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Subject to revision Major Content Supporting Content Additional Content
Curriculum and Instruction – Office of Mathematics
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
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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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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
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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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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
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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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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
The TNCore Mathematics Standards
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The 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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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.
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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:
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Curriculum Maps:
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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.
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Include daily fluency practice. Study the suggested performance assessments (tasks) and match them to your objectives. Review the CLIP 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.
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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
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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.
OverviewShelby County Schools 2015/2016
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Grade 3: Quarter 3
Engageny Module 2/Topic 17: Time Engageny Module 4: Multiplication and AreaTopic 9: Patterns and Relationships
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Engageny Module 6: Collecting and Displaying Data Engageny Module 7/ Topic 10: Shapes
Overview
At the end of Quarter 2, students explored measurements using kilograms, liters and milliliters. Students will continue their understanding of Shelby County Schools 2015/2016
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measurement in Topic 17, where they will deepen their understanding of time, building on previous concepts of time from first and second grades. Telling time is an important life skill that all students should master. In the age of advanced technologies, the era of analog clocks is receding. Students should move fluidly from an analog to a digital representation of time and accurately depict the time to the nearest hour, half hour, five minutes and to the nearest minute. They will understand time as a continuous measurement through exploration with stopwatches, and use the number line, a continuous measurement model, as a tool for counting intervals of minutes within 1 hour (3.MD.1). Students see the analog clock is a portion of the number line shaped into a circle. They will use both the number line and the clock to represent addition and subtraction problems involving intervals of minutes within 1 hour (3.MD.1).
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In Module 4 Topic A, students begin to conceptualize area as the amount of two-dimensional surface that is contained within a plane figure. They come to understand that the space can be tiled with unit squares without gaps or overlaps (3.MD.C.5). Students decompose paper strips into square inches and square centimeters, which they use to tile 3 by 4, 4 by 3, and 2 b 6 rectangles. They compare rectangles tiled with like unites and notice different side lengths but equal areas. Topic A provides students’ first experience with tiling form which they learn to distinguish between length and area by placing a ruler with the same size units (inches or centimeters) next to a tiled array. They discover that the number of tiles along a side corresponds to the length of the side (3.MD.C.6).
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In Topic B, students progress from using square tile manipulatives to drawing their own area models. Anticipating the final structure of an array, they complete rows and columns in figures such as the example shown to the right. Students connect their extensive work with rectangular arrays and multiplication to eventually discover the area formula for a rectangle, which is formally introduced in Grade 4 (3.MD.7a).In Topic C, students manipulate rectangular arrays to concretely demonstrate the arithmetic properties in
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2 cm
2 cm
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anticipation of the lessons that follow. They do this by cutting rectangular grids and rearranging the parts into new wholes using the properties to validate that area stays the same, despite the new dimensions. They apply tiling and multiplication skills to determine all whole number possibilities for the side lengths of rectangles given their areas (3.MD.7b).Topic D creates an opportunity for students to solve problems involving area (3.MD.7b). Students decompose or compose composite regions, such as the one shown to the right—into non-overlapping rectangles, find the area of each region, and then add or subtract to determine the total area of the original shape. This leads students to find the areas of rooms in a given floor plan (3.MD.7d).
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Topic 9 explores patterns and relationships. While this is not the ideal location for this topic, because it was not addressed in previous quarters, it will need to be addressed prior to Part 1 of the TN Ready Assessment. In this topic students will be asked to identify a particular arithmetic pattern. Identifying a particular arithmetic pattern is critical to understanding the complex and dynamic relationships between numbers. While it is important
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to verbally explain such things, expressing them as a numeric equation is also important (3.OA.D.9). Teachers need to guide students’ interpretation of patterns they encounter into numeric sentences. (3.OA.D.9) Introducing this topic at this time will allow students to see connections with patterns with addition and multiplication as preparation for the TN Ready Assessment.
The Q3 Curriculum map does recognize time that will be needed for TN Ready Part 1 testing. It is understood that testing schedules will vary for each school. Therefore, it is the recommendation that you continue to teach the standards based on the Curriculum Maps when you are not testing. This information is also embedded in the map.
