2013-2014 Blended School Year-5th Grade · PDF file2013-2014 Blended School Year-5th Grade Mathematics ... FL Page 1 2013-2014 Blended School Year ... has to plan for the students

2013-2014 Blended School Year-5th Grade Mathematics

Lake County, FL Page 1

2013-2014 Blended School Year Clarification:

Students will be assessed on the Next Generation Sunshine State Standards with the FCAT 2.0.

Most of the mathematics NGSSS content is addressed within the Common Core State Standards, but not all.

Understanding Common Core State Standards for Mathematics

Read the Critical Areas of Focus for your grade level on Page 2 of this document. This explains the primary focus of the CCSSM

for your grade level. It is important to be aware of these areas during this blended year.

Look at the speaking and listening standards and writing standards on Page 3 of this document that should be integrated into

your math instruction. Plan for collaboration and writing in math based on these standards.

The Mathematical Practice Standards on Page 4 are standards that proficient math students should exhibit, but the teacher

has to plan for the students to practice with these standards during the instruction of the content standards. These should be

integrated during instruction of NGSSS or CCSM.

There are fluency standards for each grade level. These should be introduced early in the year to ensure students have

enough time and practice to develop fluency by the end of the year.

Utilizing the NGSSS Task Card and the C² Connection Card to guide and enhance classroom instruction aligned to NGSSS and CCSSM.

Use the Scope and Sequence Document to determine order of instruction.This document outlines:

•CCCSS that should be taught

•NGSSS Mini Assessment that should be given to assess transfer (NGSSS Standards in red do not transfer with CCSSM, therefore should be explicitely taught accoridng tho the FCAT 2.0 Specifications.)

Refer to the C² Connection Card for a deeper understanding of the Common Core Standard. This document includes:

•Deconstructed standards

•Aligned questions

•Aligned Web Links

•Elements to assist with rigorous tasks/ student engagment

Refer to the NGSSS Task Card for elements aligned to the FCAT 2.0 Assessment. This document includes:

•FCAT 2.0 Test Specifications

•Question Stems

•Summative writing tasks

•Vocabulary

•Sample Questions

Create your Differentiated Focus Calendar based on:

•Bell Ringer- (Maintaining previous benchmarks or practicing parts of current benchmark)

•Order of instruction

•School Data (Student Achievement, Instructional Look For Visit Checklist)

•Elements that would most impact instruction at your school and therefore should be included in your focus calendar

•Copy appropriate elements from the C² Connection Cards, NGSSS Task Card and Scope and Sequence documents and embed into your Focus Calendar

•Add any additional elements you would like for your school aligned to the standards

Teachers will use the differentiated focus calendar to plan instruction. The following standards should be included in each lesson plan:

•Include specific Speaking/Listening, Reading, and Writing Standards (Promotes student discourse, writing and reading across content)

•Include specific Mathematical Practice Standards to increase the rigor and student engagement.

•Include CCSSM and NGSSS aligned content standards



Critical Areas of Focus CCSSM In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume. (1) Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.) (2) Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with multi-digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately. (3) Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.



In order for students to be College and Career ready prepared with the 21st Century skills, it is important for them to have multiple opportunities to speak, listen, and write across content. The following are the speaking and listening standards and the writing standards that should be integrated into the math curriculum.

Speaking and Listening Writing

LACC.5.SL.1.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly.

a) Come to discussions prepared having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.

b) Follow agreed-upon rules for discussions and carry out assigned roles.

c) Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others.

d) Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions.

LACC.5.W.1.2 Write informative/explanatory texts to examine a topic and convey ideas and information clearly.

a) Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.

b) Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic.

c) Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially).

d) Use precise language and domain-specific vocabulary to inform about or explain the topic.

e) Provide a concluding statement or section related to the information or explanation presented.

LACC.5.SL.1.2 Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.

LACC.5.SL.1.3 Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence.



The Mathematical Practice Standards describe the expertise that mathematics teachers should develop in their students. Teachers

should consciously plan for instruction aligned with 2-3 standards embedded in each lesson.

Student Friendly Mathematical Practice Statements

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

Make a plan!

Try different approaches when your problem is hard.

