Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 3

Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,

80% of our students will graduate from high school college or career ready 90% of students will graduate on time 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, College and Career Ready standards-aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and Career Ready Standards are rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

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Focus

The Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For grades K–8, each grade's time spent in instruction must meet or exceed the following percentages for the major work of the grade. 85% or more time spent in instruction in each grade Kindergarten, 1, and 2 align exclusively to the major work of the grade. 75% or more time spent in instruction in each grade 3, 4, and 5 align exclusively to the major work of the grade. Supporting Content - information that supports the understanding and implementation of the major work of the grade.Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency.

Coherence

Thinking across grades:The Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding on to foundations built in previous years. Each standard is not a new event, but an extension of previous learning. Linking to major topics:Instead of allowing additional or supporting topics to detract from the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.

Rigor

Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures.Application: The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.

Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 3

While the academic standards establish desired learning outcomes, the curriculum provides instructional planning designed to help students reach these outcomes. Educators will use this guide and the standards as a roadmap for curriculum and instruction. The sequence of learning is strategically positioned so that necessary foundational skills are spiraled in order to facilitate student mastery of the standards.

These standards emphasize thinking, problem-solving and creativity through next generation assessments that go beyond multiple-choice tests to increase college and career readiness among Tennessee students. In addition, assessment blueprints (http://www.tn.gov/education/article/tnready-blueprints) have been designed to show educators a summary of what will be assessed in each grade, including the approximate number of items that will address each standard. Blueprints also detail which standards will be assessed on Part I of TNReady and which will be assessed on Part II.

Our collective goal is to ensure our students graduate ready for college and career. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation and connections.

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Problem Solving

Reasoning and Proof

CommunicationRepresentation

Connection

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The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations) procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see

mathematics and sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy). Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

How to Use the Mathematics Curriculum Maps

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that ultimately our students can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their instructional practice in alignment with the three College and Career Ready shifts, as described above, in instruction for Mathematics.

Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the standards and teaching practices that teachers should consistently access:

The TNCore Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at each respective grade level.

Mathematical Teaching Practiceshttps://mathprojectsjournal.files.wordpress.com/2015/05/nctm-teaching-practices.pdf

NCTM – Mathematics Teaching Practices

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Mathematical Practices

Make sense of problems and persevere in solving them

Reason abstractly and quatitatively

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

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Locate the TDOE Standards in the left column. Analyze the language of the standards and match each standard to a learning target in the second column.

Each standard is identified as the following: Major Work, Supporting Content or Additional Content. In any single grade, students and teachers should spend the majority of their time on the major work of the grade. Consult your enVision Teachers’ Edition (TE) and other cited references to map out your week(s) of instruction. Plan your weekly and daily objectives, using the learning target statements to help. Best practices tell us that making objectives

measureable increases student mastery. Include daily fluency practice. Study the suggested performance assessments (tasks) and match them to your objectives. Review the Literacy Connections found in the right hand column. Make plans to address the Academic Vocabulary in your

instruction. Examine the other standards and skills you will need to address in order to ensure mastery of the indicated standard. Using your enVision TE and other resources cited in the curriculum map, plan your week using the SCS lesson plan template.

Remember to include differentiated activities to address the needs of all students.

Resources to Help Prepare Students for the TNReady Assessments

The following tools are available for teachers to assist them in preparing their students for the TNReady Assessments: The Item Sampler (MICA) can be found here: https://micatime.com/ TDOE TNReady Practice Tools homepage : A summary of TNReady practice tools Classroom Chronicles: Using MICA to prepare for TNReady : Hear how other teachers in TN are using MICA! Ten Things to Know about TNReady from the TDOE TNReady Blueprints: Blueprints provide a summary of what will be assessed in each grade, including the number of items that will

address each standard on each part of TNReady as well as the standards addressed in the Performance Task. This webpage also includes the calculator policy and reference sheets for Grades 5-8.

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Overview

Grade 3: Quarter 4

Engageny Module 7: Geometry and Measurement Word Problems (continued from Q3)Review: 3.NF.A/3.NBT.ATN Ready Part 2Engageny Module 7: Topic F: Year in Review/ Review Tasks

Overview

Quarter 4 begins with a continuation of Engageny Module 7. Topic A was covered in Quarter 3, therefore we will begin the final quarter with Topic B. Topic B: Attributes of Two-Dimensional FiguresTopic B introduces an exploration of geometry. Students build on Grade 2 ideas about polygons and their properties, specifically developing and expanding their knowledge of quadrilaterals. They explore the attributes of quadrilaterals and classify examples into various categories, including recognizing the characteristics of polygons (3.G.1). Students draw polygons based on their attributes, producing sketches from descriptions like, “This shape has two long sides that are parallel, two short sides, and no right angles.” Students next use tangrams and tetrominoes (see examples to the right) to compose and decompose shapes. They reason about the relationships between shapes and between attributes. For example, students understand that quadrilaterals can be decomposed into triangles, and recognize that the two smallest triangles in a tangram puzzle can be put together to form a parallelogram, a square, and a medium triangle.