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We continue with quarter 3 with Engageny Module 6, Collecting and Displaying Data. This 10-day module builds on Grade 2 concepts about data, graphing, and line plots. Topic A begins with a lesson in which students generate categorical data, organize it, and then represent it in a variety of forms. Drawing on Grade 2 knowledge, students might initially use tally marks, tables, or graphs with one-to-one correspondence. By the end of the lesson, they show data in tape diagrams where units are equal groups with a value greater than 1. In the next two lessons, students rotate the tape diagrams vertically so that the tapes become the units or bars of scaled graphs (3.MD.3). Students understand picture and bar graphs as vertical representations of tape diagrams and apply well-practiced skip-counting and multiplication strategies to analyze them. In Lesson 4, students
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synthesize and apply learning from Topic A to solve one- and two-step problems. Through problem solving, opportunities naturally surface for students to make observations, analyze, and answer questions such as, "How many more?" or "How many less?" (3.MD.3).In Topic B, students learn that intervals do not have to be whole numbers but can have fractional values that facilitate recording measurement data with greater precision. In Lesson 5, they generate a six-inch ruler marked in whole-inch, half-inch, and quarter-inch increments, using the Module 5 concept of partitioning a whole into parts. This creates a conceptual link between measurement and recent learning about fractions. Students then use the rulers to measure the lengths of precut straws and record their findings to generate measurement data (3.MD.4). Lesson 6 reintroduces line plots as a tool for displaying measurement data. Although familiar from Grade 2, line plots in Grade 3 have the added
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complexity of including fractions on the number line (2.MD.9, 3.MD.4). In this lesson, students interpret scales involving whole, half, and quarter units in order to analyze data. This experience lays the foundation for them to create their own line plots in Lessons 7 and 8. To draw line plots, students learn to choose appropriate intervals within which to display a particular set of data. For example, to show measurements of classmates’ heights, students might notice that their data fall within the range of 45 to 55 inches and then construct a line plot with the corresponding interval. Students end module 6 by applying learning from Lessons 1–8 to problem solving. They work with a mixture of scaled picture graphs, bar graphs, and line plots to problem solve using both categorical and measurement data (3.MD.3, 3.MD.4).
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Finally, the end of Q3 offers students intensive practice with word problems, as well as hands-on investigation experiences with geometry through the use of Engageny Module 7.Topic A begins with solving one- and two-step word problems based on a variety of topics studied throughout the year, using all four operations (3.OA.8). The lessons emphasize modeling and reasoning to develop solution paths. They incorporate teacher facilitated problem solving, opportunities for students to independently make sense of problems and persevere in solving them, and time for students to share solutions and critique peer strategies. Topic B introduces an exploration of geometry. Students build on Grade 2 ideas about polygons and their properties,
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Tangram Puzzle
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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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Tetrominoes
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Through the use of Engageny Module 7, students will use their understanding of shapes as they lean about perimeter as an attribute of plane figures at the onset of Quarter 4.
Focus Grade Level Standards(Note: Related Foundational Standards are noted in parenthesis after standard)
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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
Measurement and Data
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Cluster 3.MD.A: Solve problems involving measurement and estimation. 3.MD.A.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. (1.MD.B.3; 2.MD.C.7)
Cluster 3.MD.B: Represent and interpret data.
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3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. (2.MD.D.10)
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)
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Cluster 3.MD.C: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. (1.G.A.2) 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. (1.G.A.2) 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. (1.G.A.2) 3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). (3.MD.C.5) 3.MD.C.7: Understand concepts of area and relate area to multiplication and to addition. (3.OA.A.1; 3.MD.C.5)
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3.MD.C.7.A Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.(3.OA.A.1; 3.MD.C.5)
3.MD.C.7.B Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. (3.OA.A.1; 3.MD.C.5)
3.MD.C.7.C Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. (3.OA.A.1; 3MD.C.5)
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3.MD.C.7.D Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. (3.OA.A.1; 3.MD.C.5)
Geometry
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
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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)
Operations and Algebraic Thinking
Cluster 3.OA.D: Solve problems involving the four operations, and identify and explain patterns in arithmetic.
