OKALOOSA COUNTY SCHOOL DISTRICT MATH · PDF fileare taught to mastery and completed by the conclusion ... Serves as a placeholder for teachers to add ... They make conjectures and

OKALOOSA SCHOOL DISTRICT

Curriculum Guide for Math

REV 062012 Fifth Grade Math Page 1

OKALOOSA COUNTY SCHOOL DISTRICT

MATH CURRICULUM GUIDE

Fifth Grade

Office of Quality Assurance and Curriculum Support

Guyla Hendricks, Chief Officer




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




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.

http://www.okaloosa.k12.fl.us/math




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.

http://www.fldoestem.org/uploads/1/docs/2007_FL_Mathematics_Standards_9_13_07.pdf

http://www.floridastandards.org/index.aspx

http://www.floridastandards.org/downloads.aspx




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 repor t 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 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.

http://www.okaloosaschools.com/?q=employees/admin-curriculum-guides




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 arguments.

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 descr ibe 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 interpre t 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,




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 be ing 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.




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;




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.




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.

Addition • Items should not exceed four addends. • Items should not exceed four 4-digit addends, three 5-digit addends, or

two 6-digit addends.

Subtraction Subtrahends, minuends, and differences should not exceed six digits.

Multiplication Factors can have up to three digits by three digits or four digits by two digits and could include a 0 in the hundreds, tens, and/or ones places.

Division • Divisors should not exceed two digits. • Dividends should not exceed four digits. • Quotients may be expressed as mixed numbers or include remainders.

Decimals Place values could range from tenths through thousandths.

Addition Items should not require the use of more than four 4-digit addends or two 5-digit addends.

Subtraction Subtrahends, minuends, and differences should not exceed five digits.

Multiplication • Multiplication is limited to the context of money. • Factors may have up to a four-digit number multiplied by a two-digit

number.

Division • Division is limited to the context of money. • Divisors should not exceed two digits and must be whole numbers. • Dividends should not exceed four digits. • Quotients should not have remainders.

Fractions Fractions should have denominators of 1–12, 75, or 1000, or denominators that are derived from basic multiplication facts through 12 X 12 may also be used (e.g., 24 has the two factors 6 and 4; 72 has the factors 8 and 9).

Addition • Items should not require the use of more than three addends. • Items may require the use of up to two mixed numbers with unlike

denominators of 2 through 12 (excluding 11). • Items should not require the use of more than two unlike denominators.

Subtraction • Items should not require the use of more than two unlike denominators. • Subtrahends and minuends may use up to two mixed numbers with

unlike denominators of 2 through 12 (excluding 11).

Multiplication Not assessed at Grade 5.

Division Not assessed at Grade 5.

Percent • When finding equivalent fractions and decimals, items will be limited to

percents equivalent to halves, fourths, tenths, and hundredths. • Items dealing with percents will not involve computation using the percent.

Measurement Items will be limited to assessment of length (to the nearest 1/16 inch), weight/mass, elapsed time, temperature, perimeter, area, and volume/capacity.

Gridded-Response Items • Answers may not exceed five digits. • See grid types for appropriate answer formats.




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

Moderate

5 days Chapters 1,2,3

Describe the process of f inding quotients involving multi-digit dividends

using models, place value, properties and the relationship of division to

multiplication.

MA.5.G.5.1

Low

3 days Chapter 5

Identify and plot ordered pairs on the f irst quadrant of the coordinate plane.

MA.5.A.1.2

Moderate 3 days

Chapters 1,2,3

Estimate quotients or calculate them mentally depending on the context and numbers involved

MA.5.A.4.2

High 5 days

Chapter 5

Construct and describe a graph show ing continuous data, such as a graph of a quantity that changes over time.

MA.5.A.6.5

High

5 days

Ongoing

Solve non-routine problems using various strategies including “solving a

simpler problem” and “guess, check, and revise”.

MA.5.S.7.1

High

5 days

Chapter 5

Construct and analyze line graphs and double bar graphs.

MA.5.A.1.3

High

5 days

Chapter 2

Interpret solutions to division situations including those w ith remainders

depending on the context of the problem.

MA.5.S.7.2

Moderate

6 days

Chapter 5

Differentiate betw een continuous and discrete data and determine w ays to

represent those using graphs and diagrams.

MA.5.A.1.4

High 5 days

Chapters 2,3

Divide multi-digit w hole numbers f luently, including solving real-w orld

problems, demonstrating understanding of the standard algorithm

and checking the reasonableness of results.

