FINAL Grade 4 Mathematics Curriculum Map December...

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MATHEMATICS Curriculum Map

2012 - 2013

Volusia County Schools

Next Generation Sunshine State Standards

Mathematics Department ii Fourth Grade Curriculum Map

Volusia County Schools December 2012

Common Core State Standards Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them. (MACC.K12.MP.1) Solving a mathematical problem involves making sense of what is known and applying a thoughtful and logical process which

sometimes requires perseverance, flexibility, and a bit of ingenuity.

2. Reason abstractly and quantitatively. (MACC.K12.MP.2) The concrete and the abstract can complement each other in the development of mathematical understanding: representing a

concrete situation with symbols can make the solution process more efficient, while reverting to a concrete context can help make

sense of abstract symbols.

3. Construct viable arguments and critique the reasoning of others. (MACC.K12.MP.3) A well-crafted argument/critique requires a thoughtful and logical progression of mathematically sound statements and supporting

evidence.

4. Model with mathematics. (MACC.K12.MP.4) Many everyday problems can be solved by modeling the situation with mathematics.

5. Use appropriate tools strategically. (MACC.K12.MP.5) Strategic choice and use of tools can increase reliability and precision of results, enhance arguments, and deepen mathematical

understanding.

6. Attend to precision. (MACC.K12.MP.6) Attending to precise detail increases reliability of mathematical results and minimizes miscommunication of mathematical

explanations.

7. Look for and make use of structure. (MACC.K12.MP.7) Recognizing a structure or pattern can be the key to solving a problem or making sense of a mathematical idea.

8. Look for and express regularity in repeated reasoning. (MACC.K12.MP.8) Recognizing repetition or regularity in the course of solving a problem (or series of similar problems) can lead to results more

quickly and efficiently.

Mathematics Department iii Fourth Grade Curriculum Map


Next Generation Sunshine State Standards

Following a six-year cycle review and revision of K-12 Mathematics content standards, the Next Generation Sunshine State Standards (NGSSS) were adopted by the Florida State Board of Education in September 2007. The revision in the benchmark language offers greater specificity to indicate clearly what teachers should teach and student should be able to do. Support of these standards can be found at www.floridastandards.org.

Mathematics Grade 3 Program Overview

Big Idea 1: Develop quick recall of multiplication facts and related division facts and fluency with

whole number multiplication.

Big Idea 2: Develop an understanding of decimals, including the connection between fractions and decimals.

Big Idea 3: Develop an understanding of area and determine the area of two-dimensional shapes.

Supporting Idea: Algebra

Supporting Idea: Geometry and Measurement

Supporting Idea: Number and Operations

Mathematics Department iv Fourth Grade Curriculum Map


COMPONENTS OF THE CURRICULUM MAP

Unit/Organizing Principle: the overarching organizational structure used to group content and concepts within the curriculum map

Pacing: the recommended time period within the year for instruction related to the essential questions to occur

Essential Questions: the overarching question(s) that will serve to guide instruction and push students to higher levels of thinking; essential questions should guide students to the heart of the content and should be in student -friendly language.

Measurement Topics: an organized grouping of learning targets – these will be evident as headings in (Pinnacle) Gradebook

Learning Targets/Skills: the content knowledge, processes and enabling skills that will ensure successful mastery of the essential questions (tied to Common Core State Standards and/or Next Generation Sunshine State Standards)

Benchmarks ((Pinnacle)): Benchmarks for the Next Generation Sunshine State Standards until the Common Core State Standards are implemented

Academic Language: the content vocabulary and other key terms and phrases with which students should be familiar and that support mastery of the learning targets/skills and essential questions

Suggested Activities and Resources: a listing of available, appropriate materials, strategies, lessons, textbooks, videos and other media sources that are aligned with the learning targets, skills and essential questions; developed to save teachers time when planning for instruction

Assessment: a list of required assessments as well as suggested assessments that are available to use as formative or summative assessments

Mathematics Department v Fourth Grade Curriculum Map


Teachers are required to administer each of the District Interim Assessments. The assessments will be made available through the Copy Center as they are developed; the Scantron answer sheets are available through Scantron Achievement Series. Following the administration of the District Interim Assessments and the scanning of the Scantron answer sheets data will be immediately available through Scantron Achievement Series.

Weeks Grade 4 Math Interim Assessments Testing Window Weeks 1-4 04 Math Interim Assmt Number Sense/Multiplication and Division September 10-14 Weeks 5-11 04 Math Interim Assmt Multiplication October 29-November 2 Weeks 12-16 04 Math Interim Assmt Fractions and Decimals I December 3-7 Weeks 17-18 04 Math Interim Assmt Geometry I December 17-21 Weeks 19-22 04 Math Interim Assmt Fractions and Decimals II January 28-February 1 Weeks 23-27 04 Math Interim Assmt Algebra March 4-8 Weeks 28-31 04 Math Interim Assmt Geometry II April 8-12

Mathematics Department 1 Fourth Grade Curriculum Map


UNIT/ORGANIZING PRINCIPLE: NUMBER SENSE/MULTIPLICATION AND DIVISION PACING: Weeks 1 – 4 ESSENTIAL QUESTIONS: How does place value help you compare and order numbers?

MEASUREMENT TOPICS

LEARNING TARGETS/SKILLS BENCHMARKS

(Pinnacle) ACADEMIC LANGUAGE

Number Sense (T01)

NGSSS: Use and represent numbers through millions in various contexts, including estimation of relative sizes of amounts or distances.

Students will:

• identify numbers through the millions place in real-world contexts. • read and write numbers through the millions. • name the value of a given digit in whole numbers to 1,000,000 (e.g.

127,520 has 127 thousands). • compare two or more numbers using symbols, >, <, =, to 1,000,000. • order whole numbers through millions. • solve the answers to real-world problems that involve adding and

subtracting numbers through the millions.

NOTE: Numbers used to solve problems may be presented in bar graphs, pictographs, line plots, or tables.

• estimate numbers through the millions in real-world situations.

NOTE: Front-end estimation will not be an acceptable strategy.

FCAT 2.0 Sample Item:

NOTE: When modeling with mathematics, the student uses a variety of strategies to apply the math they have learned.

T01.MA.4.A.6.1 compare digit equal (=) equivalent estimate expanded form greater than (>)

greater than or equal (≥) less than (<) less than or equal (≤) millions not equal (≠) period round standard form thousand word form

continued on next page



Multiplication Fluency (T02)

NGSSS: Determine factors and multiples for specified whole numbers.

Students will:

• use the vocabulary terms factors and multiples with precision. • determine multiples for whole numbers.

NOTE: Students should be able to determine multiples of numbers 1-12, 20, 25, 50, and 100 quite easily.

• determine factors of whole numbers less than or equal to 100. • use models to identify square numbers to 100. • solve problems involving multiples or factors in a real-world or

mathematical context.


T02.MA.4.A.6.4 arrays decompose Distributive Property division dividend divisor equation expression fact family factor multiple inverse operations multiple partitioning perfect square product quotient repeated addition successive subtraction variables

NGSSS: Use and describe various models for multiplication in problem-solving situations, and demonstrate recall of basic multiplication and related division facts with ease.

Students will:

• recall fluently basic multiplication and related division facts through 12 x12.

T02.MA.4.A.1.1

Division (basic) (T03)

NGSSS: Use models to represent division as: the inverse of multiplication, as partitioning, and as successive subtraction.

Students will:

• identify inverse equations or expressions for division or multiplication problems.

• use successive (repeated) subtraction to solve a division problem. • use partitive division to solve a division problem.

NOTE: Partitive division is the mental activity of slicing/separating an object into equal-sized units including only whole numbers and whole-number remainders.

• solve division problems that result in whole numbers and whole-number remainders.