Solve your problem in more than one way.

Check whether your solution makes sense.

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

Explain the meanings of the numbers, words, pictures, symbols, and objects you and others use.

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

Explain both what to do and why it works.

Work to make sense of others’ mathematical thinking.

MACC.K.12.MP.4.1 Model with mathematics.

Apply math to real-world situations.

Use models such as graphs, drawings, tables, symbols, numbers, and diagrams to solve problems.

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

Choose appropriate tools for your problem.

Use mathematical tools correctly and efficiently.

Estimate and use what you know to check the answers you find using tools.

MACC.K12.MP.6.1 Attend to precision.

Communicate your mathematical thinking clearly and precisely.

Use the level of precision you need for your problem.

Be accurate when you count, measure, and calculate.

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

Find, extend, analyze, and create patterns.

Use patterns and structures to solve problems.

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

Use patterns and structures to create and explain rules and shortcuts.

Use properties, rules, and shortcuts to solve problems.

Reflect on your thinking before, during, and after you solve a problem.



Fluency Standards with Common Core Mathematics: Fluency in the standards means “fast and accurate.” When fluency

is used in the standards, it is referring to an endpoint. It is the end of that progression of learning. The fluency standards

should be addressed early in the year to provide time and practice in developing the necessary fluency skills.

Grade Fluency Standard Required Fluency

K MACC.K.OA.1.5

Add/subtract within 5

1 MACC.1.OA.3.6

Add/subtract within 10

2 MACC.2.OA.2.2 MACC.2.NBT.2.5

Add/subtract within 20 Add/subtract within 100 (pencil and paper)

3 MACC.3.OA.3.7 MACC.3.NBT.1.2

Multiply/divide within 100 Add/subtract within 1000

4 MACC.4.NBT.2.4 Add/subtract within 1,000,000

5 MACC.5.NBT.2.5

Multi‐digit multiplication



*This scope and sequence is not a cross-walk. It should be used to determine order of instruction

*The red NGSSS are not covered in 5th grade with the Common Core State Standards, but will need to be taught for the blended school year.

Approximate amount of time:

Should be adjusted based on school data

CCSSM-Mathematics C² Connection Card

NGSSS- Task Card Assess with Mini Benchmark

10 days MACC.5.NBT.2.5 MACC.5.NBT.2.6

MA.5.A.1.1 MA.5.A.6.5

22 days MACC.5.NBT.2.6 MA.5.A.1.1 MA.5.A.1.4

14 days MACC.5.OA.1.1 MACC.5.OA.1.2

MA.5.A.6.2 MA.5.A.4.1 MA.5.A.6.3 MA.5.A.6.4

12 days MACC.5.G.1.1 MACC.5.G.1.2 MACC.5.OA.2.3

MA.5.S.7.1 MA.5.S.7.2 MA.5.G.5.1 MA.5.A.4.2

25 days MACC.5.NF.1.1 MACC.5.NF.1.2

MA.5.A.2.1 MA.5.A.2.4 MA.5.A.2.2 MA.5.A.2.3

13 days MACC.5.NBT.1.1 MACC.5.NBT.1.2 MACC.5.NBT.1.3 MACC.5.NBT.1.4

MA.5.A.6.1 MA.5.A.2.2 MA.5.A.2.3 Adding and Subtracting Decimals

14 days MACC.5.MD.1.1 MACC.5.MD.2.2

MA.5.G.5.2 MA.5.G.5.3 Measurement

13 days MA.5.G.2.3 MA.5.G.2.4

MA.5.G.5.3 MA.5.G.3.1 Two and Three Dimensional Figures

10 days MACC.5.MD.3.3 MACC.5.MD.3.4 MACC.5.MD.3.5

MA.5.G.5.4 MA.5.G.3.2

Pre-FCAT Review concepts not mastered based on the LBA midyear and Mini-benchmark assessments. NGSSS

Post-FCAT All Common Core

MACC.5.NF.2.3 MACC.5.NF.2.4 MACC.5.NF.2.5 MACC.5.NF.2.6 MACC.5.NF.2.7 Multiply and Divide Fractions

MACC.5.NBT.2.7 Add, Subtract, Multiply, and Divide Decimals

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MATHEMATICS C² CONNECTION CARD GRADE #

Domain: Larger group of related standards (Clusters fall under these domains) Each group of cards is color coded according to the cluster.

