miami-dade county public schools district pacing guide...

MIAMI-DADE COUNTY PUBLIC SCHOOLS DISTRICT PACING GUIDE

2014-2015 YEAR-AT-A-GLANCE

Grade 4 Course Code: 5012060F1

Division of Academics – Department of Mathematics of 5

1ST

Nine Weeks 2nd

Nine Weeks 3rd

Nine Weeks 4th

Nine Weeks I. Place Value and Operations with Whole

Numbers A. Modeling Place Value Relationships B. Reading and Writing Numbers C. Comparing and Ordering Numbers D. Estimation Strategies E. Problem Solving

II. Factors, Multiples, and Patterns A. Modeling Factors and Divisibility B. Common Factors and Multiples C. Prime and Composite D. Problem Solving

III. Multiply by 1-Digit Numbers

A. Recalling Multiplication Facts 2-9 (Daily Routines)

B. Multiplication Comparisons C. Multiplication Strategies D. Estimating Products E. Multiplying with Regrouping F. Problem Solving

IV. Multiply by 2-Digit Numbers A. Multiplication Strategies B. Multiplying with Regrouping C. Problem Solving

V. Divide by 1-Digit Numbers A. Estimating Quotients B. Investigating Remainders C. Interpreting the Remainder D. Division Strategies E. Modeling Division with Regrouping F. Problem Solving

VI. Fraction Equivalence and Comparison A. Fractions B. Comparing Fractions C. Comparing and Ordering Fractions D. Problem Solving

VII. Add and Subtract Fractions A. Adding and Subtracting Fractions B. Fractions and Mixed Numbers C. Properties of Addition D. Problem Solving

VIII. Multiply Fractions by Whole Numbers A. Multiplying Fractions B. Fractions and Mixed Numbers C. Problem Solving

IX. Relate Fractions and Decimals A. Relating Tenths, Hundredths, and

Decimals B. Equivalent Forms C. Relating Fractions, Decimals, and

Money D. Adding Fractional Parts of 10 and

100 E. Comparing Decimals F. Problem Solving

X. Two-Dimensional Figures A. Lines, Rays, and Angles B. Classifying Triangles C. Parallel and Perpendicular Lines D. Classifying Quadrilaterals E. Symmetry F. Problem Solving

XI. Angles A. Angles and Fractional Parts of a

Circle B. Degrees C. Measuring and Drawing Angles D. Joining and Separating Angles E. Problem Solving

XII. Relative Sizes of Measurement Units A. Identifying Measurement

Benchmarks B. Customary Units of Length, Weight,

and Liquid Volume C. Line Plots D. Metric Length, Mass, and Liquid E. Time F. Problem Solving

XIII. Algebra: Perimeter and Area A. Perimeter B. Area C. Unknown Measures D. Problem Solving

XIV. MAFS Review XV. Addition, Subtraction, Order of

Operations, and Division FIFTH GRADE PREP

A. Adding and Subtracting Dollars and Cents

B. Order of Operations C. Dividing by Multiples of Ten D. Modeling Division

XVI. Place Value, Decimals, Multiples, and

Number Patterns FIFTH GRADE PREP

A. Place Value Through Millions B. Decimals and Place Value C. Rounding Decimals D. Using Place Value to Compare

Decimals E. Decomposing Multiples of 10, 100,

1000 F. Number Patterns

XVII. Fractions FIFTH GRADE PREP

A. Adding and Subtracting Related Fractions

B. Comparing Fractions C. Repeated Subtraction with Fractions D. Fractions and Division

XVIII. Geometry, Measurement and

Multiplication FIFTH GRADE PREP

A. Locating Points on a Grid B. Area and Tiling C. Multiplying Three Factors D. Finding the Area of the Base

Dates for Instruction and Testing:

Dates for Instruction and Testing: Fall Interim Administration

Dates for Instruction and Testing: Winter Interim Administration

Dates for Instruction and Testing: FSA Administration

Topic I 08-18-14 to 09-05-14 Topic V 10-27-14 to 11-19-14 Topic IX 01-20-15 to 01-30-15 Topic XIV 03-30-15 to 04-10-15 MAFS Review Topic II 09-08-14 to 09-17-14 Topic VI 11-20-14 to 12-05-14 Topic X 02-02-15 to 02-11-15