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3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (2.OA.A.1, 3.OA.A.3)
3.OA.D.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. (2.NBT.B.9)
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Foundational Standards
Geometry 1.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three- dimensional
shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
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Numbers and Operation Base Ten2.NBT.B.9 Explain why additions and subtraction strategies work, using place value and the properties of operations.
2.NBT.B.9 Explain why additions and subtraction strategies work, using place value and the properties of operations.
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1.MD.B.3 Tell and write time in hours and half- hours, using analog and digital clocks. 2.MD.C.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
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.
2.MD.D.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.
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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
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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
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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. Special care should be taken so that it is not seen as punitive for students that might need more time to master fluency.
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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.
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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.
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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
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http://www.nctm.org/Standards-and-Positions/Position-Statements/Procedural-Fluency-in-Mathematics/
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TN State Standards Essential Understandings Content & Tasks CLIP Connections
Engageny Module 2 Topic A/Topic 17: Time(Allow 1 1/2 weeks for instruction, review and assessment)
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TN State Standards Essential Understandings Content & Tasks CLIP ConnectionsCluster 3.MD.A: Solve problems involving measurement and estimation. 3.MD.A.1 Tell and write time to the
nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a
Enduring Understandings1. Time can be expressed using different
units that are related to each other.2. There are different units for measuring
time. Many clock times can be expressed in more than one way.
3. The duration of an event can be measured if one knows the start and end
Use the following lessons from Engageny:
https://www.engageny.org/resource/grade-3-mathematics-module-2
Model 2Topic A: Time Measurement and Problem SolvingLesson 1Lesson 2
Academic Vocabularydigital clock, analog clock, o’clock, hour, half hour, quarter hour, minute, second, A.M., P.M., elapsed time
Write to explain: The football game starts at 8:45. It takes 50 minutes to get to the stadium and 12 minutes to park and walk
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsnumber line diagram.
Cluster 3.NBT.A: Use place value understanding and properties of operations to perform multi-digit arithmetic.
times for event.4. Starting with the end result, reversing the
steps and processes, and working backward to the initial data point can solve some problems with the initial data point unknown.
Essential Questions
Lesson 3Lesson 4Lesson 5
Coordinating i-Ready Lessons Elapsed Time to the Minute Telling Time to the Minute Solve Problems about Time
inside. Should you leave at 7:45 or 7:30. Explain
Exit Ticket: Please see exit tickets located at the end of every lesson. These exit tickets usually require a written response.
Tasks: The suggested tasks allow
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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
1. How can you show time?2. Is there more than one way to show
time?3. How can you measure how long an event
takes from start to finish?4. How do we solve problems when the
beginning information is unknown?
Suggested Tasks:Insidemathematics.org:Time to get Clean
http://3-5cctask.ncdpi.wikispaces.net/3.MD.1-3.MD.23.MD.1 Task 13.MD.1 Task 2
opportunities for students to engage in mathematical conversations that require them to explain and justify their answers to their peers and in a written format where applicable.
Literature ConnectionsWorldScapes Readers: Fiji Facts and
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TN State Standards Essential Understandings Content & Tasks CLIP ConnectionsLearning Targets I can explore time as a continuous
measurement. (Topic A: Lesson 1) (3.MD.A.1)
I can measure the duration of time in minutes. Topic A: Lesson 1) (3.MD.A.1)
I can relate skip-counting by fives on the clock and telling time to a continuous
3.MD.1 Task 3
Use the following envision resources as supplementalTime17-2 Measurement: Time to the Minute17-4 Measurement: Elapsed Time17-6 Problem Solving: Work Backward
Figures
Additional Literature ConnectionsSlowpoke, Lucille Recht Penner
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsmeasurement model, the number line (Topic A: Lesson 2) (3.MD.A.1, 3.NBT.2)
I can count by fives and ones on the number line as a strategy to tell time to the nearest minute on the clock. (Topic A: Lesson 3) (3.MD.A.1, 3.NBT.2)
I can solve word problems involving time intervals within 1 hour by counting
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsbackward and forward using the number line and clock. (Topic A: Lesson 4)(3.MD.A.1)
I can solve word problems involving time intervals within 1 hour by adding and subtracting on the number line. (Topic A: Lesson 5) (3.MD.A.1)
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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
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
Fluency Resource:http://www.caboces.org/iss/resources/school-library-system/common-core-workbooks(See Grade 3 - Sprints – Grade 3 – Module 2)
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsknows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
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.