Cluster Group of related standards Associated Fluency Standard Fluency standards to be addressed with this cluster group.

These may be fluency standards from prior grade levels students have not mastered or from the current grade level they should be practicing with.

Common Core State Standard (There could be anywhere from 1-5 standards on a card because each card contains an entire cluster of standards.

Common Core State Standard

Deconstructed standard Deconstructed standard The standard is deconstructed into concise learning statements about what the students need to know and be able to do. They are organized by learning targets to make it easier to choose the correct method of instruction and assessment.

Math standards are deconstructed based on: This is the level to which teachers should teach, but may not align with the DOK for assessment. Knowledge Reasoning Demonstration Product

Suggested Mathematical Practice Standards Questions

Math Practices that should be integrated into the instruction of this cluster according to the deconstructed standards document. (Teachers may incorporate others)

Sample higher order thinking questions aligned to content and practice standards.

Vertical Progression Example Writing Connections

Prior Knowledge Upcoming knowledge in the next grade level. Example writing prompts aligned to the cluster that encourages students to explain and justify their mathematical thinking.

Web Links Common Core Task/ Assessment Next Generation Edusoft Mini-Assessment

Resources will be aligned to the cluster and sometimes aligned to multiple clusters.

Common Core Tasks and PARCC Assessment Links aligned to the cluster

Edusoft Mini-benchmark Assessment aligned to NGSSS that should be utilized to monitor transfer of knowledge. Standards in red will not transfer to CCSSM, and should therefore be explicitly taught using the NGSSS task card.

Draft 2013 Lake County Schools Academic Services Unit

MATHEMATICS C² CONNECTION CARD GRADE 5

Domain: Geometry Cluster G.1 Graph points on the coordinate plane to solve real-world and mathematical problems.

Associated Fluency Standards: MACC.5.NBT.2.5 Multiply Multi-Digit Whole Numbers MACC.4.NBT.2.4 Add and Subtract within 1,000,000

MACC.5.G.1.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

MACC.5.G.1.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

5.G.1.1 Deconstructed standard (DOK 1) 5.G.1.2 Deconstructed standard (DOK 2) Knowledge

Define the coordinate system.

Identify the x and y axis.

Locate the origin on the coordinate system.

Identify coordinates of a point on a coordinate system.

Recognize and describe the connection between the ordered pair and the x and y axis from the origin.

Knowledge

Graph points in the first quadrant. Reasoning

Interpret coordinate values of points in real world context and mathematical problems. Demonstration

Represent real world and mathematical problems by graphing points in the first quadrant.

Suggested Mathematical Practice Standards Question

MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.4.1 Model with mathematics MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

How does a coordinate system work?

How does understanding the coordinate system help you read a map?

How do you use the ordered pairs to locate ________________?

Vertical Progression TurnOnCCMath.net K-8 Learning Trajectories

Example Writing Connection

Students have no prior knowledge with coordinate graphs.

6th

Grade

Students solve real-world problems by graphing points in all four quadrants of a coordinate plane.

Students write to explain where their point is located on the coordinate plane.

Write a situational story problem using a coordinate graph.


Common Core State Standards for Mathematics (P. 89- Common Multiplication and Division situations) 5

th Grade Common Core Flip Book

Link to Depth of Knowledge (DOK) Chart

5.G.1.1 CPALMS Resources 5.G.1.2 CPALMS Resources

NCTM Lesson: Finding your Way Around NCTM Lesson: Describe the Graph Task: Battle Ship Using Grid Paper

