2013 - 2014 fifth grade...

1 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department June 2013

Fifth Grade

MATHEMATICS Curriculum Map

2013 - 2014

Volusia County Schools

Common Core State Standards Next Generation Sunshine State Standards

A Blended Approach to Teaching and Learning


Common Core State Standards

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them. (MACC.K12.MP.1) Solving a mathematical problem involves making sense of what is known and applying a thoughtful and logical process which

sometimes requires perseverance, flexibility, and a bit of ingenuity.

2. Reason abstractly and quantitatively. (MACC.K12.MP.2) The concrete and the abstract can complement each other in the development of mathematical understanding: representing a

concrete situation with symbols can make the solution process more efficient, while reverting to a concrete context can help make

sense of abstract symbols.

3. Construct viable arguments and critique the reasoning of others. (MACC.K12.MP.3) A well-crafted argument/critique requires a thoughtful and logical progression of mathematically sound statements and supporting

evidence.

4. Model with mathematics. (MACC.K12.MP.4) Many everyday problems can be solved by modeling the situation with mathematics.

5. Use appropriate tools strategically. (MACC.K12.MP.5) Strategic choice and use of tools can increase reliability and precision of results, enhance arguments, and deepen mathematical

understanding.

6. Attend to precision. (MACC.K12.MP.6) Attending to precise detail increases reliability of mathematical results and minimizes miscommunication of mathematical

explanations.

7. Look for and make use of structure. (MACC.K12.MP.7) Recognizing a structure or pattern can be the key to solving a problem or making sense of a mathematical idea.

8. Look for and express regularity in repeated reasoning. (MACC.K12.MP.8) Recognizing repetition or regularity in the course of solving a problem (or series of similar problems) can lead to results more

quickly and efficiently.


Common Core State Standards

Mathematics Grade 5 In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.

(1) Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)

(2) Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with multi-digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately.

(3) Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.


Domain: Operations and Algebraic Thinking

• Write and interpret numerical expressions.

• Analyze patterns and relationships.

Domain: Number and Operations in Base Ten

• Understand the place value system.

• Perform operations with multi-digit whole numbers and with decimals to hundredths.

Domain: Number and Operations—Fractions

• Use equivalent fractions as a strategy to add and subtract fractions.

• Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Domain: Measurement and Data

• Convert like measurement units within a given measurement system.

• Represent and interpret data.

• Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Domain: Geometry

• Graph points on the coordinate plane to solve real-world and mathematical problems.

• Classify two-dimensional figures into categories based on their properties.

Grade 5 Overview


Next Generation Sunshine State Standards

Following a six-year cycle review and revision of K-12 Mathematics content standards, the Next Generation Sunshine State Standards (NGSSS) were adopted by the Florida State Board of Education in September 2007. The revision in the benchmark language offers greater specificity to indicate clearly what teachers should teach and student should be able to do. Support of these standards can be found at www.floridastandards.org.

Mathematics Grade 5 Program Overview

Big Idea 1: Develop an understanding of and fluency with division of whole numbers.

Big Idea 2: Develop an understanding of 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.

Supporting Idea: Algebra

Supporting Idea: Geometry and Measurement

Supporting Idea: Number and Operations

Supporting Idea: Data Analysis


ENGAGEMENT EXPLORATION EXPLANATION ELABORATION EVALUATION

The engagement phase of the model is intended to capture students’ interest and focus their thinking on the concept, process, or skill

that is to be learned.

During this engagement phase, the teacher is on center stage.

The exploration phase of the model is intended to provide students with a common set of experiences from

which to make sense of the concept, process or skill that is to be learned.

During the exploration phase, the students come to center stage.

The explanation phase of the model is intended to grow students’

understanding of the concept, process, or skill and its associated

academic language.

During the explanation phase, the teacher and students

share center stage.

The elaboration phase of the model is intended to construct a deeper understanding of the concept, process, or skill through the exploration of related ideas.

During the elaboration phase, the teacher and students

share center stage.

The evaluation phase of the model is intended to be used during all phases

of the learning cycle driving the decision-making process and

informing next steps.

During the evaluation phase, the teacher and students

share center stage. What does the teacher do?

• create interest/curiosity • raise questions • elicit responses that uncover

student thinking/prior knowledge (preview/process)

• remind students of previously taught concepts that will play a role in new learning

• familiarize students with the unit

What does the teacher do?

• provide necessary materials/tools • pose a hands-on/minds-on

problem for students to explore • provide time for students to

“puzzle” through the problem • encourage students to work

together • observe students while working • ask probing questions to redirect

student thinking as needed


• ask for justification/clarification of newly acquired understanding

• use a variety of instructional strategies

• use common student experiences to: o develop academic language o explain the concept

• use a variety of instructional strategies to grow understanding

• use a variety of assessment strategies to gage understanding


• provide new information that extends what has been learned

• provide related ideas to explore • pose opportunities (examples and

non-examples) to apply the concept in unique situations

• remind students of alternate ways to solve problems

• encourage students to persevere in solving problems


• observe students during all phases of the learning cycle

• assess students’ knowledge and skills

• look for evidence that students are challenging their own thinking

• present opportunities for students to assess their learning

• ask open-ended questions: o What do you think? o What evidence do you have? o How would you explain it?

What does the student do?

• show interest in the topic • reflect and respond to questions • ask self-reflection questions:

o What do I already know? o What do I want to know? o How will I know I have learned

the concept, process, or skill? • make connections to past learning

experiences


• manipulate materials/tools to explore a problem

• work with peers to make sense of the problem

• articulate understanding of the problem to peers

• discuss procedures for finding a solution to the problem

• listen to the viewpoint of others


• record procedures taken towards the solution to the problem

• explain the solution to a problem • communicate understanding of a

concept orally and in writing • critique the solution of others • comprehend academic language

and explanations of the concept provided by the teacher

• assess own understanding through the practice of self-reflection


• generate interest in new learning • explore related concepts • apply thinking from previous

learning and experiences • interact with peers to broaden

one’s thinking • explain using information and

experiences accumulated so far


• participate actively in all phases of the learning cycle

• demonstrate an understanding of the concept

• solve problems • evaluate own progress • answer open-ended questions

with precision • ask questions

Evaluation of Engagement The role of evaluation during the

engagement phase is to gain access to students’ thinking during the

pre-assessment event/activity.

Conceptions and misconceptions currently held by students are uncovered during this phase.

These outcomes determine the concept, process, or skill to be

explored in the next phase of the learning cycle.

Evaluation of Exploration The role of evaluation during the exploration phase is to gather an

understanding of how students are progressing towards making sense of

a problem and finding a solution.

Strategies and procedures used by students during this phase are

highlighted during explicit instruction in the next phase.

The concept, process, or skill is formally explained in the next phase

of the learning cycle.

Evaluation of Explanation The role of evaluation during the

explanation phase is to determine the students’ degree of fluency (accuracy

and efficiency) when solving problems.

Conceptual understanding, skill refinement, and vocabulary acquisition

during this phase are enhanced through new explorations.

The concept, process, or skill is elaborated in the next phase

of the learning cycle.

Evaluation of Elaboration The role of evaluation during the

elaboration phase is to determine the degree of learning that occurs

following a differentiated approach to meeting the needs of all learners.

Application of new knowledge in unique problem solving situations

during this phase constructs a deeper and broader understanding.

The concept, process, or skill has been and will be evaluated as part of all phases of the learning cycle.

5E Learning Cycle: An Instructional Model


Weeks of Instruction

Grade 5 District Interim Assessments (DIA)

Testing Window

Weeks 1-5 05 Math DIA Multiplication & Division September 16 – 20 Weeks 6-8 05 Math DIA Algebra October 7 – 11 Weeks 9-11 05 Math DIA Data October 20 – November 1 Weeks 12-13 05 Math DIA Integers November 12 – 15 Weeks 14-18 05 Math DIA Decimals December 16 – 19 Weeks 19-23 05 Math DIA Fractions February 3 – 7 Weeks 24-27 05 Math DIA Measurement March 3 – 7 Weeks 28-31 05 Math DIA Geometry April 7 – 11 Week 32 FCAT 2.0 Mathematics April 14 – 17 Weeks 32-36 CCSS Decimals & Fractions Extension no assessment Week 37 CCSS Measurement & Data Extension no assessment Weeks 38-39 CCSS Algebra Extension no assessment

Formative Assessment Strategies are included in the Grade 5 Mathematics Curriculum Map on pages 53-62.

Instructional Scope and Sequence and

District Interim Assessment (DIA) Schedule Grade 5


COMPONENTS OF THE CURRICULUM MAP

The Mathematics Curriculum Map has been developed by teachers for ease of use during instructional planning. Definitions for the framework of the curriculum map components are defined below.

CCSS DOMAIN: the broadest organizational structure used to group content and concepts within the curriculum map

Unit: an overarching organizational sub-structure used to narrow the focus of the content and concepts within the map; DIA has been developed for each unit with the same name

Pacing: the recommended time frames within the year determined by teacher committee for initial delivery of instruction in preparation for the FCAT 2.0 Mathematics Test

Topics: a grouping of standards and skills that form a subset of mathematical concepts covered in each unit of study Learning Targets/Skills: the content knowledge, processes, and enabling skills that will ensure successful mastery of the standards

Notes/Examples: additional information that serves to further clarify the expectations of the learning targets/skills to assist with instructional decision-making processes

Standards: the Common Core State Standards required in the course descriptions posted on CPALMS by FLDOE

Vocabulary: the content vocabulary and other key terms and phrases that support mastery of the learning targets and skills; for teacher and student use alike

Standards for Mathematical Practice: processes and proficiencies that teachers should seek to purposefully develop in students

Resource Alignment: a listing of available, high quality and appropriate materials, strategies, lessons, textbooks, videos and other media sources that are aligned with the learning targets and skills; recommendations are not intended to limit lesson development

Assessment: a listing of summative and formative assessment opportunities available for use during each unit of instruction

Common Addition and Subtraction/Multiplication and Division Situations (Table 1 and Table 2): a comprehensive display of possible addition, subtraction, multiplication and division problem solving situations that involve an unknown number in varied locations within an equation

Formative Assessment Strategies: a collection of assessment strategies/techniques to help teachers discover student thinking, determine student understanding, and design learning opportunities that will deepen student mastery of standards

Intervention/Remediation Guide: a description of resources available within the adopted mathematics textbook resource (enVisionMATH) that provides differentiated support for struggling learners—ESE, ELL, and General Education students alike


CCSS DOMAIN: Unit:

NUMBER AND OPERATIONS IN BASE TEN Multiplication & Division

PACING: Weeks 1 – 5 August 19 – September 20

Topics Learning Targets/Skills Standards Vocabulary

Multiplication

CCSS: Fluently multiply multi-digit whole numbers using the standard algorithm. MACC.5.NBT.2.5 array compatible numbers digit divide dividend divisor equal sharing estimate expanded notation inverse operation multiple multiply partial quotients place holder zero place value product quotient reasonable remainder repeated subtraction standard algorithm

Students will:

• recall basic multiplication facts through 12 × 12. • use the standard algorithm for multi-digit whole number multiplication with ease (3-digit

by 3-digit and 4-digit by 2-digit). • explain strategies (including the standard algorithm) used to multiply multi-digit whole

numbers.