MA.5.A.2.1

Moderate 5 days

Chapter 6

Represent addition and subtraction of decimals and fractions w ith like and unlike

denominators using models, place value or properties. (See quarter 3 for unlike

fractions)

MA.5.A.4.1 Moderate

5 days

Chapter 4

Use the properties of equality to solve numerical and real w orld

situations.

MA.5.A.2.2 Moderate

5 days

Chapter 6

Add and subtract fractions and decimals f luently and verify the reasonableness

of results, including in problem situations. . (See quarter 3 for unlike fractions)

MA.5.A.6.2

Moderate

5 days

Chapter 4

Use the order of operations to simplify expressions w hich include

exponents and parentheses.

MA.5.A.2.4

Moderate

4 days

Chapter 6

Determine the prime factorization of numbers.

MA.5.A.6.3

Moderate

2 days Chapter 4

Describe real-w orld situations using positive and negative numbers.

MA.5.A.6.1

Moderate

5 days Chapters 6, 7

Identify and relate prime and composite numbers, factors and multiples w ithin the

context of fractions.

MA.5.A.6.4 Moderate

5 days

Chapter 4

Compare, order, and graph integers, including integers show n on a

number line.

40 Days w ith 5 to accommodate assessments and remediation 36 Days w ith 7 to accommodate assessment and remediation




Quarter 3 - Big Ideas 2 & 3 Quarter 4

Benchmark Description Benchmark Description

MA.5.A.2.1 Moderate

5 days

Chapter 7, 8

Represent addition and subtraction of decimals and fractions w ith like

and unlike denominators using models, place value or properties;

include fractions/percents. (See quarter 2 for like fractions)

Big Idea 1 Develop an understanding and f luency w ith division of w hole numbers.

MA.5.A.2.2

Moderate 5 days

Chapter 7, 8

Add and subtract fractions and decimals f luently and verify the reasonableness of results, including in problem situations.

Big Idea 2 Develop an understanding and f luency w ith addition and subtraction of fractions and decimals.

MA.5.A.2.3

Moderate 5 days

Chapters 7, 8

Make reasonable estimates of fraction and decimal sums and differences, and use techniques for rounding.

Big Idea 3 Describe three-dimensional shapes and analyze their properties, including volume and surface area.

MA.5.G.5.2

Moderate 5 days

Chapter 9

Compare, contrast, and convert units of measure w ithin the same dimension (length, mass, or time) to solve problems.

Tw enty Getting Ready for Grade 6 Lessons in back of book

MA.5.G.5.3

High 5 days

Chapters 9, 10

Solve problems requiring attention to approximation, selection of appropriate measuring tools, and precision of measurement.

Introduce multiplication and division of fractions, including mixed numbers.

MA.5.G.3.1

High 5 days

Chapter 10

Analyze and compare the properties of tw o-dimensional f igures and

three-dimensional solids (polyhedra), including the number of edges,

faces, vertices, and types of faces.

Introduce multiplication and division of decimals.

MA.5.G.3.2

High 5 days

Chapter 11

Describe, define and determine surface area and volume of prisms by using appropriate units and selecting strategies and tools.

MA.5.G.5.4

High

5 days Chapter 11

Derive and apply formulas for areas of parallelograms, triangles, and

trapezoids from the area of a rectangle.

40 Days w ith 5 to accommodate assessments and remediation




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

Benchmark Text Alignment

FCAT Info

Content limits

Item specs

Additional Resources/Activities Lit. Connection

Vocabulary / Reading Open: Specific to

teacher, grade, subject

MA.5.A.1.1 Describe the process of finding quotients involving multi-digit dividends using models, place value, properties and the relationship of division to multiplication. Text: Chapters 1,2, 3

Moderate complexity See Item Specifications, page 115. Content Limits: Items may include one-digit or two-digit divisor and dividends up to four digits. Items will not include quotients with remainders.

http://www.floridastandards.org/Standards/PublicPreviewBen

chmark583.aspx?kw=

Sample Item 1:

Sample Item 2:

Sample Item 3:

https://www-k6.thinkcentral.com www.brainpop.com

Division Base ten blocks, counters, ten-frame, MathBoard

New Vocabulary: divisor dividend quotient product factor distributive property inverse operations Review Vocabulary: divide dividend divisor estimate factor multiply place value product quotient rectangular arrays area models

The Grapes of Math The King’s Commissioners

Multiplications and division should be presented simultaneously to show the relationship.

http://www.floridastandards.org/Standards/PublicPreviewBenchmark583.aspx?kw


http://www.floridastandards.org/Standards/PublicPreviewSampleTestItem42.aspx



https://www-k6.thinkcentral.com/

http://www.brainpop.com/




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.

