fifth grade pacing 2014-2015 flexible depending on the...

Fifth Grade Pacing 2014-2015

Within the development of the pacing guides, it is expected that these will be

reasonably flexible depending on the needs of your class and pre-assessment data by

module. The pacing guide for Fifth Grade has 154 days of instruction including 26 days

for remediation, enrichment and assessment. In addition to the eighteen days used for

beginning of the year routines, state and district assessments, these 28 days can be flexed

based on your student needs.

Skills spiral throughout the year and students may not be at mastery by the end of

an individual lesson. In fact, many lessons anticipate that students will need more practice

in concepts. Therefore, we recommend that if re-teaching needs to happen, it occurs as a

part of the next day’s lesson. By doing this, teachers are able to present concepts in several

ways and will not get stuck within the same lesson for multiple days.

Module Map for Fifth Grade

Module 1 Module 2 Module 3 Module 4 Module 5 Module 6 10 Core Lessons

25 Core Lessons

11 Core Lessons

25 Core Lessons

20 Core Lessons

14 Core Lessons + 11 with Supplemental Materials

2 Days for Problem Solving Tasks

2 Days for Problem Solving Task



1 Day for Problem Solving Task

2 Days for Problem Solving Task

4 Days for Remediation, Enrichment and Assessment





4 Days for Remediation, Enrichment (Assessments are not recommended to be used)

Suggested 16 Days

Suggested 31 Days

Suggested 18 Days

Suggested 33 Days

Suggested 25 Days

Suggested 31 Days

EngageNY pacing guides modified by Federal Way Public SchoolsFederal Way, WA

Lesson

Modified by FWPS for the 2014/2015 School Year

New York State Common Core

Module Overview NYS COMMON CORE MATHEMATICS CURRICULUM 5•1

Module 1: Place Value and Decimal Fractions Date: 6/17/14

v

© 2013 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Overview of Module Topics and Lesson Objectives

Standards Topics and Objectives Days

5.NBT.1 5.NBT.2 5.MD.1

A Multiplicative Patterns on the Place Value Chart

Lesson 1: Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths.

Lesson 2: Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths.

Lesson 3: Use exponents to name place value units and explain patterns in the placement of the decimal point.

Lesson 4: Use exponents to denote powers of 10 with application to metric conversions.

3

5.NBT.3 B Decimal Fractions and Place Value Patterns

Lesson 5: Name decimal fractions in expanded, unit, and word forms by applying place value reasoning.

Lesson 6: Compare decimal fractions to the thousandths using like units and express comparisons with >, <, = .

2

5.NBT.4 C Place Value and Rounding Decimal Fractions

Lesson 7: Round a given decimal to any place using place value understanding and the vertical number line.

Lesson 8: Round a given decimal to any place using place value understanding and the vertical number line.

1

Mid-Module Assessment: Topics A–C (assessment ½ day, return ½ day, remediation or further applications 1 day)

2


5.NBT.2 5.NBT.3 5.NBT.7

D Adding and Subtracting Decimals

Lesson 9: Add decimals using place value strategies and relate those strategies to a written method.

Lesson 10: Subtract decimals using place value strategies and relate those strategies to a written method.

2

5.NBT.2 5.NBT.3 5.NBT.7

E Multiplying Decimals

Lesson 11: Multiply a decimal fraction by single-digit whole numbers, relate to a written method through application of the area model and place value understanding, and explain the

1

http://creativecommons.org/licenses/by-nc-sa/3.0/deed.en_US

Lesson




Module 1: Place Value and Decimal Fractions Date: 6/17/14

vi


reasoning used.

Lesson 12: Multiply a decimal fraction by single-digit whole numbers, including using estimation to confirm the placement of the decimal point.

5.NBT.3 5.NBT.7

F Dividing Decimals

Lesson 13: Divide decimals by single-digit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method.

Lesson 14: Divide decimals with a remainder using place value understanding and relate to a written method.

Lesson 15: Divide decimals using place value understanding including remainders in the smallest unit.

Lesson 16: Solve word problems using decimal operations.