• translate arrays, equal-sized groups, area models or other visual representations into expressions and equations

T03.MA.4.A.6.2




Division (basic) (T03)

• translate a word problem involving multiplication or division into an

expression or equation.

FCAT 2.0 Sample Item: NOTE: When modeling with mathematics, the student uses a variety of strategies to apply the math they have learned.

T03.MA.4.A.6.2

CCSS: Standards for Mathematical Practice Students will: (to be embedded throughout instruction as appropriate)

Make sense of problems and

persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and

critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision. Look for and make use of structure.

Look for and express regularity in repeated

reasoning.

MACC.K12.MP.1 MACC.K12.MP.2 MACC.K12.MP.3 MACC.K12.MP.4 MACC.K12.MP.5 MACC.K12.MP.6 MACC.K12.MP.7 MACC.K12.MP.8



Suggested Activities and Resources Assessment

enVisionMATH Student Edition Topic 1: Lessons 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7; Reteaching Sets: A-F p 26 Topic 2: Lessons 2-1, 2-2, 2-3, 2-4, 2-5, 2-6; Reteaching Sets: A-F p 44 Topic 3: Lessons 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8; Reteaching Sets: A-E p 66

enVisionMATH Ready-Made Centers

Topic 1: Lessons 1-3, 1-4, 1-5, 1-6, 1-7 Topic 2: Lessons 2-1, 2-2, 2-3, 2-4 Topic 3: Lessons 3-1, 3-2, 3-5, 3-6, 3-8

enVision Math Problem of the Day

Topic 1: Lessons 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7 Topic 2: Lessons 2-1, 2-2, 2-3, 2-4, 2-5, 2-6 Topic 3: Lessons 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8

envisionMath Daily Assessment and Reteaching Workbook

Topic 1: Lessons 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7 Topic 2: Lessons 2-1, 2-2, 2-3, 2-4, 2-5, 2-6 Topic 3: Lessons 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8

Everglades K-12: Grade 4 pp. 22-40 Chapter 1: Multiplication and Division Facts pp. 160-167 Numbers Through Millions pp. 168-175 Use Models to Represent Division pp. 183-189 Factors and Multiples of Whole Numbers

Required Summative

04 Math Interim Assmt Number Sense/Multiplication and Division

Optional Formatives

Florida Benchmarks Assessment Workbook

Topic 1 Florida Test Topic 2 Florida Test Topic 3 Florida Test

(Cover Pages and Answer Keys are available for each topic test through Copy Center/DOD.)

Math Focus Formatives

04 Math Focus Formative MA.4.A.6.2 04 Math Focus Formative MA.4.A.6.4

(Online and scan versions available through Scantron/Achievement Series.)

For additional formative assessment strategies,

see pages 36-45 in the Fourth Grade Mathematics Curriculum Map.

Intervention/Remediation An intervention/remediation resource guide can

be found on page 46 of the Fourth Grade Mathematics Curriculum Map.

Enrichment (Math Extension Activities organized by each

topic are available through Copy Center/DOD)




Internet Resources

http://www.floridastandards.org/homepage/index.aspx - CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). www.studyjams.scholastic (multiplication & Division) http://www.321know.com/mul74bx2.htm students identify the property demonstrated in problems-interactive www.sumdog.com www.khanacademy.org www.mathdrills.com www.multiplication.com www.mathfactcafe.com http://firefly/ (no login is required)

• A Million Fish More or Less by Patricia C. McKissack • Counting on Frank by Rod Clement • One Hundred Hungry Ants by Elinor J.Pinczes • Anno’s Mysterious Multiplying Jar by Masaichiro and Mitsumasa Anno • Math Appeal by Greg Tang • Math for All Seasons by Greg Tang • Amanda Bean’s Amazing Dream by Cindy Neuschwander • The Grapes of Math by Greg Tang • A Remainder of One by Elinor J. Pinczes • Bats on Parade by Kathi Appelt

• Bat Jamboree by Kathi Applet • One Grain of Rice: A Mathematical Folktale by Demi • The King's Chessboard, by David Birch • Twelve Plump Cookies by Larry Dane Brimner • Divide and Ride: Dividing by Stuart Murphy

http://www.prometheanplanet.com/en/resources/subjects/math/ (Common Factors,” by unknown author) http://studyjams.scholastic.com/studyjams/jams/math/index.htm (number sense)



UNIT/ORGANIZING PRINCIPLE: MULTIPLICATION PACING: Weeks 5 – 11

ESSENTIAL QUESTIONS: How does your knowledge of basic multiplication help you multiply multi-digit whole numbers? How can estimation help when you are multiplying multi-digit whole numbers?

MEASUREMENT TOPICS



Multiplication by One Digit Numbers

(T04)


Students will:

• solve real-world problems using basic multiplication and the related division facts through 12 x 12.

• solve multiplication problems that do not exceed four digits by one digit using various strategies (e.g. repeated addition, arrays, properties, etc.).

• describe the strategies used to solve multiplication problems. • use properties (commutative, associative, inverse, identity, distributive, and

zero product) to solve problems.

NOTE: Students do not need to name specific properties.

• apply the Distributive Property to a basic multiplication fact.

NOTE: Distributive Property: multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

T04.MA.4.A.1.1 Associative Property arrays Commutative Property Distributive Property factor hundreds Identity Property Inverse Property multiples ones partial product product rounding tens thousands Zero Product Property

NGSSS: Estimate and describe reasonableness of estimates determine the appropriateness of an estimate versus an exact answer.

Students will:

• use appropriate estimation strategies to determine reasonable estimates (may involve finding a number or a range of numbers that is most appropriate).

NOTE: Front-end estimation will not be an acceptable estimation strategy.

• determine whether an exact number or an estimate is more appropriate for a given real-world situation.

T04.MA.4.A.6.6




Multi-Digit Multiplication

(T05)

NGSSS: Multiply multi-digit whole numbers through four digits fluently, demonstrating understanding of the standard algorithm, and checking for reasonableness of results, including solving real-world problems.

Students will:

• solve multi-digit multiplication problems up to 3-digit by 3-digit or 4-digit by 2-digit using a variety of strategies.

• solve multi-digit problems where one of the factors contains a “0” (when it is 3-digit by 3-digit)

• find partial products of a multi-digit multiplication problem. • analyze multiplication problems to find errors.

T05.MA.4.A.1.2

Associative Property Commutative Property compatible numbers Distributive Property equation factors Identity Property Inverse partial product product round Zero Product Property


(T05)


Students will:

• use and describe various models for multiplication in problem-solving situations.

• demonstrate recall of basic multiplication and related division facts with ease. (e.g. repeated addition, arrays, etc.)

• understand and use the Distributive Property (multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products).