Benchmark

Text Alignment

FCAT Info Content limits

Item specs


Vocabulary / Reading

Open: Specific to


MA.5.A.1.2 Estimate quotients or calculate them mentally depending on the context and numbers involved. Text: Chapters 1, 2, 3

Moderate complexity Assessed with MA.5.A.1.4

https://www-k6.thinkcentral.com Aims – Solve It! 5th Grade - Three Digit Divisibility Dilemma* Counters, ten-frame

New Vocabulary:

compatible number Review Vocabulary: estimate partial quotients remainder

The Tarantula in My Purse

Suggestion: Combine lessons 1.6, 2.3, and 3.2.





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.

Benchmark

Text Alignment


Item specs



Open: Specific to


MA.5.A.6.5 Solve non-routine problems using various strategies including “solving a simpler problem” and “guess, check, and revise. ‘ Text: In each chapter

High complexity See DRAFT FCAT Mathematics Test Item Specifications, page 155 Content Limits: Items may include multistep problems with no more than three operations. Students should be able to choose their own strategies to solve problems.

http://www.floridastandards.org/Standards/PublicPreviewBe

nchmark602.aspx?kw=

A Square of Numbers (problem to solve using addition,

subtraction, multiplication, division)

Sample Item 1:

Sample Item 2:

https://www-k6.thinkcentral.com Aims Solve it! 5th www.brainpop.com

Word Problems

Review Vocabulary: basic facts mental math multi-digit number pattern

Six Dinner Sid

The King’s Chessboard

Spaghetti and Meatballs for All

Note: Discuss the term “round trip” with students.



http://www.floridastandards.org/Resources/PublicPreviewResource8302.aspx









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.

Benchmark

Text Alignment


Item specs



Open: Specific to


MA.5.A.1.3 Interpret solutions to division situations including those with remainders depending on the context of the problem. Text: Chapter 2

High complexity Assessed with MA.5.A.1.4

https://www-k6.thinkcentral.com Manipulatives: counters base-ten blocks ten-frame Students will write a word problem for which they must find a remainder. 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?

Review Vocabulary:

remainder The Alaska Purchase Math Curse A Remainder of One The Kings Chessboard





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):


4:Model with mathematics

Benchmark

Text Alignment


Item specs

Additional Resources/Activities

Lit. Connection


Open: Specific to


MA.5.A.1.4 Divide multi-digit whole numbers fluently, including solving real-world problems, demonstrating understanding of the standard algorithm and checking the reasonableness of results. Text: Chapters 2 and 3

High complexity See Item Specifications, page 118. Content Limits: Divisors have up to two digits and dividends may have up to four digits. Decimals in the context of money may be used only for the dividend or quotient. Items may require the use of two operations to solve the problem if at least one operation is division.

Problem solving may include strategies using rounding and

working backward.


nchmark586.aspx?kw=

Sample Item 1:

Sample Item 2:

Sample Item 3:

https://www-k6.thinkcentral.com Hands On Activities: www.nlvm.com - Number and Operations - Rectangle Division www.brainpop.com - Division www.aaamath.com - Click on Division on the left side

New Vocabulary: reasonableness algorithm

The Doorbell Rang A Grain of Rice







http://www.nlvm.com/


http://www.aaamath.com/




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):


2:Reason abstractly and quantitatively.

Benchmark

Text Alignment


Item specs


Lit. Connection


Open: Specific to


MA.5.A.4.1 Use the properties of equality to solve numerical and real world situations. Text: Chapter 4

Moderate complexity See Item Specifications, page 136. Content Limit: Problems may involve equalities that have no more than two operations. Properties of equality may include substituting a quantity of equal value for another quantity. Students are not expected to solve for two variables. Coefficients of variables must be whole numbers. Items will not include naming the property of equality. Numbers used in situations, and their solutions, must be whole numbers less than or equal to 150.