Example:

Student 1: 125 × 12

I broke 12 up into 10 and 2. 125 × 10 = 1,250 125 × 2 = 250 1,250 + 250 = 1,500

Student 2: 125 × 12

I broke up 225 into 200 and 25. 100 × 12 = 1,200 I broke 25 up into 5 × 5, so I had 5 × 5 × 12 or 5 × 12 × 5. 5 × 12 = 60. 60 × 5 = 300 1,200 + 300 = 1,500

Student 3: 125 × 12

I doubled 125 and cut 12 in half to get 250 × 6. I then doubled 250 and cut 6 in half to get 500 × 3 which equals 1,500.

Division Strategies

(continues on next page)

NGSSS: Describe the process of finding quotients involving multi-digit dividends using models, place value, properties, and the relationship of division to multiplication.

CCSS: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MA.5.A.1.1

MACC.5.NBT.2.6

Students will:

• explain the inverse relationship between multiplication and division.

• recall basic division facts within 100.

• represent basic division facts in multiple ways (e.g., 25 ÷ 5, 5 25 , 5

25 ).

• describe and demonstrate the process of division using a variety of models (e.g., expanded notation, partial quotients, repeated subtraction, equal sharing, place-value).

NOTE: Expanded notation is the use of the Distributive property in division problems, for

example, 639 ÷ 3 can be expressed as: (600 + 30 + 9) ÷ 3 = (600 ÷ 3) + (30 ÷ 3) + (9 ÷ 3).

Partial quotients is an alternative method to long division using groupings of multiples of the divisor and then adding the partial quotients to find the answer (example on the next page).


Division Strategies

Example:

26 r 4 partial quotients

5 134

- 50 10 84 - 50 10 34 - 25 5 9 - 5 1

4

• use multiplication as a tool for checking quotients in division problems. • describe the steps of the standard algorithm. • model and apply the standard algorithm for division to solve real-world problems with

1- or 2-digit divisors and dividends up to 4 digits. • evaluate missing steps of a partially completed division problem.

FCAT 2.0 Sample Item:

Estimation in Division

NGSSS: Estimate quotients or calculate them mentally depending on the context and numbers involved. MA.5.A.1.2

Students will:

• solve real-world problems using estimation or mental math strategies.


Multiples of 5 Find compatible numbers for use with the strategy of partial quotients. 1 × 5 = 5 2 × 5 = 10 5 × 5 = 25 10 × 5 = 50 20 × 5 = 100

NOTE: Refer to page 52 in the Fifth Grade Mathematics Curriculum Map for clarification of Table 2: Common multiplication and division situations. It is expected that students will become proficient in finding the unknown number for all situations.


Interpreting Remainders

NGSSS: Interpret solutions to division situations, including those with remainders, depending on the context of the problem.

MA.5.A.1.3

Students will:

• model and interpret solutions and remainders using real-world problems (e.g., A school bus holds 25 students. Sixty students are going on a field trip to Mosquito Lagoon. How many buses will be needed?).


• solve division problems involving quotients with fraction and decimal remainders

(e.g., 42 ÷ 8 = 5 �

�or 5.25).

NOTE: enVisionMATH does not address quotients with remainders expressed as decimals and fractions.

Applying Division

NGSSS: Divide multi-digit whole numbers fluently, including solving real-world problems, demonstrating understanding of the standard algorithm, and checking the reasonableness of results.

CCSS: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MA.5.A.1.4

MACC.5.NBT.2.6

Students will:

• use estimation to predict the relative size of answers. • divide multi-digit whole numbers fluently using a variety of strategies (e.g., arrays,

partial quotients, base-ten models, place value).

NOTE: Fluently means accurately, efficiently, and strategically.

• check the reasonableness of an answer to a multi-digit division problem. • defend the answer to the multi-digit division problem. • model and apply the standard algorithm for division to solve real-world problems with

1- or 2-digit divisors and dividends up to 4 digits. • solve real-world division problems involving money up to four digits representing

dollars and two zeros representing cents (e.g., $372.00 ÷ 24). • apply up to two operations to solve problems where at least one is division.


Non-routine Problems

NGSSS: Solve non-routine problems using various strategies including “solving a simpler problem” and “guess, check, and revise.”

MA.5.A.6.5

Students will:

• solve non-routine problems using various strategies including, but not limited to, making an educated guess, checking and revising, solving a simpler problem, drawing diagrams, looking for patterns, and using models.

• make sense of problems and persevere in solving them by applying problem solving strategies to solve multi-step problems.


CCSS: Standards for Mathematical Practice Students will: (to be embedded throughout instruction as appropriate)

Make sense of problems and

persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and

critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision. Look for and make use of structure.

Look for and express regularity in repeated reasoning.

MACC.K12.MP.1 MACC.K12.MP.2 MACC.K12.MP.3 MACC.K12.MP.4 MACC.K12.MP.5 MACC.K12.MP.6 MACC.K12.MP.7 MACC.K12.MP.8


Suggested Activities and Resources Assessment

enVisionMATH Student Edition Topic 1: Lessons 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7; Reteaching Sets: A-G p. 22 Topic 2: Lessons 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7; Reteaching Sets: A-F pp. 54-55 Topic 3: Lessons 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8; Reteaching Sets: A-F pp. 78-79

enVisionMATH Ready-Made Centers Topic 1: Lessons 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7 Topic 2: Lessons 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7 Topic 3: Lessons 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8

enVision Math Problem of the Day Topic 1: Lessons 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7 Topic 2: Lessons 2-1, 2-2, 2-3, 2-5, 2-6, 2-7 Topic 3: Lessons 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8

envisionMath Daily Assessment and Reteaching Workbook Topic 1: Lessons 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7 Topic 2: Lessons 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7 Topic 3: Lessons 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8

enVisionMATH Teacher Resource Masters pp. 73-78 Basic Timed Facts (T.E. pp. 20C & 20D)

Everglades K-12: Grade 5 pp. 24-49 Chapter 1: Division of Whole Numbers

Safari Montage

http://vsod.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=29696&location=local Division/Prime Factorization/Multiples Internet CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx https://www.everydaymathonline.com/free_resources_main.html?frnologin=1# Click on Algorithms in Everyday Mathematics, then select a grade and select an operation to see videos on various algorithms. www.pearsonsuccessnet.com http://illuminations.nctm.org/ www.rosley.cumbria.sch.uk/Division%20strategies.pdf (examples of division using partial quotients) https://www.everydaymathonline.com/free_resources_main.html?frnologin=1# - For video lesson, click on Algorithm Handbook Animations and choose one of the Division: Partial Quotient Models. See pages 14-15 for additional math internet websites and district approved math apps that may support instruction during this unit.

Summative

05 Math DIA Multiplication & Division

Optional Formatives

Florida Benchmarks Assessment Workbook

Topic 1 Florida Test Topic 2 Florida Test Topic 3 Florida Test

(Cover Pages and Answer Keys are available for each topic test through Copy Center/DOD.)

Math Focus Formatives

05 Math Focus Formative Division Form A-Optional Online

(Available through Scantron/Achievement Series.)

For additional formative assessment strategies,

see pages 53-62 in the Fifth Grade Mathematics Curriculum Map.

Intervention/Remediation An intervention/remediation resource guide

can be found on page 63 of the Fifth Grade Mathematics Curriculum Map.

Enrichment Math Extension Activities organized by each topic are available through

Copy Center/DOD.


Internet (additional math websites)

CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx

www.pearsonsuccessnet.com Sign in to view envision book and printable resources. http://thinkingblocks.com/ Shows standard method of solving word problems and bar model representations of word problems.

https://www.everydaymathonline.com/free_resources_main.html?frnologin=1# Everyday Math free resources with algorithm animations by concepts, algorithm handbook by grade and math literature lists.

http://www.k-5mathteachingresources.com/ This site provides an extensive collection of free resources, math games, and hands-on math activities. Math printables can be used in math centers, small group or whole class settings. Instructions for each activity are presented in large print on a task card in child-friendly language to enable students to work on tasks independently after a brief introduction to the task.

http://aaamath.com Interactive math lessons and practice. www.ixl.com Math practice and games for all grade levels. http://illuminations.nctm.org/ National Council of Teachers of Mathematics with activities, lessons and links. http://www.coolmath4kids.com/ Fun math lessons, practice and games. http://www.adaptedmind.com/Fifth-Grade-Math-Worksheets-And-Exercises.html Lessons and practice with math concepts. http://www.internet4classrooms.com/skills-5th-mathbuilders.htm Interactive math skill builders. www.mathplayground.com Guided, interactive model practice using bar models in solving word problems and interactive math games. http://www.learn-with-math-games.com/ Descriptions of math games that can be copied and pasted into a word document for students to use to enforce skills. http://www.bbc.co.uk/bitesize/ks2/maths/ Interactive videos where students can explore different math concepts. http://www.gregtangmath.com/Games Choose a game and a level or math practice. http://lrt.ednet.ns.ca/PD/BLM/table_of_contents.htm Multiple Math blackline masters for 100s charts, geoboards, decimal squares, fraction pieces, 2-D shapes, nets, number lines, place value charts, etc.


Math Apps Approved for School Use as of June 5th, 2013 Additional Apps are added approximately every 2 weeks.

Go to http://myvolusiaschools.org/learn-tech/Pages/default.aspx and choose “Approved Software and Apps.”

