones, Math Websites tens, and hundreds place in a given number. iPad apps Franklin County Community School Corporation - Brookville, Indiana Curriculum Map Course Title: 3rd Grade Math Quarter: 1 Academic Year: 2011-2012 Essential Questions for this Quarter: 1. How do I add and subtract numbers up to 1,000 and check my answers for reasonableness? 2. How can I extend my understanding of place value to numbers in various contexts? 3. Why is understanding time and money important? 4. What steps can students take to be better problem solvers?

3.1.2b Write the value of a digit in a number up to 1,000. 3.1.3a Use models to represent numbers up to 1,000. 3.1.3b Write the number as the sum of the value of its digits (expanded form).

3.1.4a Decompose any number up to 1,000 in various combinations of hundreds, tens, and ones (i.e., 3 hundreds, 2 tens, 5 ones).

3.1.4b Write in standard form a number up to 1,000 that is given in a different combination of hundreds, tens, and ones.

3.1.5a Compare whole numbers up to 1,000.

3.1.5b Arrange whole numbers up to 1,000 in numerical order.

3.1.6a Round numbers less than one hundred to the nearest ten.

3.1.6b Round numbers less than one thousand to the nearest hundred. Franklin County Community School Corporation - Brookville, Indiana Curriculum Map Course Title: 3rd Grade Math Quarter: 1 Academic Year: 2011-2012 Essential Questions for this Quarter: 1. How do I add and subtract numbers up to 1,000 and check my answers for reasonableness? 2. How can I extend my understanding of place value to numbers in various contexts? 3. Why is understanding time and money important? 4. What steps can students take to be better problem solvers?

3.1.7a Classify numbers up to 1,000 as even or odd.

3.1.7b Describe what determines if a number is even or odd.

Measurement and Data 3.5.10a Determine which symbol (¢ or $) to Text book Text book use after finding the value of any Understand money and collection of coins and bills. Acuity Acuity time concepts Understand that 20¢ is the same as $0.20. Observation Skills Tutor 3.5.11a Determine the total cost of more than Skills Tutor iPADs one item. 3.5.11b iPAD apps Web sites Determine whether there is enough money given a certain amount to buy Coins & Bills more than one item. 3.5.9a Clocks Tell time to the nearest 5-minutes. 3.5.9b Determine the time it would be one hour after a given time. Repeat for any number of hour intervals. 3.5.9c Determine the number of hours Franklin County Community School Corporation - Brookville, Indiana Curriculum Map Course Title: 3rd Grade Math Quarter: 1 Academic Year: 2011-2012 Essential Questions for this Quarter: 1. How do I add and subtract numbers up to 1,000 and check my answers for reasonableness? 2. How can I extend my understanding of place value to numbers in various contexts? 3. Why is understanding time and money important? 4. What steps can students take to be better problem solvers?

between two times that have the same number of minutes (Ex: How many hours between 11:15 and 3.5.9d 2:15?).

3.5.9e Tell time to the nearest minute.

Determine what time it will be in any number of five-minute intervals (up to an hour) after a given time that falls 3.5.9f on a five-minute interval.

Determine the amount of time between any two given times.Te

Geometry Not quarter 1 Math Standards for SMP1 Make sense of problems and Mathematical Practice persevere in solving them.

Unit 1: SMP2 Reason abstractly and quantitatively. Taught in first quarter and spirals throughout SMP3 Construct viable arguments and the year. critique the reasoning of others.

Problem Solving Steps: SMP4 Model with mathematics.

1. Understand SMP5 Use appropriate tools strategically. 2. Plan SMP6 Franklin County Community School Corporation - Brookville, Indiana Curriculum Map Course Title: 3rd Grade Math Quarter: 1 Academic Year: 2011-2012 Essential Questions for this Quarter: 1. How do I add and subtract numbers up to 1,000 and check my answers for reasonableness? 2. How can I extend my understanding of place value to numbers in various contexts? 3. Why is understanding time and money important? 4. What steps can students take to be better problem solvers?