The properties of equality include:

a) If you have a balanced situation, you can add, subtract,

multiply or divide by the same number on both sides

and the equality stays the same.

b) If you have one quantity equal to another, you can

substitute that quantity for the other in an equation.


nchmark593.aspx?kw=

Pan Balance - Numbers

Sample Item 1:

https://www-k6.thinkcentral.com Online Resources: www.nlvm.com

Choose Algebra, then choose Algebra Balance Scales (It is under grades 9-12.)

www.brainpop.com Equations with Variables

www.aamath.com Choose equations on the left side.

www.pbskids.org/cyberchase Double the Donuts Poddle Weigh – In

Review Vocabulary:

equality variable equation expression operation evaluate numerical expression

New Vocabulary: algebraic expression






http://www.nlvm.com/


http://www.aamath.com/

http://www.pbskids.org/cyberchase




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?


7: Look for and make use of structure.

Benchmark

Text Alignment


Item specs



Open: Specific to


MA.5.A.6.2 Use the order of operations to simplify expressions which include exponents and parentheses. Text: Chapter 4

Moderate complexity See Item Specifications, page 150. Content Limits: Items will include no more than five whole numbers (including exponents) within the expression. Numbers raised to a power must be single-digit numbers. Exponents may not be applied to the entire quantity within parentheses. Exponents used on numbers must be 2 or 3, Division will not be shown as a fraction.

http://www.floridastandards.org/Standards/PublicPreviewB

enchmark599.aspx?kw=

Balancing Algebraic Understanding

Order of Operations Bingo

Exploring Krypto (Order of Operations)

Sample Item 1:

Sample Item 2:

https://www-k6.thinkcentral.com www.brainpop.com Order of Operations Exponents

New Vocabulary:

base exponent order of operations square numbers brackets braces

Review Vocabulary: parantheses













Supporting Idea: Number and Operations Essential Question:

What real-world situations can be described using positive and negative numbers?


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.

Benchmark

Text Alignment

FCAT Info

Content limits

Item specs



Open: Specific to


MA.5.A.6.3 Describe real-world situations using positive and negative numbers. Text: Chapter 4

Moderate complexity See Item Specifications, page 152. Content Limits: Items may include integers -500 through 500.



Sample Item 1:


Absolute Value Manipulatives: Two color counters Thermometers

Examples: Owing Money Measuring Elevations Above and Below Sea Level

New Vocabulary: integer positive negative









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):


Benchmark

Text Alignment


Item specs



Open: Specific to


MA.5.A.6.4 Compare, order, and graph integers, including integers shown on a number line. Text: Chapter 4

Moderate complexity See Item Specifications, page 153 Content Limits: Items may include -500 through 500. Items may include the inequality symbols (≠, ≤, ≥, <, >) Items will not include timelines (years).



Dynamic Paper (tool to print graph paper, number lines

and grids, shapes, spinners, tessellations)

Number Line Bars

Sample Item 1:

https://www-k6.thinkcentral.com 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.

The Great Number Rumble: The Story of Math in Surprising Places








http://www.floridastandards.org/Standards/PublicPreviewBenchmark1726.aspx





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?



6: Attend to precision.

Benchmark

Text Alignment

FCAT Info

Content limits

Item specs



Open: Specific to


MA.5.G.5.1 Identify and plot ordered pairs on the first quadrant of the coordinate plane. Text: Chapter 5

Low complexity See Item Specifications, page 139. Content Limits: Items may include the following terms: coordinates, coordinate plane, ordered pairs, midpoint, x axis, y axis, but items will not assess the vocabulary of these terms.


nchmark595.aspx?kw=

What Is Your Point?

Chameleon Graphing

Sample Item 1:


Coordinate Plane Aims Activity:

Ship Shape

Aims: Finding Your Bearings

Plot Your Position

New Vocabulary:

quadrant coordinate plane axis origin ordered pair x axis y axis coordinate system horizontal vertical intersection of lines coordinates x-coordinate y-cooridnate

The Fly on the Ceiling











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?



5: Use appropriate tools strategically.



Benchmark

Text Alignment

FCAT Info

Content limits Item specs



Open: Specific to


MA.5.A.4.2

Construct and describe a

graph showing

continuous data, such as

a graph of a quantity that

changes over time.

Text: Chapter 5

High complexity In the 2007 Sunshine

State Standards for

mathematics,

continuous line graphs

are introduced for the

first time in fifth grade.


chmark594.aspx?kw=

Grid Paper (small)

Free Graph Paper

KidsZone: Create a Graph


Graphs Aims Critters:

“Mealworms on Stage”

New Vocabulary:

quantity line graph continuous data discrete data outlier line plot

Review Vocabulary:

bar graph frequency table pictograph tally table key data scale

Tiger 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?