T05.MA.4.A.1.1










Look for and express regularity

in repeated reasoning.





enVisionMATH Student Edition Topic 4: Lessons 4-1, 4-2, 4-3, 4-5, 4-6; Reteaching Sets: A-F p 86 Topic 5: Lessons 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, 5-7; Reteaching Sets: A, B, D, E p 112 Topic 6: Lessons 6-1, 6-2, 6-3, 6-4, 6-5; Reteaching Sets: A-E p 130 Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5; Reteaching Sets: A-D p 148 Topic 8: Lessons 8-1, 8-2, 8-3, 8-4, 8-5, 8-6; Reteaching Sets: A-C, E, F p 168 Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-6

enVisionMATH Ready-Made Centers Topic 4: Lessons 4-1, 4-2, 4-3 Topic 5: Lessons 5-1, 5-2, 5-3, 5-4, 5-5 Topic 6: Lessons 6-2, 6-3, 6-4 Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5 Topic 8: Lessons 8-3, 8-5, 8-6 Topic 9: Lessons 9-1, 9-2, 9-3

enVision Math Problem of the Day Topic 4: Lessons 4-1, 4-2, 4-3, 4-5, 4-6 Topic 5: Lessons 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, 5-7 Topic 6: Lessons 6-1, 6-2, 6-3, 6-4, 6-5 Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5 Topic 8: Lessons 8-1, 8-2, 8-3, 8-5, 8-6 Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-6

envisionMath Daily Assessment and Reteaching Workbook Topic 4: Lessons 4-1, 4-2, 4-3, 4-5, 4-6 Topic 5: Lessons 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, 5-7 Topic 6: Lessons 6-1, 6-2, 6-3, 6-4, 6-5 Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5 Topic 8: Lessons 8-1, 8-2, 8-3, 8-5, 8-6 Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-6

Everglades K-12: Grade 4 pp. 22-40 Chapter 1: Multiplication and Division Facts

Internet Resources

CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.studyjams.scholastic (multiplication & division) www.sumdog.com www.khanacademy.org www.mathdrills.com www.multiplication.com www.mathfactcafe.com

Required Summative

04 Math Interim Assmt Multiplication

Optional Formatives


Topic 4 Florida Test Topic 5 Florida Test Topic 6 Florida Test Topic 7 Florida Test Topic 8 Florida Test Topic 9 Florida Test



04 Math Focus Formative MA.4.A.1.2 & A.1.1 (Online and scan versions available through

Scantron/Achievement Series.)

For additional formative assessment strategies, see pages 36-45 in the

Fourth Grade Mathematics Curriculum Map.



Enrichment (Math Extension Activities organized by each topic are available through Copy Center/DOD)



UNIT/ORGANIZING PRINCIPLE: FRACTIONS AND DECIMALS I PACING: Weeks 12 – 16

ESSENTIAL QUESTIONS: How can you use your knowledge of fractions to compare and estimate them? What is a decimal? How is ordering decimals the same as ordering whole numbers and how is it different?

MEASUREMENT TOPICS



Fractions (T10)

NGSSS: Compare and order decimals, and estimate fraction and decimal amounts in real-world problems.

Students will:

• compare fractions or mixed numbers between two numbers on a number line or other graphical representation.

NOTE: Inequality symbols should be used when comparing fractions (<, ≤, >, ≥, =, or ≠).

• order up to 5 fractions or mixed numbers using a number line or other graphical representation.

• estimate fractions in real-world situations. • identify a fraction that is closest to another number or a benchmark

fraction (e.g., �

�� of a circle is closer to

�

� than 0 or 1).

T10.MA.4.A.2.4 benchmark fraction denominator equal to (=) equivalence equivalent fractions estimate fractions

fraction greater than one ( �

� )

formerly called improper fractions

generalization greater than (>)

greater than or equal to (≥) hundredths less than (<)

less than or equal to (≤) mixed numbers

not equal (≠) number line numerator one hundred tenths word form factors multiples

NGSSS: Generate equivalent fractions and simplify fractions.

Students will:

• generate equivalent fractions • simplify fractions to lowest terms.

NOTE: All common factors of the numerator and denominator should be less than or equal to 10. FCAT 2.0 Sample Item:

• rename fractions as mixed numbers or vice versa.

T10.MA.4.A.6.3




Multiplication Fluency (T02)


Students will:

• determine factors and/or multiplies for specified whole numbers to find equivalent fractions.

T02.MA.4.A.6.4

Decimals (T08)

NGSSS: Use decimals through the thousandths place to name numbers between whole numbers.

Students will:

• read, write, and identify decimals through the thousandths place. • demonstrate place value of decimals through the thousandths using

concrete materials (e.g., base-ten blocks). • identify the place value of digits to the right of the decimal point (tenths,

hundredths, and thousandths). • identify or locate a decimal between two whole numbers (up to 99) on a

number line or from a graphical representation.

• compare and order decimals through the thousandths place on a number line.

T08.MA.4.A.2.1

decimal decimal point equal to (=) equivalence equivalent decimals estimate expanded form greater than (>)

greater than or equal to (≥) hundredths less than (<) less than or equal to (≤)

not equal (≠) number line tenths thousandths

NGSSS: Describe decimals as an extension of the base-ten number system.

Students will:

• discover how decimal values can be written in multiple ways and still be equivalent (e.g., 0.2, 0.20, and 0.200 are equivalent).

• explain the relationship between the decimal place values of any number.

NOTE: Place values increase by a factor of 10 as they move to the left and decreases by a factor of 10 as they move to the right. This is easily understood at this level in the context of money.

Example: The value of a number in the tenths place is 10 times greater than the same number in the hundredths place (e,g, $5.55).

T08.MA.4.A.2.2




Decimals (T08)


Students will:

• compare and order decimals on a number line or other graphical representation.

NOTE: The number of digits in a decimal should not exceed 5 (e.g. 38.149). The number of decimals being ordered or compared should not exceed 6.

NOTE: Inequality symbols should be used when comparing decimals (<, ≤, >, ≥, =, or ≠).

• estimate decimals in real world situations. • identify a decimal that is closest to another number or a benchmark

fractions, e.g., �


�

� than

�

�.


T08.MA.4.A.2.4










Look for and express regularity in repeated reasoning.





enVisionMATH Student Edition Topic 12: Lessons 12-1, 12-2, 12-3, 12-4, 12-5, 12-6, 12-7, 12-8; Reteaching Sets: A-F p 252 Topic 13: Lessons 13-1, 13-2, 13-3, 13-4, 13-5, 13-7; Reteaching Sets: A-F p 274


Topic 12: Lessons 12-1, 12-2, 12-3, 12-4, 12-5 Topic 13: Lessons 13-3, 13-4, 13-5, 13-7




Topic 12: Lessons 12-1, 12-2, 12-3, 12-4, 12-5, 12-6, 12-7, 12-8 Topic 13: Lessons 13-1, 13-2, 13-3, 13-4, 13-5, 13-7

Everglades K-12: Grade 4 pp. 42-74 Chapter 2: Understanding Decimals and Related Fractions

Internet

http://www.floridastandards.org/homepage/index.aspx - CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). www.studyjams.scholastic (fractions) www.khanacademy.org www.mathfactcafe.com

Required Summative

04 Math Interim Assmt Fractions and Decimals I

Optional Formatives


Topic 12 Florida Test Topic 13 Florida Test



04 Math Focus Formative MA.4.A.2.4, A.2.1, A.2.2


For additional formative assessment strategies,

see pages 36-45 in the Fourth Grade Mathematics Curriculum Map.







UNIT/ORGANIZING PRINCIPLE: GEOMETRY I PACING: Weeks 17-18

ESSENTIAL QUESTIONS: How can you tell if rotations, reflections or translations have occurred? What are some ways to determine if shapes have symmetry?

MEASUREMENT TOPICS



Transformations and Symmetry

(T13)

NGSSS: Identify and describe the results of translations, reflections, and rotations of 45, 90, 180, 270, and 360 degrees, including figures with line and rotational symmetry.

Students will:

• demonstrate transformations (translation, reflection, and rotation) using 2-dimensional shapes (e.g., pattern blocks, geoboards, paper shapes, snap cubes).

Examples: Translation Reflection Rotation

• identify a shape that is the result of a translation, reflection, and/or rotation of 45˚, 90˚, 180˚, 270˚, or 360˚.

• identify and describe figures that have line symmetry (folding a figure so it has two parts that match exactly).

Examples:

• identify and describe figures that have rotational symmetry (when a figure

can rotate onto itself in less than 360°).

Examples:

• identify and describe the result of two-step transformations.


• use vocabulary associated with geometry with precision.

T13.MA.4.G.5.2

acute angle angle center clockwise counterclockwise degree line line symmetry obtuse angle reflection right angle rotation rotational symmetry transformation translation vertices/vertex





Angles (T12)

NGSSS: Classify angles of two-dimensional shapes using benchmark angles (45º, 90º, 180º and 360º).