1

End-of-Module Assessment: Topics A–F (assessment ½ day, return ½ day, remediation or further applications 1 day)

2

Total Number of Instructional Days 14

Lesson Number Instructional Notes

4 Focus is on metric conversion

7 Two lessons on vertical number line. Remove 7, keep 8.

12 Instead, incorporate estimating products into lesson 11.

13-15 These lessons are abstract – conceptual understanding is covered in Modules 2 and 4.

End of Module assessment

Remove #4.




Module 2: Multi-Digit Whole Number and Decimal Fraction Operations Date: 6/17/14

vii




5.NBT.1 5.NBT.2 5.OA.1

A Mental Strategies for Multi-Digit Whole Number Multiplication

Lesson 1: Multiply multi-digit whole numbers and multiples of 10 using place value patterns and the distributive and associative properties.

Lesson 2: Estimate multi-digit products by rounding factors to a basic fact and using place value patterns.

2

5.OA.1 5.OA.2 5.NBT.5

B The Standard Algorithm for Multi-Digit Whole Number Multiplication

Lesson 3: Write and interpret numerical expressions and compare expressions using a visual model.

Lesson 4: Convert numerical expressions into unit form as a mental strategy for multi-digit multiplication.

Lesson 5: Connect visual models and the distributive property to partial products of the standard algorithm without renaming.

Lesson 6: Connect area diagrams and the distributive property to partial products of the standard algorithm without renaming.

Lesson 7: Connect area diagrams and the distributive property to partial products of the standard algorithm with renaming.

Lesson 8: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.

Lesson 9: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems.

6

5.NBT.7 5.OA.1 5.OA.2 5.NBT.1

C Decimal Multi-Digit Multiplication

Lesson 10: Multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding to record partial products.

Lesson 11: Multiply decimal fractions by multi-digit whole numbers through conversion to a whole number problem and reasoning about the placement of the decimal.

Lesson 12: Reason about the product of a whole number and a decimal with hundredths using place value understanding and estimation.

3

5.NBT.5 D Measurement Word Problems with Whole Number and Decimal Multiplication 3





viii



5.NBT.7 5.MD.1 5.NBT.1 5.NBT.2

Lesson 13: Use whole number multiplication to express equivalent measurements.

Lesson 14: Use decimal multiplication to express equivalent measurements.

Lesson 15: Solve two-step word problems involving measurement and multi-digit multiplication.

Mid-Module Assessment: Topics A–D (assessment ½ day, return ½ day, remediation or further applications 2 days)

3

5.NBT.1 5.NBT.2 5.NBT.6

E Mental Strategies for Multi-Digit Whole Number Division

Lesson 16: Use divide by 10 patterns for multi-digit whole number division.

Lessons 17: Use basic facts to approximate quotients with two-digit divisors.

Lessons 18: Use basic facts to approximate quotients with two-digit divisors.

2

5.NBT.6

F Partial Quotients and Multi-Digit Whole Number Division

Lesson 19: Divide two- and three-digit dividends by multiples of 10 with single-digit quotients and make connections to a written method.

Lesson 20: Divide two- and three-digit dividends by two-digit divisors with single-digit quotients and make connections to a written method.

Lesson 21: Divide two- and three-digit dividends by two-digit divisors with single-digit quotients and make connections to a written method.

Lessons 22: Divide three- and four-digit dividends by two-digit divisors resulting in two- and three-digit quotients, reasoning about the decomposition of successive remainders in each place value.

Lessons 23: Divide three- and four-digit dividends by two-digit divisors resulting in two- and three-digit quotients, reasoning about the decomposition of successive remainders in each place value.

Combine lessons 22 and 23.

4

5.NBT.2 5.NBT.7

G Partial Quotients and Multi-Digit Decimal Division

Lesson 24: Divide decimal dividends by multiples of 10, reasoning about the placement of the decimal point and making connections to a written method.

Lesson 25: Use basic facts to approximate decimal quotients with two-digit divisors, reasoning about the placement of the decimal point.

Lessons 26: Divide decimal dividends by two-digit divisors, estimating

2





ix



quotients, reasoning about the placement of the decimal point, and making connections to a written method.