Topic III 09-18-14 to 10-08-14 Topic VII 12-08-14 to 12-19-14 Topic XI 02-12-15 to 02-20-15 Topic XV 04-13-15 to 05-08-15 Topic IV 10-09-14 to 10-23-14 Topic VIII 01-05-15 to 01-15-15 Topic XII 02-23-15 to 03-11-15 Topic XVI 04-23-15 to 05-08-15 Topic XIII 03-12-15 to 03-19-15 Topic XVII 05-11-15 to 05-22-15

Topic XVIII 05-26-15 to 06-04-15





1st Nine Weeks 2nd Nine Weeks 3rd Nine Weeks 4th Nine Weeks

Topic I MAFS.4.NBT.1.1 MAFS.4.NBT.1.2 MAFS.4.NBT.1.3 MAFS.4.NBT.2.4 MAFS.4.OA.1.a MAFS.4.OA.1.b

Topic II MAFS.4.OA.2.4 MAFS.4.OA.3.5

Topic III MAFS.4.NBT.2.5 MAFS.4.OA.1.1 MAFS.4.OA.1.2 MAFS.4.OA.1.3

Topic IV MAFS.4.NBT.2.5 MAFS.4.OA.1.3

Topic V MAFS.4.NBT.2.6 MAFS.4.OA.1.3

Topic VI MAFS.4.NF.1.1 MAFS.4.NF.1.2

Topic VII MAFS.4.NF.2.3a MAFS.4.NF.2.3b MAFS.4.NF.2.3c MAFS.4.NF.2.3d

Topic VIII MAFS.4.NF.2.4a MAFS.4.NF.2.4b MAFS.4.NF.2.4c

Topic IX MAFS.4.NF.3.5 MAFS.4.NF.3.6 MAFS.4.NF.3.7 MAFS.4.MD.1.2

Topic X MAFS.4.G.1.1 MAFS.4.G.1.2 MAFS.4.G.1.3 MAFS.4.OA.3.5

Topic XI MAFS.4.MD.3.5a MAFS.4.MD.3.5b MAFS.4.MD.3.6 MAFS.4.MD.3.7

Topic XII

MAFS.4.MD.1.1 MAFS.4.MD.1.2 MAFS.4.MD.2.4

Topic XIII

MAFS.4.MD.1.3

Topic XIV MAFS Review

Topic XV

Topic XVI

Topic XVII

Topic XVIII

Dates for Instruction and Testing:

Dates for Instruction and Testing: Fall Interim Administration

Dates for Instruction and Testing: Winter Interim Administration

Dates for Instruction and Testing: FSA Administration

Topic I 08-18-14 to 09-05-14 Topic V 10-27-14 to 11-19-14 Topic IX 01-20-15 to 01-30-15 Topic XIV 03-30-15 to 04-10-15 MAFS Review Topic II 09-08-14 to 09-17-14 Topic VI 11-20-14 to 12-05-14 Topic X 02-02-15 to 02-11-15

Topic III 09-18-14 to 10-08-14 Topic VII 12-08-14 to 12-19-14 Topic XI 02-12-15 to 02-20-15 Topic XV 04-13-15 to 05-08-15 Topic IV 10-09-14 to 10-23-14 Topic VIII 01-05-15 to 01-15-15 Topic XII 02-23-15 to 03-11-15 Topic XVI 04-23-15 to 05-08-15 Topic XIII 03-12-15 to 03-19-15 Topic XVII 05-11-15 to 05-22-15

Topic XVIII 05-26-15 to 06-04-15

FOURTH GRADE MAFS.4.NBT.2.4 MAFS.4.NBT.2.6

MAFS.4.OA.1.3

FOURTH GRADE

MAFS.4.NF.2.3d

FIFTH GRADE PREP MAFS.5.NF.1.2 MAFS.5.NF.2.3 MAFS.5.NF.2.5b MAFS.5.NF.2.7b

FOURTH GRADE MAFS.4.MD.1.1 MAFS.4.MD.1.3 MAFS.4.NBT.2.5

FIFTH GRADE PREP MAFS.5.G.1.1 MAFS.5.MD.3.5b

MAFS.5.NF.2.4b

FIFTH GRADE PREP MAFS.5.NBT.2.6 MAFS.5.NBT.2.7

MAFS.5.OA.1.1

FOURTH GRADE MAFS.4.NBT.1.2 MAFS.4.NBT.1.3 MAFS.4.NF.3.6 MAFS.4.NF.3.7 MAFS.4.OA.2.4 MAFS.4.OA.3.5

FIFTH GRADE PREP MAFS.5.NBT.1.1 MAFS.5.NBT.1.2 MAFS.5.NBT.1.3a MAFS.5.NBT.1.3b MAFS.5.NBT.1.4

MAFS.5.OA.2.3





Mathematical Practices (MP)

MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.K12.MP.2.1 Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.K12.MP.3.1 Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

http://www.cpalms.org/Standards/PublicPreviewBenchmark6327.aspx








MAFS.K12.MP.4.1 Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.K12.MP.5.1 Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.K12.MP.6.1 Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning









MAFS.K12.MP.7.1 Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Cognitive Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.K12.MP.8.1 Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Cognitive Complexity: Level 3: Strategic Thinking & Complex Reasoning



EQuIP Rubric for Lessons & Units: Mathematics Grade: Mathematics Lesson/Unit Title: Overall Rating:

The EQuIP rubric is derived from the Tri-State Rubric and the collaborative development process led by Massachusetts, New York, and Rhode Island and facilitated by Achieve. This version of the EQuIP rubric is current as of 06-15-13.

View Creative Commons Attribution 3.0 Unported License at http://creativecommons.org/licenses/by/3.0/. Educators may use or adapt. If modified, please attribute EQuIP and re-title.

I. Alignment to the Depth of the CCSS

II. Key Shifts in the CCSS III. Instructional Supports IV. Assessment

The lesson/unit aligns with the letter and spirit of the CCSS:

o Targets a set of grade- level CCSS mathematics standard(s) to the full depth of the standards for teaching and learning.

o Standards for Mathematical Practice that are central to the lesson are identified, handled in a grade-appropriate way, and well connected to the content being addressed.

o Presents a balance of mathematical procedures and deeper conceptual understanding inherent in the CCSS.

The lesson/unit reflects evidence of key shifts that are reflected in the CCSS:

o Focus: Lessons and units targeting the major work of the grade provide an especially in-depth treatment, with especially high expectations. Lessons and units targeting supporting work of the grade have visible connection to the major work of the grade and are sufficiently brief. Lessons and units do not hold students responsible for material from later grades.

o Coherence: The content develops through reasoning about the new concepts on the basis of previous understandings. Where appropriate, provides opportunities for students to connect knowledge and skills within or across clusters, domains and learning progressions.

o Rigor: Requires students to engage with and demonstrate challenging mathematics with appropriate balance among the following: − Application: Provides opportunities for students to

independently apply mathematical concepts in real-world situations and solve challenging problems with persistence, choosing and applying an appropriate model or strategy to new situations.

− Conceptual Understanding: Develops students’ conceptual understanding through tasks, brief problems, questions, multiple representations and opportunities for students to write and speak about their understanding.

− Procedural Skill and Fluency: Expects, supports and provides guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.

The lesson/unit is responsive to varied student learning needs:

o Includes clear and sufficient guidance to support teaching and learning of the targeted standards, including, when appropriate, the use of technology and media.

o Uses and encourages precise and accurate mathematics, academic language, terminology and concrete or abstract representations (e.g., pictures, symbols, expressions, equations, graphics, models) in the discipline.

o Engages students in productive struggle through relevant, thought-provoking questions, problems and tasks that stimulate interest and elicit mathematical thinking.

o Addresses instructional expectations and is easy to understand and use.

o Provides appropriate level and type of scaffolding, differentiation, intervention and support for a broad range of learners. − Supports diverse cultural and linguistic backgrounds, interests and styles.

− Provides extra supports for students working below grade level.

− Provides extensions for students with high interest or working above grade level.

A unit or longer lesson should:

o Recommend and facilitate a mix of instructional approaches for a variety of learners such as using multiple representations (e.g., including models, using a range of questions, checking for understanding, flexible grouping, pair-share).

o Gradually remove supports, requiring students to demonstrate their mathematical understanding independently.

o Demonstrate an effective sequence and a progression of learning where the concepts or skills advance and deepen over time.

o Expect, support and provide guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.

The lesson/unit regularly assesses whether students are mastering standards-based content and skills:

o Is designed to elicit direct, observable evidence of the degree to which a student can independently demonstrate the targeted CCSS.

o Assesses student proficiency using methods that are accessible and unbiased, including the use of grade-level language in student prompts.

o Includes aligned rubrics, answer keys and scoring guidelines that provide sufficient guidance for interpreting student performance.

A unit or longer lesson should:

o Use varied modes of curriculum-embedded assessments that may include pre-, formative, summative and self-assessment measures.

