2013-2014 blended school year-4th grade · pdf file2013-2014 blended school year-4th grade...

2013-2014 Blended School Year-4th Grade Mathematics

Lake County, FL

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 Scope and Sequence, 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


Lake County, FL

Critical Areas of Focus CCSSM In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. (1) Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems. Students apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context. (2) Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions. Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number. (3) Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry.


Lake County, FL

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.4.SL.1.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 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 to clarify or follow up on information, and make comments that contribute to the discussion and link to the remarks of others.

d) Review the key ideas expressed and explain their own ideas and understanding in light of the discussion.

LACC.4.W.1.2 Write informative/explanatory texts to examine a topic and convey ideas and information clearly.

a) Introduce a topic clearly and group related information in paragraphs and sections; 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 categories of information using words and phrases (e.g., another, for example, also, because).

d) Use precise language and domain-specific vocabulary to inform about or explain the topic. Provide a concluding statement or section related to the information or explanation presented.

LACC.4.SL.1.2 Paraphrase portions of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally.

LACC.4.SL.1.3 Identify the reasons and evidence a speaker provides to support particular points.


Lake County, FL

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.


Lake County, FL

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


Lake County, FL

*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 4th 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

9 days MACC.4.NBT.1.1 MACC.4.NBT.1.2 MACC.4.NBT.1.3 MACC.4.NBT.2.4

MA.4.A.6.1 MA.4.A.6.6 Representing and Using Numbers Through Millions.

11 days MACC.3.OA.3.7 MACC.4.OA.1.1 MACC.4.OA.1.2

MA.4.A.1.1 MA.4.A.6.4 Multiplication and Division

12 days

MACC.4.OA.1.3 MACC.4.OA.2.4 MACC.4.OA.3.5

MA.4.A.4.1 MA.4.A.4.2 MA.4.A.4.3 Algebra: Expressions, Equations, and Patterns

25 days MACC.4.OA.1.1 MACC.4.NBT.2.5

MA.4.A.1.2 MA.4.A.6.6 Multiplication

8 days MACC.4.NBT.2.6 MA.4.A.6.2 Division

14 days (Fractions) 11 days (Decimals)

MACC.4.NF.1.1 MACC.4.NF.1.2 MACC.4.NF.3.5 MACC.4.NF.3.6 MACC.4.NF.3.7

MA.4.A.6.3 MA.4.A.6.4 MA.4.A.2.1 MA.4.A.2.2 MA.4.A.2.3 Fractions and Decimals

11 days MACC.4.NF.3.5 MACC.4.NF.3.6 MACC.4.NF.3.7

MA.4.A.2.1 MA.4.A.2.4 MA.4.A.6.5 Decimal Place Value

9 days MACC.4.MD.1.1 MACC.4.MD.1.2 MACC.4.MD.1.3

MA.4.G.3.1 MA.4.G.3.2 MA.4.G.3.3 Area

10 days MACC.4.G.1.1 MACC.4.G.1.2 MACC.4.G.1.3

MA.4.G.5.1 MA.4.G.5.2 MA.4.G.5.3 Angles and 2 Dimensional Shapes

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

Post-FCAT All Common Core

MACC.4.NF.2.3 MACC.4.NF.2.4 Adding, Subtracting, and Multiplying Fractions

MACC.4.MD.3.5 MACC.4.MD.3.6 MACC.4.MD.3.7 Measuring Angles using a protractor using word problems. At the same time reinforcing fluency standard for adding and subtracting through 1,000,000.

MA

CC

.3.O

A.3

.7 M

ult

iply

an

d d

ivid

e w

ith

in 1

00

MA

CC

.4.N

BT.

2.4

Ad

d a

nd

su

btr

act

wit

hin

1,0

00,0

00


Lake County, FL

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 (DOK #) Deconstructed standard (DOK #) 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 4

Domain: Geometry Cluster G.1 Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Associated Fluency Standards: MACC.4.NBT.2.4 Add and Subtract within 1,000,000

MACC.4.G.1.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

MACC.4.G.1.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

MACC.4.G.1.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

4.G.1.1 Deconstructed standard (DOK1) 4.G.1.2 Deconstructed standard (DOK 2) 4.G.1.3 Deconstructed standard (DOK 1) Reasoning

Analyze two-dimensional figures to identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines.