Benchmark

Text Alignment

FCAT Info

Content limits

Item specs



Open: Specific to


MA.5.S.7.1 Construct and analyze line graphs and double bar graphs. MA.5.S.7.2 Differentiate between continuous and discrete data and determine

High complexity

See DRAFT FCAT Mathematics Test Item Specifications, page 158. Content Limits: Items may require students to predict if the line graph represents data that is increasing or decreasing. (Students are not expected to use the word trend.) Items should not require students to determine the type of graph to use. Items should contain no more than 20 items of raw data. Moderate complexity See DRAFT FCAT Mathematics Test Item



KidsZone: Create a Graph

Sample Item 1: (MA.5.S.7.1)

Sample Item 1: (MA.5.S.7.2)

Bar Graphs Birthdays Transportation to and from school Pets Favorite subject at school Line Graphs School enrollment Number of hurricanes over time Temperature over time https://www-k6.thinkcentral.com www.brainpop.com

Graphs

New Vocabulary:

double-bar graph On the Day You Were Born











ways to represent those using graphs and diagrams. Text: Chapter 5

Specifications, page 162. Content Limits: Items may 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.




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?




Benchmark

Text Alignment

FCAT Info




Open: Specific to


MA.5.A.2.1 Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value or properties. Text: Chapter 6

Moderate complexity See DRAFT FCAT Mathematics Test Item Specifications, page 121. Content Limits: Items may include graphic representations of models. Items may include decimals to the thousandths place or in the context of money. Items may assess the commutative or associative properties. Denominators of fractions in the stimulus must be less than or equal to 12. Items may include mixed numbers or fractions. Items may include fractions represented as parts of sets. Items will not include more than three addends.


chmark587.aspx?kw=

Fraction Track

Fraction Strips in Black and White

Sample Item 1:

Sample Item 2:

Sample Item 3:


Adding and Subtracting Fractions Hundred Chart or Grid Fraction Bars Fraction Circles Cuisenaire Rods When students add 1.45 + 3.24, they should be encouraged to say "five hundredths and 4 hundredths are added to give 9 hundredths, etc." rather than "five plus 4 is 9, etc.

New Vocabulary:

tenth hundredth thousandth Associative Property of

Addition Commutative Property of

Addition Improper fraction

Review Vocabulary : decimal / decimal point fraction numerator denominator equivalent fractions mixed number whole number common factor divisible greater than / less than equal to compare / comparison equivalent addition / add sum subtraction difference subtract like / unlike














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?





Benchmark

Text Alignment

FCAT Info

Content limits

Item specs



Open: Specific to


MA.5.A.2.2 Add and subtract fractions and decimals fluently and verify the reasonableness of results, including in problem situations. Text: Chapter 6

Moderate complexity See Item Specifications, page 126. Content Limits: Items may include up to two mixed numbers. Items may include up to three fractions, which may contain unlike 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.


nchmark588.aspx?kw=

Florida Food Round Up!

Sample Item 1:

Sample Item 2:

Sample Item 3:

https://www-k6.thinkcentral.com Students may use inverse operations to self-check sum/difference.

Vocabulary:

Fractional sides Unit fraction











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

Benchmark

Text Alignment

FCAT Info

Content limits

Item specs



Open: Specific to


MA.5.A.2.4 Determine the prime factorization of numbers. . Text: Chapter 6

Moderate complexity See Item Specifications, page 129. Content Limits: Expressions with a base of 2, 3, or 4, may have exponents up to 5, 4, or 3 respectively. Expressions with a base of 5-10 may be raised to the second power. Items will not include factoring numbers greater than 100.


nchmark590.aspx?kw=

Prime Factorization - From Fingerprints to Factorprints

Factor Trees

Sample Item 1:

https://www-k6.thinkcentral.com www.brainpop.com Factoring Prime Numbers Aims Activity:

Factor Trees Divisibility Rules Least common multiple (LCM) and the greatest common factor (GCF)

New Vocabulary

prime factorization prime number composite number factor tree ladder diagram

Review Vocabulary

factor











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?


8: Look for and express regularity in repeated reasoning.

Benchmark

Text Alignment


Item specs



Open: Specific to


MA.5.A.6.1 Identify and relate prime and composite numbers, factors and multiples within the context of fractions. Text: Chapters 6 and 7

Moderate complexity

https://www-k6.thinkcentral.com Aims Activity:

Equivalent Fractions Cards

New Vocabulary

least common multiple greatest common factor

Review Vocabulary:

factors multiples





Quarter 3


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?