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Topic C: Problem with PerimeterStudents tessellate to bridge geometry experience with the study of perimeter in Topic C. They first decompose a quadrilateral and then rearrange the parts. They use the new shape to tile. Students then define perimeter in two distinct ways: (1) as the boundary of a planar region and (2) as the length of the boundary curve. Students see varied examples from the tiles used to tessellate. As they learn about perimeter as an attribute of plane figures, students apply their knowledge to real world situations through problem solving (3.MD.8). They measure side lengths of shapes in whole number units to determine perimeter and solve problems where side lengths are given. They use string and rulers to measure the length around circles of different sizes. This variation prompts students to think more flexibly about perimeter, and to understand that it can be the boundary of any shape and that its measurements are not limited to whole numbers. The topic ends with problems in which some measurements around the perimeter of a polygon are missing but can be determined by reasoning. Students consider the efficiency of their strategies and identify tools for solving; for example, they use multiplication as a tool when measurements are repeated.

Topic D: Recording of Perimeter and Area Data on Line PlotsTopic D utilizes the line plot, familiar from Module 6, to help students draw conclusions about perimeter and area measurements (3.MD.4). Early in the topic, students find different possible perimeters or areas for rectangles based on information given about the rectangles. For example, using knowledge of factors from experience with multiplication, students determine the following:

Different perimeters of rectangles comprised of a given number of unit squares (3.MD.8). For example, given a rectangle composed of 24 unit squares, students find four possible perimeters: 50, 28, 22, and 20 length units.

Different areas of rectangles comprised of unit squares with a given perimeter. For example, students use unit squares to build rectangles with a perimeter of 12 units and determine that they can do so using 5, 8, or

9 unit squares. (Rectangles are formed with unit squares, and as a result they have whole number side lengths.)

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Students then draw their rectangles on grid paper and reason about their findings, noticing, for example, that for rectangles of a given area, those with side lengths that are equal or almost equal (more square-like) have smaller perimeters than those whose side lengths are very different (a long and narrow shape). They use line plots to show the number of rectangles they were able to construct for each set of given information. The line plots are a tool that students use to help them reason and draw conclusions about their data. As they move through the lessons in this topic, students notice and compare differences in the strategies for finding area when given a perimeter and for finding perimeter given an area. By the end of the topic they are able to conclude that there is no direct relationship between area and perimeter, meaning that if an area is given there is no way of knowing a shape’s corresponding perimeter.

Topic B: Problem Solving with Perimeter and AreaIn Topic E, students solve problems involving area and perimeter. After an initial lesson problem solving with perimeter, students apply this knowledge to create a robot composed of rectangles. Given specific perimeter measurements, they reason about the different side lengths that may be produced. Students compare and analyze their work, discussing how different choices for side lengths can affect area while conforming to the criteria for perimeter. Students synthesize their learning in the final lessons through solving word problems involving area and perimeter using all four operations (3.OA.8).We then break for a quick review of the following standards: 3.NF.A and 3.NBT.A. These standards were chosen as a review based TN 3rd Grade Blueprint. These two skills will count toward 10-15% of the TN Ready Part 2 Assessment. In this section we have included resources that are different from resources listed in previous quarters to give you a variety of ways to meet the needs of your students. It is the intent that you will use these resources to guide the instruction for your class and individual student review prior to taking TN Ready Part 2. The pacing is set up so that this review will come the week before the SCS published testing schedule.

Topic F: Year in ReviewTopic F concludes the school year with a set of engaging lessons that briefly review the fundamental Grade 3 concepts of fractions, multiplication, and division. This topic comes after the End-of-Module Assessment. It begins with a pair of lessons on fractions, engaging students in analyzing and creating unusual representations of one-half such as those shown to the right. Students analyze and discuss these representations, using their knowledge of fractions to justify their constructions and critique the work of others to make adjustments as necessary. The final lessons in this topic are fluency based and engage students in games that provide practice to solidify their automaticity with Grade 3 skills. Using simple origami techniques they create booklets of these games. The booklets go home and become resources for summer practice.