Lessons 27: Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method.

5.NBT.6 5.NBT.7

H Measurement Word Problems with Multi-Digit Division

Lesson 28: Solve division word problems involving multi-digit division with group size unknown and the number of groups unknown.

Lesson 29: Solve division word problems involving multi-digit division with group size unknown and the number of groups unknown.

1

End-of-Module Assessment: Topics A–H (assessment ½ day, return ½ day, remediation or further application 2 days)

3



10 Use for small group re-teaching if needed. Same content in lesson 11.

17 Can be used for additional practice/reteaching.

22-23 Problem set is rearranged to combine problems from each lesson.

26 Can be used for additional practice/reteaching.

27 Add problem set from lesson 27 to lesson 28 so students have one problem set to use during the lesson and one for independent practice.


Lesson


Module 3: Addition and Subtraction of Fractions Date: 6/17/14

vi





4.NF.1 4.NF.3c 4.NF.3d

A Equivalent Fractions

Lesson 1: Make equivalent fractions with the number line, the area model, and numbers.

Lesson 2: Make equivalent fractions with sums of fractions with like denominators.

2

5.NF.1 5.NF.2

B Making Like Units Pictorially

Lesson 3: Add fractions with unlike units using the strategy of creating equivalent fractions.

Lesson 4: Add fractions with sums between 1 and 2.

Lesson 5: Subtract fractions with unlike units using the strategy of creating equivalent fractions.

Lesson 6: Subtract fractions from numbers between 1 and 2.

Lesson 7: Solve two-step word problems.

4

Mid-Module Assessment: Topics A–B (assessment ½ day, return ½ day, remediation or further applications 2 day)

3

5.NF.1 5.NF.2

C Making Like Units Numerically

Lesson 8: Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies.

Lesson 9: Add fractions making like units numerically.

Lesson 10: Add fractions with sums greater than 2.

Lesson 11: Subtract fractions making like units numerically.

Lesson 12: Subtract fractions greater than or equal to one.

5

5.NF.1 5.NF.

D Further Applications

Lesson 13: Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations.

Lesson 14: Strategize to solve multi-term problems.

Lesson 15: Solve multi-step word problems; assess reasonableness of solutions using benchmark numbers.

Lesson 16: Explore part to whole relationships.

0


Lesson


Module 3: Addition and Subtraction of Fractions Date: 6/17/14

vii




End-of-Module Assessment: Topics C–D (assessment ½ day, return ½ day, remediation or further applications 1 day)

2



13-16 These would be great enrichment lessons!


Lesson

Modified by FWPS for the 2014-2015 School Year.



Module 4: Multiplication and Division of Fractions and Decimal Fractions Date: 6/17/14

ix



ix




5.MD.2 A Line Plots of Fraction Measurements

Lesson 1: Measure and compare pencil lengths to the nearest 1/2, 1/4, and 1/8 of an inch, and analyze the data through line plots.

1

5.NF.3 B Fractions as Division

Lessons 2: Interpret a fraction as division.

Lessons 3: Interpret a fraction as division.

Lesson 4: Use tape diagrams to model fractions as division.

Lesson 5: Solve word problems involving the division of whole numbers with answers in the form of fractions or whole numbers.

3

5.NF.4a

C Multiplication of a Whole Number by a Fraction

Lesson 6: Relate fractions as division to fraction of a set.

Lesson 7: Multiply any whole number by a fraction using tape diagrams.

Lesson 8: Relate fraction of a set to the repeated addition interpretation of fraction multiplication.

Lesson 9: Find a fraction of a measurement, and solve word problems.

3

5.OA.1 5.OA.2 5.NF.4a 5.NF.6

D Fraction Expressions and Word Problems

Lesson 10: Compare and evaluate expressions with parentheses.

Lesson 11–12: Solve and create fraction word problems involving addition, subtraction, and multiplication.