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)
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TN State Standards Essential Understandings Content & Tasks CLIP Connections
EngagenyModule 4: Multiplication and Area
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(Allow 3 ½ weeks for instruction, review and assessment)Cluster 3.MD.C: Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.C.5 Recognize area as an
attribute of plane figures and understand
Enduring Understandings1. The region inside a shape is its area and
can be measures using square units.2. Area can be found by adding the square
units or by multiplying.3. Measurements of solid figures can be
Use the following lessons from Engageny
Module 4:Topic A: Foundations for Understanding AreaLesson 1Lesson 2Lesson 3
Academic VocabularyNew:Area, area model, square unit, tile, unit square, whole number
Familiar:
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsconcepts 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
estimated or approximated.4. Areas of rectangles can be found by
using the distributive property.5. Areas of irregular shapes can be found
by breaking apart the original shape into other shapes in which the area can be found.
Lesson 4
Topic B: Concepts of Area MeasurementLesson 5Lesson 6Lesson 7Lesson 8
Array, commutative property, distribute, geometric shape, length, multiplications, rows and columns
Exit Ticket: Please see exit tickets located at the end of every lesson. These exit tickets usually require a written response.
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsn square units.
3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
3.MD.C.7: Understand concepts of area and relate area to multiplication and to addition.
Essential Questions1. How do you find area?2. How can you use the distributive property
to find the area of a rectangle.3. How do you estimate to find the area of
an irregular shape?
Learning Targets
Mid Module Assessment
Topic C: Arithmetic Properties Using Area ModelsLesson 9Lesson 10Lesson 11
Topic D: Applications of Area Using Side Lengths
Tasks: The suggested tasks allow opportunities for students to engage in mathematical conversations that require them to explain and justify their answers to their peers and in a written format where applicable.
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TN State Standards Essential Understandings Content & Tasks CLIP Connections 3.MD.C.7.A Find the area of a
rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
3.MD.C.7.B Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving
I can understand area as an attribute of plane figures. (Topic A Lesson 1) (3.MD.C.5)
I can decompose and recompose shapes to compare areas. (Topic A: Lesson 2) (3.MD.C.5, 3.MD.C.6, 3.MD.C.7)
I can model tiling with centimeter and inch unit squares to make arrays. (Topic A:
of Figures
Lesson 12Lesson 13Lesson 14Lesson 15Lesson 16
Literature ConnectionsWorldScapes Readers: Below Zero
Additional Literature ConnectionsMath Matters Series, ScholasticChickens on the Move, Pam Pollack & Meg Belviso
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsreal world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
3.MD.C.7.C Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b
Lesson 3) (3.MD.C.5, 3.MD.C.6, 3.MD.C.7)
I can relate side lengths with the number of tiles on a side. (Topic A: Lesson 4) (3.MD.C.5, 3.MD.C.6, 3.MD.C.7)
I can form rectangles by tiling with unit squares to make arrays. (Topic B: Lesson 5)(3.MD.C.5, 3.MD.C.6, 3.MD.C.7a,
End of Module Assessment
Coordinating i-Ready Lessons Understand Area Add and Multiply to Find Area Understanding Area and Surface Area
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsand a × c. Use area models to represent the distributive property in mathematical reasoning.