MA.5.S.7.1 (Does not transfer to CCSSM) MA.5.S.7.2 (Does not transfer to CCSSM) MA.5.G.5.1 Link to Scope and Sequence Link to Next Generation Benchmark Task Cards

http://www.insidemathematics.org/index.php/commmon-core-math-intro

http://www.turnonccmath.net/

http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

http://katm.org/wp/wp-content/uploads/flipbooks/5th-Flipbookedited2.pdf

http://lake.k12.fl.us/Page/27614

http://www.cpalms.org/Standards/PublicPreviewBenchmark5431.aspx




http://illuminations.nctm.org/LessonDetail.aspx?id=L280

http://illuminations.nctm.org/LessonDetail.aspx?id=L777

http://illuminations.nctm.org/ActivityDetail.aspx?ID=70

http://lake.k12.fl.us/site/default.aspx?PageID=1344


MATHEMATICS C² CONNECTION CARD GRADE 5 Domain: Geometry Cluster G.2 Classify two-dimensional figures into categories based on their properties. No Associated Fluency Standards

MACC.5.G.2.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

MACC.5.G.2.4 Classify two-dimensional figures in a hierarchy based on properties.

5.G.2.3 Deconstructed standard (DOK 2) 5.G.2.4 Deconstructed standard (DOK 2) Knowledge

Recognize that some two-dimensional shapes can be classified into more than one category based on their attributes.

Recognize if a two-dimensional shape is classified into a category, that it belongs to all subcategories of that category.

Knowledge

Recognize the hierarchy of two-dimensional shapes based on their attributes. Reasoning

Analyze properties of two-dimensional figures in order to place into a hierarchy.

Classify two-dimensional figures into categories and/or subcategories based on their attributes.


MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.3.1 Construct viable arguments and critique the reasoning of others. MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

Why is a square always a rectangle?

Why is a rectangle not always a square?

How can you classify the 2 –dimensional shapes?

How can angle and side measures help us to create and classify triangles?

Where is geometry found in your everyday world?

Why is geometry relevant to our everyday lives?



4th

Grade

Students classify two dimensional figures based on parallel or perpendicular lines and size of angles.

6th

Grade

Students apply techniques of composing and decomposing to find the area of triangles, special quadrilaterals, and polygons to solve mathematical and real world problems.

Students represent three-dimensional figures using nets made up of rectangles and triangles.

Write to explain how you classified the 2-dimensional shapes and why.

Develop a written summary to explain how quadrilaterals are alike and different.

Create a _____________ triangle. Prove that the triangle you created has those attributes.





5.G.2.3 CPALMS Resources 5.G.2.4 CPALMS Resources

Game: Polygon Sort

MA.5.G.5.3 MA.5.G.3.1 (Does not transfer to CCSSM) Link to Scope and Sequence Link to Next Generation Benchmark Task Cards











http://www.crickweb.co.uk/ks2numeracy-shape-and-weight.html#quad




Domain: Measurement and Data Cluster MD.1 Convert like measurement units within a given measurement system. Cluster MD.2 Represent and interpret data.

Associated Fluency Standards: MACC.5.NBT.2.5 Multiply Multi-Digit Whole Numbers

MACC.5.MD.1.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

MACC.5.MD.2.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

5.MD.1.1 Deconstructed standard (DOK 2) 5.MD.2.2 Deconstructed standard (DOK 2) Knowledge

Recognize units of measurement within the same system.

Divide and multiply to change units. Reasoning

Convert units of measurement within the same system. Demonstration

Solve multi-step, real world problems that involve converting units.

Knowledge

Identify benchmark fractions.

Make a line plot to display a data set of measurements in fractions of a unit. Demonstration

Solve problems involving information presented in line plots which use fractions of a unit by adding, subtracting, multiplying, and dividing fractions.


MACC.K12.MP.1.1 Make sense of problems and persevere in solving them. MACC.K12.MP.4.1 Model with mathematics MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

How do you convert between units in the metric system? Explain why.

Why did you________________________?



4th

Grade

Students use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money.

Students express measurements in a larger unit in terms of a smaller unit and record measurement equivalents in a two column table.

Students make a line plot to display a data set of measurements in fractions of a unit and solve problems involving addition and subtraction by using information on line plot.

6th

Grade

Students recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Students display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Students summarize numerical data sets in relation to their context

Write to explain the relationship between two units of the same system.

Display your measurement data on a line plot and analyze the data.

Construct an informative piece based on the data presented in your line plot.