Students will:

• identify and model angles as acute, obtuse, right and straight. • recognize the geometric notation for an angle ( R) and degrees ( °). • identify the benchmark angle measurements of 45º, 90º, 180º and 360º. • classify angles of 2-dimensional figures as acute, obtuse, right, or straight.



T12.MA.4.G.5.1 acute angle angle (∠) degree (°) line obtuse angle perpendicular lines protractor ray right angle straight angle vertices/vertex















enVisionMATH Student Edition Topic 16: Lessons 16-1, 16-2, 16-3, 16-4, 16-5, 16-6, 16-7; Reteaching Sets: A-E p. 360


Topic 16: Lessons 16-1, 16-2, 16-3, 16-4, 16-5

enVision Math Problem of the Day Topic 16: Lessons 16-1, 16-2, 16-3, 16-4, 16-5, 16-6, 16-7


Topic 16: Lessons 16-1, 16-2, 16-3, 16-4, 16-5, 16-6, 16-7

Everglades K-12: Grade 4 pp. 122-158 Chapter 5: Geometry and Measurement

Internet

http://www.floridastandards.org/homepage/index.aspx - CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). www.studyjams.scholastic (geometry) www.bbc.co.uk/schools/ksbitesize/maths/shape_space (matching 3-D shapes to correct “containers” based on characteristics)

Required Summative

04 Math Interim Assmt Geometry I

Optional Formatives


Topic 16 Florida Test (can be given after Geometry II)



04 Math Focus Formative MA.4.G.5.1 04 Math Focus Formative MA.4.G.5.2




Intervention/Remediation An intervention/remediation resource guide

can be found on page 46 of the Fourth Grade Mathematics Curriculum Map.





UNIT/ORGANIZING PRINCIPLE: FRACTIONS AND DECIMALS II PACING: Weeks 19 – 22 ESSENTIAL QUESTIONS: How are fractions, decimals and percents alike and different?

MEASUREMENT TOPICS



Decimal and Fraction Equivalents

(T09)

NGSSS: Relate equivalent fractions and decimals with and without models, including locations on a number line.

Students will:

• use different-sized grids (10 х 10 and 100 х 100) to represent equivalency of fractions and decimals.

• identify decimals that are equivalent to commonly used fractions or mixed numbers and vice versa.

NOTE: Commonly used fractions: �

�, �

�, �

�, �

�, all fifths, all tenths, all

hundredths, and all thousandths.

• translate commonly used fractions or mixed numbers to their decimal

equivalents (e.g. �

� = 0.25).

T09.MA.4.A.2.3 benchmark fraction

( �

� , �

� , �

� , �

� , �

� )

decimal decimal point denominator equal to (=) equivalence equivalent decimals equivalent fractions estimate expanded form fractions


� )

formerly called improper fractions

generalization greater than (>) greater than or equal to (≥) hundredths less than (<) less than or equal to (≤) mixed numbers not equal (≠) number line numerator one hundred percent standard form tenths thousandths word form


Students will:

• compare and order two different forms of numbers (decimals, fractions, or mixed numbers).

NOTE: When comparing a combination of decimals and fractions, it should not exceed 5.

NOTE: Inequality symbols should be used when comparing fractions and decimals (<, ≤, >, ≥, =, or ≠).

• identify a fraction or decimal that is closest to another number or a

benchmark fraction, e.g., �


�

� than

�

�.

T09.MA.4.A.2.4


Students will:

• locate whole numbers, fractions, decimals (to thousandths) and mixed numbers on a number line.

T09.MA.4.A.2.1




NGSSS: Relative halves, fourths, tenths, and hundredths to decimals and percents.

Students will:

• convert a percent to a fraction or a decimal (e.g., 25 % = �

� , 50% =

�

� ,

75% = �

� , 25% = 0.25, 60% = 0.6, 36% = 0.36).

• convert a fraction or a decimal to a percent (e.g. �

� = 25% , 0.83 = 83%).

T09.MA.4.A.6.5











reasoning.





enVisionMATH Student Edition Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6, 14.7; Reteaching Sets: A-E p 300


Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6, 14.7

enVision Math Problem of the Day Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6, 14.7


Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6, 14.7

Everglades K-12: Grade 4 pp. 56-62 Equivalent Fractions and Decimals

Internet Resources

http://www.floridastandards.org/homepage/index.aspx - CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). www.studyjams.scholastic (decimals, fractions and percents)

Required Summative

04 Math Interim Assmt Fractions and Decimals II

Optional Formatives


Topic 14 Florida Test (Cover Pages and Answer Keys are available for each topic test through Copy Center/DOD.)


04 Math Focus Formative MA.4.A.2.3, A.2.1, & A.2.2

04 Math Focus Formative MA.4.A.6.5 (Online and scan versions available through

Scantron/Achievement Series.)









UNIT/ORGANIZING PRINCIPLE: ALGEBRA PACING: Weeks 23 – 27

ESSENTIAL QUESTIONS: How can you identify and describe patterns and relationships? Why do we use variables?

MEASUREMENT TOPICS



Patterns (T06)

NGSSS: Generate algebraic rules and use all four operations to describe patterns, including nonnumeric growing or repeating patterns.

Students will:

• identify and demonstrate numeric or nonnumeric patterns (repeating and growing).

NOTE: A repeating pattern must be shown with at least three examples of the repeated pattern.

• describe in words the algebraic rule of a pattern.

NOTE: Only one operation (+, −, х, ÷) will be used in each numeric pattern. Patterns involving multiplication or division are limited to the multiplication facts of 0 х 0 through 12 х 12 and the related division facts.

• extend a pattern beyond its next step or find a missing number, graphic, or figure in a pattern.

T06.MA.4.A.4.1 algebraic expression difference equal (=) equations expressions factors multiples not equal (≠) operations patterns products quotient rules solution variables

Equations and Expressions

(T07)

NGSSS: Describe mathematics relationships using expressions, equations, and visual representations.

Students will:

• translate a written description or a graphic to an expression (e.g., 6 + 5, x – 7) or equation (e.g., y ÷ 2 = 4, 2 х 5 = 10) using up to one variable.

• translate an expression or equation to a written or graphic description to solve a real-world problem.

NOTE: An equation ALWAYS contains an equal sign.

• identify a missing number or element in a numeric or graphic relationship. • describe the rule of a visual relationship using an expression, equation, or

description of the graphic. • describe an algebraic rule from a list of numbers or a function table.

T07.MA.4.A.4.2





(T07)

NGSSS: Recognize and write algebraic expressions for functions with two operations.

Students will:

• identify and write an expression to represent a real-world situation using one variable

Example: Marty has 15 video games. He buys some more on eBay. This can be represented as 15 + v.

• identify and write an expression involving two operations representing a real-world situation or graphic relationships.

Example: Equal amounts of coins in two bags and 5 coins outside the bags can be represented as 2x + 5 (multiplication and addition).

• identify and write an algebraic rule with two operations from a list of

numbers or a function table .