Demonstration

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines.

Knowledge:

Identify parallel or perpendicular lines in two dimensional figures.

Recognize acute, obtuse, and right angles.

Identify right triangles. Reasoning:

Classify two-dimensional figures based on parallel or perpendicular lines and size of angles.

Classify triangles as right triangles or not right.

Knowledge:

Recognize lines of symmetry for a two-dimensional figure

Recognize a line of symmetry as a line across a figure that when folded along creates matching parts.

Identify line-symmetric figures. Demonstration:

Draw lines of symmetry for two-dimensional figures.


MACC.K12.MP.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

How are the figures similar and different?

How did you reach your answer?

What makes it a ________ angle?

Why would it be necessary to classify shapes?

Vertical Progression TurnOnCCMath.net K-8 Learning Trajectories

Example Writing Connection

3rd Grade

Students understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category.

Students partition shapes into parts with equal areas.

5th

Grade

Students understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories.

Students classify two-dimensional figures in a hierarchy based on properties.

Write to explain the classification used.

Compare and contrast the two shapes.

Explain how you can prove the number of lines of symmetry a shape has, if any.

Develop a design using two dimensional figures. Then write step-by-step directions using mathematical vocabulary for a peer to reconstruct your design.


4

th Grade Common Core Flip Book

Link to Depth of Knowledge (DOK) Chart

4.G.1.1 CPALMS Resources 4.G.1.2 CPALMS Resources 4.G.1.3 CPALMS Resources

MA.4.G.5.1 MA.4.G.5.2 (Does not transfer with CCSSM) MA.4.G.5.3 (Does not transfer with CCSSM) 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://katm.org/wp/wp-content/uploads/flipbooks/4FlipBookedited.pdf

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

http://www.cpalms.org/Standards/PublicPreviewBenchmark5406.aspx





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


MATHEMATICS C² CONNECTION CARD GRADE 4 (1 of 2)

Domain: Measurement and Data Cluster MD.1 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Cluster MD.2 Represent and interpret data.

Associated Fluency Standards: MACC.3.OA.3.7 Multiply and Divide within 100

MACC.4.NBT.2.4 Add and Subtract within 1,000,000

MACC.4.MD.1.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

MACC.4.MD.1.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

MACC.4.MD.1.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

MACC.4.MD.2.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

4.MD.1.1 Deconstructed standard (DOK 1)




Knowledge

Know relative size of measurement units (km, m; kg, g; lb, oz; L, mL; hrs, min, sec).

Reasoning

Compare the different units within the same system of measurement.

Demonstration

Convert larger units of measurement within the same system to smaller units and record conversions in a 2-column table.

Knowledge

Express measurements given in a larger unit in terms of a smaller unit.

Reasoning

Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Demonstration

Add, subtract, multiply, and divide fractions and decimals.

Solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money.

Solve world problems involving measurement that include simple fractions or decimals.

Solve word problems that require expressing measurements given in a larger unit in terms of a smaller unit.

Knowledge

Know that the formula for the perimeter of a rectangle is 2L + 2W or L + L + W + W.

Know that the formula for the area of a rectangle is L x W.

Demonstration

Apply the formula for perimeter of a rectangle to solve real world and mathematical problems.

Apply the formula for area of a rectangle to solve real world and mathematical problems.

Solve area and perimeter problems in which there is an unknown factor (n).

Reasoning

Analyze and interpret a line plot to solve problems involving addition and subtraction of fractions.

Demonstration

Add and subtract fractions.



Domain: Measurement and Data Cluster MD.1 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Cluster MD.2 Represent and interpret data.




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.4.1 Model with mathematics. MACC.K12.MP.6.1 Attend to precision. Link to Inside Mathematics 8 Mathematical Practice Standards

Can different size containers hold the same capacity? How do you know?

How are units within the same system of measurement related?

Why did you use that unit of measurement?

How does a line plot help you organize your data?