5.MD.1.1 CPALMS Resources 5.MD.2.2 CPALMS Resources

Illuminations Lesson: Do You Measure Up? Activity: Fractions in Every Day Life

MA.5.G.5.2 MA.5.G.5.3 Link to Scope and Sequence Link to Next Generation Benchmark Task Cards














MATHEMATICS C² CONNECTION CARD GRADE 5 Domain: Measurement and Data Cluster MD.3 Geometric measurement understands concepts of volume and relate volume

to multiplication and to addition. Associated Fluency Standards:

MACC.5.NBT.2.5 Multiply Multi-Digit Whole Numbers

MACC.5.MD.3.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a) A cube with side length 1 unit, called a “unit

cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

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

MACC.5.MD.3.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

MACC.5.MD.3.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a) Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and

show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

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

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

5.MD.3.3 Deconstructed standard (DOK 1)



Knowledge

Recognize that volume is the measurement of the space inside a solid three-dimensional figure.

Recognize a unit cube has 1 cubic unit of volume and is used to measure volume of three-dimensional shapes.

Recognize any solid figure packed without gaps or overlaps and filled with n unit cubes indicates the total cubic units or volume.

Knowledge

Measure volume by counting unit cubes, cubic cm, cubic in, cubic ft, and improvised units.

Knowledge

Identify a right rectangular prism.

Multiply the three dimensions in any order to calculate volume (Commutative and Associative Properties.)

Know that “B” is the area of the base.

Recognize volume as additive. Reasoning

Develop volume formula for a rectangle prism by comparing volume when filled with cubes to volume by multiplying the height by the area of the base, or when multiplying the edge lengths (L x W x H)

Apply the following formulas to right rectangular prisms having whole number edge lengths in the context of real world mathematical problems: Volume = length x width x height, Volume = area of base x height.

Demonstration

Solve real world problems by decomposing a solid figure into two non-overlapping right rectangular prisms and adding their volumes.

Find the volume of a right rectangular prism with whole number side lengths by packing it with unit cubes.


MACC.K12.MP.1.1 Make sense of problems and persevere in solving them. MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.3.1 Construct viable arguments and critique the reasoning of others. MACC.K12.MP.4.1 Model with mathematics MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.8.1 Look for and express regularity in repeated reasoning. Link to Inside Mathematics 8 Mathematical Practice Standards

How are area and volume alike and different?

Why is volume represented with cubic units?

How can you find the volume of cubes and rectangular prisms?

How can you find the combined volume of two or more rectangular prisms?

How do you determine if your solution is correct?



4th Grade

Students applied the area and perimeter formulas for rectangles in real world and mathematical problems.

6th Grade

Students find the area of triangles, quadrilaterals, and polygons.

Students find the volume of a right rectangular prism with fractional edge lengths.

Write to explain the relationship between area and volume.

Think about your home. What would you measure in square units and why? What would you measure in cubic units and why?

Construct an informational piece explaining why it is necessary to use square units when building a house.


Common Core State Standards for Mathematics (P. 89- Common Multiplication and Division situations) 5th Grade Common Core Flip Book Link to Depth of Knowledge (DOK) Chart

5.MD.3.3 CPALMS Resources 5.MD.3.4 CPALMS Resources 5.MD.3.5 CPALMS Resources

Task: Box of Clay Link to Depth of Knowledge (DOK) Chart

MA.5.G.5.4(Does not transfer with CCSSM) MA.5.G.3.2 (Does not transfer with CCSSM) Link to Scope and Sequence Link to Next Generation Benchmark Task Cards











http://www.illustrativemathematics.org/illustrations/1031

../../../../DOK_Chart.pdf



MATHEMATICS C² CONNECTION CARD GRADE 5 Domain: Numbers and Operations in Base Ten Cluster NBT.1 Understand the place value system. Associated Fluency Standards:

MACC.5.NBT.2.5 Multiply Multi-Digit Whole Numbers

MACC.5.NBT.1.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

MACC.5.NBT.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

MACC.5.NBT.1.3 Read, write, and compare decimals to thousandths. a) Read and write decimals to thousandths using

base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

b) Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MACC.5.NBT.1.4 Use place value understanding to round decimals to any place.