3. Solve Attend to precision 4. Check SMP7 Look for and make use of structure.

SMP8 Look for and express regularity in repeated reasoning.

3.6.1a Analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

3.6.2a Decide when and how to break a problem into simpler parts.

Apply strategies and results from 3.6.3a simpler problems to solve more complex problems.

Express solutions clearly and logically 3.6.4a by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work. Franklin County Community School Corporation - Brookville, Indiana Curriculum Map Course Title: 3rd Grade Math Quarter: 1 Academic Year: 2011-2012 Essential Questions for this Quarter: 1. How do I add and subtract numbers up to 1,000 and check my answers for reasonableness? 2. How can I extend my understanding of place value to numbers in various contexts? 3. Why is understanding time and money important? 4. What steps can students take to be better problem solvers?

Recognize the relative advantages of exact and approximate solutions to 3.6.5a problems and give answers to a specified degree of accuracy.

Know and use strategies for estimating results of whole-number 3.6.6a addition and subtraction.

Make precise calculations and check the validity of the results in the context of the problem. 3.6.7a Explain whether a solution is reasonable in the context of the original situation. 3.6.8a Note the method of finding the solution and show a conceptual understanding of the method by 3.6.9a solving similar problems. Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS

Represent and solve problems involving addition and subtraction. 3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. 3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ☐ ÷ 3, 6 × 6 = ? Understand properties of multiplication and the relationship between multiplication and division. 3.OA.5 Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) 3.OA.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. Multiply and divide within 100. 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. 1 See Glossary, Table 2. 2 Students need not use formal terms for these properties. Mathematics Academic Standards: Grade 3 Solve problems involving the four operations, and identify and explain patterns in arithmetic. 3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3 Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS 3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. Number and Operations in Base Ten NBT Use place value understanding and properties of operations to perform multi-digit arithmetic.4 3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100. 3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. 3 This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parenthesis to specify a particular order (Order of Operations). 4 A range of algorithms may be used. Mathematics Academic Standards: Grade 3 Number and Operations- Fractions5 NF Develop understanding of fractions as numbers. 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS Of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 5 Grade 3 expectations in this domain are limited to fractions with denominators 2,3,4,6, and 8. Mathematics Academic Standards: Grade 3 Measurement and Data MD Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. 3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. 3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.7 Represent and interpret data. 3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. 3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters. Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. 3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 3.MD.7 Relate area to the operations of multiplication and addition. Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. 6 Excludes compound units such as cm3 and finding the geometric volume of a container. 7 Excludes multiplicative comparison problems (problems involving notions of “times as much”; see Glossary, Table 2). Mathematics Academic Standards: Grade 3 b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Geometry G Reason with shapes and their attributes. 3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ of the area of the shape. Mathematics Academic Standards: Grade 3 Standards for Mathematical Practice The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. 1. Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, �Does this make sense?� They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. 2. Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Mathematics Academic Standards: Grade 3 3. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. 4. Model with mathematics. Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Mathematics Academic Standards: Grade 3 5. Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. 6. Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Mathematics Academic Standards: Grade 3 7. Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. 8. Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Standard 1 Number Sense

Students understand the relationships among numbers, quantities, and place value in whole numbers* up to 1,000. They understand the relationship among whole numbers, simple fractions, and decimals.

