OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
OKALOOSA COUNTY SCHOOL DISTRICT MATH CURRICULUM GUIDE
Fifth Grade
Office of Quality Assurance and Curriculum Support Guyla Hendricks, Chief Officer REV 062012 Fifth Grade Math Page 1 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
CONTENTS Mission Statement...... 3 Suggestions for Implementing Curriculum Guides ...... 3 Florida Department of Education ≠ Office of Math and Science Essential Websites ...... 4 OCSD Curriculum and Pacing Guide ∞ Overview ...... 4 Mathematics | Standards for Mathematical Practice ...... 5 Cognitive Complexity/Depth of Knowledge Rating for Mathematics ...... 8 Grade 5 General Content Limits ...... 10 Quarterly Benchmarks ...... 11 Grade-level Curriculum Guide ...... 13 Quarter 1 ...... 13 Quarter 2...... 22 Quarter 3...... 30 Quarter 4...... 39 Go Math! Online Math Concept Readers ...... 40 OCSD Curriculum Alignment ...... 42 Math Resources Guide ...... 43 Literature Connection Chart ...... 44
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Mission Statement
Develop the highest quality math instruction to maximize student achievement through alignment of grade-level benchmarks to appropriate instructional practices, materials, resources, and pacing.
Suggestions for Implementing Curriculum Guides
The role of the teacher is to:
Teach students the Next Generation Standards as dictated by state law for their grade-level. Provide learning-rich classroom activities that teach the benchmarks in depth. Enhance the curriculum by using resources and instructional technology. Differentiate instruction by varying methods of instruction and frequently offering relevant lab activities. Regularly administer assessment to include higher-level questions, and performance task assessment.
In addition, teachers should:
Collaborate with other grade-level teachers to maximize school resources and teacher expertise. Consult with other grade-levels to define absolute skill goals for each grade-level. Document questions and suggestions for improvement of the curriculum Guide. Integrate science into math and reading curriculum. Consider applying for a grant to support project-based learning for their school. Visit the Okaloosa Math Central Website at: http://www.okaloosa.k12.fl.us/math
Days allotted to each benchmark are approximate and have been suggested based on the level of the complexity of the benchmark. To insure benchmarks are taught to mastery and completed by the conclusion of the school year, it is recommended that teache rs not veer significantly from the suggested pacing.
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Florida Department of Education ≠ Office of Math and Science Essential Websites
Next Generation Sunshine State Standards: http://www.fldoestem.org/uploads/1/docs/2007_FL_Mathematics_Standards_9_13_07.pdf
Searchable Next Generation Sunshine State Standards Database: http://www.floridastandards.org/index.aspx
Printable Downloads of Next Generation Sunshine State Standards with or without remarks: http://www.floridastandards.org/downloads.aspx
OCSD Curriculum and Pacing Guide ∞ Overview
This document provides a math curriculum and pacing guide. It is designed to help teachers to efficiently pace the delivery o f quality instruction for each nine-week period. Purpose: This guide was created by a team of grade-level teachers to correlate to the Next Generation Standards with the goal of providing teachers ready access to resources for teaching those new standards and a pace for accomplishing benchmark mastery. Description: The OCSD Math Curriculum Guide specifies the math content to be covered within each nine-week instructional period. Their guide identifies Next Generation Standards (NGS) Benchmarks. Furthermore, it allows teachers to input information specific to their students or sch ool needs.
Top Block – Big Idea and Essential Questions Identifies the Big Idea and the components of the Big Idea Lists the Essential Questions addressed in the section’s Benchmarks. Column One – Benchmark/Text Alignment Lists the specific Benchmark by number and states the Benchmark. Cites the Harcourt Textbook chapters that correlate to the Benchmark. Column Two – FCAT Info Serves as a placeholder for future FCAT information; to include content limits, assessment status, and crosswalk correlation. Column Three – Additional Resources/Activities Suggests instructional activities, including media (DVD/Video/CD), websites, and student involvement tasks. Column Four – Literacy Connection/Vocabulary/Reading Lists vocabulary terms, and books or stories connected to the Benchmark goals.
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Column Five – Open: Specific to Teacher/Grade/Subject/School Serves as a placeholder for teachers to add information that is specific to their school’s or student’s needs.
NOTE: Addendums to this curriculum guide, as well as additional information/forms will be posted at http://www.okaloosaschools.com/?q=employees/admin-curriculum-guides
Mathematics | Standards for Mathematical Practice
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to dev elop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a bel ief in diligence and one’s own efficacy). 1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and 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 so lution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the orig inal 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 informat ion 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 c oncrete 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 ref erents—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.
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3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in construct ing 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 othe rs, 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 th e arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the argume nts. 4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, a nd 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 pro blem 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 ab le 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. 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 o f these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically pro ficient 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 ident ify 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,
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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 d efinitions. 7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for 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 expre ssion 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 numb ers 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 slop e 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, mathematicall y proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of t heir intermediate results.
Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary , middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction. The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack unde rstanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices. In this respect, those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mat hematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in the school mathematics curriculum that most merit the time, resources, innovative energies, and focus necessary to qualitatively improve the curriculum, instruction, assessment, profess ional development, and student achievement in mathematics.
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Cognitive Complexity/Depth of Knowledge Rating for Mathematics
Florida’s revised mathematics standards emphasize teaching and learning the most important K-12 mathematics concepts in depth at each grade level. After adoption of the new math standards, the Florida Center for Research in Science, Technology, Engineering and Mathematics (FCR-STEM) at Florida State University convened a group of Florida math teachers, district math supervisors, and math education faculty to rate the cognitive demand of each benchmark. Meeting in teams for each body of knowledge, they reviewed and discussed each benchmark, then reached consensus on level of cognitive complexity using a classification system adapted from the “depth of knowledge” system developed by Dr. Norman Webb at the University of Wisconsin. Cognitive complexity refers to the cognitive demand of tasks associated with the benchmark. The depth of knowledge levels (We bb, 1999) reflect the relative complexity of thinking that a given benchmark demands of students — what it requires the student to recall, understand, analyze, and do. Florida’s depth of knowledge rating system focuses on expectations of students at three levels: Low Complexity This category relies heavily on the recall and recognition of previously learned concepts and principles. Items typically specify what the student is to do, which is often to carry out some procedure that can be performed mechanically. It is not left to the student to come up with a low complexity original method or solution. Skills required to respond to low complexity items include solving a one-step problem; computing a sum, difference, product, or quotient; evaluating a variable expression, given specific values for the variables; recognizing or constructing an equivalent representation; recalling or recognizing a fact, term, or property; retrieving information from a graph, table, or figure; identifying appropriate units or tools for common measurements; or performing a single-unit conversion.
Moderate Complexity Items in the moderate complexity category involve more flexible thinking and choice among alternatives than low complexity it ems. They require a response that goes beyond the habitual, is not specified, and ordinarily has more than a single step. The student is expected to decide what to do—using informal methods of reasoning and problem-solving strategies—and to bring together skill and knowledge from various domains. Skills required to respond to moderate complexity items include solving a problem requiring multiple operations; solving a problem involving spatial visualization and/or reasoning; selecting and/or using different representations, depending on situation and purpose; retrieving information from a graph, table, or figure and using it to solve a problem; determining a reasonable estimate; extending an algebraic or geometric pattern; providing a justification for steps in a solution process; comparing figures or statements;
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representing a situation mathematically in more than one way; or formulating a routine problem, given data and conditions.