5.NBT.1.1 Deconstructed standard (DOK1) 5.NBT.1.2 Deconstructed Standard (DOK 2)

5.NBT.1.3 Deconstructed standard (DOK 1)

5.NBT.1.4 Deconstructed standard (DOK 1)

Knowledge

Recognize that in a multi-digit number, a digit in the one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Knowledge

Translate between powers of 10 written as 10 raised to a whole number exponent, in expanded form, and standard notation.

Reasoning

Explain the patterns in the number of zeros of the product when multiplying a number by powers of 10.

Explain the relationship of the placement of the decimal point when a decimal is multiplied or divided by a power of 10.

Demonstration

Represent powers of 10 using whole number exponents.

Knowledge

Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

Use >, =, and < symbols to record the results of comparisons between decimals.

Use knowledge of base ten and place value to round decimals to any place.

Reasoning

Compare two decimals to the thousandths, based on the place value of each digit.

Knowledge

Use knowledge of base ten and place value to round decimals to any place.


MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.4.1 Model with mathematics MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. MACC.K12.MP.8.1 Look for and express regularity in repeated reasoning. Link to Inside Mathematics 8 Mathematical Practice Standards

How can you represent a quantity of a multiple of ten?

Why is that number greater than the other?

How can we use models to demonstrate decimal values?

Why is place value different from digit value?

How does the position of a number determine its value?


Example Writing Connections

4th Grade

Students recognize that multi-digit whole numbers a digit in one place represents ten times what it represents to its right.

Students compare decimals through hundredths.

6th Grade

Students understand that positive and negative numbers are used together to describe quantitates having opposite directions or values.

Write to explain and justify how you reached your answer.

Compare and Contrast two numbers according to their place value.

Write to explain why the position of a number determines the value.



5.NBT.1.1 CPALMS Resources 5.NBT.1.2 CPALMS Resources 5.NBT.1.3 CPALMS Resources 5.NBT.1.4 CPALMS Resources

MA.5.A.6.1 (Does not transfer with CCSSM) MA.5.A.2.2 (Includes fractions) MA.5.A.2.3 (Includes fractions)

Link to Scope and Sequence Link to Next Generation Benchmark Task Cards
















Domain: Numbers and Operations in Base Ten Cluster NBT.2 Perform operations with multi-digit whole numbers and with decimals to hundredths.

Associated Fluency Standards: MACC.5.NBT.2.5 Multiply Multi-Digit Whole Numbers

MACC.5.NBT.2.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

MACC.5.NBT.2.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MACC.5.NBT.2.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

5.NBT.2.5 Deconstructed standard (DOK 1) 5.NBT.2.6 Deconstructed standard (DOK 2) 5.NBT.2.7 Deconstructed standard (DOK 3) Demonstration

Fluently multiply multi-digit whole numbers using the standard algorithm.

Knowledge

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.

Demonstration

Use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division to solve division problems.

Illustrate and explain division calculations by using equations, rectangular arrays, and/or area models.

Knowledge

Add, subtract, multiply, and divide decimals to hundredths using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Demonstration

Relate the strategy to a written method and explain the reasoning used to solve decimal operation calculations.


MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.4.1 Model with mathematics MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

Why is place value important when adding/subtracting whole numbers and decimal numbers?

How can we use models to multiply and divide decimals?

How can we check for errors in multiplication or division of decimals?



4th

Grade

Students multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers using strategies based on place value and the properties of operations.

Students find whole number quotients and remainders with up to four-digit dividends and one-digit divisors based on place value and the properties of operation.

6th Grade

Students fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Write to explain and justify how you solved your problem.

Write to explain how you could use a model to solve the problem and why.

Compare one strategy for multiplication to the standard algorithm.