App Name Content Area iPad iPod

App Tutoe MT - Multiplication Tables Math 3 - 5 Free Yes Yes

Basic Fraction Math 3 - 5 Free Yes No

Candy Factory Math 3 - 5 Free Yes Yes

Coop Fractions Math 3 - 5 Free Yes Yes

Everyday Mathematics Divisibility Math K - 6 Free Yes Yes

Fast Facts Multiplication Math 3 - 5 Free Yes Yes

Flash to Pass Free Math K - 6 Free Yes Yes

Master the Math Math K - 5 Free Yes No

Math Concentration Math K - 5 Free Yes Yes

Motion Math HD Math 3 - 5 Free Yes Yes

Motion Math: Hungry Fish Math K - 5 Free Yes Yes

Rocket Math Math 3 - 5 Free Yes Yes

Sushi Monster Math K - 5 Free Yes Yes

Virtual Manipulatives! Math K - 5 Free Yes No


CCSS DOMAIN:

Unit:

OPERATIONS AND ALGEBRAIC THINKING NUMBER AND OPERATIONS IN BASE TEN Algebra

PACING: Weeks 6 – 8 September 24 – October 11


Expressions

NGSSS: Use the order of operations to simplify expressions, which include exponents and parentheses.

CCSS: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

CCSS: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 x (8 + 7). Recognize that 3 x (18932 + 921) as three times as large as 18932 + 921, without having to calculate the indicated sum or product.

CCSS: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

MA.5.A.6.2

MACC.5.OA.1.1

MACC.5.OA.1.2

MACC.5.NBT.1.2

balance base number braces brackets cubed (power of 3) equality equation exponent expression growing pattern order of operations parentheses power squared (power of 2) variable (also known as unknown number)

Students will:

• express powers of 10 using whole-number exponents (e.g., 10 = 10¹, 100 = 10², 1000= 10³).

• illustrate and explain a pattern for how the number of zeros of a product- when multiplying a whole number by power of 10-relates to the power of 10 (e.g., 500-is the same as 5 x 100, or 5 x 10² -- has two zeros in its product).

• evaluate a base number with exponents up to power of 3 (e.g., 43 = 64).

• follow steps in the order of operations to simplify expressions which include exponents and parentheses, brackets, and/or braces.

Examples: 48 ÷ ( 20 – 8 ) + 2 x 3³ {[24 ÷ (3 + 5)] – 1}

48 ÷ 12 + 2 x 33 {[24 ÷ 8] – 1}

48 ÷ 12 + 2 x 27 {3 – 1} 4 + 54 2 58

NOTE: PEMDAS is a popular mnemonic used to teach order of operations when evaluating expressions. Be aware of misconceptions students form with the use of this strategy.

• write an numeric expression given a description, graphic, or scenario. • create a description, graphic, or scenario given an numeric expression.

Note: Exponents will be limited to: - power of 2 (squared) - power of 3 (cubed).

Order of Operations Steps

1. Perform calculations inside (parentheses) first, then [brackets], and finally {braces}. 2. Do calculations involving exponents. 3. Complete all multiplication/division as it appears from left to right. 4. Complete all addition/subtraction as it appears from left to right.


Equations

NGSSS: Use the properties of equality to solve numerical and real-world situations. MA.5.A.4.1

Students will:

• reason abstractly and quantitatively to demonstrate knowledge of how to apply properties of equality (addition, subtraction, multiplication, and division).

NOTE: Equalities will involve no more than two operations.

Examples of balanced equations (equality):

1) 5 + 2 = 7 3(5 + 2) = 3 • 7 2) 12 = 15 – 3 12 ÷ 4 = (15 – 3) ÷ 4 When the same operation is performed on both sides of an equation, the equation remains balanced.

Another example of equality:

If the scale is balanced, what is the weight of one rectangle?

• solve equations with up to two variables by substituting a quantity for one of the variables in the equation.

NOTE: When a two variable equation is used, the value of one variable must be provided (e.g., If c = 6, solve for y in the following equation: 4c + y = 28).

• differentiate between an expression and an equation. • translate a written description or graphic into an expression or equation (using a

variable for the unknown number). NOTE: Notation for an unknown number may include, but is not limited to, the following:

o 72 ÷ ? = 8 o m × 4 = 24 o 40 ÷ 10 = __ o ᴥ × 5 = 60 o 56 ÷ = 8



Non-routine Problems

NGSSS: Solve non-routine problems using various strategies including “solving a simpler problem” and “guess, check, and revise.”

MA.5.A.6.5

Students will:

• make sense of and persevere in solving non-routine problems using various strategies (e.g., drawing diagrams, making tables or lists, looking for patterns, using models, estimating, solving a simpler problem, and/or make an educated guess, check, and revise).

• reason abstractly and quantitatively to extend growing patterns.

FCAT 2.0 Sample Item: NOTE: Practice with growing patterns can be found in the enVisionMATH Diagnostic & Intervention System. Go to Booklet F: Numeration, Patterns, and Relationships in Grades 4-6. Page F25 Geometric Growth Patterns.














enVisionMATH Student Edition Topic 4: Lessons 4-1, 4-2, 4-3, 4-4, 4-5, 4-6, 4-7; Reteaching Sets: A-C, E, F p. 102-103

enVisionMATH Ready-Made Centers Topic 4: Lessons 4-1, 4-2, 4-3, 4-4, 4-5, 4-6

enVision Math Problem of the Day Topic 4: Lessons 4-1, 4-2, 4-3, 4-4, 4-5, 4-6, 4-7

envisionMath Daily Assessment and Reteaching Workbook Topic 4: Lessons 4-1, 4-2, 4-3, 4-4, 4-5, 4-6, 4-7

Everglades K-12: Grade 5 pp. 104-144 Chapter 4: Algebra pp. 152-155 Chapter 6: Order of Operations

Safari Montage http://vsod.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=21311&location=local “Variables, Expressions, and Equations, Order of Operations http://safari4.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=20298&location=local (Algebraic Thinking)

Internet CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.pearsonsuccessnet.com http://illuminations.nctm.org/ http://www.homeschoolmath.net/teaching/equations-1.php (balance as a model of an equation) See pages 14-15 for additional math internet websites and district approved math apps that may support instruction during this unit.

Summative

05 Math DIA Algebra

Formatives


Topic 4 Florida Test (Cover Pages and Answer Keys are available for each topic test through Copy Center/DOD.)


05 Math Focus Formative Algebra Form A-Optional Online

05 Math Focus Formative Algebra Form B-Optional Online







Copy Center/DOD.


CCSS DOMAIN:

Unit:

OPERATIONS AND ALGEBRAIC THINKING GEOMETRY Data

PACING: Weeks 9 – 11 October 14 – November 1


Ordered Pairs


NGSSS: Identify and plot ordered pairs on the first quadrant of the coordinate plane.

CCSS: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

CCSS: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

MA.5.G.5.1

MACC.5.G.1.1

MACC.5.G.1.2

bar graph continuous data (measured data) coordinate grid coordinate plane coordinates decreasing discrete data (counted data) double bar graph equidistant frequency table graph horizontal increasing intervals key line graph line plot midpoint ordered pairs origin pictograph plot point quadrant scale survey trend Venn diagram vertical x- and y-coordinates x-axis y-axis

Students will:

• draw a coordinate plane with two intersecting perpendicular lines. • identify the intersection as the origin and the point where 0 lies on each of the lines. • label the horizontal axis as the x-axis, and the vertical axis as the y-axis. • identify an ordered pair such as (3,2) as an x-coordinate followed by a y-coordinate. • use appropriate tools strategically to identify, locate and plot ordered pairs of whole

numbers on a graph in the first quadrant of the coordinate plane.

NOTE: The first quadrant includes only positive numbers.

• explain the relationship between an ordered pair and its location on the coordinate plane.

• describe the horizontal and vertical movements (translations) necessary to get from one point to another on a coordinate plane.

• determine the distance between two ordered pairs using appropriate tools or strategies. • locate a point equidistant from two other points in the first quadrant of the coordinate

plane.


NOTE: A point that is equidistant from two other points may, but does not have to, lie in the same horizontal or vertical line that connects the two points.


Data Analysis

NGSSS: Construct and analyze line graphs and double bar graphs.

NGSSS: Construct and describe a graph showing continuous data, such as a graph of a quantity that changes over time.

MA.5.S.7.1

MA.5.A.4.2

Students will:

• identify the title, label for each axis, scale, interval, and key for a given single bar graph, double bar graph, and line graph.

• analyze and compare information from a given graph. • predict and explain data trends in a line graph (increasing, decreasing, or constant). • draw conclusions and predictions based on evidence in a graph. • collect data through events such as a survey, research, or experiment, • select an appropriate graph for a given set of data. • determine scales and intervals for a given set of data. • construct a graph representing a given set of data including title, label for each axis,

scale, interval, and key (as needed). • defend and critique the appropriateness of a graph to the data it represents including

real-world scenarios.

Continuous and Discrete Data

(continues on

next page)

NGSSS: Differentiate between continuous and discrete data, and determine ways to represent those using graphs and diagrams.

MA.5.S.7.2

Students will:

• differentiate between continuous data and discrete data using evidence.

NOTE: Discrete data (finite) is counted and can only take certain values. Possible representations of discrete data may include, but are not limited to,:

� the number of students in a class (you can’t have half a student) � the number of problems on a test (you can’t have half a question) � total amount of money to the nearest penny in a bank account (you can’t

withdraw/deposit half a penny)

Continuous data (infinite) is measured and can take an unlimited number of values within a range. Possible representations of continuous data may include, but are not limited to:

� infinite measurable data (time, weight, mass, height, depth, length, speed) � measuring plant growth which can be represented with decimals such as 2.7 in.

or 2.78 in. or 2.7843893 in. to show increments between the data points (limited by the measurement tool)

� measuring the burning of a candle; the time and length are both continuous measurements

� includes measurements such as seconds (part of a minute) and ounces (part of a pound)


Continuous and Discrete Data











Look for and express regularity in repeated

reasoning.



Suggested Activities and Resources Assessment enVisionMATH Student Edition Topic 4: Lessons 15-1, 15-2, 15-3, 15-4, 15-5, 15-6, 15-7; Reteaching Sets: A-G p. 358

enVisionMATH Ready-Made Centers Topic 4: Lessons 15-1, 15-2, 15-3, 15-4, 15-5, 15-6, 15-7

enVision Math Problem of the Day Topic 4: Lessons 15-1, 15-3, 15-4, 15-5, 15-6, 15-7

envisionMath Daily Assessment and Reteaching Workbook Topic 4: Lessons 15-1, 15-2, 15-3, 15-4, 15-5, 15-6, 15-7

Everglades K-12: Grade 5 pp. 180-199 Chapter 7: Data Analysis

Internet CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx http://lrt.ednet.ns.ca/PD/BLM/table_of_contents.htm Multiple Math blackline masters. www.pearsonsuccessnet.com http://illuminations.nctm.org/ http://www.mathsisfun.com/data/pictographs.html (Shows different types of graphs, describes the type of data they represent and provides questions that go with the graph)

See pages 14-15 for additional math internet websites and district approved math apps that may support instruction during this unit.