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The final review includes specific tasks that can reinforce the concepts that students will need going forward into fourth grade. If fluency practice has continued daily as suggested in the curriculum maps, students should now feel confident in their increased procedural fluency and prepared to enter the next level of their mathematics progression in fourth grade.

Focus Grade Level Standards(Note: Related Foundational Standards are noted in parenthesis after standard)Cluster 3.G.A: Reason with shapes and their attributes. 3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and

that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. (1.G.A.1, 2.G.A.1)

Cluster 3.MD.B: Represent and interpret data.

3.MD.B.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters. (2.MD.D.9)

Cluster 3.MD.D: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.MD.D.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths,

finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. (3.MD.C.5)

Cluster 3.NF.A: Develop the understanding of fractions as numbers. 3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is portioned into b equal parts; understand a fraction a/bas the

quantity formed by a parts of size 1/b. (1.G.A.3, 2.G.A.3) 3.NF.A.2 Represent a fraction 1/b on a number line diagram (3.NF.A.1) 3.NF.A.2.a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal

parts. Recognize that each part has a size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (3.NF.A.1) 3.NF.A.2b Represent a fraction a/b on a number line diagram by marking of a lengths 1/b from 0. Recognize that the resulting interval has size a/b and

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3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (3.NF.A.1, 3.NF.A.2) 3.NF.A.3.a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (3.NF.A.1, 3.NF.A.2) 3.NF.A.3.b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using

a visual fraction model. (3.NF.A.1, 3.NF.A.2) 3.NF.A.3.c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. (3.NF.A.1, 3.NF.A.2) 3.NF.A.3.d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons

are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model 1/b. (3.NF.A.1, 3.NF.A.2)

Cluster 3.NBT.A: Use place value understanding and properties of operations to perform multi-digit arithmetic.

3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100. (1.NBT.B.2, 2.NBT.A.1, 2.NBT.A.2) 3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the

relationship between addition and subtraction. (2.NBT.B.7, 2.NBT.B.8, 2.NBT.A.1)

Cluster 3.NBT.A: Use place value understanding and properties of operations to perform multi-digit arithmetic.

3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. (2.NBT.A.1, 3.OA.B.5)

Cluster 3.OA.A: Represent and solve problems involving multiplication and division. 3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. (2.NBT.A.2, 2.OA.C.3, 2.OA.C.4) 3.OA.A.2 Interpret whole-number quotients of whole numbers. (2.OA.C.4, 2.NBT.A.2, 3.OA.A.1) 3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawing and equations with a symbol for the unknown number to represent the problem. (3.OA.A.1, 3.OA.A.2)

Cluster 3.OA.C: Multiply and divide within 100. Shelby County Schools

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3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. (3.OA.A.1, 3.OA.A.2)

Foundational StandardsGeometry 1.G.A.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non- defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use

the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

2.G.A.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Measurement and Data

2.MD.D.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. 3.MD.C.5.a A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. 3.MD.C.5.b A plane figure, which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

Numbers and Operations Base 10 1.NBT.B.2. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

a) 10 can be thought of as a bundle of ten ones – called a “ten.” b) The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. C) The numbers 10, 20, 10, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight or nine tens (and 0 ones).

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2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the special cases.

2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s. 2.NBT.B.7 Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes is necessary to compose or decompose tens or hundreds.

2.NBT.B.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

Operations and Algebraic Thinking 2.OA.C.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by

2s; write an equation to express an even number as a sum of two equal addends. (1.OA.D.7) 2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation

to express the total as a sum of equal addends. (1.OA.D.7)

Fluency Practice

NCTM Position

Procedural fluency is a critical component of mathematical proficiency. Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another. To develop procedural fluency, students need experience in integrating concepts and procedures and building on familiar procedures as they create their own informal strategies and procedures. Students need opportunities to justify both informal strategies and commonly used procedures mathematically, to support and justify their choices of appropriate procedures, and to strengthen their understanding and skill through distributed practice.

Fluency is designed to promote automaticity by engaging students in practice in ways that get their adrenaline flowing. Automaticity is critical so that students avoid using up too many of their attention resources with lower-level skills when they are addressing higher-level problems. The automaticity prepares students with the computational foundation to enable deep understanding in flexible ways. Therefore it is recommended that students participate in fluency practice daily. It should be high-paced and energetic, celebrating improvement and focusing on recognizing patterns

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and connections within the material. Special care should be taken so that it is not seen as punitive for students that might need more time to master fluency.

Standards for Mathematical Practice

The eight Standards for Mathematical Practice are an important component of the mathematics standards for each grade and course, K-12.  The Standards for Mathematical Practice describe the varieties of expertise, habits of minds, and productive dispositions that educators seek to develop in all students.