What do you think would happen if…?



3rd

Grade

Students find area of a rectangle and relate it to addition and multiplication.

Students tell time and write time to the nearest minute.

Students measure and estimate liquid volume and masses of objects.

Students solve addition and subtraction problems based on time, volume, and mass.

Students generate data measuring lengths and show data on a line plot in whole numbers, halves, or quarters.

5th

Grade

Students convert among different-sized measurement units within a given measurement system and use the conversions in multi-step word problems.

Write to explain how you convert units within the same system of measurement.

Using your line plot, write as many interpretations of the data you can make.

Write to explain how you reached the solution.

Compose an informational piece to fit the given equation.


4th

Grade Common Core Flip Book Link to Depth of Knowledge (DOK) Chart

4.MD.1.1 CPALMS Resources 4.MD.1.2 CPALMS Resources 4.MD.1.3 CPLAMS Resources 4.MD.2.4 CPALMS Resources

PARCC Prototype: Deer in the Park

MA.4.G.3.1 MA.4.G.3.2 MA.4.G.3.3 Link to Scope and Sequence Link to Next Generation Benchmark Task Cards












http://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html




Domain: Measurement and Data Cluster MD.3 Geometric measurement: understand concepts of angle and measure angle.


MACC.4.MD.3.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a) An angle is measured with reference to a circle with its center at

the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one‐degree angle,” and can be used to measure angles.

b) An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

MACC.4.MD.3.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

MACC.4.MD.3.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

4.MD.3.5 Deconstructed standard (DOK 1) 4.MD.3.6 Deconstructed standard (DOK 1) 4.MD.3.7 Deconstructed standard (DOK 2) Knowledge

Define angle.

Recognize a circle as a geometric figure that has 360 degrees.

Recognize and identify an angle as a geometric shape formed from 2 rays with a common endpoint.

Recognize that an angle is a fraction of a 360 degree circle.

Explain the angle measurement in terms of degrees. Reasoning

Compare angles to circles with the angles point at the center of the circle to determine the measure of the angle.

Calculate angle measurement using the 360 degrees of a circle.

Knowledge

Recognize that angles are measured in degrees (°.)

Read a protractor. Reasoning

Determine which scale on the protractor to use, based on the direction the angle is open.

Determine the kind of angle based on the specified measure to decide reasonableness of the sketch.

Demonstration

Measure angles in whole-number degrees using a protractor.

Sketch angles of specified measure.

Knowledge

Recognize that an angle can be divided into smaller angles.

Demonstration

Solve addition and subtraction equations to find unknown angle measurements on a diagram.

Find an angle measure by adding the measurements of the smaller angles that make up the larger angle.

Find an angle measure by subtracting the measurements of the smaller angle from the larger angle.


MACC.K12.MP.2.1 Reason abstractly and quantitatively. MACC.K12.MP.5.1 Use appropriate tools strategically. 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 are angles and circles related?

How will a protractor help you?

Describe a real world situation that would involve angles.

Describe a real world situation that would involve angles as they relate to circles.



3rd

Grade

Students compare and classify shapes by attributes, sides, and angles.

7th

Grade

Students draw geometric shapes with given conditions focusing on constructing triangles from three measures of angles or sides.

Compose a written summary to justify your conclusion.

Compare and contrast two shapes based on their angles.

Explain how you determined the measurement of an angle.

Write about a job in which the employee would need to understand the relationship of circles and angles.


4th


4.MD.3.5 CPALMS Resources 4.MD.3.6 CPALMS Resources 4.MD.3.7 CPALMS Resources

*No Mini-Assessment Correlation Link to Scope and Sequence Link to Next Generation Benchmark Task Cards













Domain: Numbers and Operations in Base Ten Cluster NBT.1 Generalize place value understanding for multi-digit whole numbers.


MACC.4.NBT.1.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

MACC.4.NBT.1.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MACC.4.NBT.1.3 Use place value understanding to round multi-digit whole numbers to any place.