5.NBT.1.1 CPALMS Resources

5.NBT.2.5 CPALMS Resources 5.NBT.2.6 CPALMS Resources 5.NBT.2.7 CPALMS Resources

MA.5.A.1.1 MA.5.A.6.5 MA.5.A.1.4 Link to Scope and Sequence Link to Next Generation Benchmark Task Cards

















Domain: Numbers and Operations-Fractions Cluster NF.1 Use equivalent fractions as a strategy to add and subtract fractions. Associated Fluency Standards: MACC.4.NBT.2.4 Add and Subtract within 1,000,000

MACC.5.NF.1.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

MACC.5.NF.1.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

5.NF.1.1 Deconstructed standard (DOK 1) 5.Nf.1.2 Deconstructed standard (DOK 3) Knowledge

Generate equivalent fractions to find the like denominator. Demonstration

Solve addition and subtraction problems involving fractions (including mixed numbers) with like and unlike denominators using an equivalent fraction strategy.

Knowledge

Generate equivalent fractions to find like denominators. Reasoning

Evaluate the reasonableness of an answer, using fractional number sense, by comparing it to a benchmark fraction.

Demonstration

Solve word problems, involving addition and subtraction of fractions with unlike denominators referring to the same whole.


MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.4.1 Model with mathematics MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. MACC.K12.MP.8.1 Look for and express regularity in repeated reasoning. Link to Inside Mathematics 8 Mathematical Practice Standards

How was that strategy similar/different than…?

How are equivalent fractions helpful when solving problems?

Why is it important to know how close a fraction is to one whole?

How can addition/subtraction of fractions be represented by objects, pictures, words, numbers, and models?



4th

Grade

Students generate equivalent fractions and compare fractions.

Students add and subtract fractions with like denominators.

6th

Grade

Students apply understanding of fractions within expressions and equations.

Students compare their strategy to another strategy.

Write to explain how fractions of different denominators area added together and why you would solve it that way.





5.NF.1.1 CPALMS Resources 5.NF.1.2 CPALMS Resources

MA.5.A.2.1 MA.5.A.2.4 (Does not transfer to CCSSM) MA.5.A.2.2 (Also includes decimals) Link to Scope and Sequence Link to Next Generation Benchmark Task Cards












MATHEMATICS C² CONNECTION CARD GRADE 5 (1 of 2)

Domain: Numbers and Operations-Fractions Cluster NF.2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions.


MACC.5.NF.2.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

MACC.5.NF.2.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a) Interpret the product (a/b) × q as a parts of a

partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

b) Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

MACC.5.NF.2.5 Interpret multiplication as scaling (resizing), by: a) Comparing the size of a product to

the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

b) Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

MACC.5.NF.2.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

MACC.5.NF.2.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a) Interpret division of a unit fraction

by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

b) Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?


MATHEMATICS C² CONNECTION CARD GRADE 5 (2 of 2) Domain: Numbers and Operations-Fractions

Cluster NF.2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions.


5.NF.2.3 Deconstructed standard (DOK 2)





Knowledge

Interpret a fraction as division of the numerator by the denominator.

Reasoning

Interpret the remainder as a fractional part of the problem.

Demonstration

Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

Knowledge

Multiply fractions by whole numbers.

Multiply fractions by fractions. Reasoning

Interpret the product of fractions times a whole number as total number of parts of the whole.

Determine the sequence of operations that results in the total number of parts of the whole.

Interpret the product of a fractions times a fractions as the total number of parts of the whole.

Represent fraction products as rectangular areas.

Justify multiplying fractional side lengths to find the area is the same as tiling a rectangle with unit squares of the appropriate unit fraction side lengths.

Demonstration

Find area of a rectangle with fractional side lengths using different strategies.

Model the area of rectangles with fractional side lengths with unit squares to show the area of rectangles.

Knowledge

Know that scaling (resizing) involves multiplication.

Know that multiplying whole numbers and fractions results in products greater than or less than one depending upon the factors.

Reasoning

Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Draw a conclusion multiplying that a fraction greater than one will result in a product greater than the given number.

Draw a conclusion that when you multiply a fraction by one, the resulting fraction is equivalent.

Draw a conclusion that when you multiply a fraction by a fraction, the product will be smaller than the given number.

Knowledge

Represent word problems involving multiplication of fractions and mixed numbers.

Demonstration

Solve real world problems involving multiplication of fractions and mixed numbers.

Knowledge

Know the relationship between multiplication and division.

Reasoning

Interpret division of a unit fraction by a whole number and justify your answer using the relationship between multiplication and division, by creating story problems, using visual models, and relationship to multiplication, etc.