Benchmark

Text Alignment

FCAT Info

Content limits

Item specs



Open: Specific to


MA.5.A.2.1 Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value or properties. Text: Chapters 7 and 8

Moderate complexity See Item Specifications, page 121. See previous MA.5.A.2.1


nchmark587.aspx?kw=

Fraction Track

Fraction Strips in Black and White

Sample Item 1:

Sample Item 2:

Sample Item 3:


Adding and Subtracting Fractions

Hundred Chart or Grid Fraction Bars Fraction Circles Cuisenaire Rods

New Vocabulary:

simplest form reduce

*Note: Grade 5 Content Limits specify: When finding equivalent fractions and decimals, items will be limited to percents equivalent to halves, fourths, tenths, and hundredths. *Items dealing with percent will not involve computation using the percent.














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):



4: Model with mathematics

8: Look for and express regularity in repeated reasoning.]

Benchmark

Text Alignment


Item specs



Open: Specific to


MA.5.A.2.2 Add and subtract fractions and decimals fluently and verify the reasonableness of results, including in problem situations. Text: Chapters 7 and 8

Moderate complexity See Item Specifications, page 126. See previous MA.5.A.2.2

www.floridastandards.org/Standards/PublicPreviewBenchmark588.aspx

Florida Food Round Up!

Sample Item 1:

Sample Item 2:

Sample Item 3:

https://www-k6.thinkcentral.com

Suggestions: Review decimal place value Combine lessons 8.1 & 8.2 Combine lessons 8.4 &8.5











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 ?):



8: Look for and express regularity in repeated reasoning.

Benchmark

Text Alignment

FCAT Info




Open: Specific to


MA.5.A.2.3 Make reasonable estimates of fraction and decimal sums and differences, and use techniques for rounding. Text: Chapters 7 and 8

Moderate complexity


nchmark589.aspx?kw=

https://www-k6.thinkcentral.com Use a variety of strategies for estimating sums and differences of fractions and decimals including benchmark fractions and decimals, and rounding techniques.

New Vocabulary:

Benchmark

Review Words: sum difference round

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)


4:Model with mathematics

6: Attend to precision







Benchmark

Text Alignment

FCAT Info




Open: Specific to


MA.5.G.5.2 Compare, contrast, and convert units of measure within the same dimension (length, mass, or time) to solve problems.

Text: Chapter 9

Moderate complexity See Item Specifications, page 141. Content Limits: Items may include linear measure, weight/mass, time, or elapsed time (to the nearest minute). Items will not include time zones. Items may include either analog or digital clocks. Items will not convert between different measurement systems. Items may include up to two conversions within the same system. Items may include multiplying or dividing by multiples of ten. Items may require students to add or subtract measurements.

http://www.floridastandards.org/Standards/PublicPrev

iewBenchmark596.aspx?kw=

Sample Item 1:

Sample Item 2:

https://www-k6.thinkcentral.com Aims Activities: Weight Watchers

Big Banana Peel Metric Scavenger Hunt Are You a Square Now That’s Using Your Head

Flexible Feet Wreck Tangles Be sure to discuss with children why we must have consistent unit of measure.

New Vocabulary:

dimension convert decimeter decameter milliliter millimeter

Review Words:

capacity gallon gram length ounce pound ton weight customary units 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

Suggestion: Combine Lessons 9.1 &9.2 Combine Lessons 9.3 & 9.4










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):




Benchmark

Text Alignment


Item specs



Open: Specific to


MA.5.G.5.3 Solve problems requiring attention to approximation, selection of appropriate measuring tools, and precision of measurement.

Text: Chapters 9 and 10

High complexity See Item Specifications, page 144. Content Limits: Linear measure in inches may be to the nearest 1/16 of an in Chapter Metric measures of mass may be to the nearest milligram. Linear metric measures may be to the nearest millimeter. Capacity metric measure may be to the nearest milliliter. Elapsed time may be to the nearest minute.

http://www.floridastandards.org/Standards/PublicPreviewBenc

hmark597.aspx?kw=

How Long? How Wide? How Tall? How Deep?

Let's Make Fudge

Makeshift Measurements

Sample Item 1:

Aims Activities: Hands on the Giant Mini Metric Olympics Student-Made measurement tools Rulers Line Up Are you a Square? Now That’s Using Your Head Pleased as Punch Flexible Feet 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).