3.1.1 Count, read, and write whole numbers up to 1,000. Example: Write 349 for the number “three hundred forty-nine.” 3.1.2 Identify and interpret place value in whole numbers up to 1,000.Example: Understand that the 7 in 479 represents 7 tens or 70. 3.1.3 Use words, models, and expanded form to represent numbers up to 1,000. Example: Recognize that 492 = 400 + 90 + 2. 3.1.4 Identify any number up to 1,000 in various combinations of hundreds, tens, and ones. Example: 325 can be written as 3 hundreds, 2 tens, and 5 ones, or as 2 hundreds, 12 tens,and 5 ones, etc. Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS 3.1.5 Compare whole numbers up to 1,000 and arrange them in numerical order. Example: What is the smallest whole number you can make using the digits 4, 9, and 1?Use each digit exactly once. 3.1.6 Round numbers less than 1,000 to the nearest ten and the nearest hundred. Example: Round 548 to the nearest ten. 3.1.7 Identify odd and even numbers up to 1,000 and describe their characteristics. Example: Find the even number: 47, 106, 357, 629. 3.1.8 Show equivalent fractions* using equal parts. 3 6 9 Example: Draw pictures to show that 5 , 1 0 , and 1 5 are equivalent fractions. 3.1.9 Identify and use correct names for numerators and denominators. 3 Example: In the fraction 5 , name the numerator and denominator. 3.1.10 Given a pair of fractions, decide which is larger or smaller by using objects or pictures. 3 1 Example: Is 4 of a medium pizza larger or smaller than 2 of a medium pizza? Explain your answer. 3.1.11 Given a set* of objects or a picture, name and write a decimal to represent tenths and hundredths. Example: You have a pile of 100 beans and 72 of them are lima beans. Write the decimal that represents lima beans as a part of the whole pile of beans. 3.1.12 Given a decimal for tenths, show it as a fraction using a place-value model. 7 Example: Shade the part of a square that represents 0.7 and write the number 1 0 . 3.1.13 Interpret data displayed in a circle graph and answer questions about the situation. Example: Have the students in your class choose the pizza they like best from these choices: cheese, sausage, pepperoni. Use a spreadsheet to enter the number of students who chose each kind and make a circle graph of the data. Determine the most popular and the least popular kind of pizza, and explain what the circle and each pie slice represent. 3.1.14 Identify whether everyday events are certain, likely, unlikely, or impossible. Example: It is raining in your neighborhood. Is it certain, likely, unlikely, or impossible that the tree in your front yard will get wet? 3.1.15 Record the possible outcomes for a simple probability experiment. Example: Have a partner toss a coin while you keep a tally of the outcomes. Exchange places with your partner and repeat the experiment. Explain your results to the class.    * whole number: 0, 1, 2, 3, etc. 1 2 3 * equivalent fractions: fractions with the same value (e.g., 2 , 4 , 6 , etc.)  * set: collection of objects, numbers, etc.

  Standard 2 Computation

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   Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS Students solve problems involving addition and subtraction of whole numbers. They model and solve simple problems involving multiplication and division.

3.2.1 Add and subtract whole numbers up to 1,000 with or without regrouping, using relevant properties of the number system. Example: 854 – 427 = ?. Explain your method. 3.2.2 Represent the concept of multiplication as repeated addition. Example: Lynn made 3 baskets each week for 4 weeks. Draw a picture to show how many baskets she made. 3.2.3 Represent the concept of division as repeated subtraction, equal sharing, and forming equal groups. Example: Bob shared 10 cookies among 5 friends. Draw a picture to show how many cookieseach friend got. 3.2.4 Know and use the inverse relationship between multiplication and division facts, such as 6  7 = 42, 42  7 = 6, 7  6 = 42, 42  6 = 7. Example: Find other facts related to 8  3 = 24. 3.2.5 Show mastery of multiplication facts for 2, 5, and 10. Example: Know the answer to 6  5. 3.2.6 Add and subtract simple fractions with the same denominator. 3 1 Example: Add 8 and 8 . Explain your answer. 3.2.7 Use estimation to decide whether answers are reasonable in addition and subtraction problems. Example: Your friend says that 79 – 22 = 27. Without solving, explain why you think the answeris wrong. 3.2.8 Use mental arithmetic to add or subtract with numbers less than 100. Example: Subtract 35 from 86 without using pencil and paper.