T07.MA.4.A.4.3















enVisionMATH Student Edition Topic 10: Lessons 10-1, 10-2, 10-3, 10-4, 10-5, 10-6, 10-7; Reteaching Sets: A-E p 212 Topic 11: Lessons 11-1, 11-2, 11-3, 11-4, 11-5; Reteaching Sets: A-E p 228




Topic 10: Lessons 10-1, 10-2, 10-3, 10-4, 10-5, 10-6 Topic 11: Lessons 11-2, 11-3, 11-4, 11-5


Topic 10: Lessons 10-1, 10-2, 10-3, 10-4, 10-5, 10-6, 10-7 Topic 11: Lessons 11-1, 11-2, 11-3, 11-4, 11-5

Everglades K-12: Grade 4 pp. 100-120 Chapter 4: Algebra

Internet Resources

http://www.floridastandards.org/homepage/index.aspx - CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). www.studyjams.scholastic (algebra)

Required Summative

04 Math Interim Assmt Algebra

Optional Formatives


Topic 10 Florida Test Topic 11 Florida Test



04 Math Focus Formative MA.4.A.4.1 04 Math Focus Formative MA.4.A.4.2 04 Math Focus Formative MA.4.A.4.3










UNIT/ORGANIZING PRINCIPLE: GEOMETRY II PACING: Weeks 28 – 31

ESSENTIAL QUESTIONS: What is area and how is it measured? How do you find the area of a rectangle?

MEASUREMENT TOPICS



Area (T11)

NGSSS: Describe and determine area as the number of same-sized units that cover a region in the plane, recognizing that a unit square is the standard unit for measuring area.

Students will:

• recognize that a unit square is the standard unit for measuring area. • recognize that area is found using same-size units. • describe area (the number of same-sized units that cover a region in a

plane). • determine the area of polygons using manipulatives (e.g., graph paper,

color tiles, geoboards).

NOTE: Use of the area formula is not appropriate at this time.

• estimate the area of irregular shapes found in the real-world (e.g., shape of a pond, a mitten, a foot, the sole of a shoe) using manipulatives such as graph paper, color tiles, geoboards.

NOTE: Students are expected to find the area of polygons and irregular shapes using countable units that estimate to a whole or half unit.


T11.MA.4.G.3.1 area centimeter composite shape feet height inches irregular shape kilometer meter mile millimeter perimeter regular shape square units




NGSSS: Justify the formula for the area of the rectangle “area = base x height.”

Students will:

• identify situations that require the use of the area formula in real-world contexts (e.g., amount of paint needed to cover a wall, amount of ground the bottom of a pool will cover).

• explain that the number of square units of a rectangle can be represented as the base times the height.

NOTE: Students will NOT be given the formula of the area of a rectangle during a testing situation.


T11.MA.4.G.3.2

NGSSS: Select and use appropriate units, both customary and metric, strategies, and measuring tools to estimate and solve real-world area problems.

Students will:

• find the area of a rectangle by multiplying the base by the height. • solve problems involving the area of a rectangle or a composite shape

composed of adjacent rectangles, such as L-or E-Shaped figures (irregular shapes).

• select appropriate units and/or tools to estimate and/or solve real-world area problems, (e.g., recognize that the area of a room is expressed as square feet, compared to an area of land expressed in square miles or square kilometers).

• use a ruler to determine the dimensions of a figure


T11.MA.4.G.3.3




2- and 3-Dimensional Shapes

(T14)

NGSSS: Identify and build a three-dimensional object from a two-dimensional representation of that object and vice versa.

Students will:

• use nets (a 2-dimensional shape that can be folded into a 3-dimensional figure) to compose and decompose figures.

• identify a three-dimensional object from two-dimensional views of that object.

• identify one or more of the two-dimensional views of a three-dimensional object.

• use appropriate geometric vocabulary to describe properties and attributes of 2- and 3-dimensional objects

• draw and classify 2- and 3-dimensional objects. • identify one or more 2-dimensional views (top, sides, front or base) of a 3-

dimensional object (not nets). FCAT 2.0 Sample Item:

T14.MA.4.G.5.3 cone cube cylinder edge face net perspective (view) prism pyramid quadrilateral rectangular pyramid rhombus sphere square pyramid triangle triangular prism triangular pyramid vertices/vertex











reasoning.





enVisionMATH Student Edition Topic 15: Lessons 15-1, 15-2, 15-3, 15-4, 15-5, 15-6, 15-7, 15-8; Reteaching Sets: A, D, F p 324 Topic 16: Lessons 16-9, 16-10, 16-11, 16-12; Reteaching Sets: F-I p 360-361


Topic 15: Lessons 15-1, 15-2, 15-3, 15-4, 15-5, 15-6, 15-7, 15-8 Topic 16: Lessons 16-9, 16-10, 16-11, 16-12





Everglades K-12: Grade 4 pp. 76-98 Chapter 3: Understanding Area and Area of Two-Dimensional Shapes

Internet Resources

http://www.floridastandards.org/homepage/index.aspx - CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). www.studyjams.scholastic (measurement) www.studyjams.scholastic (geometry) www.fi.uu.nl/toepassingen/02015/toepassing_wisweb.en.html - The Freudenthal Institute for Science and Mathematics Education (FIsme) is a research institute of Utrecht Universiteit, faculty of Science. “Building houses with side views” a great interactive site on perspective. www.bbc.co.uk/schools/ks2bitesize/maths.shape_space (games) www.fi.uu.nl/toepassingen/02015/toepassing_wisweb.en.html - “Building houses with side views” a great interactive site on perspective.

Required Summative

04 Math Interim Assmt Geometry II

Optional Formatives


Topic 15 Florida Test Topic 16 Florida Test (if not already given)



04 Math Focus Formative MA.4.G.3.1 04 Math Focus Formative MA.4.G.3.2 04 Math Focus Formative MA.4.G.3.3 04 Math Focus Formative MA.4.G.5.3










UNIT/ORGANIZING PRINCIPLE: EXTENSION OF MULTIPLICATION PACING: Weeks 32 – 33

ESSENTIAL QUESTIONS: Why is place value important when multiplying multi-digit numbers? How does estimating an answer help justify the reasonableness of a product?

MEASUREMENT TOPICS




(T04)

NGSSS: Estimate and describe reasonableness of estimates; determine the appropriateness of an estimate versus an exact answer.

Students will:

• use appropriate estimation strategies, including rounding, benchmarking, and compatible numbers to determine reasonable estimates.

• determine whether an exact number or an estimate is more appropriate for a given real-world situation.

T04.MA.4.A.6.6 factors multiple product round


(T05)

NGSSS: Multiply multi-digit whole numbers through four digits fluently, demonstrating understanding of the standard algorithm and checking for reasonableness of results, including solving real-world problems.

Students will:

• solve real-world problems using basic multiplication and the related division facts.

• solve multidigit whole-number multiplication problems or supply partial products in real-world multiplication problems through 4-digits.

T05.MA.4.A.1.2


(T04)

NGSSS: Multiply multi-digit whole numbers through four digits fluently, demonstrating understanding of the standard algorithm and checking for reasonableness of results, including solving real-world problems.

Students will:

• solve real-world problems using basic multiplication and the related division facts.

• solve multidigit whole-number multiplication problems or supply partial products in real-world multiplication problems through 4-digits.

T04.MA.4.A.1.2















enVisionMATH Student Edition

* These materials may have been used in earlier units. They should be used now, as needed, to help students reach mastery of these concepts.

Topic 4: Lessons 4-1, 4-2, 4-3, 4-4, 4-5, 4-6 Reteaching Sets: A-F p 86

Topic 5: Lessons 5-1, 5-2, 5-3, 5-5, 5-6, 5-7 Reteaching Sets: A, B, D, E p 112

Topic 6: Lessons 6-1, 6-2, 6-3, 6-4 Reteaching Sets: A-E p 130

Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5 Reteaching Sets: A-D p 148

Topic 8: Lessons 8-1, 8-2, 8-3, 8-5, 8-6 Reteaching Sets: A-C, E, F p 168

Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-5, 9-6 Reteaching Sets: A-E p 188

enVisionMATH Daily Assessment and Reteaching Workbook

* These materials may have been consumed in earlier units. They should be used now, as needed, to help students reach mastery of these concepts. They can be accessed online at www.pearsonsuccessnet.com.