Summative

05 Math DIA Data

Formatives




05 Math Focus Formative Data Analysis Form A-Optional Online


For additional formative assessment strategies, see pages 53-62 in the

Fifth Grade Mathematics Curriculum Map.




Copy Center/DOD.


CCSS DOMAIN: Unit:

NONE Integers

PACING: Weeks 12 – 13 November 4 – November 15


Integers

NGSSS: Compare, order, and graph integers, including integers shown on a number line. MA.5.A.6.4 ascend compare descend decrease distance elevations equal to (=) greater than (>) greater than or equal to (≥) increase inequality integer less than (<) less than or equal to (≤) negative number number line not equal (≠) positive number sea level

Students will:

• demonstrate knowledge and understanding of integers (the set of positive and negative numbers).

• identify and graph integers (the set of positive and negative numbers) on a number line.

NOTE: Graph means to plot integers on a number line.

Graph -3 on the number line.

• explain that numbers are larger or increase when moving to the right on a number line and smaller or decrease when moving to the left on a number line.

• explain the location of a positive or negative number as the distance from 0 on a number line.

• find the distance between any two integers on a number line. • compare integers using inequalities ( >, <, ≥, ≤, ≠ ).

NOTE: Numbers may range between -500 and 500.

• order up to five integers from a set of given data.



Integers

NGSSS: Describe real-world situations using positive and negative numbers. MA.5.A.6.3 Students will:

• apply and solve real-world problems using positive and negative integers (e.g., owing money - My allowance is $4. Mom loans me $3 to buy a $7 book. I owe Mom $3; therefore, I have -3 dollars).

NOTE: Other appropriate real-world situations may include, but are not limited to, measuring elevations, above and below sea level, riding elevators up and down, temperature, ascending and descending mountains, depositing and withdrawing money from a bank account, and football yardage.

NOTE: In fifth grade this does not include adding and subtracting positive and negative numbers. It does include recognizing the distance between the numbers in relation to the amount above and below (less than and greater than) zero.















enVisionMATH Student Edition Topic 4: Lessons 16-1, 16-2, 16-3, 16-4, 16-5; Reteaching Sets: A-D pp. 378-379

enVisionMATH Ready-Made Centers Topic 4: Lessons 16-1, 16-2, 16-3, 16-4, 16-5

enVision Math Problem of the Day Topic 4: Lessons 16-1, 16-2, 16-3, 16-4, 16-5

envisionMath Daily Assessment and Reteaching Workbook Topic 4: Lessons 16-1, 16-2, 16-3, 16-4, 16-5

Everglades K-12: Grade 5 pp. 156-178 Chapter 6: Number and Operations

Safari Montage http://safari4.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=19637&location=local (Introduction to Integers – Chapter 1 and Chapter 2) Internet CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.pearsonsuccessnet.com http://illuminations.nctm.org/ See pages 14-15 for additional math internet websites and district approved math apps that may support instruction during this unit.

Summative

05 Math DIA Integers

Formatives




05 Math Focus Formative Integers Form A-Optional Online

05 Math Focus Formative Integers Form B-Optional Online







Copy Center/DOD.


CCSS DOMAIN: Unit:

NUMBER AND OPERATIONS IN BASE TEN Decimals

PACING: Weeks 14 – 18 November 18 – December 19


Decimal Place Value

CCSS: Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g.,

347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <

symbols to record the results of comparisons.

MACC.5.NBT.1.3 MACC.5.NBT.1.3a

MACC.5.NBT.1.3b

base ten numerals (standard form) decimal difference equivalent decimals estimate expanded form hundredths place value rounding sum tenths thousandths whole number word form

Students will:

• represent decimals using place value, models, and graphics of place value through the thousandths place.

Examples: Place Value Charts

• represent decimals to the thousandths place numerically.

Example: Equivalent forms of 0.34 are: 34/100 3/10 + 4/100 30/100 + 4/100 0.30 + 0.02 340/1000 3 × (1/10) + 4 × (1/100) 3 × (1/10) + 4 × (1/100) + 0 × (1/1000)

• read and write decimals to thousandths in word form, base ten numerals, and expanded form.

• compare two decimals to the thousandths using place value and record the comparison using symbols <, >, or =.

• order up to five decimals from least to greatest and vice versa.

Represent Addition and Subtraction of

Decimals


NGSSS: Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value, or properties.

MA.5.A.2.1

Students will:

• represent addition and subtraction of decimals using place value, models, and graphics of place value through the thousandths place. FCAT 2.0 Sample Item:

NOTE: Be aware that some students will struggle with relating the unshaded box in the key with the shaded sections in the diagram.


Representing Addition and

Subtraction of Decimals

• represent addition and subtraction of decimals using the associative or distributive properties through the thousandths place.

Examples:

NOTE: Decimals may also be used in the context of money.

Addition and Subtraction of

Decimals

NGSSS: Add and subtract fractions and decimals fluently, and verify the reasonableness of results, including in problem situations.

CCSS: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

MA.5.A.2.2

MACC.5.NBT.2.7

Students will:

• add and subtract decimals fluently (accurately and efficiently) using a variety of strategies including proper alignment of place value.

Example: Use a model to solve 3 – 0.6.

NOTE: Decimals may also be used in the context of money.

• solve real-world problems involving addition and subtraction of decimals.


• justify the reasonableness of the solution.

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

CCSS: Use place value understanding to round decimals to any place.

MA.5.A.2.3

MACC.5.NBT.1.4

Students will:

• round decimals up to thousandths to any place value. • use estimation strategies such as rounding, benchmark numbers, or number lines, to

predict the relative size of answers when adding or subtracting decimals.











reasoning.


NOTE: Refer to page 51 in the Fifth Grade Mathematics Curriculum Map for clarification of Table 1: Common addition and subtraction situations. It is expected that students will become proficient in finding the unknown number for all situations.



enVisionMATH Student Edition Topic 6: Lessons 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7, 6-8, 6-9, 6-10; Reteaching Sets: A-J p. 156

enVisionMATH Ready-Made Centers Topic 6: Lessons 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7, 6-8, 6-9, 6-10

enVision Math Problem of the Day Topic 6: Lessons 6-3, 6-4, 6-5, 6-6, 6-7, 6-8, 6-9, 6-10

envisionMath Daily Assessment and Reteaching Workbook Topic 6: Lessons 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7, 6-8, 6-9, 6-10

Everglades K-12: Grade 5 pp. 55-56 Modeling Addition and Subtraction of Decimals

Safari Montage

Internet CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx http://www.adaptedmind.com/Fifth-Grade-Math-Worksheets-And-Exercises.html www.pearsonsuccessnet.com http://illuminations.nctm.org/ http://lrt.ednet.ns.ca/PD/BLM/table_of_contents.htm Collection of blackline masters for all math concepts. http://www.k-5mathteachingresources.com/5th-grade-number-activities.html Math Centers for decimals You Tube video on adding and subtracting decimals See pages 14-15 for additional math internet websites and district approved math apps that may support instruction during this unit.

Summative

05 Math DIA Decimals

Formatives




(Online and scan versions available through Scantron/Achievement Series.)






Copy Center/DOD.


CCSS DOMAIN: Unit:

NUMBER AND OPERATIONS – FRACTIONS Fractions

PACING: Weeks 19 – 23 January 7 – February 7


Prime and Composite Numbers

NGSSS: Determine the prime factorization of numbers. MA.5.A.2.4 base number benchmark fractions common factors composite denominator difference divisible equivalent estimate exponents factor factor tree fraction fraction greater than

one ( �

� )

(formerly called improper fractions) greatest common factor (GCF) least common denominator (LCD) least common multiple (LCM) like denominator mixed number number lines numerator power prime prime factorization reasonableness simplest form (lowest terms) sum unlike denominator whole number

Students will:

• model the use of factor trees to determine the prime factorization of numbers.

Example:

• express composite numbers as the product of prime factors (e.g., 36 = 2² • 3²).

NOTE: If the base number is 2 or 3, the exponents are to be limited to 3, 4, or 5. If the base number is greater than 3, the exponent is to be limited to 2 (second power).

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

Students will:

• explain and apply the divisibility rules for 2, 3, 4, 5, 6, 9, and 10.

NOTE: This will not be assessed, but is a good strategy for finding factors.

• identify and explain prime and composite numbers to 100. • list multiples of a given number. • list factors of a given number. • determine the greatest common factor (GCF) and least common multiple (LCM) for up to

three numbers.



Fractions


NGSSS: Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value, or properties.

CCSS: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc) / bd.)

MA.5.A.2.1

MACC.5.NF.1.1

Students will:

• review equivalent fractions using fraction bars, models and graphics. • simplify a fraction into lowest terms. • find the Least Common Denominator (LCD) in a set of fractions using various strategies

(e.g., manipulatives, listing of multiples, prime factorization).

Example: Find the LCD of 12

5 and 8

3 .

First Way:

Record the first few multiples for each denominator and circle the first number that is

common.

12 – 12, 24, 36, 48

8 – 8, 16, 24

Second Way:

Step 1: Write the product of prime factors for each denominator.

12 = 2 • 2 • 3 = 22 • 3¹

8 = 2 • 2 • 2 = 23

Step 2: Sort the prime factors according to the same bases. 2

2 and 2

3 AND

3¹

Step 3: Choose the base with the highest exponent.

For 22 and 2

3 , choose 2

3 because the highest exponent is 3.

For 3¹ , choose 3¹ because the highest (and only) exponent is 1.

Step 4: Multiply the factors with the highest exponent for each base together. 2

3 • 3¹

8 • 3 = 24 (LCD is 24.)

• relate prime and composite numbers to finding common multiples (denominators), finding equivalent fractions and simplifying fractions.

• represent addition and subtraction of fractions with like and unlike denominators using concrete and graphical models.

NOTE: Concrete models include, but are not limited to, fraction strips, fraction circles, pattern blocks, Geoboards, and other tangible objects. Graphical models include, but are not limited to, pictures of base-ten blocks and drawings.



Fractions

• add and subtract mixed numbers with like and unlike denominators (with and without regrouping) using concrete and graphical models.

• add and subtract fractions greater than one with like and unlike denominators using concrete and graphical models.


NGSSS: Add and subtract fractions and decimals fluently, and verify the reasonableness of results, including in problem situations.