3

Mid-Module Assessment: Topics A–D (assessment ½ day, return ½ day, remediation or further applications 1 day)

2

5.NBT.7 5.NF.4a 5.NF.6 5.MD.1 5.NF.4b

E Multiplication of a Fraction by a Fraction

Lesson 13: Multiply unit fractions by unit fractions.

Lesson 14: Multiply unit fractions by non-unit fractions.

Lesson 15: Multiply non-unit fractions by non-unit fractions.

Lesson 16: Solve word problems using tape diagrams and fraction-by-fraction multiplication.

Lessons 17: Relate decimal and fraction multiplication.

Lessons 18: Relate decimal and fraction multiplication.

7



Lesson





x



x



Lesson 19: Convert measures involving whole numbers, and solve multi-step word problems.

Lesson 20: Convert mixed unit measurements, and solve multi-step word problems.

5.NF.5 5.NF.6

F Multiplication with Fractions and Decimals as Scaling and Word Problems

Lesson 21: Explain the size of the product, and relate fraction and decimal equivalence to multiplying a fraction by 1.

Lessons 22–23: Compare the size of the product to the size of the factors.

Lesson 24: Solve word problems using fraction and decimal multiplication.

2

5.OA.1 5.NBT.7 5.NF.7

G Division of Fractions and Decimal Fractions

Lesson 25: Divide a whole number by a unit fraction.

Lesson 26: Divide a unit fraction by a whole number.

Lesson 27: Solve problems involving fraction division.

Lesson 28: Write equations and word problems corresponding to tape and number line diagrams.

Lessons 29: Connect division by a unit fraction to division by 1 tenth and 1 hundredth.

Lessons 30–31: Divide decimal dividends by non‐unit decimal divisors.

5

5.OA.1 5.OA.2

H Interpretation of Numerical Expressions

Lesson 32: Interpret and evaluate numerical expressions including the language of scaling and fraction division.

Lesson 33: Create story contexts for numerical expressions and tape diagrams, and solve word problems.

1

End-of-Module Assessment: Topics A–H (assessment ½ day, return ½ day, remediation or further applications 2 days)

3





Lesson





xi



xi


3 This concept is thoroughly covered in lesson 2 and 4.

7 Move from concrete to abstract in tape diagrams by replacing or connecting counters with numbers when working with greater values.

9 This lesson would be a good extension or spiral review of measurement conversions.

10 This lesson needs contextual connections.

12 Remove given application problem and ask students to create a

word problem for (7+5)×

using school lunch and students.

14 & 15 Combine these if your students are ready to move on.

18 Covered in Module 3. Use for re-teaching or review as needed.

21 Could use this as enrichment.

24 Could use this as enrichment.

28 Any model is acceptable for modeling division of fractions. Remove page 1 of problem set and problems 1 and 2 from lesson.

30 This is a great strategy to teach, but is not required for mastery.

31-32 Could use this as enrichment.

33 Remove #6.

End of Module Assessment Remove #2e, #2f and #3c



Lesson


Module 5: Addition and Multiplication with Volume and Area Date: 6/17/14

vii






5.MD.3 5.MD.4

A Concepts of Volume

Lesson 1: Explore volume by building with and counting unit cubes.

Lesson 2: Find the volume of a right rectangular prism by packing with cubic units and counting.

Lesson 3: Compose and decompose right rectangular prisms using layers.

3

5.MD.3 5.MD.5

B Volume and the Operations of Multiplication and Addition

Lesson 4: Use multiplication to calculate volume.

Lesson 5: Use multiplication to connect volume as packing with volume as filling.

Lesson 6: Find the total volume of solid figures composed of two non-overlapping rectangular prisms.

Lesson 7: Solve word problems involving the volume of rectangular prisms with whole number edge lengths.

Lessons 8–9: Apply concepts and formulas of volume to design a sculpture using rectangular prisms within given parameters.

6

Mid-Module Assessment: Topics A–B (assessment 1 day, return ½ day, remediation or further applications ½ day)

2

5.NF.4b 5.NF.6

C Area of Rectangular Figures with Fractional Side Lengths

Lesson 10: Find the area of rectangles with whole-by-mixed and whole-by-fractional number side lengths by tiling, record by drawing, and relate to fraction multiplication.