Lessons: 4-1, 4-2, 4-3, 4-4, 4-5, 4-6 5-1, 5-2, 5-3, 5-5, 5-6, 5-7 6-1, 6-2, 6-3, 6-4 7-1, 7-2, 7-3, 7-4, 7-5 8-1, 8-2, 8-3, 8-5, 8-6 9-1, 9-2, 9-3, 9-4, 9-5, 9-6

Everglades K-12: Grade 4

Chapter 1

Internet

CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.studyjams.scholastic (multiplication & Division) http://www.321know.com/mul74bx2.htm students identify the property demonstrated in problems-interactive www.sumdog.com www.khanacademy.org www.mathdrills.com www.multiplication.com www.mathfactcafe.com



UNIT/ORGANIZING PRINCIPLE: EXTENSION OF FRACTIONS PACING: Weeks 34 – 35 ESSENTIAL QUESTIONS: How can you use your knowledge of fractions to compare and estimate them?

MEASUREMENT TOPICS



Fractions (T10)

NGSSS: Compare and order decimals through the thousandths place to name numbers between whole numbers.

Students will:

• compare (using the symbols: <, ≤, >, ≥, =, ≠) and order mixed numbers and decimals through the thousandths place with no more than five digits.

• compare and order decimals, fractions, and/or mixed numbers between two numbers.

• estimate fractions and/or decimals in real-world situations • identify a fraction or decimal that is closest to another number or a

benchmark fraction �


�

� than

�

� .


( �

� , �

� , �

� , �

� , �

� )

common factors denominator equivalent fractions


� )

formerly called improper fractions factors generalization

mixed numbers (1�

� )

multiples numerator


Students will:

• locate whole numbers, fractions and mixed numbers on a number line. • identify or locate a fraction or mixed number between two whole numbers

on a number line.

T10.MA.4.A.2.1

NGSSS: Generate equivalent fractions and simplify fractions.

Students will:

• find equivalent fractions or simplify fractions to lowest terms. • rename fractions as mixed numbers or vice versa

T10.MA.4.A.6.3


Students will:

• determine factors and/or multiplies for specified whole numbers to find equivalent fractions.

T10.MA.4.A.6.4

















Topic 13: Lessons 13-1, 13-2, 13-3, 13-4, 13-5, 13-7 Reteaching Sets: A-F p 274

Topic 14: Lessons 14-6 Reteaching Sets: E p 301



Lessons: 13-1, 13-2, 13-3, 13-4, 13-5, 13-7 14-6


Chapter 2

Internet

CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.studyjams.scholastic (fractions) www.khanacademy.org www.mathfactcafe.com



UNIT/ORGANIZING PRINCIPLE: EXTENSION OF DECIMALS PACING: Week 36

ESSENTIAL QUESTIONS: How are fractions, decimals and percents alike and different?

MEASUREMENT TOPICS



Decimals (T08)


Students will:

• compare (using the symbols: <, ≤, >, ≥, =, ≠) and order mixed numbers and decimals through the thousandths place.

• compare or order decimals, fractions, and/or mixed numbers between two numbers.

• estimate fractions and/or decimals in real-world situations.

��Front-end estimation will not be an acceptable estimation strategy.


( �

� , �

� , �

� , �

� , �

� )

decimal decimal point denominator equivalence equivalent decimals equivalent fractions estimate expanded form fractions


� )

formerly called improper fractions generalization greater than hundredths less than

mixed numbers (1�

� )

number line number line numerator one hundred percent standard form tenths thousandths word form

NGSSS: Describe decimals as an extension of the base-ten number system.

Students will:

• use manipulatives to model decimals as an extension of the base-ten number system

• recognize the relationship between the place values (e.g. place values increase by a factor of 10 as they move to the left)

T08.MA.4.A.2.2











reasoning.







Topic 12: Lessons 12-1, 12-2, 12-4, 12-5, 12-6, 12-7, 12-8 Reteaching Sets: A, C-F p 252

Topic 13: Lessons 13-1 Reteaching Sets: A p 274

Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6, 14-7 Reteaching Sets: A-E p 300

Topic 16: Lessons 16-12 Reteaching Sets: I p 363



Lessons: 12-1, 12-2, 12-4, 12-5, 12-6, 12-7, 12-8 13-1 14-1, 14-2, 14-3, 14-4, 14-5, 14-6 16-12


Chapter 2

Internet

CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.studyjams.scholastic www.khanacademy.org



UNIT/ORGANIZING PRINCIPLE: EXTENSION OF ALGEBRAIC THINKING PACING: Week 37

ESSENTIAL QUESTIONS: How can you identify and describe patterns and relationships? Why do we use variables?

MEASUREMENT TOPICS



Patterns (T06)

NGSSS: Generate algebraic rules and use all four operations to describe patterns, including nonnumeric growing or repeating patterns.

Students will:

• complete a graphic or numeric pattern. • describe or generalize the algebraic rule of a pattern. • predict and extend a pattern beyond its next step or find a missing

number, graphic, or figure in a pattern. • analyze number patterns and state rules for relationships involving all four

operations

T06.MA.4.A.4.1 algebraic expression difference equations expressions factors multiples operations patterns products protractor quotient rules solution variables


(T07)

NGSSS: Describe mathematics relationships using expressions, equations, and visual representations.

Students will:

• translate a written description or a graphic to an expression or equation or translate an expression or equation to a written or graphic description to solve a real-world problem.

• identify a missing number or element in a numeric or graphic relationship • describe or generalize the rule of a visual relationship using an

expression, equation, or description of the graphic.

T07.MA.4.A.4.2

NGSSS: Recognize and write algebraic expressions for functions with two operations.

Students will:

• identify an expression having two operations including the use of the

symbols =, ≠ or two procedural steps representing a real-world situation or graphic relationship.

T07.MA.4.A.4.3


Make sense of problems and persevere in solving them.


Construct viable arguments and critique the reasoning of others.









enVisionMATH Student Edition * These materials may have been used in earlier units. They should be used now, as needed, to help students reach mastery of these concepts.

Topic 10: Lessons 10-1, 102, 10-3, 10-4 Reteaching Sets: A-C p 212

Topic 11: Lessons 11-4



Lessons: 10-1, 102, 10-3, 10-4 11-4


Chapter 4

Internet

CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.studyjams.scholastic (algebra)



UNIT/ORGANIZING PRINCIPLE: EXTENSION OF AREA OF 2-DIMENSIONAL SHAPES PACING: Weeks 38-39 ESSENTIAL QUESTIONS: What is area and how is it measured? How do you find the area of a rectangle?

MEASUREMENT TOPICS



Area (T11)

NGSSS: Describe and determine area as the number of same-sized units that cover a region in the plane, recognizing that a unit square is the standard unit for measuring area.

Students will:

• determine the area of a figure or a region on a plane by counting units rather than multiplying dimensions.

• recognize that a unit square is the standard unit for measuring area • recognize that area is found using same size units • estimate and solve real-world problems to find area including irregular

shapes

T11.MA.4.G.3.1 area centimeter composite shape feet height inches irregular shape kilometer meter mile millimeter perimeter regular shape square units

NGSSS: Justify the formula for the area of the rectangle “area = base x height.”

Students will:

• identify situations that require the use of the area formula in real-world contexts.

• identify the number of square units of a rectangle as the base times the height.

T11.MA.4.G.3.2

NGSSS: Select and use appropriate units, both customary and metric, strategies, and measuring tools to estimate and solve real-world area problems.

Students will:

• find the area of a rectangle by multiplying the base by the height. • solve problems involving the area of a rectangle or a composite shape

composed of adjacent rectangles, such as L-or E-shaped figures. • select appropriate units and/or tools to estimate and/or solve real-world

area problems, (e.g., recognized that the area of a room is expressed as square feet, compared to an area of land expressed in square miles or square kilometers).