3.MD.C.7.D Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts,
3.MD.C.7b, 3.MD.C.7d) I can draw rows and columns to
determine the area of a rectangle given an incomplete array. (Topic B: Lesson 6) )(3.MD.C.5, 3.MD.C.6, 3.MD.C.7a, 3.MD.C.7b, 3.MD.C.7d)
I can interpret area models to form rectangular arrays. (Topic B: Lesson 7) )
Using Area for Multiplication: Facts for 3, 4 and 5
Using Area for Multiplication: Facts for 6, 7 and 8
Concepts of Area in Two-Dimensional Shapes
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsapplying this technique to solve real world problems.
(3.MD.C.5, 3.MD.C.6, 3.MD.C.7a, 3.MD.C.7b, 3.MD.C.7d)
I can find the area of a rectangle through multiplication of the side lengths. (Topic B: Lesson 8) )(3.MD.C.5, 3.MD.C.6, 3.MD.C.7a, 3.MD.C.7b, 3.MD.C.7d)
I can analyze different rectangles and reason about their area. (Topic C: Lesson
Task Bank (TNCore 3rd Grade Task)Measurement: Solving for Area of Figures
http://tncore.org/math/assessment_tasks/grades/g3.aspx
Area of Squares Finding Area Two Areas
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TN State Standards Essential Understandings Content & Tasks CLIP Connections9) )(3.MD.C.5, 3.MD.C.7a, 3.MD.C.7b, 3.MD.C.7c, 3.MD.C.7d)
I can apply the distributive property as a strategy to find the total are of a large rectangle by adding two products. (Topic C: Lesson 10) (3.MD.C.5, 3.MD.C.7a, 3.MD.C.7b, 3.MD.C.7c, 3.MD.C.7d)
I can demonstrate the possible whole
Using Simpler Problems
Supplemental enVision Resources:
16-5 Problem Solving: Understanding Area16-6 Estimating and Measuring Area16-6A Covering Regions
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsnumber side lengths of rectangles with areas of 24, 36, 48, or 72 square units using the associative property. (Topic C: Lesson 11) (3.MD.C.5, 3.MD.C.7a, 3.MD.C.7b, 3.MD.C.7c, 3.MD.C.7d)
I can solve word problems involving area. (Topic D: Lesson 12) (3.MD.C.6, 3.MD.C.7a, 3.MD.C.7b, 3.MD.C.7c,
16-6B Area and Units16-7A Area of Squares & Rectangles16-7B Area and the Distributive Property16-7C Area of Irregular Shapes16-7D Equal Areas and Fractions16-8 Problem Solving: Solve a Simpler Problem
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TN State Standards Essential Understandings Content & Tasks CLIP Connections3.MD.C.7d, 3.MD.5)
I can find areas by decomposing into rectangles or completing composite figures to form rectangles.(Topic D: Lesson 13-14) (3.MD.C.6, 3.MD.C.7a, 3.MD.C.7b, 3.MD.C.7c, 3.MD.C.7d, 3.MD.5)
I can apply knowledge of area to
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsdetermine areas of rooms in a given floor plan. (Topic D: Lesson 15-16) (3.MD.C.6, 3.MD.C.7a, 3.MD.C.7b, 3.MD.C.7c, 3.MD.C.7d, 3.MD.5)
Cluster 3.OA.C: Multiply and divide within 100.
Daily Fluency Practice Fluency Resource:http://www.caboces.org/iss/resources/school-
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TN State Standards Essential Understandings Content & Tasks CLIP Connections 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.
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
library-system/common-core-workbooks(See Grade 3 - Sprints – Grade 3 – Module 4)
http://biloxischools.schoolwires.net/Page/5280
http://maccss.ncdpi.wikispaces.net/3rd+Grade+Instructional+Resources
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionscan be used to supplement the fluency to meet the individual needs of your students.
(Click on resource Building Conceptual Understanding and Fluency Through Games)
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Topic 9: Patterns & Relationships(Allow 1 weeks for instruction, review and assessment)
Cluster 3.OA.D: Solve problems Enduring Understandings Patterns and Relationships Academic Vocabulary
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsinvolving the four operations, and identify and explain patterns in arithmetic. 3.OA.D.9 Identify arithmetic patterns
(including patterns in the addition table or multiplication table), and explain them using properties of operations.