High Complexity High complexity items make heavy demands on student thinking. Students must engage in more abstract reasoning, p lanning, analysis, judgment, and creative thought. The high-complexity item requires that the student think in an abstract and sophisticated way. Skills required to respond correctly to high complexity items include performing a procedure having multiple steps and multiple decision points; solving a non-routine problem (as determined by grade-level appropriateness); solving a problem in more than one way; describing how different representations can be used for different purposes; generalizing an algebraic or geometric pattern; explaining and justifying a solution to a problem; describing, comparing, and contrasting solution methods; providing a mathematical justification; analyzing similarities and differences between procedures and concepts; formulating an original problem, given a situation; formulating a mathematical model for a complex situation; or analyzing or producing a deductive argument.
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Grade 5 General Content Limits
The content limits described below are applicable to all items developed for Grade 5; however, the content limits defined in the individual benchmark specifications can supersede these general content limits.
Whole numbers • Items should not require the use of more than three operations. • Integers may range from -500 through 999,999,999. Fractions Addition Fractions should have denominators of 1–12, 75, or 1000, or denominators • Items should not exceed four addends. that are derived from basic multiplication facts through 12 X 12 may also be • Items should not exceed four 4-digit addends, three 5-digit addends, or used (e.g., 24 has the two factors 6 and 4; 72 has the factors 8 and 9). two 6-digit addends. Addition Subtraction • Items should not require the use of more than three addends. Subtrahends, minuends, and differences should not exceed six digits. • Items may require the use of up to two mixed numbers with unlike Multiplication denominators of 2 through 12 (excluding 11). Factors can have up to three digits by three digits or four digits by two • Items should not require the use of more than two unlike denominators. digits and could include a 0 in the hundreds, tens, and/or ones places. Subtraction Division • Items should not require the use of more than two unlike denominators. • Divisors should not exceed two digits. • Subtrahends and minuends may use up to two mixed numbers with • Dividends should not exceed four digits. unlike denominators of 2 through 12 (excluding 11). • Quotients may be expressed as mixed numbers or include remainders. Multiplication Decimals Not assessed at Grade 5. Place values could range from tenths through thousandths. Division Addition Not assessed at Grade 5. Items should not require the use of more than four 4-digit addends or two 5- Percent digit addends. • When finding equivalent fractions and decimals, items will be limited to Subtraction percents equivalent to halves, fourths, tenths, and hundredths. Subtrahends, minuends, and differences should not exceed five digits. • Items dealing with percents will not involve computation using the percent. Multiplication Measurement • Multiplication is limited to the context of money. Items will be limited to assessment of length (to the nearest 1/16 • Factors may have up to a four-digit number multiplied by a two-digit inch), weight/mass, elapsed time, temperature, perimeter, area, and number. volume/capacity. Division Gridded-Response Items • Division is limited to the context of money. • Divisors should not exceed two digits and must be whole numbers. • Answers may not exceed five digits. • Dividends should not exceed four digits. • See grid types for appropriate answer formats. • Quotients should not have remainders.
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Quarterly Benchmarks Each quarter shows when a concept or skill is introduced. It is understood that these skills and concepts will be ongoing throughout the year.
Quarter 1 - Big Idea 1 Quarter 2 - Big Idea 2 Benchmark Description Benchmark Description MA.5.A.1.1 MA.5.G.5.1 Describe the process of finding quotients involving multi-digit dividends Moderate Low using models, place value, properties and the relationship of division to Identify and plot ordered pairs on the first quadrant of the coordinate plane. 5 days 3 days multiplication. Chapters 1,2,3 Chapter 5 MA.5.A.1.2 MA.5.A.4.2 Moderate Estimate quotients or calculate them mentally depending on the context High Construct and describe a graph show ing continuous data, such as a graph of a 3 days and numbers involved 5 days quantity that changes over time. Chapters 1,2,3 Chapter 5 MA.5.A.6.5 MA.5.S.7.1 High Solve non-routine problems using various strategies including “solving a High Construct and analyze line graphs and double bar graphs. 5 days simpler problem” and “guess, check, and revise”. 5 days Ongoing Chapter 5 MA.5.A.1.3 MA.5.S.7.2 High Interpret solutions to division situations including those w ith remainders Moderate Differentiate betw een continuous and discrete data and determine w ays to 5 days depending on the context of the problem. 6 days represent those using graphs and diagrams. Chapter 2 Chapter 5 MA.5.A.1.4 MA.5.A.2.1 Divide multi-digit w hole numbers fluently, including solving real-w orld Represent addition and subtraction of decimals and fractions w ith like and unlike High Moderate problems, demonstrating understanding of the standard algorithm denominators using models, place value or properties. (See quarter 3 for unlike 5 days 5 days and checking the reasonableness of results. fractions) Chapters 2,3 Chapter 6 MA.5.A.4.1 MA.5.A.2.2 Moderate Use the properties of equality to solve numerical and real w orld Moderate Add and subtract fractions and decimals fluently and verify the reasonableness 5 days situations. 5 days of results, including in problem situations. . (See quarter 3 for unlike fractions) Chapter 4 Chapter 6 MA.5.A.6.2 MA.5.A.2.4 Moderate Use the order of operations to simplify expressions w hich include Moderate Determine the prime factorization of numbers. 5 days exponents and parentheses. 4 days Chapter 4 Chapter 6 MA.5.A.6.3 MA.5.A.6.1 Moderate Moderate Identify and relate prime and composite numbers, factors and multiples w ithin the Describe real-w orld situations using positive and negative numbers. 2 days 5 days context of fractions. Chapter 4 Chapters 6, 7 MA.5.A.6.4 Moderate Compare, order, and graph integers, including integers show n on a 5 days number line. Chapter 4
40 Days w ith 5 to accommodate assessments and remediation 36 Days w ith 7 to accommodate assessment and remediation
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Quarter 3 - Big Ideas 2 & 3 Quarter 4
Benchmark Description Benchmark Description
MA.5.A.2.1 Represent addition and subtraction of decimals and fractions w ith like Moderate and unlike denominators using models, place value or properties; Big Idea 1 Develop an understanding and fluency w ith division of w hole numbers. 5 days include fractions/percents. (See quarter 2 for like fractions) Chapter 7, 8 MA.5.A.2.2 Moderate Add and subtract fractions and decimals fluently and verify the Develop an understanding and fluency w ith addition and subtraction of fractions and Big Idea 2 5 days reasonableness of results, including in problem situations. decimals. Chapter 7, 8 MA.5.A.2.3 Moderate Make reasonable estimates of fraction and decimal sums and Describe three-dimensional shapes and analyze their properties, including volume Big Idea 3 5 days differences, and use techniques for rounding. and surface area. Chapters 7, 8 MA.5.G.5.2 Moderate Compare, contrast, and convert units of measure w ithin the same
5 days dimension (length, mass, or time) to solve problems. Tw enty Getting Ready for Grade 6 Lessons in back of book Chapter 9 MA.5.G.5.3 High Solve problems requiring attention to approximation, selection of Introduce multiplication and division of fractions, including mixed numbers. 5 days appropriate measuring tools, and precision of measurement. Chapters 9, 10 MA.5.G.3.1 Analyze and compare the properties of tw o-dimensional figures and High three-dimensional solids (polyhedra), including the number of edges, Introduce multiplication and division of decimals. 5 days faces, vertices, and types of faces. Chapter 10 MA.5.G.3.2 High Describe, define and determine surface area and volume of prisms by
5 days using appropriate units and selecting strategies and tools. Chapter 11 MA.5.G.5.4 High Derive and apply formulas for areas of parallelograms, triangles, and
5 days trapezoids from the area of a rectangle. Chapter 11
40 Days w ith 5 to accommodate assessments and remediation
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Grade-level Curriculum Guide
Quarter 1
Big Idea 1: Develop an Understanding of and fluency with division of whole numbers.