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

CCSS: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

MA.5.A.2.2

MA.5.A.2.3

MACC.5.NF.1.2

Students will:

• add and subtract mixed numbers with like and unlike denominators (with and without regrouping) represented graphically and numerically set in real-world scenarios.

• add and subtract fractions greater than one with like and unlike denominators represented graphically and numerically set in real-world scenarios.

Examples: NOTE: Appropriate denominators include 1-12, 14, 15, 16, 18, 21, 24, 25, 32, 35, 36, 45, 75, or any multiple of 10 through 100.


• use estimation to verify the reasonableness of answers using benchmark fractions and number sense.

Example: Question: Jerry was making two different types of cookies. One recipe called for 3/4 cup of sugar and the other needed 2/3 cup of sugar. How much sugar is needed to make both recipes? Student Response: Jerry needs more than one cup but less than 2 cups. I compared both fractions to 1/2 and found that both are more than 1/2. When the denominator is 4, half of that is 2 so 2/4 is the same as 1/2. 3/4 is more than that. When the denominator is 3, half of that is 1.5 so 1.5/3 would be the same as 1/2. 2/3 is more than that. Adding two fractions that are more than 1/2 and less than 1 would put it between 1 and 2 cups.

NOTE: Benchmark fractions are common fractions that you can judge other numbers against such as 0, 1/2, and 1.











reasoning.


mark

3

4

2

3

1

2



enVisionMATH Student Edition Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5, 7-6, 7-7, 7-8, 7-9, 7-10, 7-11; Reteaching Sets: A-J p. 156,

F-J p. 196 Topic 8: Lessons 8-1, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7; Reteaching Sets: A-F p. 218 Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-5, 9-6; Reteaching Sets: A-F p. 240

enVisionMATH Ready-Made Centers Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5, 7-6, 7-7, 7-8, 7-9, 7-10, 7-11 Topic 8: Lessons 8-1, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7 Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-5, 9-6

enVision Math Problem of the Day Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5, 7-6, 7-7, 7-8, 7-9, 7-10, 7-11 Topic 8: Lessons 8-1, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7 Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-5, 9-6

envisionMath Daily Assessment and Reteaching Workbook Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5, 7-6, 7-7, 7-8, 7-9, 7-10, 7-11 Topic 8: Lessons 8-1, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7 Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-5, 9-6

Everglades K-12: Grade 5 pp. 52-84 Chapter 2: Addition and Subtraction of Fractions

Safari Montage http://safari4.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=29696&location=local&chapterskeyindex=52831&play=1(Chapter 6: Prime Factorization)

Internet CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.pearsonsuccessnet.com http://illuminations.nctm.org/ www.abcya.com/fraction_tiles.htm http://www.visualfractions.com/Games.htm (visual fractions games) http://www.softschools.com/math/fractions/ (fraction games, worksheets and quizzes www.factorsamurai.com (free ipad app on prime factorization http://www.internet4classrooms.com/grade_level_help/prime_factorization_math_fifth_5th_grade.htm (prime factorization videos, games and resources) http://www.mathgoodies.com/games/ (math games including prime factorization See pages 14-15 for additional math internet websites and district approved math apps that may support instruction during this unit.

Summative

05 Math DIA Fractions

Formatives



(Cover Pages and Answer Keys are available for each topic test through Copy

Center/DOD.)

Math Focus Formatives 05 Math Focus Formative MA.5.A.2.1

05 Math Focus Formative MA.5.A.2.2 & MA.5.A.2.3

05 Math Focus Formative MA.5.A.2.4 & MA.5.A.6.1

(Online and scan versions available

through Scantron/Achievement Series.)

For additional formative assessment strategies, see pages 53-62 in the

Fifth Grade Mathematics Curriculum Map.




Copy Center/DOD.


CCSS DOMAIN: Unit:

MEASUREMENT AND DATA Measurement

PACING: Weeks 24 – 27 February 10 – March 7


Measurement

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

MA.5.G.5.3

accurate balance Celsius customary units degrees elapsed time Fahrenheit foot gallons gram hours inch liter mass meter meter stick metric units mile milligram milliliter millimeter minutes ounces pint pounds precise quart ruler scale seconds thermometer tons yard yard stick

Students will:

• select and use appropriate units of measurement. • select and use appropriate tools strategically for:

� weight/mass (down to the nearest ounce and milligram) � capacity/volume (down to the nearest ounce and milliliter) � length (down to the nearest 1/16 inch and millimeter) � area (base/height instead of length/width) � temperature (be familiar with reading both Celsius and Fahrenheit) � time (down to the nearest minute) including elapsed time

NOTE: Tools may include, but are not limited to, scales, rulers, yardsticks, tape measures, meter sticks, measuring cups, stopwatches, analog and digital clocks, and thermometers. Students should be able to measure objects with linear measurement tools that do not start at “0” (e.g., a broken ruler).

• determine when to use an approximate measure or a more precise measure in real-world contexts.

• recognize and explain precision of measurement (measuring to the nearest 1/4 inch is more precise than measuring to the nearest 1/2 inch; 1/2 inch is more precise than 1/4 foot).


• solve real-world problems involving measurement. • defend solutions.


Converting Units of Measurement

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

CCSS: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

MA.5.G.5.2

MACC.5.MD.1.1

Students will:

• compare units of measure within the same system and same dimensions (inches to feet, ounces to pounds, millimeters to meters, grams to kilograms, seconds to minutes).

• convert within the same system (customary or metric) with up to two conversions using the Grade 5 FCAT 2.0 Mathematics Reference Sheet found on page 64 in the Grade 5 Mathematics Curriculum Map.


• determine elapsed time to the nearest minute using analog and digital clocks.


• apply knowledge of length, weight, mass, calendars and elapsed time to solve problems.










Look for and express regularity in

repeated reasoning.




enVisionMATH Student Edition Topic 10: Lessons 10-1, 10-2, 10-3, 10-4, 10-5; Reteaching Sets: A-D pp. 256-257 Topic 11: Lessons 11-1, 11-2, 11-3, 11-4, 11-5, 11-6; Reteaching Sets: A-E pp. 274-275

enVisionMATH Ready-Made Centers Topic 10: Lessons 10-1, 10-2, 10-3, 10-4, 10-5 Topic 11: Lessons 11-1, 11-2, 11-3, 11-4, 11-5, 11-6

enVision Math Problem of the Day Topic 10: Lessons 10-1, 10-2, 10-3, 10-4, 10-5 Topic 11: Lessons 11-1, 11-2, 11-3, 11-4, 11-5, 11-6

envisionMath Daily Assessment and Reteaching Workbook Topic 10: Lessons 10-1, 10-2, 10-3, 10-4, 10-5 Topic 11: Lessons 11-1, 11-2, 11-3, 11-4, 11-5, 11-6

Everglades K-12: Grade 5 pp. 131-134 Measurement Problems with Approximations and Precision

Internet CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.ixl.com www.pearsonsuccessnet.com http://illuminations.nctm.org/ http://www.internet4classrooms.com/skills-5th-mathbuilders.htm (choose a topic for fun math games) www.mathplayground.com (shapes, geometry) http://bbc.co.uk/schools/ks2bitesize/maths/shape_space (interactive math site - 2-D shapes, 3-D shapes, angles, measures, symmetry, time) See pages 14-15 for additional math internet websites and district approved math apps that may support instruction during this unit.

Summative

05 Math DIA Measurement

Formatives


Topic 10 Florida Test Topic 11 Florida Test



05 Math Focus Formative MA.5.G.5.2 05 Math Focus Formative MA.5.G.5.3







Copy Center/DOD.


CCSS DOMAIN: Unit:

GEOMETRY Geometry

PACING: Weeks 28 – 31 March 10 – April 11


Two-dimensional Shapes

NGSSS: 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

CCSS: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

CCSS: Classify two-dimensional figures in a hierarchy based on properties.

MA.5.G.3.1

MACC.5.G.2.3

MACC.5.G.2.4

2-dimensional figures 3-dimensional solids area (A) area of base (B) attributes base (b) cube cubic unit edges faces height (h) length (l) parallelogram perimeter polygon polyhedron prisms pyramid rectangle right angle solid square unit surface areas.(S.A.) trapezoid triangle vertex/vertices volume (V) width (w)

Students will:

• review whether a shape is a polygon or not.

NOTE: A polygon is a closed figure whose sides are all line segments. Students should be given exposure to regular and irregular polygons.

Examples:

Hexagons

Pentagons

• compare and describe the geometric properties (attributes) of two-dimensional figures (triangle, quadrilateral, rectangle, square, rhombus, trapezoid, pentagon, hexagon, circle, half-circle, quarter circle).

• categorize two-dimensional figures according to their individual and shared geometric properties (attributes).

NOTE: Geometric properties include properties of sides (parallel, perpendicular, congruent), properties of angles (type, measurement, congruent), and properties of symmetry (point and line).

• explain the reasoning for the determined categories. • organize figures into a hierarchy diagram.

Examples:


Three-dimensional Solids

NGSSS: 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

MA.5.G.3.1

• use appropriate geometric vocabulary to describe three-dimensional solids including polyhedra.

NOTE: Polyhedra (prisms and pyramids) are three-dimensional solids in which all surfaces are polygons.

• determine the types of faces (e.g., rectangle, triangle) and the number of edges, faces, bases, and vertices in polyhedra.

• compose/decompose solids such as cereal boxes (from a solid to a net and vice versa). • identify and name the three-dimensional solid formed by a net and vice versa, based on

the number of faces, types of faces, or bases. • identify different views of a composite solid composed of cubes. • determine the number of cubes needed to build a composite solid.

NOTE: A composite solid is a 3-dimensional shape formed by combining geometric solids to build a new shape (assessment will be limited to composite solids formed by cubes only).

Area


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

Students will:

• explore the area of a rectangle based on the number of squares it takes to fill or cover the inside of a rectangle

• review the formula for finding area of a rectangle (A = bh). • justify why the formula for finding the area of a parallelogram is the same as a rectangle

(A = bh).

NOTE: Cutting off a right triangle from one side of a rectangle and translating it to the other side of the shape forms a parallelogram with the same area as the original rectangle.

• derive and apply the area formula of a triangle (A = ½bh) from the area formula of a rectangle.

NOTE: Cutting a rectangle in half diagonally (joining nonadjacent vertices of a polygon) gives two triangles, each with half the area of the original rectangle.


Area

• derive and apply the area formula for an isosceles trapezoid from the area formula of a rectangle [A = ½ h(b1 + b2) or A = h(b1 + b2) ÷ 2].