4.NBT.1.1 Deconstructed standard (DOK 1) 4.NBT.1.2 Deconstructed standard (DOK 1) 4.NBT.1.3 Deconstructed standard (DOK 1) Knowledge

Recognize that a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Reasoning

Compare two multi-digit numbers based on meanings of the digits in each place, using >,=, and < to record the results of comparisons.

Demonstration

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.

Knowledge

Round multi-digit whole numbers to any place using place value.


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 would you need to round a number?

How are the numbers similar? How are they different?

Why did you________________?



3rd

Grade

Students round to the nearest 10 or 100.

5th

Grade

Students recognize that the number to the right is 1/10 of what it represents in the in the place to its left.

Write to explain how you rounded the number.

Explain how you compared the numbers.

Write a real life problem in which rounding a number makes sense to solve the problem.

Explain how the value of a digit changes.


Common Core State Standards for Mathematics (P. 89- Common Multiplication and Division situations) 4



4.NBT.1.1 CPALMS Resources 4.NBT.1.2 CPALMS Resources 4.NBT.1.3 CPLAMS Resources

PARCC Prototype: Number of Stadium Seats

MA.4.A.6.1 MA.4.A.6.6 Link to Scope and Sequence Link to Next Generation Benchmark Task Cards



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













Domain: Numbers and Operations in Base 10 Cluster NBT.2 Use place value understanding and properties of operations to perform multi-digit arithmetic.



MACC.4.NBT.2.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

MACC.4.NBT.2.5 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MACC.4.NBT.2.6 Find whole-number quotients and remainders with up to four-digit dividends and one-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.

4.NBT.2.4 Deconstructed standard (DOK 1) 4.NBT.2.5 Deconstructed standard (DOK 2) 4.NBT.2.6 Deconstructed standard (DOK 2) Demonstration

Fluently add and subtract multi-digit whole numbers less than or equal to 1,000,000 using the standard algorithm.

Knowledge

Multiply a whole number of up to four digits by a one-digit whole number.

Multiply two two-digit numbers. Reasoning

Use strategies based on place value and the properties of operations to multiply whole numbers.

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

Knowledge

Find whole number quotients and remainders with up to four digit dividends and one digit divisors.

Reasoning

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

Illustrate and explain the calculation by using written equations, rectangular array, and/or area models.


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 would someone break apart the numbers when (adding, subtracting, multiplying, or dividing)?

How does the distributive property help with…?

How could you model the problem? Why did you choose that model?

How did you solve the problem using mental math?



3rd

Grade

Students fluently add and subtract within 1,000.

Students fluently multiply and divide through 100.

Students multiply one-digit numbers by multiples of 10 using strategies based on place value.

5th

Grade

Students fluently multiply multi-digit whole numbers using the standard algorithm.

Students find whole number quotients using two-digit divisors.

Write to explain how you solved the problem.

Write to justify your conclusion.

Write a word problem that fits a given equation.

Compare and contrast a peer’s solution method to yours. Write about what you learned.





4.NBT.2.4 CPALMS Resources 4.NBT.2.5 CPALMS Resources 4.NBT.2.6 CPALMS Resources

PARCC Prototype: Buses, vans, and cars PARCC Prototype: Ordering Juice Drinks Link to Depth of Knowledge (DOK) Chart

MA.4.A.1.2 MA.4.A.6.2 Link to Scope and Sequence Link to Next Generation Benchmark Task Cards











http://ccsstoolbox.agilemind.com/parcc/elementary_3775_1.html





Domain: Number and Operations- Fractions

Cluster NF.1 Extend understanding of fraction equivalence and ordering. Associated Fluency Standards: MACC.3.OA.3.7 Multiply and Divide within 100

MACC.4.NF.1.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

MACC.4.NF.1.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

4.NF.1.1 Deconstructed standard (DOK 3) 4.NF.1.2 Deconstructed standard (DOK 3) Knowledge

Recognize and identify equivalent fractions with unlike denominators. Reasoning

Explain why a/b is equal to (n x a)/ (n x b) by using fraction models with attention to how the number and size of the parts differ even though the two fractions themselves are the same size.

Use visual fraction models to show why fractions are equivalent.

Generate equivalent fractions using visual fraction models and explain why they can be called “equivalent.”