1. Some patterns consist of shapes or numbers arranged in a unit that repeats.
2. Some numerical sequences have a rule that tells how to generate more numbers in the sequence.
3. Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know
Please complete lessons in the following order:Envision Lessons:9-2 Number Sequences9-3 Extending Tables9-4 Writing Rules for Situations
Engage NY: Module 3 Lessons:
repeating pattern, numerical expression, equation, inequality
Explain Your Thinking• Do you Understand? (See Guided
Practice)• Writing to Explain (See Problem Solving
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsthe value of the other quantity.
Essential Questions1. How can you continue a repeating
pattern?2. What is the pattern?3. What pairs of numbers fit a pattern?Learning Targets I can identify and describe arithmetic
Topic E: Lesson 17
Coordinating i-Ready Lessons Understand Patterns
Task Bankhttps://www.illustrativemathematics.org/3.OA.D.9
Section of each lesson)
Reading Comprehension & Problem SolvingTeaching Tool 1, p. 304F
Literature Connections
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionspatterns in number charts, addition tables, and multiplication tables. (3.OA.D.9)
I can explain arithmetic patterns using properties of operations. (3.OA.D.9)
Addition Patterns Patterns in the Multiplication Table
http://tncore.org/math/assessment_tasks/grades/g3.aspx
Basketball Schedule
WorldScapes Readers: Perfect Patterns
Additional Literature ConnectionsPatterns, Michele Koomen
Cluster 3.OA.C: Multiply and divide within 100.
Daily Fluency Practice Fluency Resource:http://www.caboces.org/iss/resources/school-
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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
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.
The resources provided to the right can be to meet the individual needs of your students.
library-system/common-core-workbooks(See Grade 3 - Sprints – Grade 3 – Module 3)
http://biloxischools.schoolwires.net/Page/5280
http://maccss.ncdpi.wikispaces.net/3rd+Grade+Instructional+Resources(Click on resource Building Conceptual
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsnumbers. Understanding and Fluency Through Games
TN Ready Testing(Allow 1 week for assessment and review)
Note: Please continue to teach topics as shown in curriculum maps until scheduled testing dates
Engageny Module 6: Collecting and Displaying Data
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TN State Standards Essential Understandings Content & Tasks CLIP Connections(Allow 2 weeks for instruction, review and assessment)
Cluster 3.MD.B: Represent and interpret data.3.MD.B.3 Draw a scaled picture graph and a
scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in
Enduring Understandings1. Tally charts are useful in recording
and organizing some kinds of data.2. Each type of graph is most
appropriate for certain kinds of data.3. The likelihood of an event occurring
can be found using data on a line
Please use the following resources from Engageny:Engage NY Module 6:Topic A: Generate and Analyze Categorical DataLesson 1Lesson 2Lesson 3
Academic Vocabulary
New:Frequent, key, measurement data, scaled graphs
Familiar:Shelby County Schools 2015/2016
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsscaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
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
plot.
Essential Questions1. How do you determine how much a
symbol in a pictograph represents?2. How can you choose a scale to
make a bar graph?3. How do outcomes compared to
Lesson 4
Topic B: Generate and Analyze Measurement DataLesson 5Lesson 6Lesson 7Lesson 8Lesson 9
Bar graph, data, fraction, line plot, picture graph, scale, survey
Exit Ticket: Please see exit tickets located at the end of every lesson. These exit tickets usually require a written response.
Tasks: The suggested tasks allow
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsscale is marked off in appropriate units— whole numbers, halves, or quarters.
predictions?4. How do you make and use a line
plot?
Learning Targets I can generate and organize data.
(Topic A: Lesson 1) (3.MD.3) I can rotate diagrams vertically)
End of Module Assessment
Coordinating i-Ready Lessons Scaled Pictographs and Bar Graphs Picture Graphs and Bar Graphs Interpreting Bar Graphs and Pictographs Measure Length and Plot Data on Line
opportunities for students to engage in mathematical conversations that require them to explain and justify their answers to their peers and in a written format where applicable.