Essential Questions: How can you use base-ten blocks to model and understand how to divide whole numbers? How is multiplication used to solve a division problem? How can you use place value to solve a division problem? Standards for Mathematical Practice (see page 7): 7: Look for and make use of structure 8: Look for and express regularity in repeated reasoning FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.1.1 Moderate complexity http://www.floridastandards.org/Standards/PublicPreviewBen New Vocabulary: Multiplications and Describe the process of chmark583.aspx?kw= divisor division should be finding quotients See Item Specifications, Sample Item 1: dividend presented involving multi-digit page 115. quotient simultaneously to dividends using models, Sample Item 2: product show the relationship. place value, properties Content Limits: Items Sample Item 3: factor and the relationship of may include one-digit or distributive property division to multiplication. two-digit divisor and https://www-k6.thinkcentral.com inverse operations dividends up to four Review Vocabulary: Text: digits. Items will not www.brainpop.com divide Chapters 1,2, 3 include quotients with Division dividend remainders. divisor Base ten blocks, counters, ten-frame, MathBoard estimate factor multiply place value product quotient rectangular arrays area models
The Grapes of Math The King’s Commissioners
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Big Idea 1: Develop an Understanding of and fluency with division of whole numbers.
Essential Questions How can basic facts and the Distributive Property help you estimate a quotient or calculate the quotient mentally? How can you use compatible numbers to estimate quotients? Standards for Mathematical Practices (see page 7) 8. Look for and express regularity in repeated reasoning. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.1.2 Moderate complexity https://www-k6.thinkcentral.com New Vocabulary: Suggestion: Estimate quotients or compatible number Combine lessons 1.6, calculate them mentally Assessed with Aims – Solve It! 5th Grade 2.3, and 3.2. depending on the MA.5.A.1.4 - Three Digit Divisibility Dilemma* Review Vocabulary: context and numbers estimate involved. Counters, ten-frame partial quotients remainder Text: Chapters 1, 2, 3 The Tarantula in My Purse
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Supporting Idea: Number and Operations
Essential Question: How can you solve problems by using the strategy guess, check and revise? How can you solve a problem by solving a simpler problem? How can the strategy draw a diagram help you solve a division problem? Standards for Mathematical Practices (see page 5) 1:Make sense of problems and persevere in solving them. 2:Reason abstractly and quantitatively. 3:Construct viable arguments and critique the reasoning of others. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.6.5 High complexity http://www.floridastandards.org/Standards/PublicPreviewBe Review Vocabulary: Note: Discuss the Solve non-routine nchmark602.aspx?kw= basic facts term “round trip” with problems using various See DRAFT FCAT A Square of Numbers (problem to solve using addition, mental math students. strategies including Mathematics Test Item multi-digit number subtraction, multiplication, division) “solving a simpler Specifications, page 155 pattern problem” and “guess, Sample Item 1: check, and revise. ‘ Content Limits: Items Sample Item 2: Six Dinner Sid may include multistep Text: problems with no more https://www-k6.thinkcentral.com The King’s Chessboard In each chapter than three operations.
Students should be able Aims Solve it! 5th Spaghetti and Meatballs for All to choose their own strategies to solve www.brainpop.com problems. Word Problems
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Big Idea 1: Develop an Understanding of and fluency with division of whole numbers.
Essential Questions: What does the remainder represent within the context of a division problem? What three forms can show a remainder? (R5, ¼, .25) Standards of Mathematical Practices (See page 5): 3:Construct viable arguments and critique the reasoning of others. 4:Model with mathematics. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.1.3 High complexity https://www-k6.thinkcentral.com Review Vocabulary: Interpret solutions to remainder division situations Assessed with Manipulatives: including those with MA.5.A.1.4 . counters The Alaska Purchase remainders depending . base-ten blocks on the context of the . ten-frame Math Curse problem. Students will write a word problem for which they must find a A Remainder of One Text: remainder. Chapter 2 The Kings Chessboard Examples: . Five classes of 18 students each are going on the same fieldtrip. Each bus holds 35 people. How many buses will they need? . Mrs. Smith is ordering pizza for the class party. Each pizza is cut into 8 slices. There are 21 students in the class. How many pizzas are needed for each student to receive 2 slices each? . For the same class party, Mrs. Smith is supplying juice. Remember there are 21 students. How many liters/quarts of juice are needed for each student to receive 200ml/6oz?
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Big Idea 1: Develop an understanding of and fluency with division of whole numbers.
Essential Questions: How can you tell where to place the first digit of a quotient without dividing? How do you use the remainder to solve a division problem? How do you solve and check division problems? Standards for Mathematical Practices (see page 5): 1:Make sense of problems and persevere in solving them. 4:Model with mathematics FCAT Info Benchmark Additional Resources/Activities Lit. Connection Open: Specific to Content limits Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.1.4 High complexity Problem solving may include strategies using rounding and New Vocabulary: Divide multi-digit whole working backward. reasonableness numbers fluently, See Item Specifications, algorithm including solving real- page 118. http://www.floridastandards.org/Standards/PublicPreviewBe world problems, The Doorbell Rang demonstrating Content Limits: Divisors nchmark586.aspx?kw= understanding of the have up to two digits and Sample Item 1: A Grain of Rice standard algorithm dividends may have up Sample Item 2: and checking the to four digits. Sample Item 3: reasonableness of Decimals in the context results. of money may be used https://www-k6.thinkcentral.com only for the dividend or Text: quotient. Hands On Activities: Chapters 2 and 3 Items may require the . www.nlvm.com use of two operations to - Number and Operations solve the problem if at - Rectangle Division least one operation is . www.brainpop.com division. - Division . www.aaamath.com - Click on Division on the left side
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Supporting Idea: Algebra
Essential Questions: How can you use a pan balance to solve an equation with a variable? How can you write and solve addition and subtraction equations in real world situations? How can you solve equations with multiplication by using division or division equations by using multiplication? Standard for Mathematical Practices (see page 5): 1:Make sense of problems and persevere in solving them. 2:Reason abstractly and quantitatively. FCAT Info Benchmark Additional Resources/Activities Lit. Connection Open: Specific to Content limits Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.4.1 Moderate complexity The properties of equality include: Review Vocabulary: Use the properties of a) If you have a balanced situation, you can add, subtract, equality equality to solve See Item Specifications, multiply or divide by the same number on both sides variable numerical and real page 136. equation world situations. and the equality stays the same. expression Content Limit: Problems b) If you have one quantity equal to another, you can operation Text: may involve equalities substitute that quantity for the other in an equation. evaluate Chapter 4 that have no more than numerical expression two operations. http://www.floridastandards.org/Standards/PublicPreviewBe Properties of equality nchmark593.aspx?kw= New Vocabulary: may include substituting algebraic expression a quantity of equal value Pan Balance - Numbers for another quantity. Sample Item 1: Students are not expected to solve for two https://www-k6.thinkcentral.com variables. Coefficients of variables must be whole Online Resources: numbers. Items will not . www.nlvm.com include naming the Choose Algebra, then choose Algebra Balance Scales (It property of equality. is under grades 9-12.) Numbers used in . www.brainpop.com situations, and their Equations with Variables solutions, must be whole . www.aamath.com numbers less than or Choose equations on the left side. equal to 150. . www.pbskids.org/cyberchase Double the Donuts Poddle Weigh – In
REV 062012 Fifth Grade Math Page 18 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Supporting Idea: Number and Operations
Essential Questions: How would you describe the purpose of an exponent? Demonstrate using arrays. In what order must operations be evaluated to find the correct solution to a problem? Standards for Mathematical Practices (see page 7): 7: Look for and make use of structure. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.6.2 Moderate complexity http://www.floridastandards.org/Standards/PublicPreviewB New Vocabulary: Use the order of enchmark599.aspx?kw= base operations to simplify See Item Specifications, Balancing Algebraic Understanding exponent expressions which page 150. order of operations include exponents and Order of Operations Bingo square numbers parentheses. Content Limits: Items will Exploring Krypto (Order of Operations) brackets include no more than five Sample Item 1: braces Text: whole numbers Sample Item 2: Review Vocabulary: Chapter 4 (including exponents) parantheses within the expression. https://www-k6.thinkcentral.com Numbers raised to a power must be single- www.brainpop.com digit numbers. Exponents . Order of Operations may not be applied to the . Exponents entire quantity within parentheses. Exponents used on numbers must be 2 or 3, Division will not be shown as a fraction.