Knowledge

Recognize fractions as being greater than, less than, or equal to other fractions.

Record comparison results with >, =, or <. Use benchmark fractions such as ½ for comparison purposes.

Make comparisons based on parts of the same whole. Reasoning

Compare two fractions with different numerators or denominators.

Justify the results of a comparison of two fractions by using a visual fraction model.


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.5.1 Use appropriate tools strategically. Link to Inside Mathematics 8 Mathematical Practice Standards

How can equivalent fractions be identified?

How do we apply our understanding of fractions in everyday life?

How can a _______ be represented?

What is the problem asking you?

What is another way to solve the problem?



3rd

Grade

Students describe, recognize, and explain simple equivalent fractions (1/2= 2/4, 4/6=2/3 using a visual model.

Students compare fractions by reasoning about their size, same numerator, or same denominator.

5th

Grade

Students determine equivalent fractions in order to add and subtract fractions with unlike denominators.

Students use benchmark fractions and number sense of fractions to estimate mentally and assess reasonableness of answers.

Write to justify why the fractions are equivalent.

Write to explain how you can use benchmark fractions to compare fractions.

Write to explain how you placed the fractions in order from least to greatest.

Write a word problem where it would be appropriate to order the fractions.


Fractions Progressions Videos Illuminations: Equivalent Fractions Online Manipulative 4



4.NF.1.1 CPALMS Resources 4.NF.1.2 CPALMS Resources

Instructional Unit: Farmer Fred

MA.4.A.6.3 Link to Scope and Sequence Link to Next Generation Benchmark Task Cards



http://www.illustrativemathematics.org/pages/fractions_progression

http://illuminations.nctm.org/activitydetail.aspx?id=80

http://illuminations.nctm.org/activitydetail.aspx?id=80







http://schools.nyc.gov/NR/rdonlyres/04CC9ECB-C5AB-47DA-891B-6D8F6B6EFE88/0/NYCDOEG4MathFarmerFred_Final.pdf




Domain: Number and Operations- Fractions Cluster NF.2 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.



MACC.4.NF.2.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a) Understand addition and subtraction of fractions as joining and separating parts referring to the

same whole. b) Decompose a fraction into a sum of fractions with the same denominator in more than one way,

recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

c) Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

MACC.4.NF.2.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

a) Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by

the equation 5/4 = 5 × (1/4). b) Understand a multiple of a/b as a multiple of 1/b, and use this understanding to

multiply a fraction by a whole number. For example, use a visual fraction

model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

4.NF.2.3 Deconstructed standard (DOK 3) 4.NF.2.4 Deconstructed standard (DOK 2) Knowledge

Understand accumulating unit fractions (1/b) results in (a/b), where a is greater than 1.

Recognize multiple representations of one whole using fractions with the same denominator.

Replace mixed numbers with equivalent fractions, using visual fraction models.

Replace improper fractions with a mixed number, using visual fraction models. Reasoning

Using fraction models, reason that addition of fractions is joining parts that are referring to the same whole.

Using fraction models, reason that subtraction of fractions is separating parts that are referring to the same whole.

Using visual fraction models, decompose a fraction into the sum of fractions with the same denominator in more than one way.

Record decompositions of fractions as an equation and explain the equation and explain the equation using visual.

Demonstration

Add and subtract mixed numbers with like denominators by using properties of operations and the relationship between addition and subtraction.

Add and subtract fractions with like denominators.

Add and subtract mixed numbers by replacing each mixed number with an equivalent fraction.

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction models and equations to represent the problem.

Knowledge

Represent a fraction a/b as a multiple of 1/b (unit fractions)

Multiply a fraction by a whole number. Reasoning

Apply multiplication of whole numbers to multiplication of a fraction by a whole number using visual fraction models.

Explain that a multiple of a/b is a multiple of 1/b (unit fractions) using a visual fraction model.

Multiply a fraction by a whole number by using the idea that a/b is a multiple of 1/b.

Use fraction models and equations to represent the problem. Demonstration

Solve word problems involving multiplication of a fraction by a whole number.



Domain: Number and Operations- Fractions

Cluster NF.2 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.