Standard 3 Algebra and Functions

Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number and functional relationships.

3.3.1 Represent relationships of quantities in the form of a numeric expression or equation. Example: Bill’s mother gave him money to buy three drinks that cost 45 cents each at the concession stand. When he returned to the bleachers, he gave 25 cents change to his mother.Write an equation to find the amount of money Bill’s mother originally gave him. 3.3.2 Solve problems involving numeric equations. Example: Use your equation from the last example to find the amount of money that Bill’s mother gave him, and justify your answer. 3.3.3 Choose appropriate symbols for operations and relations to make a number sentence true. Example: What symbol is needed to make the number sentence 4 _ 3 = 12 true?   Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS 3.3.4 Understand and use the commutative* and associative* properties of multiplication. Example: Multiply the numbers 7, 2, and 5 in this order. Now multiply them in the order 2, 5, and 7. Which was easier? Why? 3.3.5 Create, describe, and extend number patterns using multiplication. Example: What is the next number: 3, 6, 12, 24, …? How did you find your answer? 3.3.6 Solve simple problems involving a functional relationship between two quantities. Example: Ice cream sandwiches cost 20 cents each. Find the costs of 1, 2, 3, 4, … ice cream sandwiches. What pattern do you notice? Continue the pattern to find the cost of enough ice cream sandwiches for the class. 3.3.7 Plot and label whole numbers on a number line up to 10. Example: Mark the position of 7 on a number line up to 10. * commutative property: the order when adding or multiplying numbers makes no difference (e.g., 5 + 3 = 3 + 5), but note that this rule is not true for subtraction or division * associative property: the grouping when adding or multiplying numbers makes no difference (e.g., in 5 + 3 + 2, adding 5 and 3 and then adding 2 is the same as 5 added to 3 + 2), but note that this rule is not true for subtraction or division

Standard 4 Geometry

Students describe and compare the attributes of plane and solid geometric shapes and use their understanding to show relationships and solve problems.

3.4.1 Identify quadrilaterals* as four-sided shapes. Example: Which of these are quadrilaterals: square, triangle, rectangle? 3.4.2 Identify right angles in shapes and objects and decide whether other angles are greater or less than a right angle. Example: Identify right angles in your classroom. Open the classroom door until it makes a right angle with one wall and explain what you are doing. 3.4.3 Identify, describe, and classify: cube, sphere*, prism*, pyramid, cone, and cylinder. Example: Describe the faces of a pyramid and identify its characteristics. 3.4.4 Identify common solid objects that are the parts needed to make a more complex solid object. Example: Describe and draw a house made from a prism and a pyramid. 3.4.5 Draw a shape that is congruent* to another shape. Example: Draw a triangle that is congruent to a given triangle. You may use a ruler and pencil or the drawing program on a computer. Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS 3.4.6 Use the terms point, line, and line segment in describing two-dimensional shapes. Example: Describe the way a triangle is made of points and line segments and how you know it is a triangle. 3.4.7 Draw line segments and lines. Example: Draw a line segment three inches long. 3.4.8 Identify and draw lines of symmetry in geometric shapes (by hand or using technology). Example: Use pencil and paper or a drawing program to draw lines of symmetry in a square. Discuss your findings. 3.4.9 Sketch the mirror image reflections of shapes. Example: Hold up a cardboard letter F to a mirror. Draw the letter and the shape you see in the mirror. 3.4.10 Recognize geometric shapes and their properties in the environment and specify their locations. Example: Write the letters of the alphabet and draw all the lines of symmetry that you see.

* quadrilateral: a two-dimensional figure with four sides

* sphere: a shape best described as that of a round ball, such as a baseball, that looks the same when seen from all directions.

* prism: a solid shape with fixed cross-section (a right prism is a solid shape with two parallel faces that are congruent polygons and other faces that are rectangles)

* congruent: the term to describe two figures that are the same shape and size

Standard 5 Measurement

Students choose and use appropriate units and measurement tools for length, capacity, weight, temperature, time, and money.