Literature ConnectionsShelby County Schools 2015/2016
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TN State Standards Essential Understandings Content & Tasks CLIP Connections(Topic A: Lesson 2) (3.MD.B.3)
I can create scaled bar graphs. (Topic A: Lesson 3) (3.MD.B.3)
I can solve one and two step problems involving graphs (Topic A: Lesson 4) (3.MD.B.3)
I can create and use a ruler to measure lengths in whole, half, and
Plots Interpreting Line Plots
Suggested Tasks:Pick a PocketParking Carshttp://3-5cctask.ncdpi.wikispaces.net/3.MD.3-3.MD.4
WorldScapes Readers: Rainforest Math
Additional Literature ConnectionsLemonade for Sale, Stuart MurphyGreat Graph Contest, Loreen LeedyTiger Math, Ann Whitehead NagdaFamily Reunion, Bonnie Bader
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsquarter inches. (Topic B: Lesson 5) (3.MD.B.4)
I can interpret measurement data from various line plots. (Topic B: Lesson 6) (3.MD.B.4)
I can represent measurement data with line plots (Topic B Lesson 7-8)(3.MD.B.4)
Supplemental Envision Lessons:20-3 Statistics: Making Pictographs20-4 Statistics: Making Bar Graphs20-8 Statistics: Line Plot and Probability20-9A Length and Line Plots
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TN State Standards Essential Understandings Content & Tasks CLIP Connections I can analyze data to problem solve.
(Topic B: Lesson 9) (3.MD.B.4)
Cluster 3.OA.C: Multiply and divide within 100.
Daily Fluency Practice Fluency Resource:http://www.caboces.org/iss/resources/school-
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TN State Standards Essential Understandings Content & Tasks CLIP Connections 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.
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
library-system/common-core-workbooks(See Grade 3 - Sprints – Grade 3 – Module 3)
http://biloxischools.schoolwires.net/Page/5280
http://maccss.ncdpi.wikispaces.net/3rd+Grade+Instructional+Resources
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TN State Standards Essential Understandings Content & Tasks CLIP ConnectionsLessons. The resources provided to the right can be used to supplement the fluency to meet the individual needs of your students.
(Click on resource Building Conceptual Understanding and Fluency Through Games)
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Engageny Module 7: Geometry and Measurement Word Problems(Allow 2 weeks for instruction, review and assessment to be continued in Q4)
Cluster 3.OA.D: Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Enduring Understandings1. Shapes can be used to describe
some attributes of some solids.
Solids and ShapesPlease complete the following lessons in Engage NY:
Academic VocabularyNew:Attribute, diagonal, perimeter, property,
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3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
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. Commonalities in attributes of objects or situations can be found
Module 7: Geometry and Measurement Word ProblemsTopic A: Solving Word ProblemsLesson 1Lesson 2Lesson 3
regular polygon, tessellate, tessellate, tetrominoes
Familiar:Area, compose, decompose, heptagon, hexagon, octagon, parallel lines, parallelogram, pentagon, polygon,
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TN State Standards Essential Understandings Content & Tasks CLIP 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
and used to make and test generalizations about relationships.
Essential Questions1. What is a polygon?2. How can you describe triangles?
Topic B: Attributes of Two-Dimensional FiguresLesson 4Lesson 5Lesson 6Lesson 7
quadrilaterals, rectangle, rhombus, right angle, square, tangram, trapezoid, triangle
Exit Ticket: Please see exit tickets located at the end of every lesson. These exit tickets usually require a written response.
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TN State Standards Essential Understandings Content & Tasks CLIP Connections
attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
3. What are some special names for quadrilaterals?
4. How can you use the attributes of two- and three-dimensional shapes to classify them?
Learning Targets I can solve word problems in varied
Lesson 8Lesson 9
Coordinating i-Ready Lessons Solve Two-Step Word Problems Using the
Four Operations
Tasks: The suggested tasks allow opportunities for students to engage in mathematical conversations that require them to explain and justify their answers to their peers and in a written format where applicable.