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.5.1 Use appropriate tools strategically. 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 are fractions used in problem-solving situations?

How can I add and subtract fractions of a given set?

How do we apply our understanding of fractions in everyday life?

Why does the denominator stay the same when I add fractions with like denominators?

How can I represent fractions in different ways?

How can I be sure fractional parts are the same size?

How can I represent multiplication and division of a whole number by a fraction?

How is multiplication of fractions similar to division of a whole number?

How is multiplication of fractions similar to repeated addition of fraction?



3rd

Grade

Student gain an understanding of fractions and fraction equivalence.

Students have no prior experience with performing operations with fractions.

5th

Grade

Students add and subtract fractions or mixed numbers with unlike denominators.

Students divide fractions.

Write a situational story problem that requires addition, subtraction, multiplication, or division of fractions.

Write to explain how you solved the problem.

Write examples of how we apply fractions in everyday life.

Write a situational story problem that requires addition or subtraction of mixed numbers and explain your strategy for solving your problem.


4th


4.NF.2.3 CPALMS Resources 4.NF.3.4 CPALMS Resources

Instructional Unit: Chocolate Bar Fractions

*No Mini-Assessment Correlation Link to Scope and Sequence Link to Next Generation Benchmark Task Cards













Domain: Number and Operations- Fractions Cluster NF.3 Understand decimal notation for fractions, and compare decimal fractions.


MACC.4.NF.3.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

MACC.4.NF.3.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

MACC.4.NF.3.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

4.NF.3.5 Deconstructed standard (DOK 1) 4.NF.3.6 Deconstructed standard (DOK 1) 4.NF.3.7 Deconstructed standard (DOK 3) Knowledge

Rename and recognize a fraction with a denominator of 10 as a fraction with a denominator with 100.

Recognize that two fractions with unlike denominators can be equivalent.

Reasoning

Use knowledge of renaming tenths to hundredths to add two fractions with denominators 10 and 100.

Knowledge

Explain the values of digits in the decimal places.

Read and write decimals through hundredths.

Rename fractions with 10 and 100 in the denominator as decimals.

Recognize multiple representations of fractions with denominators 10 and 100.

Reasoning

Represent fractions with denominators 10 or 100 with multiple representations and decimal notation.

Explain how decimals and fractions are alike.

Knowledge

Recognize that comparisons are valid only when the two decimals refer to the same whole.

Reasoning

Compare two decimals to hundredths by reasoning about their size.

Justify the conclusions using visual models and other methods.


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.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

What is a decimal fraction and how can it be represented?

What strategies did you use, and why did you choose that strategy?

How are they alike?

How are they different?

Can you provide an example of what you mean?



Students have no prior experience with decimal notation.

5th

Grade

Students read, write, and compare decimals to thousandths.

Students add, subtract, multiply, and divide decimals to hundredths using concrete models and strategies based on place value.

Write to justify your solution.

Explain the meaning of the problem.

Give a detailed description of the process you used to solve the problem.

Explain your comparison of two decimals and justify your comparisons.


4



4.NF.3.5 CPALMS Resources 4.NF.3.6 CPALMS Resources 4.NF.3.7 CPALMS Resources

MA.4.A.2.4 MA.4.A.2.3 (Does not transfer with CCSSM) MA.4.A.6.5 (Does not transfer with CCSSM) Link to Scope and Sequence Link to Next Generation Benchmark Task Cards













Domain: Operations and Algebraic Thinking Cluster OA.1: Use the four operations with whole numbers to solve problems.



MACC.4.OA.1.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

MACC.4.OA.1.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

MACC.4.OA.1.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

4.OA.1.1 Deconstructed standard (DOK 2) 4.OA.1.2 Deconstructed standard (DOK 2) 4.OA.1.3 Deconstructed standard (DOK 3) Knowledge

Know multiplication strategies. Reasoning

Interpret a multiplication equation as a comparison. Demonstration

Represent verbal statements of multiplicative comparisons as multiplication equations.

Knowledge

Describe multiplicative comparison.

Describe additive comparison. Reasoning

Determine and use a variety of representations to model a problem involving multiplicative comparison.