REV 062012 Fifth Grade Math Page 19 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Supporting Idea: Number and Operations
Essential Question: What real-world situations can be described using positive and negative numbers? Standards for Mathematical Practices (see page 5): 1: Make sense of problems and persevere in solving them. 2: Reason abstractly and quantitatively. 3: Construct viable arguments and critique the reasoning of others. 4: Model with mathematics. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.6.3 Moderate complexity http://www.floridastandards.org/Standards/PublicPreviewB New Vocabulary: Describe real-world enchmark600.aspx?kw= . integer situations using positive See Item Specifications, Sample Item 1: . positive and negative numbers. page 152. . negative
https://www-k6.thinkcentral.com Text: Content Limits: Items
Chapter 4 may include integers - www.brainpop.com 500 through 500. Absolute Value
Manipulatives: . Two color counters . Thermometers
Examples: . Owing Money . Measuring Elevations Above and Below Sea Level
REV 062012 Fifth Grade Math Page 20 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Supporting Idea: Number and Operations
Essential Questions: Using a number line, where would you locate positive or negative integers? How do you order a given set of integers? Explain with words, numbers or pictures. Standards for Mathematical Practices (See page 6): 4: Model with mathematics. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.6.4 Moderate complexity http://www.floridastandards.org/Standards/PublicPreviewB The Great Number Rumble: The Compare, order, and enchmark601.aspx?kw= Story of Math in Surprising graph integers, including See Item Specifications, Dynamic Paper (tool to print graph paper, number lines Places integers shown on a page 153 and grids, shapes, spinners, tessellations) number line. Content Limits: Items Number Line Bars Text: may include -500 through Sample Item 1: Chapter 4 500. Items may include the inequality symbols (≠, https://www-k6.thinkcentral.com ≤, ≥, <, >) Items will not include timelines (years). Students may explore negative and positive integers in science class through the following two science benchmarks: SC.5.P.8.1 and SC.5.P.9.1.
REV 062012 Fifth Grade Math Page 21 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Quarter 2
Supporting Idea: Geometry and Measurement
Essential Questions Which axis is named first and which axis is named second in an ordered pair? What is the process for identifying and plotting ordered pairs? How can you identify and plot points on a coordinate grid? Standards for Mathematical Practices (see page 6): 4: Model with mathematics. 6: Attend to precision. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.G.5.1 Low complexity http://www.floridastandards.org/Standards/PublicPreviewBe New Vocabulary: Identify and plot ordered nchmark595.aspx?kw= quadrant pairs on the first quadrant See Item Specifications, What Is Your Point? coordinate plane of the coordinate plane. page 139. axis Chameleon Graphing origin Text: Content Limits: Items Sample Item 1: ordered pair Chapter 5 may include the x axis following terms: https://www-k6.thinkcentral.com y axis coordinates, coordinate coordinate system plane, ordered pairs, www.brainpop.com horizontal midpoint, x axis, y axis, Coordinate Plane vertical but items will not assess intersection of lines the vocabulary of these Aims Activity: coordinates terms. Ship Shape x-coordinate y-cooridnate Aims: Finding Your Bearings Plot Your Position
The Fly on the Ceiling
REV 062012 Fifth Grade Math Page 22 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Supporting Idea: Algebra
Essential Questions: How would you identify a graph with a specific scenario? What would a graph look like that shows a quantity changing over time? Standards for Mathematical Practices (see page 5): 1: Make sense of problems and persevere in solving them. 5: Use appropriate tools strategically. 4: Model with mathematics. 6: Attend to precision. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.4.2 High complexity http://www.floridastandards.org/Standards/PublicPreviewBen New Vocabulary: Construct and describe a chmark594.aspx?kw= quantity graph showing In the 2007 Sunshine Grid Paper (small) line graph State Standards for continuous data continuous data, such as Free Graph Paper mathematics, discrete data a graph of a quantity that KidsZone: Create a Graph outlier continuous line graphs changes over time. line plot are introduced for the https://www-k6.thinkcentral.com Text: first time in fifth grade. Review Vocabulary: Chapter 5 www.brainpop.com bar graph Graphs frequency table pictograph Aims Critters: tally table “Mealworms on Stage” key data scale
Tiger Math
REV 062012 Fifth Grade Math Page 23 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Supporting Idea: Data Analysis
Essential Questions: How is a double-bar graph useful for displaying two sets of data? How would you construct a line graph? How can you use a line graph to display and analyze data? What is the difference between continuous data and discrete data? Which type of graph is appropriate for displaying discrete data, and which for displaying continuous data? How does using a Venn diagram help you solve problems? Standards for Mathematical Practices (see page 5): 1: Make sense of problems and persevere in solving them. 2: Reason abstractly and quantitatively. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.S.7.1 High complexity http://www.floridastandards.org/Standards/PublicPreviewB New Vocabulary: Construct and analyze enchmark603.aspx?kw= double-bar graph line graphs and double See DRAFT FCAT KidsZone: Create a Graph bar graphs. On the Day You Were Born Mathematics Test Item Sample Item 1: (MA.5.S.7.1)
Specifications, page 158. Sample Item 1: (MA.5.S.7.2)
Content Limits: Items may require students to predict Bar Graphs if the line graph . Birthdays represents data that is . Transportation to and from school . Pets increasing or decreasing. . Favorite subject at school
(Students are not Line Graphs expected to use the word trend.) Items should not . School enrollment require students to . Number of hurricanes over time determine the type of . Temperature over time graph to use. Items should https://www-k6.thinkcentral.com contain no more than 20 items of raw data. www.brainpop.com Graphs
MA.5.S.7.2 Moderate complexity Differentiate between continuous and discrete See DRAFT FCAT data and determine Mathematics Test Item
REV 062012 Fifth Grade Math Page 24 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math ways to represent those Specifications, page 162. using graphs and diagrams.
Text: Content Limits: Items may Chapter 5 include only the first quadrant in a graph. Items may include frequency tables, single bar graphs, double bar graphs, pictographs, line plots, line graphs, or Venn diagrams.
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Big Idea 2: Develop an understanding of and fluency with addition and subtraction of fractions and decimals.