New Vocabulary:

approximate measure precise measure measurement

*Note: Students need to distinguish between fractional measurements of different units. Example: Students will find which is most precise: ¾ foot 1 inch *The students tend to look at the fraction and assume that is the most precise unit.












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.


Benchmark

Text Alignment

FCAT Info

Content limits

Item specs



Open: Specific to


MA.5.G.3.1 Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces. Text: Chapter 10

High complexity See Item Specifications, page 130. Content Limits: Polyhedra used in items must be prisms or pyramids with bases having no more than eight sides, or composite three-dimensional figures constructed from only cubes. Items dealing with composite three-dimensional solids will not require students to determine the number of edges, sides, or faces; however, they may be asked to identify different views of the solid or the number of cubes used to build the solid.


Dynamic Paper (tool to print graph paper, number lines and grids, shapes, spinners, tessellations)

Three-Dimensional Play Dough

A Plethora of Polyhedra Sample Item 1: https://www-k6.thinkcentral.com www.brainpop.com Geometry Polyhedrons Polygons Aims: Hardhatting in a Geo-world Constructing with Straws Geo Panes

New Vocabulary:

edge face Base vertex solid volume surface area plane figure attributes polyhedron polygon net lateral faces protractor regular polygon corresponding sides corresponding angles category subcategory hierarchy properties

Review Vocabulary:

acute triangle congruent decagon equilateral triangle














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




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?


3: construct viable arguments and critique the reason of others.


Benchmark

Text Alignment

FCAT Info

Content limits

Item specs


Lit. Connection


Open: Specific to


MA.5.G.3.2 Describe, define and determine surface area and volume of prisms by using appropriate units and selecting strategies and tools. Text: Chapter 11

High complexity See Test Item Specifications, page 133. Content Limits: Dimensions of prisms must be whole numbers no larger than 12, and the surface area or calculated volume must be less than 1000. Items will not include volume and surface areas or nonrectangular prisms. Items including surface area must include a net or graphic of the three-dimensional shape.


nchmark592.aspx?kw

Measuring Volume

Block Party (Nets, Volume. Surface Area)

Finding Surface Area and Volume

Sample Item 1:

https://www-k6.thinkcentral.com www.brainpop.com Area of Polygons Volume of Prisms Aims: Hardhatting in a Geo-World

Net-Sense

New Vocabulary:

surface area volume right rectangular prism unit unit cube gap overlap cubic centimeter cubic inch cubic foot

Teachers should develop definitions by interpreting surface area as "covering all surfaces" or "wrapping with no gaps or overlaps" and volume as "filling".













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):


7: Look for and make use of structure.

Benchmark

Text Alignment

FCAT Info

Content limits

Item specs



Open: Specific to


MA.5.G.5.4 Derive and apply formulas for areas of parallelograms, triangles, and trapezoids from the area of a rectangle. Text: Chapter 11

High complexity See Test Item Specifications, page 146. Content Limits: Items assessing areas of trapezoids must use only isosceles trapezoids. Areas must include whole numbers.


nchmark666.aspx?kw=

Dynamic Paper (tool to print graph paper, number lines

and grids, shapes, spinners, tessellations)

Sample Item 1:


Area of Polygons Aims Activity:

Wrec-Tangles Hands On Activity:

Pattern Blocks

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".

Review Vocabulary:

parallelogram triangle trapezoid rectangle multiplication division dimensions composite

New Vocabulary:

edge lengths area of base diagonal height square unit cubic unit











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




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





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

6 Music To Our Ears Addition equations, subtraction equations, multiplication and division

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




OCSD Curriculum Alignment Example Benchmark Complexity Tasks

Math

LOW MODERATE HIGH

1. Make models of arrays for numbers 1-10 to

determine if it is a prime or a composite number

2. Define/Identify prime #’s using 100’s chart 3. Express all possible arrays of given numbers 4. Identify place figures 5. Using your tiles, create a model of square

mirrors that are 2,3,4,5,6 feet on each side. How many of each kind of tile will you need for the mirror that is vie feet on each side

6. Subtracting whole dollars from whole dollars 7. Given a number, express the prime

factorization through a factor tree or a CAKE method

8. Choose 2 cities of extreme temperatures. Get daily temperatures from computer (over time)

1. Create factor trees. Use the factor trees to

find prime factorization. Then find prime factorization with exponents. Explain how you used the trees to find prime factorization and then prime factorization with exponents.