Lesson 11: Find the area of rectangles with mixed-by-mixed and fraction-by-fraction side lengths by tiling, record by drawing, and relate to fraction multiplication.

Lesson 12: Measure to find the area of rectangles with fractional side lengths.

Lessons 13: Multiply mixed number factors, and relate to the distributive property and the area model.

Lessons 14–15: Solve real world problems involving area of figures with fractional side lengths using visual models and/or equations.

6

5.G.3 D Drawing, Analysis, and Classification of Two-Dimensional Shapes 5


Lesson


Module 5: Addition and Multiplication with Volume and Area Date: 6/17/14

viii




5.G.4

Lesson 16: Draw trapezoids to clarify their attributes, and define trapezoids based on those attributes.

Lesson 17: Draw parallelograms to clarify their attributes, and define parallelograms based on those attributes.

Lesson 18: Draw rectangles and rhombuses to clarify their attributes, and define rectangles and rhombuses based on those attributes.

Lesson 19: Draw kites and squares to clarify their attributes, and define kites and squares based on those attributes.

Lesson 20: Classify two-dimensional figures in a hierarchy based on properties.

Lesson 21: Draw and identify varied two-dimensional figures from given attributes.

End-of-Module Assessment: Topics A–D (assessment 1 day, return ½ day, remediation or further applications ½ day)

2



14 & 15 Consider choosing one question from these lessons to go deeper with as a performance task. Focusing on one problem as a lesson will build stamina for students instead of switching between 4 different problems.

21 Use remediation/enrichment day for “guess my shape” game for further practice classifying.


Lesson




Module 6: Problem Solving with the Coordinate Plane Date: 6/17/14

viii


In developing the pacing for this module, we found that EngageNY develops these standards

significantly beyond the standard/s expectations at the 5th grade level. These standards serve to

introduce students to proportional relationships and the coordinate grid to prepare them for deeper

work in 6th grade. In backwards planning through possible items on SmarterBalanced, many lessons

were removed. Some are replaced with supplemental material. It is important to read all

instructional notes for this module to decide how best to teach these concepts in your classroom.



5.G.1

A Coordinate Systems

Introduce Coordinate Systems with Whole Numbers using

Georgia Grade 5 Unit 5

Shoo-Fly (1 day)

Air Traffic Controller (1 day)

Lesson 1: Construct a coordinate system on a line.

Lesson 2: Construct a coordinate system on a plane.*

Lesson 3: Name points using coordinate pairs, and use the coordinate pairs to plot points. *

Lesson 4: Name points using coordinate pairs, and use the coordinate pairs to plot points. *

Lesson 5: Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes.

Lesson 6: Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes.

*see instructional notes

6

5.OA.2 5.OA.3 5.G.1

B Patterns in the Coordinate Plane and Graphing Number Patterns from Rules

Georgia Unit 5: Earth Day Project (1 day)

Lesson 7: Plot points, use them to draw lines in the plane, and describe patterns within the coordinate pairs.*

Lesson 8: Generate a number pattern from a given rule, and plot

Time Varies 6- 10 days


https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_5_Unit5FrameworkSE.pdf


Lesson





ix



the points. *

Georgia Unit 5: First to Arrive (1 day)

Lesson 9: Generate two number patterns from given rules, plot the points, and analyze the patterns.

Spend as much time as needed for students to explore relationships in the coordinate grid.

1-5 days Contextual Problems: Real Life Scenarios and Patterns with changes in x and y (see instructional notes)

Lesson 10: Compare the lines and patterns generated by addition rules and multiplication rules.

Lesson 11: Analyze number patterns created from mixed operations.

Lesson 12: Create a rule to generate a number pattern, and plot the points.

Mid-Module Assessment: Topics A–B (assessment 1 day, return 1 day, remediation or further applications 1 day)

Do not use mid-module

assessment 3

5.G.1 5.G.2

C Drawing Figures in the Coordinate Plane

Lesson 13: Construct parallel line segments on a rectangular grid.

Lesson 14: Construct parallel line segments, and analyze relationships of the coordinate pairs.