Interpret division of a whole number by a unit fraction and justify your answer using the relationship between multiplication and division, and by representing the quotient with a visual fraction model.

Demonstration

Solve real world problems involving division of unit fractions by whole numbers other than 0 and division of whole numbers by unit fractions using strategies such as visual fractions models and equations.

Suggested Mathematical Practice Standards Question

MACC.K12.MP.1.1 Make sense of problems and persevere in solving them. MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.3.1 Construct viable arguments and critique the reasoning of others. MACC.K12.MP.4.1 Model with mathematics MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

How can decomposing fractions help us multiply fractions?

Why should we use models to solve problems with fractions?

How would you model the equations?



4th Grade

Students solve word problems involving multiplication of a fraction by a whole number.

6th Grade

Students solve word problems involving division of fractions by fractions.

Student will write a context (story problem) for a given equation.

Write to explain why multiplying a given number by a fraction less than one results in a product smaller than the given number.

Represent the problem you are solving and explain the reasoning.


Common Core State Standards for Mathematics (P. 89- Common Multiplication and Division situations) 5th Grade Common Core Flip Book 5.NF.2.3 CPALMS Resources Link to Depth of Knowledge (DOK) Chart

5.NF.2.4 CPALMS Resources 5.NF.2.5 CPALMS Resources 5.NF.2.6 CPALMS Resources 5.NF.2.7 CPALMS Resources

Lesson: Stuffed with Pizza Lesson: Time for Recess

No correlation to NGSSS.

Link to Scope and Sequence












http://schools.nyc.gov/NR/rdonlyres/D0A70F2D-1133-418C-B68F-95E6D714F357/0/NYCDOEG5MathStuffedwithPizza_Final.pdf

http://schools.nyc.gov/NR/rdonlyres/B8B8BDAD-2EF2-4BF8-AE93-114C48B563E2/130938/NYCDOEG5Math_TimeforRecess_Final.pdf



Domain: Operations and Algebraic Thinking Cluster OA.1: Write and interpret numerical expressions. Cluster OA.2: Analyze patterns and relationships.


MACC.5.OA.1.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

MACC.5.OA.1.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

MACC.5.OA.2.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6”and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

5.OA.1.1 Deconstructed standard (DOK 1) 5.OA.1.2 Deconstructed standard (DOK 2) 5.OA.2.3 Deconstructed standard (DOK 2) Knowledge

Use order of operations including parentheses, brackets, or braces.

Reasoning

Evaluate expressions using the order of operations (including using parentheses, brackets, or braces.)

Reasoning

Interpret numerical expressions without evaluating them. Demonstration

Write numerical expressions for given numbers with operation words.

Write operations words to describe a given numerical expression.

Knowledge

Generate two numerical patterns using two given rules.

Form ordered pairs consisting of corresponding terms for the two patterns.

Reasoning

Analyze and explain the relationships between corresponding terms in the two numerical patterns.

Demonstration

Graph generated ordered pairs on a coordinate plane.


MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.6.1 Attend to precision. MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

Why is it important to follow the order of operations?

What kind of real world situations might we use equations and expressions?



4th

Grade

Students represent multistep problems using equations with a letter standing for the unknown quantity.

6th

Grade

Students write and evaluate numerical expressions involving whole-number exponents.

Students read, write, and evaluate expressions in which letters stand for numbers.

Students apply the properties of operation to generate equivalent expressions.

Students write to explain the relationship between the quantities and the written expression.

Students write to evaluate the expression.



5.OA.1.1 CPALMS Resources 5.OA.1.2 CPALMS Resources 5.OA.2.3 CPALMS Resources

Illuminations: Pan Balance

MA.5.A.6.2 (Does not transfer with CCSSM) MA.5.A.4.1 MA.5.A.6.3 MA.5.A.6.4 (Does not transfer with CCSSM)

Link to Scope and Sequence Link to Next Generation Benchmark Task Cards














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2013-2014 Blended School Year-5th Grade · PDF file2013-2014 Blended School Year-5th Grade Mathematics ... FL Page 1 2013-2014 Blended School Year ... has to plan for the students