Essential Questions: How can you use models to add and/or subtract fractions with like denominators? How can you rename fractions greater than 1 as mixed numbers and rename mixed numbers as fractions greater than 1? How can you rename a mixed number to subtract a larger fraction? Standards for Mathematical Practices (see page 5): 2: Reason abstractly and quantitatively. 4: Model with mathematics. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.2.1 Moderate complexity http://www.floridastandards.org/Standards/PublicPreviewBen New Vocabulary: Represent addition and chmark587.aspx?kw= tenth subtraction of decimals See DRAFT FCAT hundredth Fraction Track and fractions with like Mathematics Test Item thousandth and unlike denominators Specifications, page Fraction Strips in Black and White Associative Property of using models, place 121. Sample Item 1: Addition value or properties. Sample Item 2: Commutative Property of Content Limits: Items Sample Item 3: Addition Text: may include graphic Improper fraction
Chapter 6 representations of https://www-k6.thinkcentral.com models. Items may Review Vocabulary :
include decimals to the decimal / decimal point www.brainpop.com thousandths place or in fraction Adding and Subtracting Fractions the context of money. numerator
Items may assess the denominator Hundred Chart or Grid commutative or equivalent fractions Fraction Bars associative properties. mixed number Fraction Circles Denominators of whole number Cuisenaire Rods fractions in the stimulus common factor
must be less than or divisible When students add 1.45 + 3.24, they should be encouraged equal to 12. Items may greater than / less than to say "five hundredths and 4 hundredths are added to give 9 include mixed numbers equal to hundredths, etc." rather than "five plus 4 is 9, etc. or fractions. Items may compare / comparison
include fractions equivalent represented as parts of addition / add sets. Items will not sum include more than three subtraction addends. difference subtract like / unlike
REV 062012 Fifth Grade Math Page 26 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Big Idea 2: Develop an understanding of and fluency with addition and subtraction of fractions and decimals.
Essential Questions: How can I add and/or subtract fractions with like denominators? How can I add and/or subtract mixed numbers with like denominators? How do you verify the reasonableness of results when you add and subtract fractions? Standards for Mathematical Practices (see page 5): 1: Make sense of problems and persevere in solving them. 2: Reason abstractly and quantitatively. 4: Model with mathematics. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.2.2 Moderate complexity http://www.floridastandards.org/Standards/PublicPreviewBe Vocabulary: Add and subtract nchmark588.aspx?kw= Fractional sides fractions and decimals See Item Florida Food Round Up! Unit fraction fluently and verify the Specifications, page reasonableness of 126. Sample Item 1: results, including in Sample Item 2: problem situations. Content Limits: Items Sample Item 3: may include up to two Text: mixed numbers. Items https://www-k6.thinkcentral.com Chapter 6 may include up to three fractions, which may Students may use inverse operations to self-check contain unlike sum/difference. denominators. Denominators of fractions may be 1-12, 14, 15, 16, 18, 21, 24, 25, 32, 36, 35, 45, 75, or any multiple of 10 through 100. Items may include decimals through the thousandths place or money.
REV 062012 Fifth Grade Math Page 27 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Big Idea 2: Develop and understanding of and fluency with addition and subtraction of fractions and decimals
Essential Questions How can you explain when a number is prime or composite? How can you find all the prime factors of a number? Standards for Mathematical Practices (see page 7 ): 8: Look for and express regularity in repeated reasoning FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.2.4 Moderate complexity http://www.floridastandards.org/Standards/PublicPreviewBe New Vocabulary Determine the prime nchmark590.aspx?kw= prime factorization factorization of numbers. See Item Specifications, Prime Factorization - From Fingerprints to Factorprints prime number . page 129. composite number Text: Factor Trees factor tree Chapter 6 Content Limits: Sample Item 1: ladder diagram Expressions with a base of 2, 3, or 4, may have https://www-k6.thinkcentral.com Review Vocabulary exponents up to 5, 4, or factor 3 respectively. www.brainpop.com Expressions with a base Factoring of 5-10 may be raised Prime Numbers to the second power. Items will not include Aims Activity: factoring numbers Factor Trees greater than 100. Divisibility Rules
Least common multiple (LCM) and the greatest common factor (GCF)
REV 062012 Fifth Grade Math Page 28 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Supporting Idea: Number Operations
Essential Questions: How can you find the greatest common factor of two numbers? How can you find the least common multiples and least common denominators? Standards for Mathematical Practices (see page 7): 8: Look for and express regularity in repeated reasoning. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.6.1 Moderate complexity https://www-k6.thinkcentral.com New Vocabulary Identify and relate prime least common multiple and composite numbers, Aims Activity: greatest common factor factors and multiples Equivalent Fractions Cards within the context of Review Vocabulary: fractions. factors multiples Text: Chapters 6 and 7
REV 062012 Fifth Grade Math Page 29 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Quarter 3
Big Idea 2: Develop an understanding of and fluency with addition and subtraction of fractions and decimals.
Essential Questions: How can you use models to add and/or subtract fractions do not have the same denominator? How can properties help you add fractions with unlike denominators? How can you use the base ten-blocks to model addition and/or subtraction of decimals? How can place value help you add or subtract decimals? Standards for Mathematical Practices (see page 5): 1: Make sense of problems and persevere in solving them. 2: Reason abstractly and quantitatively. 4: Model with mathematics. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.2.1 Moderate complexity http://www.floridastandards.org/Standards/PublicPreviewBe New Vocabulary: *Note: Grade 5 Represent addition and nchmark587.aspx?kw= simplest form Content Limits specify: subtraction of decimals See Item Specifications, Fraction Track reduce When finding and fractions with like page 121. equivalent fractions and unlike denominators Fraction Strips in Black and White and decimals, items using models, place See previous Sample Item 1: will be limited to value or properties. MA.5.A.2.1 Sample Item 2: percents equivalent Sample Item 3: to halves, fourths, Text: tenths, and Chapters 7 and 8 https://www-k6.thinkcentral.com hundredths. *Items dealing with www.brainpop.com percent will not involve Adding and Subtracting Fractions computation using the percent. Hundred Chart or Grid Fraction Bars Fraction Circles Cuisenaire Rods
REV 062012 Fifth Grade Math Page 30 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Big Idea 2: Develop an understanding of and fluency with addition and subtraction of fractions and decimals.
Essential Questions: How can you use common denominators to add and subtract fractions? How can you add and subtract mixed numbers with unlike denominators? How can you rename to find the difference of two mixed numbers? How can you record addition and subtraction of decimals through thousandths? Standards for Mathematical Practices (see page 5-7): 1: Make sense of problems and persevere in solving them. 2: Reason abstractly and quantitatively. 4: Model with mathematics 8: Look for and express regularity in repeated reasoning.] FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs Suggestions: MA.5.A.2.2 Moderate complexity www.floridastandards.org/Standards/PublicPreviewBenchm Review decimal place Add and subtract ark588.aspx value fractions and decimals See Item Specifications, Florida Food Round Up! fluently and verify the page 126. Sample Item 1: Combine lessons 8.1 & reasonableness of 8.2 Sample Item 2: results, including in See previous problem situations. MA.5.A.2.2 Sample Item 3: Combine lessons 8.4 &8.5 Text: https://www-k6.thinkcentral.com Chapters 7 and 8
REV 062012 Fifth Grade Math Page 31 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Big Idea 2: Develop an understanding of and fluency with addition and subtraction of fractions and decimals.