Lesson 15: Construct perpendicular line segments on a rectangular grid.

Lesson 16: Construct perpendicular line segments, and analyze relationships of the coordinate pairs.

Lesson 17: Draw symmetric figures using distance and angle measure from the line of symmetry.

0

5.OA.3 5.G.2

D Problem Solving in the Coordinate Plane

Lesson 18: Draw symmetric figures on the coordinate plane. Problem Solving Task: Granny’s Balloon Trip (1 day) Lesson 19: Plot data on line graphs and analyze trends.

Lesson 20: Use coordinate systems to solve real world problems.

Georgia Unit 5: What’s the Better Buy? (1 day)

4



http://www.insidemathematics.org/common-core-math-tasks/5th-grade/5-2007%20Granny%27s%20Balloon%20Trip.pdf


Lesson





x



End-of-Module Assessment: Topics A–D (assessment 1 day, return 1 day, remediation or further applications 1 day)

Do not use end of module

assessment. 3

5.NF.2 5.NF.3 5.NF.6 5.NF.7c 5.MD.1 5.MD.5 5.G.2

E Multi-Step Word Problems

Lessons 21–25: Make sense of complex, multi-step problems and persevere in solving them. Share and critique peer solutions.

5

F The Years in Review: A Reflection on A Story of Units

Lessons 26–27: Solidify writing and interpreting numerical expressions.

Lesson 28: Solidify fluency with Grade 5 skills.

Lessons 29─30: Solidify the vocabulary of geometry.

Lesson 31: Explore the Fibonacci sequence.

Lesson 32: Explore patterns in saving money.

Lessons 33–34: Design and construct boxes to house materials for summer use.

Time Varies

Total Number of Instructional Days

28- 33


1 This lesson is a review of the number line.

3 For whole class instruction, only use the Application problem and spend more time on it. Another activity that could be involved in this lesson is to have students create a treasure map and work together to solve each other’s coordinate grid treasure map. The problem set is extension. Feel free to use to review points.


Lesson





xi


2,4 Make sure to teach whole numbers in a coordinate plane prior to teaching fractions.

5 Read through the problem set prior to using this to know where to focus time during instruction. If wanted, remove some items to go deeper with key concepts.

6 This is extension.

7 and 8 Both of these lessons extend above the standard. To teach this standard, only use page 1 of each problem set. Do not use page 2 of either homework.

10 This is extension and could be used for enrichment for students to work on independently (if needed).

26-34 Choose enrichment/review activities as needed.

Contextual Situations in the Coordinate Grid (1-5 days)

Possible Resources to Use:

Tri-Triangles Level B or C, SmarterBalanced released items (on following pages)

Video Examples: Input and Output Table , Intro to Ratios (create a free account to watch this video)

Students must be able to generate rules from a graphed equation, coordinate pairs and tables. For example if given a table, they must be able to say, “The rule for x is add 3 and the rule for y is multiply by 2”

The following examples are things that they may be asked to do on the SmarterBalanced assessment:

Evaluate the relationship between variables in a coordinate plane

Plot points based on rules for X and Y (x,y)

Identify the nth term in a sequence

Identify or create coordinate pairs based on rules

On the following three pages, you will find examples of released items. It is important for students to see the connection to real world context in these to make sense of the rules.


http://www.insidemathematics.org/problems-of-the-month/pom-tritriangles.pdf

http://www.insidemathematics.org/index.php/classroom-video-visits/public-lessons-numerical-patterning/221-numerical-patterning-introduction-part-c

http://commoncore.americaachieves.org/module/8

Evaluate the relationship between an input (A) and an output (B) of terms

Identify or create coordinate pairs given rules (P, Q)

Create a graph or choose a graph based on rules in (x,y)

Identify the (nth) term in a sequence based on pattern

All examples are from SmarterBalanced

Item Specifications http://www.smarterbalanced.org/smarter-balanced-assessments/#item

http://www.smarterbalanced.org/smarter-balanced-assessments/%23item

fifth grade pacing 2014-2015 flexible depending on the...

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