• use a ruler to determine the dimensions of a figure • estimate and solve real-world problems to find area including irregular

shapes.

T11.MA.4.G.3.3

















Topic 15: Lessons 15-1, 15-2, 15-3, 15-4, 15-5, 15-6, 15-7, 15-8 Reteaching Sets: A, D, F p 324

enVisionMATH Daily Assessment and Reteaching Workbook * These materials may have been consumed in earlier units. They should be used now, as needed, to help students reach mastery of these concepts. They can be accessed online at www.pearsonsuccessnet.com.

Lessons: 15-1, 15-2, 15-3, 15-4, 15-5, 15-6, 15-7, 15-8


Chapter 3

Internet

CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.studyjams.scholastic (measurement)



Formative Assessment Strategies

Mathematics K-5

Name Description Additional Information

A & D Statements

A & D Statements analyze a set of “fact or fiction” statements. First, students may choose to agree or disagree with a statement or identify whether they need more information. Students are asked to describe their thinking about why they agree, disagree, or are unsure. In the second part, students describe what they can do to investigate the statement by testing their ideas, examining what is already known, or using other means of mathematical inquiry.

• http://www.mathsolutions.com/documents/Ho

w_to_Get_Students_Talking.pdf • http://www.sagepub.com/upm-

data/37758_chap_1_tobey.pdf

• http://formativeassessment.barrow.wikispaces

.net/Agreement+Circles

Statement How can you find out?

9/16 is larger than 5/8. __agree __disagree __ not sure __it depends on My thoughts:

Agreement Circles

Agreement Circles provide a kinesthetic way to activate thinking and engage students in discussing and defending their mathematical ideas. Students stand in a circle as the teacher reads a statement. Students who agree with the statement step to the center of the circle. Those who disagree remain on the outside circle. Those on the inner circle face their peers on the outer circle and divide themselves into small groups who agree and disagree. Small groups then discuss to defend their thinking.

• Are there 20 cups in a gallon? Agree or disagree.

• Is 2/3 equivalent to 4/6? Additional Questioning: Teacher can ask if others have been swayed. If so, stand up. If not, what are your thoughts? Why did you disagree? After hearing those who disagree, does anyone who has agreed want to change their minds? Use when students have had some exposure to the content.

Annotated Student Drawings

Annotated Student Drawings are student-made, labeled illustrations that visually represent and describe students’ thinking about mathematical concepts. Modification for younger students: verbally describe and name parts of their drawing s while the teacher annotates it for them.

• http://formativeassessment.barrow.wikispaces

.net/Annotated+Student+Drawings

• Represent the number 747 drawing rods and cubes.

• Represent 3x2=2x3 using arrays.



Formative Assessment Strategies Mathematics K-5, continued


Card Sorts

Card Sorts is a sorting activity in which students group a set of cards with pictures, numbers, symbols, or words according to certain characteristics or category. Students sort the cards based on their preexisting ideas about the concepts or procedures. As students sort the cards they discuss their reasons or placing each card into a designated group. This activity promotes discussion and active thinking. Card sorts are best used in small groups to encourage students to share their thinking with their peers. Teacher circulates around the classroom listening to students hearing and seeing their levels of understanding. Make sure that the students explain their reasons for placing the card in one of the rows.

• http://teachingmathrocks.blogspot.com/2012/

09/vocabulary-card-sort.html

• Use with equivalent fractions • Place value (standard form, expanded

form, written form) • Measurement conversions • Fact families • Number to number word and drawing of

numbers

Commit and Toss

Commit and Toss is an anonymous technique used to get a quick read on the different ideas students have in the class. Students are given a question and asked to answer it AND explain their thinking. They write this on a piece of paper. The paper is crumpled into a ball. Once the teacher gives the signal, they either toss/pass/or place the ball in a basket. Students take turns reading their "caught" response. Once all ideas have been made public and discussed, engage students in a class discussion to decide which ideas they believe are the most plausible and to provide justification for the thinking. THIS IS A FUN, ENGAGING TECHNIQUE! BE CAREFUL NOT TO OVERUSE IT OR IT WILL LOSE ITS EFFECTIVENESS.

Stephanie stood with both feet on the bathroom scale. She recorded her weight. She lifted her left foot and stood on the scale with only one foot on it. Which best describes what happened to the reading on the scale? a. The weight shown on the scale increased. b. The weight shown on the scale decreased. c. The weight shown on the scale stayed the same. Explain your thinking. Describe the reason for the answer you selected.

Concept Card Mapping

Concept Card Mapping is provides an opportunity for students to activate their prior knowledge, think about relationships between familiar concepts and make visual representation of connections in their own knowledge network. Students are given cards with the concepts written on them. They move the cards around and arrange them as a connected web of knowledge. They create linkages between the concept cards that describe the relationship between concepts.





Concept Cartoons

Concept Cartoons are cartoon drawings that visually depict children or adults sharing their ideas about common everyday math. Students decide which character in the cartoon they agree with most and why. This formative is designed to engage and motivate students to uncover their own ideas and encourage mathematical argumentation. Concept Cartoons are most often used at the beginning of a new concept or skill. These are designed to probe students’ thinking about everyday situations they encounter that involve the use of mathematics. Not all cartoons have one “right answer”. Allow students time to for ideas to simmer and stew to increase cognitive engagement.

• www.pixton.com (comic strip maker)

Four corners

Four Corners provides an opportunity for students to make their ideas public. By meeting “in the corner” with students with similar ideas, students can further discuss and clarify their own thinking with others before returning to their seats and engage in mathematical discussion with the class. Present a controversial text-based statement and have students go to the corner that best fits their opinion. Students then pair up to defend their opinion with text based evidence. The teacher circulates and records comments. Next, there can be a whole group discussion, where opinions are defended and/or students can return to their desks to write a brief defense of their opinion.

• http://debbiedespirt.suite101.com/four-

corners-activities-a170020

• http://wvde.state.wv.us/teach21/FourCorners.

html

Corners are labeled: Strongly agree, agree, disagree and strongly disagree.

Frayer Model

Frayer Model graphically organizes prior knowledge about a concept into an operational definition, characteristics, examples, and non-examples. It provides students with the opportunity to clarify a concept or mathematical term and communicate their understanding. For formative assessment purposes, they can be used to determine students’ prior knowledge about a concept or mathematical term before planning the lesson. Barriers that can hinder learning may be uncovered with this assessment. This will then in turn help guide the teacher for beneficial instruction.

Frayer ModelDefinition in your own words Facts/characteristics

Examples NonexamplesQuadrilateral

A quadrilateral is a shape

with 4 sides.

•4 sides

• may or may not be of equal

length

• sides may or may not be

parallel

• square

• rectangle

• trapezoid

• rhombus

• circle

• triangle

• pentagon

• dodecahedron





Friendly Talk Probes

Friendly Talk Probes are two-tiered questions that consist of a selected-response section followed by a justification. The probe is set in a real-life scenario in which “friends” talk about a mathematical concept. Students are asked to pick the person they most agree with and explain why. Distracters are based on commonly held ideas from the research on students’ misconceptions and common errors. The conversation between the characters draws students into the ideas almost as if they are participating in the conversation.

Human Scatterplots

Human Scatterplots is a quick, visual way for teacher and students to get an immediate classroom snapshot of students’ thinking and the level of confidence students have in their ideas. This formative can be used at the beginning of a lesson or sequence of instruction to bring out students initial ideas and motivate them to want to further explore and discover mathematical ideas. Label the wall (Y-axis) on one side of the room with the choices: for example, A, B, C (and D, if there are four responses). Label the adjacent wall (X-axis) with a range of low confidence to high confidence. Have students position themselves based on where they feel they fall on the graph. A paper version can be used instead of a human graph.