Rating: 3 2 1 0 Rating: 3 2 1 0 Rating: 3 2 1 0 Rating: 3 2 1 0

EQuIP Rubric for Lessons & Units: Mathematics

Directions: The Quality Review Rubric provides criteria to determine the quality and alignment of lessons and units to the Common Core State Standards (CCSS) in order to: (1) Identify exemplars/ models for teachers’ use within and across states; (2) provide constructive criteria-based feedback to developers; and (3) review existing instructional materials to determine what revisions are needed. Step 1 – Review Materials

Record the grade and title of the lesson/unit on the recording form. Scan to see what the lesson/unit contains and how it is organized. Read key materials related to instruction, assessment and teacher guidance. Study and work the task that serves as the centerpiece for the lesson/unit, analyzing the content and mathematical practices the tasks require.

Step 2 – Apply Criteria in Dimension I: Alignment Identify the grade-level CCSS that the lesson/unit targets. Closely examine the materials through the “lens” of each criterion. Individually check each criterion for which clear and substantial evidence is found. Identify and record input on specific improvements that might be made to meet criteria or strengthen alignment. Enter your rating 0 – 3 for Dimension I: Alignment.

Note: Dimension I is non-negotiable. In order for the review to continue, a rating of 2 or 3 is required. If the review is discontinued, consider general feedback that might be given to developers/teachers regarding next steps. Step 3 – Apply Criteria in Dimensions II – IV

Closely examine the lesson/unit through the “lens” of each criterion. Record comments on criteria met, improvements needed and then rate 0 – 3.

When working in a group, individuals may choose to compare ratings after each dimension or delay conversation until each person has rated and recorded their input for the remaining Dimensions II – IV. Step 4 – Apply an Overall Rating and Provide Summary Comments

Review ratings for Dimensions I – IV adding/clarifying comments as needed. Write summary comments for your overall rating on your recording sheet. Total dimension ratings and record overall rating E, E/I, R, N – adjust as necessary.

If working in a group, individuals should record their overall rating prior to conversation. Step 5 – Compare Overall Ratings and Determine Next Steps

Note the evidence cited to arrive at final ratings, summary comments and similarities and differences among raters. Recommend next steps for the lesson/unit and provide recommendations for improvement and/or ratings to developers/teachers.

Additional Guidance on Dimension II: Shifts - When considering Focus it is important that lessons or units targeting additional and supporting clusters are sufficiently brief – this ensures that students will spend the strong majority of the year on major work of the grade. See the K-8 Publishers Criteria for the Common Core State Standards in Mathematics, particularly pages 8-9 for further information on the focus criterion with respect to major work of the grade at www.corestandards.org/assets/Math_Publishers_Criteria_K-8_Summer%202012_FINAL.pdf. With respect to Coherence it is important that the learning objectives are linked to CCSS cluster headings (see www.corestandards.org/Math). Rating Scales Rating for Dimension I: Alignment is non-negotiable and requires a rating of 2 or 3. If rating is 0 or 1 then the review does not continue.

Rating Scale for Dimensions I, II, III, IV: 3: Meets most to all of the criteria in the dimension 2: Meets many of the criteria in the dimension

1: Meets some of the criteria in the dimension 0: Does not meet the criteria in the dimension

Overall Rating for the Lesson/Unit: E: Exemplar – Aligned and meets most to all of the criteria in dimensions II, III, IV (total 11 – 12) E/I: Exemplar if Improved – Aligned and needs some improvement in one or more dimensions (total 8 – 10)

R: Revision Needed – Aligned partially and needs significant revision in one or more dimensions (total 3 – 7) N: Not Ready to Review – Not aligned and does not meet criteria (total 0 – 2)

Descriptors for Dimensions I, II, III, IV: 3: Exemplifies CCSS Quality - meets the standard described by criteria in the dimension, as explained in criterion-based observations. 2: Approaching CCSS Quality - meets many criteria but will benefit from revision in others, as suggested in criterion-based observations.

1: Developing toward CCSS Quality - needs significant revision, as suggested in criterion-based observations. 0: Not representing CCSS Quality - does not address the criteria in the dimension.

Descriptor for Overall Ratings: E: Exemplifies CCSS Quality – Aligned and exemplifies the quality standard and exemplifies most of the criteria across Dimensions II, III, IV of the rubric. E/I: Approaching CCSS Quality – Aligned and exemplifies the quality standard in some dimensions but will benefit from some revision in others.

R: Developing toward CCSS Quality – Aligned partially and approaches the quality standard in some dimensions and needs significant revision in others. N: Not representing CCSS Quality – Not aligned and does not address criteria.

http://www.corestandards.org/assets/Math_Publishers_Criteria_K-8_Summer%202012_FINAL.pdf

http://www.corestandards.org/Math

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