NOTE: An isosceles trapezoid is a trapezoid with two equal sides. Cutting off a right triangle from one side of a rectangle and reflecting, rotating, and translating it to the other side of the shape forms a trapezoid with the same area as the original rectangle.

NOTE: The Grade 5 FCAT 2.0 Mathematics Reference Sheet (page 64) should be used consistently for finding area AFTER the students understand the relationship that exists between the area of a rectangle and the areas of a parallelogram, triangle, and trapezoid.

• label appropriate units of measure for area.

Surface Area

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

MA.5.G.3.2

Students will:

• describe and define surface area using nets and solids of rectangular prisms and cubes.

• model and choose appropriate strategies and tools for determining surface area. • calculate surface area of rectangular prisms and cubes (S.A. = 2bh + 2bw + 2hw) using

appropriate tools. • label appropriate units of measure for surface area.

NOTE: The Grade 5 FCAT 2.0 Mathematics Reference Sheet (page 64) should be used consistently AFTER the students have explored and developed the concept of surface area.


Volume

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

CCSS: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used

to measure volume. b. A solid figure which can be packed without gaps or overlaps using n units cubes is said to have a volume of n

cubic units.

CCSS: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

CCSS: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

b. Apply the formula V= l x w x h and V= b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of non-overlapping parts, applying this technique to solve real world problems.

MA.5.G.3.2

MACC.5.MD.3.3 MACC.5.MD.3.3a

MACC.5.MD.3.3b

MACC.5.MD.3.4

MACC.5.MD.3.5

MACC.5.MD.3.5a

MACC.5.MD.3.5b

MACC.5.MD.3.5c

Students will:

• identify volume as an attribute of a solid figure. • explain that a cube with 1 unit side length is “one cubic unit” of volume. • explain a process for finding the volume of a solid figure by filling it with unit cubes

without gaps and overlaps. • measure the volume of a hollow three-dimensional figure (rectangular prism and cube)

by filling it with unit cubes without gaps and counting the number of unit squares. • explain how to find area of a rectangular prism or cube.

Example: 1. Find the area of the base by multiplying its length by its width (B = l × w). 2. Multiply the area of the base by the height (V = Bh).

• relate finding the product of three numbers (length, width, and height) to finding volume. • relate the associative property of multiplication to finding volume. • calculate volume of rectangular prisms and cubes using the formula for volume

(V = bwh or V = Bh) using appropriate tools.


Volume

• label appropriate units of measure for volume. • decompose a composite solid into non-overlapping rectangular prisms to find the

volume of the solid by finding the sum of the volumes of each of the decomposed prisms.

Example: What is the volume of concrete needed to build the steps in the diagram?

• solve real world problems involving volume.

NOTE: The Grade 5 FCAT 2.0 Mathematics Reference Sheet (page 64) should be used consistently AFTER the students have explored and developed the concept of volume.











reasoning.


The lowest step measures 2 ft. × 2 ft. × 1.5 ft. making the volume 6 cubic feet.

The highest step measures 3 ft. × 2 ft. × 3 ft. making the volume 18 cubic feet.

6 cubic feet + 18 cubic feet = 24 cubic feet



enVisionMATH Student Edition Topic 12: Lessons 12-1, 12-2, 12-3, 12-4, 12-5, 12-6, 12-7; Reteaching Sets: B-E pp. 294-295 Topic 13: Lessons 13-1, 13-2, 13-3, 13-4, 13-5; Reteaching Sets: A-D pp. 312-313 Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6; Reteaching Sets: A-F pp. 334-335

enVisionMATH Ready-Made Centers Topic 12: Lessons 12-1, 12-2, 12-3, 12-4, 12-5, 12-6, 12-7 Topic 13: Lessons 13-1, 13-2, 13-3, 13-4, 13-5 Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6

enVision Math Problem of the Day Topic 12: Lessons 12-1, 12-2, 12-3, 12-4, 12-5, 12-6, 12-7 Topic 13: Lessons 13-1, 13-2, 13-3, 13-4, 13-5 Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6

envisionMath Daily Assessment and Reteaching Workbook Topic 12: Lessons 12-1, 12-2, 12-3, 12-4, 12-5, 12-6, 12-7 Topic 13: Lessons 13-1, 13-2, 13-3, 13-4, 13-5 Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6

Everglades K-12: Grade 5 pp. 86-99 Chapter 3: 3-Dimensional Shapes: Volume and Surface Area pp. 135-139 Chapter 5: Derive and Apply Area Formulas

Safari Montage http://vsod.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=33061&location=local (area of rectangle, parallelogram, and triangle) http://safari4.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=51311&location=local&chapterskeyindex=122406&play=1 (area of geometric shapes, surface area, and volume)

Internet www.fi.uu.nl/toepassingen/02015/toepassing_wisweb.en.html - The Freudenthal Institute for Science and Mathematics Education (FIsme) is a research institute of Utrecht Universiteit, faculty of Science. “Building houses with side views” a great interactive site on perspective. CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx http://www.internet4classrooms.com/skills-5th-mathbuilders.htm (choose a topic for fun math games) www.mathplayground.com (shapes, geometry) http://bbc.co.uk/schools/ks2bitesize/maths/shape_space (interactive math site- 3-D shapes) http://www.coolmath.com/reference/areas.html (site for area of geometric shapes and where the formula comes from) http://www.studyzone.org/testprep/math4/d/formareal.cfm (formulas for area of geometric shapes including a link to practice finding area) See pages 14-15 for additional math internet websites and district approved math apps that may support instruction during this unit.

Summative

05 Math DIA Geometry

Formatives





05 Math Focus Formative MA.5.G.3.1 05 Math Focus Formative MA.5.G.3.2 05 Math Focus Formative MA.5.G.5.4







Copy Center/DOD.


CCSS DOMAIN: Unit:

NUMBER AND OPERATIONS IN BASE TEN CCSS Decimals & Fractions Extension

PACING: Weeks 32 – 36 April 14 – May 16


Decimal Placement

CCSS: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

MACC.5.NBT.1.2 area model decimal decimal point denominator divide fair share model fraction mixed number multiply numerator power product quotient whole number

Students will:

• illustrate and explain a pattern for how multiplying or dividing any decimal by a power of 10 relates to the placement of the decimal point (e.g., dividing 15.3 by 100, or 15.3 ÷ 10², results in 0.153--where the decimal point in the quotient is 2 places to the left of where it was in the dividend).

Multiplication and Division of Decimals

CCSS: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

MACC.5.NBT.2.7

Students will:

• multiply and divide decimals fluently (accurately and efficiently) using a variety of strategies.

• Illustrate and explain strategies using concrete models or drawings.

Example: Area Model for Multiplication Fair Share Model for Division

• solve real-world problems involving multiplication and division of decimals.

Example: Joe has 1.6 meters of rope. He has to cut pieces of rope that are 0.2 meters long. How many pieces can he cut?


Relating Fractions and Division

CCSS: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret ¾ as the result of dividing 3 by 4, noting that ¾ multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size ¾. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

MACC.5.NF.2.3

Students will:

• explain that the fraction (a/b) can be represented as a division of the numerator by the denominator (a ÷ b)

• illustrate why a ÷ b can be represented by the fraction a/b.

Example: Show how 3 ÷ 7 can also be represented as 3/7. Divide each of 3 rectangles into 7 equal parts resulting in a total of 21 equal parts. Divide the 21 parts into 7 equal groups. The result is 3/7 of 1 whole.

• solve word problems involving the division of whole numbers and interpret the quotient – which could be a whole number, mixed number, or fraction - in the context of the problem.

• explain or illustrate the solution strategy using visual fraction models or equations that represent the problem.











reasoning.




enVisionMATH Student Edition Topic 1: Lessons 1-1A (online) Topic 6: Lessons 6-11A, 6-11B, 6-11C, 6-11D, 6-11E, 6-11F, 6-11G (online) Topic 9: Lesson 9-7A (online)

enVisionMATH Ready-Made Centers Topic 1: Lessons 1-1A (online) Topic 6: Lessons 6-11A, 6-11B, 6-11C, 6-11D, 6-11E, 6-11F, 6-11G (online) Topic 9: Lesson 9-7A (online)

envisionMath Daily Assessment and Reteaching Workbook Topic 1: Lessons 1-1A (online) Topic 6: Lessons 6-11A, 6-11B, 6-11C, 6-11D, 6-11E, 6-11F, 6-11G (online) Topic 9: Lesson 9-7A (online)


Summative

There is no district interim assessment available for this unit.

Formatives

For formative assessment strategies, see pages 53-62 in the

Fourth Grade Mathematics Curriculum Map.

Enrichment

Math Extension Activities organized by each topic are available through Copy Center/DOD.


CCSS DOMAIN: Unit:

MEASUREMENT AND DATA CCSS Measurement & Data Extension

PACING: Week 37 May 19 – May 23


Line Plots

CCSS: Make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

MACC.5.MD.2.2 length line plot liquid volume mass measurement

Students will:

• measure and record objects to the nearest 1/2, 1/4, or 1/8 unit.

NOTE: Measures for length, mass, and liquid volume will be the focus for this standard.

• display the collected data on a line plot.

Example: Ten beakers, measured in liters, are filled with a liquid.

• solve problems using data on line plots.

NOTE: Refer to pages 51-52 in the Fifth Grade Mathematics Curriculum Map for clarification of Table 1 and 2: Common addition, subtraction, multiplication and division situations. It is expected that students will become proficient in finding the unknown number for all situations.











reasoning.




enVisionMATH Student Edition Topic 15: Lessons 15-1A (online)

enVisionMATH Ready-Made Centers Topic 15: Lessons 15-1A (online)

envisionMath Daily Assessment and Reteaching Workbook Topic 15: Lessons 15-1A (online)


Summative


Formatives



Enrichment



CCSS DOMAIN: Unit:

OPERATIONS AND ALGEBRAIC THINKING CCSS Algebra Extension

PACING: Weeks 38 – 39 May 27 – June 6


Patterns

CCSS: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

MACC.5.OA.2.3 coordinate plane graph ordered pair origin pattern plot rule x-axis y-axis

Students will:

• generate two numerical patterns with the same starting number for two given rules. Example:

• explain the relationship between the two numerical patterns by comparing how each pattern grows or by comparing the relationship between each of the corresponding terms from each pattern.