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.

Resources:

https://www.engageny.org/resource/grade-2-mathematics https://www.pearsonsuccessnet.com/snpapp/iText/getTeacherHomepage.do?newServiceId=6000&newPageId=10100 http://www.nctm.org/Standards-and-Positions/Position-Statements/Procedural-Fluency-in-Mathematics/

TN State Standards Essential Understandings Content & Tasks Literacy Connections

Engageny Module 7: Geometry and MeasurementTopic B-E

(Continued from Q3 - Allow 6 weeks for instruction, review and assessment)

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TN State Standards Essential Understandings Content & Tasks Literacy Connections

Cluster 3.G.A: Reason with shapes and their attributes.

3.G.A.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Cluster 3.MD.B: Represent and interpret data.

3.MD.B.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

Cluster 3.MD.D: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.MD.D.8 Solve real world and

mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Enduring Understandings1. Shapes can be used to describe some

attributes of some solids.2. Two-dimensional or plane shapes have

many properties that make them different from one another. Polygons can be described and classified by their sides and angles.

3. The distance around a figure is its perimeter, which is the sum of the length of the sides.

4. Different shapes can have the same perimeter.

5. Measurements of solid figures can be estimated or approximated.

Essential Questions6. What is a solid figure?7. How can you describe parts of solid

figures?8. What is a polygon?9. How can you describe triangles?10. What are some special names for

quadrilaterals?11. How do you find perimeter?12. How do you find the perimeter of common

shapes?13. How do you find the perimeter of shapes?14. What shapes can you make when you

know the perimeter?Learning Targets

I can compare and classify quadrilaterals. (Topic B: Lesson 4)

Please use the following Resources from Engageny: (Continued from Q3)(Note: Objectives are restated as Learning Targets in the previous column)

Week 1(Suggested – This may vary depending on individual class needs as well as the use of tasks in instruction)Module 7: Geometry and MeasurementTopic B: Attributes of Two-Dimensional FiguresLesson 4 : Objective: Compare and classify quadrilaterals.Lesson 5 : Objective: Compare and classify other polygons.Lesson 6 : Objective: Draw polygons with specified attributes to solve problemsLesson 7 : Objective: Reason about composing and decomposing polygons using tetrominoes.Lesson 8 : Objective: Create a tangram puzzle and observe relationships among the shapes.Lesson 9 : Objective: Reason about composing and decomposing polygons using tangrams.Week 2(Suggested – This may vary depending on individual class needs as well as the use of tasks in instruction)

Topic C: Problem with Perimeter

VocabularyAttribute, diagonal, perimeter, property, regular polygon, tessellate, tetrominoes

Familiar VocabularyArea, compose, decompose, heptagon, hexagon, octagon, parallel, parallelogram, pentagon, polygon, quadrilateral

Literature ConnectionsWorldScapes Readers: Below ZeroWorldScapes Readers: Fiji Facts and Figures

Additional Literature ConnectionsMath Matters series by ScholasticChickens on the Move, Pam Pollack & Meg Belviso

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TN State Standards Essential Understandings Content & Tasks Literacy Connections

(3.G.A.1) I can compare and classify other

polygons. (Topic B: Lesson 5) (3.G.A.1)

I can draw polygons with specified attributes to solve problems. (Topic B: Lesson 6) (3.G.A.1)

I can reason about composing and decomposing polygons using tetraminioes. (Topic B: Lesson 7) (3.G.A.1)

I can create a tangram puzzle and observe relationships among the shapes. (Topic B: Lesson 8) (3.G.A.1)

I can reason about composing and decomposing polygons using tangrams. (Topic B: Lesson 9) (3.G.A.1)

I can decompose quadrilaterals to understand perimeter as the boundary of a shape. (Topic C: Lesson 10) (3.G.A.1, 3.MD.D.8)

I can tessellate to understand perimeter as the boundary of a shape. (Topic C: Lesson 11) 3.G.A.1, 3.MD.D.8)

I can measure side lengths in whole number units to determine the perimeter of polygons. (Topic C: Lesson 12) (3.MD.D.8)

I can explore perimeter as an attribute of plane figures and solve problems. (Topic C: Lesson 13)

Lesson 10 : Objective: Decompose quadrilaterals to understand perimeter as the boundary of a shape.Lesson 11 : Objective: Tessellate to understand perimeter as the boundary of a shape. (Optional lesson)Lesson 12 : Objective: Measure side lengths in whole number units to determine the perimeter of polygons.Lesson 13 : Objective: Explore perimeter as an attribute of plane figures and solve problems.Lesson 14 : Objective: Determine the perimeter of regular polygons and rectangles when whole number measurements are missing.