Essential Question: How can you make reasonable estimates of fraction or decimal sums and differences? Standards for Mathematical Practices (see page ?): 1: Make sense of problems and persevere in solving them. 2: Reason abstractly and quantitatively. 8: Look for and express regularity in repeated reasoning. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.A.2.3 Moderate complexity http://www.floridastandards.org/Standards/PublicPreviewBe New Vocabulary: Make reasonable nchmark589.aspx?kw= Benchmark estimates of fraction and decimal sums and https://www-k6.thinkcentral.com Review Words: differences, and use sum techniques for rounding. Use a variety of strategies for estimating sums and difference differences of fractions and decimals including benchmark round Text: fractions and decimals, and rounding techniques. Chapters 7 and 8 Fraction Action
Supporting Idea: Geometry and Measurement
Essential Questions: How would you compare and contrast the units of measure within the same dimension? How would you convert units of measure within the same dimension to solve problems? (i.e. length, mass, or time) Standards for Mathematical Practices (see page 6): 4:Model with mathematics 6: Attend to precision
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FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.G.5.2 Moderate complexity http://www.floridastandards.org/Standards/PublicPrev New Vocabulary: Suggestion: Compare, contrast, and iewBenchmark596.aspx?kw= dimension Combine Lessons 9.1 convert units of measure See Item Specifications, page 141. Sample Item 1: convert &9.2 within the same dimension decimeter (length, mass, or time) to Content Limits: Items may include Sample Item 2: decameter Combine Lessons solve problems. linear measure, weight/mass, time, milliliter 9.3 & 9.4 or elapsed time (to the nearest https://www-k6.thinkcentral.com millimeter Text: minute). Items will not include time Chapter 9 zones. Items may include either Aims Activities: Review Words: analog or digital clocks. Items will Weight Watchers capacity not convert between different Big Banana Peel gallon measurement systems. Items may Metric Scavenger Hunt gram include up to two conversions Are You a Square length within the same system. Items may Now That’s Using Your Head ounce include multiplying or dividing by Flexible Feet pound multiples of ten. Items may require Wreck Tangles ton students to add or subtract weight measurements. Be sure to discuss with children why we must have customary units consistent unit of measure. metric units time relative size liquid volume mass kilometer meter centimeter kilogram liter inch / foot / yard / mile cup / pint / quart hour / minute/ second
How Big is a Foot
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Supporting Idea: Geometry and Measurement
Essential Questions: How can you use benchmarks to estimate measurements? Within the same dimension what units of measurement would be most precise and why? Which measuring tool(s) would be most appropriate for a specific measure? How can you determine whether you can use an estimate or need an actual measurement? Standards for Mathematical Practices (see page 5-6): 1: Make sense of problems and persevere in solving them. 5: Use appropriate tools strategically. 6: Attend to precision. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.G.5.3 High complexity http://www.floridastandards.org/Standards/PublicPreviewBenc New Vocabulary: *Note: Students need Solve problems hmark597.aspx?kw= approximate measure to distinguish requiring attention to See Item Specifications, How Long? How Wide? How Tall? How Deep? precise measure between fractional approximation, selection page 144. measurement measurements of of appropriate Let's Make Fudge different units. measuring tools, and Content Limits: Linear Makeshift Measurements Example: precision of measure in inches may Sample Item 1: Students will find measurement. be to the nearest 1/16 of which is most precise: an in Chapter Metric Aims Activities: ¾ foot Text: measures of mass may . Hands on the Giant 1 inch Chapters 9 and 10 be to the nearest . Mini Metric Olympics milligram. Linear metric . Student-Made measurement tools *The students tend to measures may be to the . Rulers Line Up look at the fraction nearest millimeter. . Are you a Square? and assume that is Capacity metric measure . Now That’s Using Your Head the most precise unit. may be to the nearest . Pleased as Punch milliliter. Elapsed time . Flexible Feet may be to the nearest minute. https://www-k6.thinkcentral.com
www.brainpop.com . Precision and Accuracy . Metric vs. Imperial
Students recognize that a smaller unit provides a more precise measure and that precision is determined by the measure being used (for example, if using inches, you can measure to fractional parts of inches).
REV 062012 Fifth Grade Math Page 34 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Big Idea 3: Describe three-dimensional shapes and analyze their properties, including volume and surface area.
Essential Questions: How would you compare and contrast a two dimensional figure with a three-dimensional solids (polyhedra)? How would you describe the attributes of a given plane figure? How would you describe the attributes of a given polyhedra? How would you compare and contrast two given plane figures? How would you compare and contrast two given polyhedra? Standards for Mathematical Practices (see page ?): 3: Construct viable arguments and critique the reasoning of others. 4: Model with mathematics. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.G.3.1 High complexity http://www.floridastandards.org/Standards/P New Vocabulary: Analyze and compare the ublicPreviewBenchmark591.aspx?kw edge properties of two- See Item Specifications, page 130. Dynamic Paper (tool to print graph paper, face dimensional figures and number lines and grids, shapes, Base three-dimensional solids Content Limits: Polyhedra used in items spinners, tessellations) vertex (polyhedra), including the must be prisms or pyramids with bases Three-Dimensional Play Dough solid number of edges, faces, having no more than eight sides, or A Plethora of Polyhedra volume vertices, and types of composite three-dimensional figures Sample Item 1: surface area faces. constructed from only cubes. Items plane figure dealing with composite three- https://www-k6.thinkcentral.com attributes Text: dimensional solids will not require polyhedron Chapter 10 students to determine the number of www.brainpop.com polygon edges, sides, or faces; however, they . Geometry net may be asked to identify different views . Polyhedrons lateral faces of the solid or the number of cubes . Polygons protractor used to build the solid. regular polygon corresponding sides corresponding angles Aims: category Hardhatting in a Geo-world subcategory . Constructing with Straws hierarchy . Geo Panes properties
Review Vocabulary: acute triangle congruent decagon equilateral triangle
REV 062012 Fifth Grade Math Page 35 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
hexagon isosceles triangle nets base obtuse triangle octagon parallelogram polygon quadrilateral rectangle rhombus right triangle scalene triangle trapezoid circle square pentagon half/quarter circle
The Greedy Triangle
Marvelous Math
REV 062012 Fifth Grade Math Page 36 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Big Idea 3: Describe three-dimensional shapes and analyze their properties, including volume and surface area.
Essential Questions Which net identifies a given prism? How would you describe and determine the surface area and volume of a given prism? Standards for Mathematical Practices (see page 6): 3: construct viable arguments and critique the reason of others. 5: Use appropriate tools strategically. FCAT Info Benchmark Additional Resources/Activities Lit. Connection Open: Specific to Content limits Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.G.3.2 High complexity http://www.floridastandards.org/Standards/PublicPreviewBe New Vocabulary: Describe, define and nchmark592.aspx?kw surface area determine surface area See Test Item Measuring Volume volume and volume of prisms by Specifications, page right rectangular prism using appropriate units 133. Block Party (Nets, Volume. Surface Area) unit and selecting strategies Finding Surface Area and Volume unit cube and tools. Content Limits: Sample Item 1: gap Dimensions of prisms overlap Text: must be whole numbers https://www-k6.thinkcentral.com cubic centimeter Chapter 11 no larger than 12, and cubic inch the surface area or www.brainpop.com cubic foot calculated volume must . Area of Polygons be less than 1000. . Volume of Prisms Teachers should develop Items will not include definitions by interpreting surface volume and surface Aims: area as "covering all surfaces" or areas or nonrectangular Hardhatting in a Geo-World "wrapping with no gaps or prisms. Items including Net-Sense overlaps" and volume as "filling". surface area must include a net or graphic of the three-dimensional shape.
REV 062012 Fifth Grade Math Page 37 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Supporting Idea: Geometry and Measurement
Essential Questions: How can the area of a rectangle help you find the area of a parallelogram, triangle, or trapezoid? How can a parallelogram help you find the area of an isosceles trapezoid? What formula can you use to find the area of a trapezoid? Standards for Mathematical Practices (see page 6-7): 6: Attend to precision. 7: Look for and make use of structure. FCAT Info Benchmark Lit. Connection Open: Specific to Content limits Additional Resources/Activities Text Alignment Vocabulary / Reading teacher, grade, subject Item specs
MA.5.G.5.4 High complexity http://www.floridastandards.org/Standards/PublicPreviewBe Review Vocabulary: Derive and apply nchmark666.aspx?kw= parallelogram formulas for areas of See Test Item Dynamic Paper (tool to print graph paper, number lines triangle parallelograms, triangles, Specifications, page trapezoid and grids, shapes, spinners, tessellations) and trapezoids from the 146. rectangle area of a rectangle. Sample Item 1: multiplication Content Limits: Items division Text: assessing areas of https://www-k6.thinkcentral.com dimensions Chapter 11 trapezoids must use composite only isosceles www.brainpop.com trapezoids. Areas must Area of Polygons New Vocabulary: include whole numbers. edge lengths Aims Activity: area of base Wrec-Tangles diagonal height Hands On Activity: square unit Pattern Blocks cubic unit
The formula for the area of a rectangle, "base x height", can be applied to develop formulas for the area of parallelograms, triangles, and trapezoids. Triangles can be constructed from diagonals of parallelograms to explore the formula "base x height divided by 2".