Distinguish between multiplicative comparison and additive comparison (repeated addition.)

Demonstration

Multiply or divide to solve word problems.

Demonstration: Determine appropriate operation and solve word problems involving multiplicative comparison.

Knowledge

Divide whole numbers including division with remainders. Reasoning

Represent multi-step word problems using equations with a letter standing for the unknown quantity.

Interpret multi-step word problems (including problems in which remainders must be interpreted) and determine the appropriate operations to solve.

Assess the reasonableness of an answer is solving a multi-step word problem using mental math and estimation strategies (including rounding.)


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.7.1 Look for and make use of structure. Link to Inside Mathematics 8 Mathematical Practice Standards

How are multiplication and division related?

How are remainders and divisors related?

What are some methods for solving multiplication and division?

What real life situations require multiplication or division?

How do you know your answer is reasonable?



3rd

Grade

Students represent and solve problems involving multiplication and division.

Students fluently multiply and divide through 100.

5th

Grade

Students use order of operations and evaluate expressions.

Students write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them.

Summarize the mathematical ideas and concepts learned today.

Use a flow/sequence map to sequence the process through the word problem, then write to explain how you solved the problem.

Explain how you assessed the reasonableness of your answer in solving a multi-step word problem using mental math and estimation strategies.

Write multi-step word problems with remainders that must be interpreted in a variety of ways.





4.OA.1.1 CPALMS Resources 4.OA.1.2 CPALMS Resources 4.OA.1.3 CPLAMS Resources

MA.4.A.6.4 Link to Scope and Sequence Link to Next Generation Benchmark Task Cards














Domain: Operations and Algebraic Thinking Cluster OA.2 Gain familiarity with factors and multiples. Cluster OA.3 Generalize and analyze patterns



MACC.4.OA.2.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one‐digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

MACC.4.OA.3.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example,

given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

4.OA.2.4 Deconstructed standard (DOK 1) 4.OA.3.5 Deconstructed standard (DOK 2) Knowledge

Define prime and composite numbers.

Know strategies to determine whether a whole number is prime or composite.

Identify all factor pairs for any given number 1-100.

Recognize that a whole number is a multiple of each of its factors. Reasoning

Determine if a given whole number (1-100) is a multiple of a given one-digit number.

Evaluate if a given whole number (1-100) is a prime or composite number.

Knowledge

Identify a number or shape pattern. Reasoning

Analyze a pattern to determine features not apparent in the rule. Demonstration

Generate a number or shape pattern that follows a given rule.


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.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 are the factors and products of a multiplication problem related?

How do you know the number is prime or composite?

How can an array help you determine if a number is primer or composite?

Why is it important to look for patterns prior to determining the rule?



3rd Grade

Students work with understanding properties of multiplication and the relationship between multiplication and division.

5th

Grade

Students generate numerical patterns using two given rules and identify relationships.

Describe your number using key vocabulary.

Write to explain your pattern.

Explain the thoughts processes you went through to determine the “not so obvious” pattern.

Explain how you evaluated a number to determine if it is a prime or composite.





4.OA.2.4 CPALMS Resources 4.OA.3.5 CPALMS Resources

Activity: The Factor Game Activity: The Product Game Lessons: Multiplication- It’s in the Cards Lessons: Patterns that Grow

MA.4.A.4.1 MA.4.A.4.2 MA.4.A.4.3 (Does not transfer with CCSSM) Link to Scope and Sequence Link to Next Generation Benchmark Task Cards











http://illuminations.nctm.org/LessonDetail.aspx?ID=L620

http://illuminations.nctm.org/LessonDetail.aspx?ID=U100

http://illuminations.nctm.org/LessonDetail.aspx?ID=U110

http://10.0.30.50:8080/ibreports/ibp/pp.html?fn=Default&fp=1&ip=10.3.64.81&ibip=10.0.30.50&ldu=0&re=0&bu=216.255.77.73&bc=Direct%20IP%20Address%20access%20not%20allowed.


2013-2014 blended school year-4th grade · pdf file2013-2014 blended school year-4th grade...

Documents