Week 3(Suggested – This may vary depending on individual class needs as well as the use of tasks in instruction)Lesson 15 : Objective: Solve word problems to determine perimeter with given side lengthsLesson 16 : Objective: Use String to measure the perimeter of various circles to the nearest quarter inch.Lesson 17 : Objective: Use all four operations to solve problems involving perimeter and missing measurements.Mid Module AssessmentOptional: Tasks (See Task Bank)

Week 3(Suggested – This may vary depending on

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(3.MD.D.8) I can determine the perimeter of

regular polygons and rectangles when whole number measurements are missing. (Topic C: Lesson 14) (3.MD.D.8)

I can solve word problems to determine perimeter with given side lengths. (Topic C: Lesson 15) (3.MD.D.8)

I can use string to measure the perimeter of various circles to the nearest quarter inch. (Topic C: Lesson 16) (3.MD.D.8)

I can use all four operations to solve problems involving perimeter and missing measurements. (Topic C: Lesson 17) (3.MD.D.8)

I can construct rectangles from a given number of unit squares and determine the perimeters. (Topic D: Lesson 18) (3.MD.D.8)

I can use a line plot to record the number of rectangles constructed from a given number of unit squares. (Topic D: Lesson 19) (3.MD.B.4, 3.MD.D.8)

I can construct rectangles with a given perimeter using unit squares and determine their areas. (Topic D: Lesson 20-21) (3.MD.D.8)

I can use a line plot to record the number of rectangles constructed in Lessons 20 and 21. (Topic D: Lesson

individual class needs as well as the use of tasks in instruction)

Topic D: Recording Perimeter and Area Data on Line PlotsLesson 18 : Objective: Construct rectangles from a given number of unit squares and determine the perimeters.Lesson 19 : Objective: Use a line plot to record the number of rectangles constructed from a given number of unit squares.Lesson 20 : Objective: Construct rectangles with a given perimeter using unit squares and determine their area.Lesson 21 : Objective: Construct rectangles with a given perimeter using unit squares and determine their area.Lesson 22 : Objective: Use a line plot to record the number of rectangles constructed in Lessons 20 and 21.Week 4(Suggested – This may vary depending on individual class needs as well as the use of tasks in instruction)Topic E: Problem Solving with Perimeter and AreaLesson 23 : Objective: Solve a variety of word problems with perimeter.Lesson 24 : Objective: Use rectangles to draw a robot with specified perimeter measurements, and reason about the different areas that may be produced.Lesson 25 : Objective: Use rectangles to draw

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TN State Standards Essential Understandings Content & Tasks Literacy Connections

22) (3.MD.B.4, 3.MD.D.8) I can solve a variety of word

problems with perimeter (Topic E: Lesson 23) (3.MD.D.8)

I can use rectangles to draw a robot with specified perimeter measurements, and reason about the different areas that may be produced. (Topic E: Lesson 24-27) (3.MD.D.8, 3.G.A.1)

I can solve a variety of word problems involving area and perimeter using all four operations. (Topic E: Lesson 28-29) (3.MD.D.8, 3.G.A.1)

I can share and critique peer strategies for problem solving. (3.MD.D.8)

a robot with specified perimeter measurements, and reason about the different areas that may be produced.Lesson 26 : Objective: Use rectangles to draw a robot with specified perimeter measurements, and reason about the different areas that may be produced.Lesson 27 : Objective: Use rectangles to draw a robot with specified perimeter measurements, and reason about the different areas that may be produced.

Week 5(Suggested – This may vary depending on individual class needs as well as the use of tasks in instruction)Lesson 28 : Objective: Solve a variety of word problems involving area and perimeter.Lesson 29 : Objective: Solve a variety of word problems involving area and perimeter.End of Module Assessment

Coordinating i-Ready Lessons Quadrilaterals Classifying Polygons Understand Perimeter Connect Area and Perimeter Measure Length and Plot Data on

Line Plots Interpreting Line Plots

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TN State Standards Essential Understandings Content & Tasks Literacy Connections

Task BankKatie's KitchenMaking A Doll HouseGarden DesignSchool Mural : 3rdGrade TaskShapes and Their Insides