REV 062012 Fifth Grade Math Page 38 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
Quarter 4
Big Idea 1 Develop an understanding and fluency with division of whole numbers.
Big Idea 2 Develop and understanding and fluency with addition and subtraction of fractions and decimals.
Big Idea 3 Describe three-dimensional shapes and analyze their properties, including volume and surface area.
Twenty Getting Ready for Grade 6 Lessons in back of book
Introduce multiplication and division of fractions, including mixed numbers
Introduce multiplication and division of decimals
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Go Math! Online Math Concept Readers https://www-k6.thinkcentral.com
Level Title Math Content Description K I Know Big and Small Big and small K I Know Alike and Different Sort and classify K I Know Numbers Numbers 6-10 K I Know Shapes Geometry K Counting at the Market Numbers 11-30 K Shortest and Longest Where I Live Measurement K Numbers at the Lake Addition/Subtraction K Summertime Math Numbers 0 to 30
1 Counting in the City Counting up and counting down 0-30 1 My Counting Trip to the Zoo Number sense (0 to 20) 1 Math Club Relate addition and subtraction to 12 1 Miss B.'s Class Makes Tables and Graphs Data and graphs 1 Our Lemonade Stand Counting coins 1 Pattern Parade Patterns: AAB, ABC, ABB, AB 1 The Dog Show Length: Nonstandard measurement 1 The Class Party One-digit addition and subtraction
2 All the Time Time: reading analog and digital clocks 2 Doubles Fun on the Farm Addition facts and strategies: Doubles 2 Party Plans Use 2-digit addition and subtraction 2 Time To Go Shopping Use money 2 Building a Mini-Park Solid and plane figures 2 Time to Take a Trip! Compare and order greater numbers 2 Treasure Hunts Length: Nonstandard measurement 2 What Do You Like? Data and graphs
3 A Nose for News and Numbers Understand place value; Compare, order, and round numbers 3 Party Plans by the Numbers! Multiplication facts and strategies 3 The Garden Fence Division facts 3 Surprising Solids Solid figures
REV 062012 Fifth Grade Math Page 40 OKALOOSA SCHOOL DISTRICT Curriculum Guide for Math
3 Sports Camp Divide by 1-digit numbers 3 Pizza Parts! Understand fractions 3 Fun and Games Data and probability 3 A Trip to the Pond Metric measurement
4 Exercising for Beads Algebra: Use addition and subtraction 4 On the Menu: Bamboo, Figs, and Other Tasty Treats Multiplication and division facts 4 Putting the World on a Page Multiply by 1-digit numbers, multiply by 2-digit numbers 4 The Thirst Quencher Practice division 4 Diego’s Perfect Fit Collect, organize, and represent Data; Interpret and graph data 4 Elizabeth’s Groovy Green Racing Machine Add and subtract decimals and money 4 A New Angle on Trains and Train Stations Lines, rays, angles, and plane figures 4 Fighting Fire with Fire Perimeter
5 The World’s Tallest Buildings Place value, addition, and subtraction 5 Fundraising Fair Fraction concepts 5 Table Soccer, Anyone? Add and subtract mixed numbers 5 Halfpipe Add and subtract decimals 5 Forecast: Sunny Skies! Percent 5 City of the Future Geometric figures, plane and solid figures 5 Designing a Skatepark Perimeter and area 5 Park Visitors Analyze data
6 Model Rocket Math Fraction concepts, add and subtract fractions 6 Expedition: Antarctica Add and subtract integers 6 Take Your Math to Work Analyze data, graph data Addition equations, subtraction equations, multiplication and division 6 Music To Our Ears equations 6 The Truth About Pi Circles 6 Walk the Distance Proportions 6 What Are the Chances? Probability of simple events 6 Room Makeover: Serving the Community Surface area and volume
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OCSD Curriculum Alignment Example Benchmark Complexity Tasks Math
LOW MODERATE HIGH
1. Make models of arrays for numbers 1-10 to 1. Create factor trees. Use the factor trees to 1. Explain how you know that 1,250 is equivalent determine if it is a prime or a composite find prime factorization. Then find prime to 2x54. Use words, pictures and/or numbers to number factorization with exponents. Explain how defend your thinking. 2. Define/Identify prime #’s using 100’s chart you used the trees to find prime factorization 2. Relate knowledge between prime and 3. Express all possible arrays of given numbers and then prime factorization with exponents. composite #s to determine if a fraction is in 4. Identify place figures 2. Construct/display arrays (extending simplest form, students will 5. Using your tiles, create a model of square /connecting knowledge) justify/explain/support fraction cards in simplest mirrors that are 2,3,4,5,6 feet on each side. 3. Compare and contrast the properties of two form/not simplest form, students will be able to How many of each kind of tile will you need place figures (sides, angles, vertices) state their reason for the mirror that is vie feet on each side 4. Create a table to record the numbers of each 3. Explain the similarities and differences in 6. Subtracting whole dollars from whole dollars type of tile that is required for each size rectangles, parallelograms, and trapezoids and 7. Given a number, express the prime mirror. Graph all the information from your use this knowledge to formulate a definition for factorization through a factor tree or a CAKE table onto a single graph each shape. method 5. Subtract an amount which requires you to 4. Find a rule for the number of tiles (two-beveled 8. Choose 2 cities of extreme temperatures. make change or “swap out” money//choice, and one-beveled sides) needed to make any Get daily temperatures from computer (over more than one step. Justify your steps. square mirror (“n” sides). Explain and defend time) 6. Construct two different prime factorization your rules. Which type of tile do you expect the models, then compare and contrast Many Mirrors Company will sell the most? 7. Construct a double line graph using collected Explain your reasoning in complete sentences. data 5. When making change determine all the different combinations and explain the benefits of one combination over another. 6. Reflect on the two different solution methods for finding prime factorization; select your favorite method and explain why it is your favorite. 7. Construct a double bar graph and make future predictions based on the data shown.