2. Construct/display arrays (extending /connecting knowledge)

3. Compare and contrast the properties of two place figures (sides, angles, vertices)

4. Create a table to record the numbers of each type of tile that is required for each size mirror. Graph all the information from your table onto a single graph

5. Subtract an amount which requires you to make change or “swap out” money//choice, more than one step. Justify your steps.

6. Construct two different prime factorization models, then compare and contrast

7. Construct a double line graph using collected data

1. Explain how you know that 1,250 is equivalent

to 2x54.

Use words, pictures and/or numbers to defend your thinking.

2. Relate knowledge between prime and composite #s to determine if a fraction is in simplest form, students will justify/explain/support fraction cards in simplest form/not simplest form, students will be able to state their reason

3. Explain the similarities and differences in rectangles, parallelograms, and trapezoids and use this knowledge to formulate a definition for each shape.

4. Find a rule for the number of tiles (two-beveled and one-beveled sides) needed to make any square mirror (“n” sides). Explain and defend your rules. Which type of tile do you expect the Many Mirrors Company will sell the most? Explain your reasoning in complete sentences.

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.




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

http://www.nctm.org/standards/default.aspx?id=58

http://www.center.edu/index.shtml

http://wwws.aimsedu.org/aims_store/home.php

http://investigations.terc.edu/library/mathactivities/children_lit2.cfm

http://www.amazon.com/Teaching-Favorite-Picture-Books-Grades/dp/0590762508

http://www.ablongman.com/vandewalleseries/

http://www.allynbaconmerrill.com/search/index.aspx

http://www.eaieducation.com/501832.html

http://www.greatsource.com/

http://fcat.fldoe.org/pdf/specifications/MathGrades3-5.pdf




Literature Connection Chart

Title Author Concept or Skills Grade

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

Inch by Inch Leo Lionni Estimating and measuring with standard and nonstandard

units, Graphing 1

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

Sea Sums Joy N. Hulme Counting, Basic addition, Basic Subtraction, Addition with more

than two addends, Classification 1

Seven Blind Mice Ed Young Ordinal Numbers 1

12 Ways to Get to 11 Eve Merriam Number and operations 2

Alexander Who Used to Be Rich Last Sunday Judith Viorst Measurement, Money, Concept of whole number operations,

Fractions, Decimals 2

Amanda’s Bean’s Amazing Dream: A

Mathematical Story Cindy Neuschwander Beginning multiplication, Multiples, Skip counting 2

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

Button Box (The) Margarette S. Reid Counting, Sorting, Classification, Estimation, Ordinal numbers,

Ordering by size 2




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

Imogene’s Antlers David Small Whole number computation, Whole number operations,

Number sense, Numeration 2

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

Pigs Will Be Pigs Amy Axelrod Measurement, Money, , Whole number computation, Fractions,

Decimals 2

Pizza Pizzazz! Carol A. Losi Fractions 2

Ready, Set, Hop! Stuart J. Murphy Basic addition, Measurement of length, Addend, Equation, Fact

families 2

So You Want to Be President Judith St. George Sorting, Graphing 2

Village of Round and Square Houses (The) Ann Grifalconi Identifying geometric shapes, Identifying three-dimensional

shapes, Describing vertices, faces, and edges 2

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

Grandfather’s Tang’s Story Ann Tompert Spatial sense, Geometric shapes, Similar triangles, Area,

Problem solving 3

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




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

Quilt Story (The) Tony Johnston and Tomie

DePaola Geometry and spatial sense, Patterns and relationships 3

Sea Squares Joy N. Hulme Counting, Basic addition, Beginning multiplication, Square

numbers, Problem solving 3

Six Dinner Sid Inga Moore Counting, Skip counting, addition, Multiplication, Problem

Solving 3

$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

Jamie O’Rourke and the Big Potato Tomie dePaola Estimating and measuring with standard and nonstandard

units, Graphing, Estimation of quantity, weight and length 4

Lost at the White House Lisa Griest Estimation of quantity, Measurement of circumference and

weight, Problem solving 4

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

Math for Smarty Pants Marilyn Burns Whole Number Computation, Algebraic Equivalence, Logical

Reasoning 5

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

Documents

OKALOOSA COUNTY SCHOOL DISTRICT MATH · PDF fileare taught to mastery and completed by the conclusion ... Serves as a placeholder for teachers to add ... They make conjectures and