MICA Sample Items:3.G.A.1 IDs 41844, 41845, 41846, 41847, and 418483.MD.B.4 ID 421173.MD.D.8 IDs 21744, 41863, 41864, 41865, and 44044Supplemental Resources:enVision Resources: (use as supplemental resources as needed to meet the needs of your students)Solids and Shapes10-1: Geometry: Solid Figures (3.G.A.1)10-2: Geometry: Relating Solids and Shapes (3.G.A.1)10-3: Geometry: Lines and Line Segments (3.G.A.1)10-5: Geometry: Polygons (3.G.A.1)10-6: Geometry: Triangles (3.G.A.1)10-7: Geometry: Quadrilaterals (3.G.A.1)10-8: Problem Solving (3.G.A.1)10-8A - (3.G.A.1) Combining and Separating Shapes10-8B Making New Shapes (3.G.A.1)16-1: Measurement: Understanding Perimeter

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(3.MD.D.8 ) 16-2: Measurement: Perimeter of Common Shapes (3.MD.D.8 ) 16-2A:Tools and Units for Perimeter (3.MD.D.8 ) 16-3 Different Shapes with the Same Perimeter (3.MD.D.8 )

Cluster 3.OA.C: Multiply and divide within 100. 3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Daily Fluency Practice

It is recommended that students participate in fluency practice daily. It should be high-paced and energetic, celebrating improvement and focusing on recognizing patterns and connections within the material.

Fluency lessons are part of all Engageny

Lessons. The resources provided to the right can be used to supplement the fluency to meet the individual needs of your students.

Fluency Resource:http://www.caboces.org/iss/resources/school-library-system/common-core-workbooks(See Grade 3 - Sprints – Grade 3 – Module 7)

http://biloxischools.schoolwires.net/Page/5280

http://maccss.ncdpi.wikispaces.net/3rd+Grade+Instructional+Resources(Click on resource Building Conceptual Understanding and Fluency Through Games)

Review of the following standards:3.NF.A and 3.NBT.ATN Ready Testing

(Allow 1 week for assessment and review)Note: Adjust instruction to accommodate revised testing schedule

Cluster 3.NF.A: Develop the understanding of fractions as numbers. 3.NF.A.1 Understand a fraction 1/b as the

quantity formed by 1 part when a whole is

Enduring Understandings (3.NF.A)1. A region can be divided into equal-

sized parts in different ways.2. A fraction describes the division of a

Please use the following resources based on the individual needs of your students to review the 3.NF.A and 3.NBT.A standards.

Vocabulary(Note: These words should be familiar to students)

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TN State Standards Essential Understandings Content & Tasks Literacy Connectionsportioned into b equal parts; understand a fraction a/bas the quantity formed by a parts of size 1/b.

3.NF.A.2 Represent a fraction 1/b on a number line diagram

3.NF.A.2.a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has a size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

3.NF.A.2b Represent a fraction a/bon a number line diagram by marking offa lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

3.NF.A.3.a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

3.NF.A.3.b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

3.NF.A.3.c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

3.NF.A.3.d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the

whole (region, set, segment) into equal parts.

3. A fraction is relative to the size of a whole.

4. Each fraction can be associated with the unique point on a number line.

5. Fractions can be approximated by other fractions that are close.

6. The same fractional amount can be represented by an infinite set of different but equivalent fractions.

7. Fractions allow for quantities to be expressed with greater precision than with just whole numbers.

Essential Questions (3.NF.A)8. How can you divide a region into

equal parts?9. How can you show and name part of

a region?10. How can a fraction name a part of a

group?11. How can different fractions name the

same part of a whole?How can you compare fractions?12. How can you locate and compare

fractions and mixed numbers on a number line?

Enduring Understandings (3.NBT.A)13. Our number system is based on

groups of ten.14. Addition can be used to solve real

world problems that involve joining, separating, part-part whole or comparison.

(Note: These standards were chosen for review based on how the concepts were weighted on the TN 3rd Grade Blueprints)

Review resources for 3.NF.A:Learnzillion 3.NF.A ResourcesCoordinating I-Ready Lessons:

Fractions: Part of a Whole in Real-World Problems

Fraction of a Whole: Denominators through 12

Understand Fractions on a Number Line

Find Equivalent Fractions

Task Bank:3.NF.AGrade 3 | Candy Bars (3.NF.A.1, 3.NF.A.3)Grade 3 | Fractions (3.NF.A.1, 3.NF.A.3)***Grade 3 | Number Line (3.NF.A.2, 3.NF.A.3)Grade 3 | Sharing Pizza (3.NF.A.3)

MICA Sample Items:3.NF.A.1: ID 407963.NF.A.2: IDs 19475, 42113, 194743.NF.A.3: IDs 44023, 43685, and 43811

Review resources for 3.NBT.A:Learnzillion 3.NBT.A Resources

3.NF.Anumerator, denominator, fractions, benchmark fraction, unit fraction, equivalent fraction, mixed numbers, halves, thirds, fourths, sixths, eighths, tenths, twelfths