Example: Since Joe catches 4 fish each day, and Melissa catches 2 fish, the amount of Joe’s fish is always greater. Joe’s fish is also twice as much as Melissa’s fish. Today, both Melissa and Joe have no fish. They both go fishing each day. Melissa catches 2 fish each day. Joe catches 4 fish each day.

• form ordered pairs out of corresponding terms from each pattern and graph them on a coordinate plane.

Example:



enVisionMATH Student Edition Topic 5: Lessons 5-5A (online)

enVisionMATH Ready-Made Centers Topic 5: Lessons 5-5A (online)

envisionMath Daily Assessment and Reteaching Workbook Topic 5: Lessons 5-5A (online)


Summative


Formatives



Enrichment



Table 1. Common addition and subtraction situations.6

Result Unknown Change Unknown Start Unknown

Add to

Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?

2 + 3 = ?

Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two?

2 + ? = 5

Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before?

? + 3 = 5

Take from

Five apples were on the table. I ate two apples. How many apples are on the table now?

5 – 2 = ?

Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?

5 - ? = 3

Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before?

? – 2 = 3

Total Unknown Addend Unknown Both Addends Unknown1

Put Together/

Take Apart2

Three red apples and two green apples are on the table. How many apples are on the table?

3 + 2 = ?

Five apples are on the table. Three are red and the rest are green. How many apples are green?

3 + ? = 5, 5 – 3 = ?

Grandma has five flowers. How many can she put in her red vase and how many in her blue vase?

5 = 0 + 5, 5 = 5 + 0 5 = 1 + 4, 5 + 4 + 1 5 = 2 + 3, 5 = 3 + 2

Difference Unknown Bigger Unknown Smaller Unknown Compare 3

(“How many more?” version):

Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy?

(“How many fewer?” version):

Lucy has two apples. Julie has five apples. How may fewer apples does Lucy have than Julie?

2 + ? = 5, 5 – 2 = ?

(Version with “more”):

Julie has 3 more apples than Lucy. Lucy has two apples. How many apples does Julie have?

(Version with “fewer”):

Lucy has three fewer apples than Julie. Lucy has two apples. How many apples does Julie have?

2 + 3 = ?, 3 + 2 = ?

(Version with “more”):

Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?

(Version with “fewer”):

Lucy has three fewer apples than Julie. Julie has five apples. How many apples does Lucy have? 5 – 3 = ?, ? + 3 = 5

1 These take apart situations can be used to show all the decompositions of a given number. The associated equations, which have the total on the left of the equal sign, help children understand that the = sign does not always mean makes or results in, but always does mean is the same number as. 2 Either addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown is a productive extension of this basic situation, especially for small numbers less than or equal to 10. 3 For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for the bigger unknown and using less for the smaller unknown). The other versions are more difficult. 6 Adapted from Box 2-4 of Mathematics Learning in Early Childhood, National Research Council (2009, pp. 32, 33).


Table 2. Common multiplication and division situations.38

Unknown Product

Group Size Unknown (“How many in each group?”

Division)

Number of Groups Unknown (“How many groups?” Division)

3 × 6 = ? 3 × ? = 18 and 18 ÷ 3 = ? ? × 6 = 18 and 18 ÷ 6 = ?

Equal Groups

There are 3 bags with 6 plums in each bag. How many plums are there in all?

Measurement example. You need 3 lengths of string, each 6 inches long. How much string will you need altogether?

If 18 plums are shared equally into 3 bags, then how many plums will be in each bag?

Measurement example. You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be?

If 18 plums are to be packed 6 to a bag, then how many bags are needed?

Measurement example. You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have?

Arrays39, Area40

There are 3 rows of apples with 6 apples in each row. How many apples are there?

Area example. What is the area of a 3 cm by 6 cm rectangle?

If 18 apples are arranged into 3 equal rows, how many apples will be in each row?

Area example. A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it?

If 18 apples are arranged into equal rows of 6 apples, how many rows will there be?

Area example. A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it?

Compare

A blue hat costs $6. A red hat cost 3 times as much as the blue hat. How much does the red hat cost?

Measurement example. A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long?

A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does the blue hat cost?

Measurement example. A rubber band is stretched to be 18 cm long and that is 3 times as longs as it was at first. How long was the rubber band at first?

A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat?

Measurement example. A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first?

General a × b = ? a × ? = p and p ÷ a = ? ? × b = p and p ÷ b = ? 38

The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples. 39

The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How m any apples are in there? Both forms are valuable. 40

Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations.


Formative Assessment Strategies

Mathematics K-5

Name Description Additional Information

A & D Statements

A & D Statements analyze a set of “fact or fiction” statements. First, students may choose to agree or disagree with a statement or identify whether they need more information. Students are asked to describe their thinking about why they agree, disagree, or are unsure. In the second part, students describe what they can do to investigate the statement by testing their ideas, researching what is already known, or using other means of inquiry.

http://www.mathsolutions.com/documents/How_to_Get_Students_Talking.pdf

Statement How can I find out? 9/16 is larger than 5/8. __agree __disagree __not sure __it depends on My thoughts:

Agreement Circles

Agreement Circles provide a kinesthetic way to activate thinking and engage students in mathematical argumentation. Students stand in a circle as the teacher reads a statement. They face their peers still standing and match themselves up in small groups of opposing beliefs. Students discuss and defend their positions. After some students defend their answers, the teacher can ask if others have been swayed. If so, stand up. If not, what are your thoughts? Why did you disagree? After hearing those who disagree, does anyone who has agreed want to change their minds? This should be used when students have had some exposure to the content.

There 20 cups in a gallon. Agree or disagree? 2/3 equivalent to 4/6. Agree or disagree? A square is a rectangle. Agree or disagree? Additional Questioning: Has anyone been swayed into new thinking? What is your new thinking? Why do you disagree with what you have heard? Does anyone want to change their mind? What convinced you to change your mind? Use when students have had sufficient exposure to content.

http://formativeassessment.barrow.wikispaces.net/Agreement+Circles

Annotated Student

Drawings

Annotated Student Drawings are student-made, labeled illustrations that visually represent and describe students’ thinking about mathematical concepts. Younger students may verbally describe and name parts of their drawings while the teacher annotates it for them.

Represent 747 by drawing rods and cubes. Represent 3x2=2x3 by drawing arrays. Describe the meaning of 5.60.

http://formativeassessment.barrow.wikispaces.net/Annotated+Student+Drawings


Formative Assessment Strategies/Mathematics K-5 (continued)


Card Sorts

Card Sorts is a sorting activity in which students group a set of cards with pictures or words according to certain characteristics or category. Students sort the cards based on their preexisting ideas about the concepts, objects, or processes on the cards. As students sort the cards, they discuss their reasons for placing each card into a designated group. This activity promotes discussion and active thinking.

http://teachingmathrocks.blogspot.com/2012/09/vocabulary-card-sort.html

Commit and Toss

Commit and Toss is a technique used to anonymously and quickly assess student understanding on a topic. Students are given a question. They are asked to answer it and explain their thinking. They write this on a piece of paper. The paper is crumpled into a ball. Once the teacher gives the signal, they toss, pass, or place the ball in a basket. Students take turns reading their "caught" response. Once all ideas have been made public and discussed, engage students in a class discussion to decide which ideas they believe are the most plausible and to provide justification for the thinking.

Stephanie eats 5 apple slices during lunch. When she gets home from school she eats more. Which statement(s) below indicates the number of apple slices Stephanie may have eaten during the day?

a. She eats 5 apple slices. b. She eats 5 apple slices at least. c. She eats more than 5 apple slices. d. She eats no more than 5 apple slices. e. I cannot tell how many apple slices were eaten.

Explain your thinking. Describe the reason for the answer(s) you selected.

Concept Card Mapping

Concept Card Mapping is a variation on concept mapping. Students are given cards with the concepts written on them. They move the cards around and arrange them as a connected web of knowledge. This strategy visually displays relationships between concepts.




Concept Cartoons

Concept Cartoons are cartoon drawings that visually depict children or adults sharing their ideas about common everyday mathematics. Students decide which character in the cartoon they agree with most and why. This formative is designed to engage and motivate students to uncover their own ideas and encourage mathematical argumentation. Concept Cartoons are most often used at the beginning of a new concept or skill. These are designed to probe students’ thinking about everyday situations they encounter that involve the use of math. Not all cartoons have one “right answer.” Students should be given ample time for ideas to simmer and stew to increase cognitive engagement.

• www.pixton.com (comic strip maker)

Four corners

Four Corners is a kinesthetic strategy. The four corners of the classroom are labeled: Strongly Agree, Agree, Disagree and Strongly Disagree. Initially, the teacher presents a math-focused statement to students and asks them to go to the corner that best aligns with their thinking. Students then pair up to defend their thinking with evidence. The teacher circulates and records student comments. Next, the teacher facilitates a whole group discussion. Students defend their thinking and listen to others’ thinking before returning to their desks to record their new understanding.

A decimal is a fraction.

http://debbiedespirt.suite101.com/four-corners-activities-a170020

http://wvde.state.wv.us/teach21/FourCorners.html

Frayer Model

Frayer Model graphically organizes prior knowledge about a concept into an operational definition, characteristics, examples, and non-examples. It provides students with the opportunity to clarify a concept or mathematical term and communicate their understanding. For formative assessment purposes, they can be used to determine students’ prior knowledge about a concept or mathematical term before planning the lesson. Barriers that can hinder learning may be uncovered with this assessment. This will then in turn help guide the teacher for beneficial instruction.

Frayer ModelDefinition in your own words Facts/characteristics

Examples NonexamplesQuadrilateral

A quadrilateral is a shape

with 4 sides.

•4 sides

• may or may not be of equal

length

• sides may or may not be

parallel

• square

• rectangle

• trapezoid

• rhombus

• circle

• triangle

• pentagon

• dodecahedron

Agree

Disagree Strongly Disagree

Strongly Agree




Friendly Talk Probes

Friendly Talk Probes is a strategy that involves a selected response section followed by justification. The probe is set in a real-life scenario in which friends talk about a math-related concept or phenomenon. Students are asked to pick the person they most agree with and explain why. This can be used to engage students at any point during a unit. It can be used to access prior knowledge before the unit begins, or assess learning throughout and at the close of a unit.

http://www.sagepub.com/upm-data/37758_chap_1_tobey.pdf

Human Scatterplots

Human Scatterplot is a quick, visual way for teacher and students to get an immediate classroom snapshot of students’ thinking and the level of confidence students have in their ideas. Teachers develop a selective response question with up to four answer choices. Label one side of the room with the answer choices. Label the adjacent wall with a range of low confidence to high confidence. Students read the question and position themselves in the room according to their answer choice and degree of confidence in their answer.