3.5.1 Measure line segments to the nearest half-inch. Example: Measure the length of a side of a triangle. 3.5.2 Add units of length that may require regrouping of inches to feet or centimeters to meters. Example: Add the lengths of three sheets of paper. Give your answer in feet and inches. 3.5.3 Find the perimeter of a polygon*. Example: Find the perimeter of a table in centimeters. Explain your method. 3.5.4 Estimate or find the area of shapes by covering them with squares. Example: How many square tiles do we need to cover this desk? Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS 3.5.5 Estimate or find the volumes of objects by counting the number of cubes that would fill them. Example: How many of these cubes will fill the box? 3.5.6 Estimate and measure capacity using quarts, gallons, and liters. Example: This bottle holds one liter. Estimate how many liters the sink holds. 3.5.7 Estimate and measure weight using pounds and kilograms. Example: Estimate the weight of your book bag in pounds. 3.5.8 Compare temperatures in Celsius and Fahrenheit. Example: Measure the room temperature using a thermometer that has both Celsius and Fahrenheit units. If the temperature in the room measures 70ºF, will the Celsius measurement be higher or lower? 3.5.9 Tell time to the nearest minute and find how much time has elapsed. Example: You start a project at 9:10 a.m. and finish the project at 9:42 a.m. How much time has passed? 3.5.10 Find the value of any collection of coins and bills. Write amounts less than a dollar using the ¢ symbol and write larger amounts in decimal notation using the $ symbol. Example: You have 5 quarters and 2 dollar bills. How much money is that? Write the amount. 3.5.11 Use play or real money to decide whether there is enough money to make a purchase. Example: You have $5. Can you buy two books that cost $2.15 each? What about three books that cost $1.70 each? Explain how you know. 3.5.12 Carry out simple unit conversions within a measurement system (e.g., centimeters to meters, hours to minutes). Example: How many minutes are in 3 hours? * polygon: a two-dimensional shape with straight sides (e.g., triangle, rectangle, pentagon)

Standard 6 Problem Solving

Students make decisions about how to approach problems and communicate their ideas.

3.6.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. Example: Solve the problem: “Start with any number. If it is even, halve it. If it is odd, add 1. Do the same with the result and keep doing that. Find what happens by trying different numbers.”Try two or three numbers and look for patterns. 3.6.2 Decide when and how to break a problem into simpler parts. Example: In the first example, find what happens to all the numbers up to 10.

Students use strategies, skills, and concepts in finding and communicating solutions to problems. Franklin County Community School Corporation - Brookville, Indiana COMMON CORE AND INDIANA ACADEMIC STANDARDS 3.6.3 Apply strategies and results from simpler problems to solve more complex problems. Example: In the first example, use your results for the numbers up to 10 to find what happens to all the numbers up to 20. 3.6.4 Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work. Example: In the first example, explain what happens to all the numbers that you tried. 3.6.5 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. Example: Measure the length and width of a room to the nearest meter to find how many student desks will fit in it. Would this be an accurate enough method if you were carpeting the room? 3.6.6 Know and use strategies for estimating results of whole-number addition and subtraction. Example: You buy 2 bags of candy for $1.05 each. The cashier tells you that will be $1.70. Does that surprise you? Why or why not? 3.6.7 Make precise calculations and check the validity of the results in the context of the problem. Example: In the first example, notice that the result of adding 1 to an odd number is always even. Use this to check your calculations.

Students determine when a solution is complete and reasonable and move beyond a particular problem by generalizing to other situations.

3.6.8 Decide whether a solution is reasonable in the context of the original situation. Example: In the example about fitting desks into a room, would an answer of 1,000 surprise you? 3.6.9 Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems. Example: Change the first example so that you multiply odd numbers by 2 or 3 or 4 or 5, before adding 1. Describe the pattern you see.