3.NBT.Adigit, place value, standard form, expanded form, word form, round, estimate, compatible numbers, addends, sum, regrouping, difference, fact family

Literature Connections3.NF.AFraction Fun David AdlerFull House Dayle Ann DoddsEating Fractions Bruce McMillanPiece = Part = Portion Scott GiffordPolar Bear Math Cindy BickelThe Hershey’s Fraction Book Jerry PallottaJump, Kangaroo, Jump! Stuart MurphyWorking With Fractions David Adler

The Wishing Club A Story about Fractions Donna Napoli

If You Were a Fraction Trisha ShaskanWhole-y Cow! Fractions are Fun! Taryn Souders

3.NBT.AA Place for Zero Angeline LoPresti

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TN State Standards Essential Understandings Content & Tasks Literacy Connectionssymbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model 1/b.

Cluster 3.NBT.A: Use place value understanding and properties of operations to perform multi-digit arithmetic.

3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100.

3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Cluster 3.NBT.A: Use place value understanding and properties of operations to perform multi-digit arithmetic.

3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

15. There are properties that are used to govern arithmetic and algebra that are always true.

16. Numbers can be approximated with numbers that are close.

17. Replacing numbers with other numbers that are close can approximate calculations.

18. Some real-world problems involving joining, separating, part part whole, or comparison can be solved using subtraction.

Essential Questions (3.NBT.A)1. Is place value important when

comparing and ordering numbers?2. How can addition properties be used

to show relationships that always hold true?

3. How can you use patterns on a hundreds chart to add two digit numbers?

4. How can you break apart numbers to help you add 2 digit numbers using mental math?

5. How can you round numbers?6. How can you estimate sums?7. How can you use addition to solve

problems?8. When do we subtract?9. How can you subtract on a hundreds

chart?10. How can you subtract using mental

math?11. How can we use estimation and

rounding to check to see if our

Coordinating I-Ready Lessons: Use Place Value to Round Numbers Subtracting Three-Digit Numbers Adding Three-Digit Numbers Add and Subtract within 1000 Multiply by multiples of 10

Task Bank:3.NBT.AGrade 3 | Fluency (3.OA.C.7, 3.NBT.A.2)Grade 3 | Fluency II (3.OA.C.7, 3.NBT.A.2)Grade 3 | Fluency III (3.OA.C.7, 3.NBT.A.2)Rounding to the Nearest 100 and 1000Rounding to 50 or 500Rounding to the nearest 10 or 100Classroom SuppliesHow many colored pencils?

MICA Sample Items:3.NBT.A.1: IDs 43875, 43873, and 438743.NF.A.2: IDs 42280, 42281, 42282, and 422833.NF.A.3: ID 43788

Count to a Million Jerry PallottaBetcha! Stuart j. MurphyMission Addition, Loreen LeedySubtraction Action, Loreen Leedy

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Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 3

TN State Standards Essential Understandings Content & Tasks Literacy Connectionsanswers are reasonable?

Learning Targets Create class and individual targets

as needed for students based on the review of the following standards: 3.NF.A and 3.NBT.A

Cluster 3.OA.C: Multiply and divide within 100. 3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Daily Fluency Practice

It is recommended that students participate in fluency practice daily. It should be high-paced and energetic, celebrating improvement and focusing on recognizing patterns and connections within the material.

Fluency lessons are part of all Engageny

Lessons. The resources provided to the right can be used to supplement the fluency to meet the individual needs of your students.

Fluency Resource:http://www.caboces.org/iss/resources/school-library-system/common-core-workbooks(See Grade 3 - Sprints – Grade 3 – Module 7)

http://biloxischools.schoolwires.net/Page/5280

http://maccss.ncdpi.wikispaces.net/3rd+Grade+Instructional+Resources(Click on resource Building Conceptual Understanding and Fluency Through Games)

Engageny Module 7: Geometry and Measurement (Continued)Topic F

Tasks – 3rd Grade Content (Allow 2 week for instruction, review and assessment)

Cluster 3.NF.A: Develop the understanding of fractions as numbers.