I Used to Think… But Now I Know…

I Used to Think…But Now I Know is a self-assessment and reflection exercise that helps students recognize if and how their thinking has changed at the end of a sequence of instruction. An additional column can be added to include…And This Is How I Learned It to help students reflect on what part of their learning experiences helped them change or further develop their ideas.

I USED TO THINK… BUT NOW I KNOW…

AND THIS IS HOW I LEARNED IT




Justified List

Justified List begins with a statement about an object, process, concept or skill. Examples and non-examples for the statement are listed. Students check off the items on the list that are examples of the statement and provide a justification explaining the rule or reasons for their selections. This can be done individually or in small group. Small groups can share their lists with the whole class for discussion and feedback. Pictures or manipulatives can be used for English-language learners.

Example 1

Put an X next to the examples that represent 734.

___700+30+4 ___7 tens 3 hundreds 4 ones ___730 tens 4 ones ___7 hundreds 3 tens 4ones ___734 ones ___seven hundred thirty-four ___seventy-four ___ 400+70+3

Explain your thinking. What “rule” or reasoning did you use to decide which objects digit is another way to state that number.

Example 2

K-W-L Variations

K-W-L is a general technique in which students describe what they Know about a topic, what they Want to know about a topic, and what they have Learned about the topic. It provides an opportunity for students to become engaged with a topic, particularly when asked what they want to know. K-W-L provides a self-assessment and reflection at the end, when students are asked to think about what they have learned. The three phrases of K-W-L help students see the connections between what they already know, what they would like to find out, and what they learned as a result.

K-This what I already KNOW

W-This is what I WANT to find out

L-This is what I LEARNED

Learning Goals Inventory (LGI)

Learning Goals Inventory (LGI) is a set of questions that relate to an identified learning goal in a unit of instruction. Students are asked to “inventory” the learning goal by accessing prior knowledge. This requires them to think about what they already know in relation to the learning goal statement as well as when and how they may have learned about it. The LGI can be given back to students at the end of the instructional unit as a self-assessment and reflection of their learning.

What do you think the learning goal is about?

List any concepts or ideas you are familiar with related to this learning goal.

List any terminology you know of that relates to this goal.

List any experiences you have had that may have helped you learn about the ideas in this learning goal.




Look Back

Look Back is a recount of what students learned over a given instructional period of time. It provides students with an opportunity to look back and summarize their learning. Asking the students “how they learned it” helps them think about their own learning. The information can be used to differentiate instruction for individual learners, based on their descriptions of what helped them learn.

What I Learned How I Learned it

Muddiest Point

Muddiest Point is a quick-monitoring technique in which students are asked to take a few minutes to jot down what the most difficult or confusing part of a lesson was for them. The information gathered is then to be used for instructional feedback to address student difficulties.

Scenario: Students have been learning about the attributes of three-dimensional shapes. Teacher states, “I want you to think about the muddiest point for you so far when it comes to three-dimensional shapes. Jot it down on this notecard. I will use the information you give to me to think about ways to help you better understand three-dimensional shapes in tomorrow’s lesson.”

Odd One Out

Odd One Out combines similar items/terminology and challenges students to choose which item/term in the group does not belong. Students are asked to justify their reasoning for selecting the item that does not fit with the others. Odd One Out provides an opportunity for students to access scientific knowledge while analyzing relationships between items in a group.

Show students three figures and ask: Which is the odd one out?

Explain your thinking. Ask students to choose a different odd one out and explain their thinking.

Partner Speaks

Partner Speaks provides students with an opportunity to talk through an idea or question with another student before sharing with a larger group. When ideas are shared with the larger group, pairs speak from the perspective of their partner’s ideas. This encourages careful listening and consideration of another’s ideas.

Today we are going to explore different ways to add three-digit numbers together.

What different kinds of strategies can you use to add 395+525?

Turn to your partner and take turns discussing your strategies. Listen carefully and be prepared to share your partner’s ideas.




A Picture Tells a

Thousand Words

A Picture Tells a Thousand Words, students are digitally photographed during a mathematical investigation using manipulatives or other materials. They are given the photograph and asked to describe what they were doing and learning in the photo. Students write their description under the photograph. The images can be used to spark student discussions, explore new directions in inquiry, and probe their thinking as it relates to the moment the photograph was snapped. By asking students to annotate a photo that shows the engaged in a mathematics activity or investigation helps them activate their thinking about the mathematics, connect important concepts and procedures to the experience shown in the picture and reflect on their learning. Teachers can better understand what students are gaining from the learning experience and adjust as needed.

Question Generating

Question Generating is a technique that switches roles from the teacher as the question generator to the student as the question generator. The ability to formulate good questions about a topic can indicate the extent to which a student understands ideas that underlie the topic. This technique can be used any time during instruction. Students can exchange or answer their own questions, revealing further information about the students’ ideas related to the topic.

Question Generating Stems:

• Why does___? • Why do you think___? • Does anyone have a different way to

explain___? • How can you prove___? • What would happen if___? • Is___always true? • How can we find out if___?

Sticky Bars

Sticky Bars is a technique that helps students recognize the range of ideas that students have about a topic. Students are presented with a short answer or multiple-choice question. The answer is anonymously recorded on a Post-it note and given to the teacher. The notes are arranged on the wall or whiteboard as a bar graph representing the different student responses. Students then discuss the data and what they think the class needs to do in order to come to a common understanding.




Thinking Log

Thinking Logs is a strategy that informs the teacher of the learning successes and challenges of individual students. Students choose the thinking stem that would best describe their thinking at that moment. Provide a few minutes for students to write down their thoughts using the stem. The information can be used to provide interventions for individuals or groups of students as well as match students with peers who may be able to provide learning support.

• I was successful in… • I got stuck… • I figured out… • I got confused when…so I… • I think I need to redo… • I need to rethink… • I first thought…but now I realize… • I will understand this better if I… • The hardest part of this was… • I figured it out because…

• I really feel good about the way…

Think-Pair-Share

Think-Pair-Share is a technique that combines thinking with communication. The teacher poses a question and gives individual students time to think about the question. Students then pair up with a partner to discuss their ideas. After pairs discuss, students share their ideas in a small-group or whole-class discussion. (Kagan)

NOTE: Varying student pairs ensures diverse peer interactions.

Three-Minute Pause

Three-Minute Pause provides a break during a block of instruction in order to provide time for students to summarize, clarify, and reflect on their understanding through discussion with a partner or small group. When three minutes are up, students stop talking and direct their attention once again to the teacher, video, lesson, or reading they are engaged in, and the lesson resumes. Anything left unresolved is recorded after the time runs out and saved for the final three-minute pause at the end.

Traffic Light Cards/Cups/Dots

Traffic Light Cards/Cups/Dots is a monitoring strategy that can be used at any time during instruction to help teachers gauge student understanding. The colors indicate whether students have full, partial, or minimal understanding. Students are given three different-colored cards, cups, or dots to display as a form of self-assessment revealing their level of understanding about the concept or skill they are learning.




Two-Minute Paper

Two-Minute Paper is a quick way to collect feedback from students about their learning at the end of an activity, field trip, lecture, video, or other type of learning experience. Teacher writes two questions on the board or on a chart to which students respond in two minutes. Responses are analyzed and results are shared with students the following day.

• What was the most important thing you learned today?

• What did you learn today that you didn’t know before?

• What important question remains unanswered for you?

• What would help you learn better tomorrow?

Two Stars and a Wish

Two Stars and a Wish is a way to balance positive and corrective feedback. The first sentence describes two positive commendations for the student’s work. The second sentence provides one recommendation for revision. This strategy could be used teacher-to-student or student-to-student.

Two-Thirds Testing

Two-Thirds Testing provides an opportunity for students to take an ungraded “practice test” two thirds of the way through a unit. It helps to identify areas of difficulty or misunderstanding through an instructional unit so that interventions and support can be provided to help them learn and be prepared for a final summative assessment. Working on the test through discussions with a partner or in a small group further develops and solidifies conceptual understanding.




What Are You Doing and Why?

What Are You Doing and Why? is a short, simple monitoring strategy to determine if students understand the purpose of the activity or how it will help them learn. At any point in an activity the teacher gets the students’ attention and asks “What are you doing and why are you doing it?” Responses can be shared with the class, discussed between partners, or recorded in writing as a One-Minute Paper to be passed in to the teacher. The data are analyzed by the teacher to determine if the class understands the purpose of the activity they are involved in.

Scenario: Students are decomposing a fraction into the sum of two or more of its parts.

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Teacher stops students in their tracks and asks,

“What are you do and why are you doing it?”

Whiteboarding

Whiteboarding is a technique used in small groups to encourage students to pool their individual thinking and come to a group consensus on an idea that is shared with the teacher and the whole class. Students work collaboratively around the whiteboard during class discussion to communicate their ideas to their peers and the teacher.

http://www.educationworld.com/a_lesson/02/lp251-01.shtml

3-2-1

3-2-1 is a technique that provides a structured way for students to reflect upon their learning. Students respond in writing to three reflective prompts. This technique allows students to identify and share their successes, challenges, and questions for future learning. Teachers have the flexibility to select reflective prompts that will provide them with the most relevant information for data-driven decision making.

Sample 1 • 3 – Three key ideas I will remember • 2 – Two things I am still struggling with

• 1 – One thing that will help me tomorrow Sample 2


Intervention/Remediation Guide

Resource Location Description Intervention Lessons (Student and Teacher pages)

Math Diagnosis and Intervention System

Use for pre-requisite skills or remediation. For grades K-2, the lessons consist of a teacher-directed activity followed by problems. In grades 3-5, the student will first answer a series of questions that guide him or her to the correct answer of a given problem, followed by additional, but similar problems.

Meeting Individual Needs Planning section of each Topic in the enVision Math Teacher’s Edition

Provides topic-specific considerations and activities for differentiated instruction of ELL, ESE, Below-Level and Advanced students.

Differentiated Instruction Close/Assess and Differentiate step of each Lesson in the enVision Math Teacher’s Edition

Provides lesson-specific activities for differentiated instruction for Intervention, On-Level and Advanced levels.

Error Intervention Guided Practice step of each Lesson in the enVision Math Teacher’s Edition

Provides on-the-spot suggestions for corrective instruction.

ELL Companion Lesson Florida Interactive Lesson Support for English Language Learners

Includes short hands-on lessons designed to provide support for teachers and their ELL students, useful for struggling students as well

2013 - 2014 fifth grade...

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