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Math Resources Guide
Principals and Standards for School Mathematics and Curriculum Focal Points National Council of Teachers of Mathematics http://www.nctm.org/standards/default.aspx?id=58 Illuminations NCTM Educational Resources http://illuminations.nctm.org/ Math Their Way, Center for Innovation in Education, Inc http://www.center.edu/index.shtml AIMS Education Foundation On-line Store Books, Free Resources and $1-2 E-Activities http://wwws.aimsedu.org/aims_store/home.php Investigations: Finding and Using Mathematical Children’s Literature with Elementary Students (1999). Teaching Math with Favorite Picture Books (Grades 1-3). NY: Scholastic Professional Books. http://investigations.terc.edu/library/mathactivities/children_lit2.cfm Teaching Math with Favorite Picture Books (Grades 1-3) By: Hechtman, J., Ellermeyer, D. and Grove, S. F. ISBN: 978-0-87355-243-1 http://www.amazon.com/Teaching-Favorite-Picture-Books-Grades/dp/0590762508 Professional Math Series: Teaching Student Centered Mathematics Grades k-3, Grades 3-5, Grades 5-8 By John A. Van de Walle http://www.ablongman.com/vandewalleseries/ http://www.allynbaconmerrill.com/search/index.aspx Good Questions for Math Teaching (Grades 5-8) By Lainie Schuster and Nancy Canavan Anderson Marilyn Burns Books http://www.eaieducation.com/501832.html Everyday Counts Partner Games Great Source Education Group http://www.greatsource.com Math Benchmark Specifications http://fcat.fldoe.org/pdf/specifications/MathGrades3-5.pdf
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Literature Connection Chart Grade Title Author Concept or Skills Level Beep, Beep, Vroom, Vroom Stuart J. Murphy Patterning K Chrysanthemum Keven Henkes Addition, Subtraction K Those Calculating Crows Alice Wakefield Counting by ones, Graphing, One-to-one correspondence K Splash! Ann Jonas Addition 1 Ten Black Dots Donald Crews Number sense, Numeration 1 A Three Hat Day Laura Geringer Statistics and probability, Patterns and relationships 1 Best Bug Parade (The) Stuart J. Murphy Counting, Ordering by length, and other attributes 1 Billy’s Buttons William Accorsi Patterns and relationships 1 Caps for Sale Esphyr Slobodkina Patterns and relationships 1 Fat Frogs on a Skinny Log Sara Riches Addition, Subtraction 1 Lilly’s Purple Plastic Purse Kevin Henkes Money 1 Estimating and measuring with standard and nonstandard Inch by Inch Leo Lionni 1 units, Graphing Lots and Lots of Zebra Stripes Stephen R. Swinburne Patterning, Classification 1 Napping House (The) Audrey Wood Addition 1 One Monday Morning Uri Shulevitz Counting, Number sense 1 One More Bunny Rick Walton Addition 1 Penny Pot (The) Stuart J. Murphy Coin values, Problem solving 1 Counting, Basic addition, Basic Subtraction, Addition with more Sea Sums Joy N. Hulme 1 than two addends, Classification Seven Blind Mice Ed Young Ordinal Numbers 1 12 Ways to Get to 11 Eve Merriam Number and operations 2 Measurement, Money, Concept of whole number operations, Alexander Who Used to Be Rich Last Sunday Judith Viorst 2 Fractions, Decimals Amanda’s Bean’s Amazing Dream: A Cindy Neuschwander Beginning multiplication, Multiples, Skip counting 2 Mathematical Story Band-Aids Shel Silverstein Number sense, Numeration 2 Betcha! Stuart J. Murphy Estimate length, Measure length, Estimate quantity 2 Biggest, Strongest, Fastest Steve Jenkins Length 2 Blast Off!! Norma Cole Estimation, Statistics and Probability 2 Counting, Sorting, Classification, Estimation, Ordinal numbers, Button Box (The) Margarette S. Reid 2 Ordering by size
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Cucumber Soup Vickie Leigh Krudwig Estimation of quantity, weight, and length 2 Doorbell Rang (The) Pat Hutchins Beginning division, Multiples, Skip counting 2
Harriet’s Halloween Candy Nancy Carlson Classification of objects, Graphing 2 How Big is a Foot? Rolf Myller Measurement with standard and non-standard units 2 How Many Feet in the Bed Jonston Hamm Skip counting, Number patterns 2 Whole number computation, Whole number operations, Imogene’s Antlers David Small 2 Number sense, Numeration
Jim and the Beanstalk Raymond Briggs Measurement of length, Problem Solving, Estimation 2 Just a Little Bit Ann Tompert Counting, Basic addition, Missing Addends, Adding 1` 2 Look at Annette Marion Walter Geometry and spatial sense, Patterns and relationships 2 My Monster Mama Loves Me So Laura Leuck Doubles 2 Only One Marc Harshman Number sense 2 Measurement, Money, , Whole number computation, Fractions, Pigs Will Be Pigs Amy Axelrod 2 Decimals Pizza Pizzazz! Carol A. Losi Fractions 2 Basic addition, Measurement of length, Addend, Equation, Fact Ready, Set, Hop! Stuart J. Murphy 2 families So You Want to Be President Judith St. George Sorting, Graphing 2 Identifying geometric shapes, Identifying three-dimensional Village of Round and Square Houses (The) Ann Grifalconi 2 shapes, Describing vertices, faces, and edges Annabelle Swift, Kindergartner Amy Schwartz Money, Addition, Subtraction, Multiplication, Division 3 Boy Who Stopped Time (The) Anthony Taber Measuring Time 3 Dave’s Down-To-Earth Rock Shop Stuart J. Murphy Classification, Patterning, Venn diagrams 3 Spatial sense, Geometric shapes, Similar triangles, Area, Grandfather’s Tang’s Story Ann Tompert 3 Problem solving Draw Me a Star Eric Carle Estimation, Number sense 3 George Shrinks William Joyce Proportional reasoning, Fractions, Length 3 Important Book (The) Margret Wise Brown Patterns and relationships 3 Math Curse Jon Scieszka and Lane Smith Number sense, Numeration 3 Night Noises Mem Fox Addition, Mental computation 3 One Duck Stuck Phyllis Root Additon 3 One Hundred Hungry Ants Elinor J. Pinczes Multiplication 3 One Hungry Cat Joanne Rocklin Division, Number sense, Geometry 3
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Pepper’s Journal Stuart J. Murphy Time, Calendars, Time lines, Graphing 3 Purse (The) Kathy Caple Money, Number sense, Problem solving using tables and lists 3 Tony Johnston and Tomie Quilt Story (The) Geometry and spatial sense, Patterns and relationships 3 DePaola Counting, Basic addition, Beginning multiplication, Square Sea Squares Joy N. Hulme 3 numbers, Problem solving Counting, Skip counting, addition, Multiplication, Problem Six Dinner Sid Inga Moore 3 Solving $1..00 Word Riddle Book (The) Marilyn Burns Addition 4 A Reminder of One Elinor J. Pinczes Number and Operations 4 Amazing Book of Mammal Records (The) Samuel G. Woods Subtraction, Proportional Reasoning, Length, Weight 4 Among the Odds & Evens Priscilla Turner Properties of Numbers 4 Cut Down to Size at High Noon Scott Sundby Length, Proportional reasoning 4 How Much Is a Million? David M. Schwartz Number and Operations 4 One Tiny Turtle Nicola Davies Whole number computation 4 Qwen and Mzee Word Problems 4 Estimating and measuring with standard and nonstandard Jamie O’Rourke and the Big Potato Tomie dePaola 4 units, Graphing, Estimation of quantity, weight and length Estimation of quantity, Measurement of circumference and Lost at the White House Lisa Griest 4 weight, Problem solving Martha Blah Blah Susan Meddaugh Frequency Distribution 4 Math Appeal Greg Tang Whole Number Computation, Number Sense 4 Spaghetti and Meatballs for All! Marilyn Burns Area, Perimeter 4 Anno’s Mysterious Multiplying Jar Masaichiro Anno Multiplication 5 Fly on the Ceiling (The) Dr. Julie Glass Coordinate Graphing 5 Whole Number Computation, Algebraic Equivalence, Logical Math for Smarty Pants Marilyn Burns 5 Reasoning One Grain of Rice Demi Addition, Number sense, Exponential numbers 5 Roman Numbers 1 to MM Artur Geisert Number and Operations 5 Tiger Math: Learning to Graph from a Baby Tiger Ann Whitehead Nagda Statistics 5 Tikki Tikki Tempo Arlene Mosel Graphing, Averages 5 Wilma Unlimited Kathleen Krull Computation, Graphing, Pounds and ounces 5
If You Hopped Like a Frog David M. Schwartz Length, Proportional reasoning 5
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