3.NF.A.3.a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Learning Targets: I can explore and create

unconventional representations of one-half. (Topic F: Lesson 31-32)

I can solidify fluency with Grade 3 skills. (Topic F: Lesson 33)

Please use the following Resources from Engageny: Module 7

(Note: Objectives are restated as Learning Targets in the previous column)

VocabularyReview vocabulary from quarters 1-4 based on individual class and student needs

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 3

TN State Standards Essential Understandings Content & Tasks Literacy Connections

3.NF.A.3.b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Cluster 3.NBT.A: Use place value understanding and properties of operations to perform multi-digit arithmetic.3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.Cluster 3.OA.A: Represent and solve problems involving multiplication and division. 3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. 3.OA.A.2 Interpret whole-number quotients of whole numbers. 3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays,Cluster 3.OA.C: Multiply and divide within 100. 3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end

I can create resource booklets to support fluency with Grade 3 skills. (Topic F: Lesson 34)

Week 1(Suggested – This may vary depending on individual class needs as well as the use of tasks in instruction)Topic F: Year in ReviewLesson 31 : Objective: Explore and create unconventional representations of one-half.Lesson 32 : Objective: Explore and create unconventional representations of one-half.Lesson 33 : Objective: Solidify fluency with Grade 3 skillsLesson 34 : Objective: Create resource booklets to support fluency with Grade 3 skills.

Week 2(Suggested – This may vary depending on individual class needs as well as the use of tasks in instruction)Task: Relating Multiplication and Division (3.OA.C.7 ) Task : The Wheel Shop (3.OA.C.7 ) Task: Carpet Squares (3.OA.A.1 , 3.OA.A.2 , 3.OA.A.3 ) Task: The Bakery (3.OA.A.1 , 3.OA.A.3 ) Task: Party Treats (3.OA.A.3 )

MICA Sample Items:3.OA.A.1: IDs 41867 and 422693.OA.A.2: ID 418683.OA.A.3: IDs 21600, 21745, and 418703.OA.C.7: IDs 42276, 42277, 42278, and

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 3

TN State Standards Essential Understandings Content & Tasks Literacy Connections

of Grade 3, know from memory all products of two one-digit numbers.

42279

Cluster 3.OA.C: Multiply and divide within 100. 3.OA.C.7 Fluently multiply and divide

within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Daily Fluency Practice

It is recommended that students participate in fluency practice daily. It should be high-paced and energetic, celebrating improvement and focusing on recognizing patterns and connections within the material.

Fluency lessons are part of all Engageny

Lessons. The resources provided to the right can be used to supplement the fluency to meet the individual needs of your students.

Fluency Resource:http://www.caboces.org/iss/resources/school-library-system/common-core-workbooks(See Grade 3 - Sprints – Grade 3 – Module 7)

http://biloxischools.schoolwires.net/Page/5280

http://maccss.ncdpi.wikispaces.net/3rd+Grade+Instructional+Resources(Click on resource Building Conceptual Understanding and Fluency Through Games)

RESOURCE TOOLBOX

NWEA MAP Resources: https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum)https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.

Textbook ResourcesVisual Animation CDCenter GamesQuick CheckDaily Spiral ReviewProblem of the DayMath Diagnosis and Intervention System

www.tncore.orghttp://www.corestandards.org/Math/7 Things You Need to Know about TNReady MathTNReady Math Blueprint

VideosDiscovery EducationLesson 2: Multiplying Numbers in ColumnsLesson 4: Multiplying by a Single DigitLearn Zillion videosUse an array to multiply a two digit by a one digit number

Calculator Interactive Manipulatives Additional Sites

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Curriculum and Instruction – Office of Mathematics4th Nine Weeks Grade 3

Skip Counting by 5 Calculator ActivityRelated ProceduresMeet my Friend the CalculatorMean Machine100 or Bust Constant Weight Gain

http://www.eduplace.comhttp://www.illuminations.nctm.orghttp://interactivesites.weebly.com/math.htmlMath Playground: Common Core StandardsCreate a GraphPattern Blocks

Word Problem Practice: Word Problems with KatieInterpreting Remainders: Interpreting Remainders

Children’s LiteratureThe Reading NookMath and Literature:A Match Made in the ClassroomMath for Kids-Best Children’s BooksScholastic: Books and Programs to Improve Elementary Math

NCTM: Common Core Videoshttp://www.nctm.org/Standards-and-Positions/Common-Core-State-Standards/Teaching-and-Learning-Mathematics-with-the-Common-Core/TNCore: Videos for the TN State Standardshttp://tn.pbslearningmedia.org/collection/professional-learning-common-core/?topic_id=1078Achieve the Corehttp://achievethecore.org

Achieve the Core Mini-Assessmentshttp://achievethecore.org/page/858/annotated-mini-assessmentsAchieve the Core: Aligned Instructional Materialshttp://achievethecore.org/aligned/?utm_source=Aligned%20Launch%20expanded%20partners_claires_email&utm_medium=email&utm_campaign=Aligned

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