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TN State Standards Essential Understandings Content & Tasks CLIP Connections
contexts using a letter to represent the unknown. (Topic A: Lesson 1-2) (3.OA.D.8)
I can share and critique peer solution strategies to varied word problems. (Topic A: Lesson 3)(3.OA.D.8)
Quadrilaterals Classifying Polygons
Suggested Tasks:Katie's KitchenMaking A Doll House
Literature ConnectionsWorldScapes Readers: Fiji Facts and FiguresThe Greedy Triangle: by Marilyn Burns
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TN State Standards Essential Understandings Content & Tasks CLIP Connections
I can compare and classify quadrilaterals. (Module 7 – Topic B: Lesson 4) (3.G.1)
I can compare and classify other polygons. (Module 7 – Topic B: Lesson 5) (3.G.1)
I can draw polygons with specified
Please supplement with the following envision lessons:10-1: Geometry: Solid Figures10-2: Geometry: Relating Solids and Shapes10-3: Geometry: Lines and Line Segments10-5: Geometry: Polygons
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TN State Standards Essential Understandings Content & Tasks CLIP Connections
attributes to solve problems. (Module 7 – Topic B: Lesson 6) (3.G.1)
I can reason about composing and decomposing polygons using tetrominoes. (Module 7 – Topic B: Lesson 7) (3.G.1)
10-6: Geometry: Triangles10-7: Geometry: Quadrilaterals10-8: Problem Solving10-8A Combining and Separating Shapes10-8B Making New Shapes
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TN State Standards Essential Understandings Content & Tasks CLIP Connections
I can create a tangram puzzle and observe relationships among the shapes. (Module 7 – Topic B: Lesson 8) (3.G.1)
I can reason about composing and decomposing polygons using tangrams. (Module 7 – Topic B:
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Lesson 9) (3.G.1)
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.,
Daily Fluency PracticeIt 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
Fluency Resource:http://www.caboces.org/iss/resources/school-library-system/common-core-workbooks(See Grade 3 - Sprints – Grade 3 – Module 3)
http://biloxischools.schoolwires.net/Page/5280
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TN State Standards Essential Understandings Content & Tasks CLIP Connectionsknowing 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.
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.
http://maccss.ncdpi.wikispaces.net/3rd+Grade+Instructional+Resources(Click on resource Building Conceptual Understanding and Fluency Through Games)
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Textbook ResourcesenVision MathenVision Common Core Addendum Lessons
Interactive Manipulativeswww.eduplace.comwww.illuminations.nctm.org
CCSS/PARCCTNCoreCCSS ToolboxPARCCCore StandardsPARCC GamesInside Mathematics
Additional Sites3rd Grade Math JournalsSCS All Things Mathematics(Weebly)Grade 3 Number TalksDigit Detective ResourcesWriting Across the Curriculum: Mathematics
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http://interactivesites.weebly.com/math.htmlMath Playground: Common Core StandardsThinking Blocks Computer and iPad basedPARCC GamesMath Playground: Word Problem Solving GameUsing a Ruler: Length-strength2-Inches
Engage NY MathIllustrative MathematicsGenerated Word Problems: KidZone Math Word Problems
ReadTennessee: 3rd Grade Math Teaching ResourcesMath Interactive Games: Grade 3
Accountable Talk SourcebookStructures and Routines of A LessonStrategies for Modifying Textbook TasksTask Analysis GuideMath Instructional ResourcesInteractive Game: Measuring-InchesMeasurement: long or shortCalculator Videos
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It's the Place that CountsCalculator Pattern Puzzles
Children’s LiteratureChildren's Literature on MeasurementChildren's Literature on GeometryChildren's Literature on Time
LearnZillionDiscovery EducationBubblegum Task Instructional VideoFractions of a Whole Instructional VideoVideo: Metric RulerVideo: Exploring Measurement
Ruler GameMeasuring LengthVideos and gamesLength-MeasurementMath Game: Capacity
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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=1078
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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