What’s the Substitute? When you substitute ½ for x in 4x and simplify the results, what is the correct answer?

A. 4 ½ B. 2 C. 8

Human Scatterplot for “What’s the Substitute?”

I Used to think… But now I know…

I Used to Think…But now I know is a self assessment and reflection exercise that helps students recognize if and how their thinking has changed at the end of a concept or skill. An additional column can be added to include…And This Is How I Learned It to help students reflect on what part of their learning experiences helped them change or further develop their ideas.

I USED TO THINK… BUT NOW I KNOW…





Justified List

Justified List begins with a statement or question about a mathematical concept or procedure. Multiple examples that fit or do not fit the statement are listed. Students choose the examples on the list that fit the statement or answer the question and provide a justification explaining their rule or reasons for their selections. This can be done individually or in small group. Small groups can share their lists with the whole class for discussion and feedback. You can also use pictures of manipulatives for English-language learners.

Ways to Make 734 All the numbers listed below are digits. Put an X next to the number that represents 734. ___ 700+30+4 ____7tens 3hundreds 4 ones ___730tens 4 ones ____7hundreds 3tens 4ones ___734 ones ____seven hundred thirty four ___seventy four ____ 400+70+3 Explain your thinking. What “rule” or reasoning did you use to decide which objects digit is another way to state that number.

KWL Variations

K-W-L is a general technique in which students describe what the Know about a topic, Want to know about a topic, and Learned about the topic. It provides an opportunity for students to become engaged with a topic, particularly when asked what they would like to learn. K-W-L provides a self-assessment and reflection at the end, when students are asked to think about what they learned. The three phrases of K-W-L help students see the connections between what they already know, what they would like to find out, and what they learned as a result.

K-This what I already KNOW

W-This is what I WANT to find out

L-This is what I LEARNED

Learning Goals Inventory (LGI)

Learning Goals Inventory (LGI) is a set of questions that relate to an identified learning goal in a unit of instruction. Students are asked to “inventory” the area they feel they have prior knowledge about the learning goal. This requires them to think about what they already know in relation to the learning goal statement as well as when and how they may have learned about it. A key principle of learning is that students must know what the learning target is. The LGI can be given back to students at the end of the instructional unit as a self assessment and reflection of their learning.

What do you think the learning goal is about? List any facts, concepts or skills you are familiar with related to this learning goal: List any terminology you know of that relates to this goal: List any experiences you have had that may have helped you learn about the ideas in this learning goal:





Look Back

Look Back is a recount of what students learned over a given instructional period of time. It also provides students with an opportunity to look back on and summarize their learning. Asking the students “how they learned it” helps them think about their own learning. The information can be used to differentiate instruction for individual learners, based on their descriptions of what helped them learn.

What I Learned How I Learned it

Muddiest Point

Muddiest Point is a commonly used, quick monitoring technique in which students are asked to take a few minutes to jot down what the most difficult or confusing part of a lesson was for them. The information is used as instructional feedback to address student difficulties.

You have been learning about three dimensional shapes. What is the muddiest point for you so far when it comes to three dimensional shapes? I will use the information you give to me to think about ways to help you better understand three dimensional shapes in tomorrow’s lesson.

Odd One Out

Odd One Out combines seemingly similar items and challenges students to choose which item in the group does not belong. Students are asked to justify their reasoning for selecting the number, symbol, representation, or mathematical term that does not fit with the others. Odd One Out can be used at the beginning of instruction to find out what students already know about a mathematic topic. It can also be used during the development of conceptual understanding to examine the reasoning students use in comparing and contrasting the items on the list. Teachers can use this strategy to examine how their students make connections among concepts.

Show students three objects. "Which is the odd one out?" "Describe properties that two share that the third does not." "Now choose a different object from the three and justify it as the odd one out."

Partner Speaks

Partner Speaks provides students with an opportunity to talk through a concept or problem solution with another student and receive feedback before sharing with a larger group. When ideas are shared with the larger group, pairs speak from the perspective of their partner’s ideas. This changes the emphasis from student’s ideas to consider the ideas of his or her partner and encourages careful listening between student pairs. This can be used to promote deeper engagement with an idea, especially when there is a need to have students think through a new idea or difficult question.

Today we are going to explore different ways to add three-digit numbers together. What different kinds of strategies can you use to add 345+525? Turn to your partner and take turns discussing your strategies. Be sure to listen carefully, without interrupting, as your partner shares his/her thinking. Then the partner shares. When you are finished taking turns, each of you will need to be prepared to share one way your partner added the numbers with the rest of class.





A Picture Tells a Thousand Words

A Picture Tells a Thousand Words, students are digitally photographed during a mathematical investigation using manipulatives or other materials. They are given the photograph and asked to describe what they were doing and learning in the photo. Students write their description under the photograph. The images can be used to spark student discussions, explore new directions in inquiry, and probe their thinking as it relates to the moment the photograph was snapped. By asking students to annotate a photo that shows the engaged in a mathematics activity or investigation helps them activate their thinking about the mathematics, connect important concepts and procedures to the experience shown in the picture and reflect on their learning. Teachers can better understand what students are gaining from the learning experience and adjust as needed.

Question Generating

Question Generating is a technique that switches roles from the teacher as the generator of questions to the student as the question generator. The ability to formulate good questions about a topic can indicate the extent to which a student understands ideas that underlie the topic. This technique can be used at the beginning of instruction in a topic to find out what students already know about the topic. Teachers can have students exchange or answer their own questions, revealing further information about the students’ ideas related to the topic.

Question Generating Stems: • Why does___? • Why do you think___? • Does anyone have a different way to

explain___? • How can you prove___? • What would happen if___? • Is___always true? • How could we find out if___?

Sticky Bars

Sticky Bars help students recognize that there is often a range of ideas students in the class have about a topic. Students are presented with a short answer or multiple-choice question. The answer is anonymously recorded on a Post-it note and passed in to the teacher. The teacher or a student arranges the notes on the wall or whiteboard, as a bar graph, representing the different student responses. Students then discuss the data and what they think the class needs to do in order to come to a common understanding.





Thinking Log

Thinking Logs help the teacher identify areas where the students are aware of their own learning successes or challenges. The information can be used to provide interventions for individual or groups of students as well as match students with peers who may provide learning support. Use impromptu moments during a learning experience or at the end of a lesson for students to record in their Thinking Logs. Students choose the thinking stem that would best describe their thinking at that moment. Provide a few minutes for students to write down their thoughts using the stem.

• I was successful in… • I got stuck… • I figured out… • I got confused when…so I… • I think I need to redo… • I need to rethink… • I first thought…but now I realize… • I will understand this better if I… • The hardest part of this was… • I figured it out because… • I really feel good about the way…

Think-Pair-Share

Think-Pair-Share combines thinking with communication. The teacher poses a question and gives individual students time to think about the question. Students then pair up with a partner to discuss their ideas. After pairs discuss, students share their ideas in a small-group or whole-class discussion. (Kagan)

This formative can be used during any stage of the mathematics assessment and instruction cycle. Using different pairing strategies to ensure that students have the opportunity to form pairs with students other than the ones who sit next to them in order to avoid having students always interact with the same group of peers.

Three-Minute Pause

Three-Minute Pause provides a break during a block of instruction in order to provide time for students to summarize, clarify, and reflect on their understanding through discussion with a partner or small group. When three minutes are up, students stop talking and direct their attention once again to the teacher, video, lesson, or reading they are engaged in, and the lesson resumes. Anything left unresolved is recorded after the time runs out and saved for the final three-minute pause at the end.

3-2-1

3-2-1 provides a structured way for students to reflect on their learning. Students respond in writing to three reflective prompts; providing six responses that describe what they learned from a lesson or instructional sequence. This technique scaffolds students’ reflections providing an opportunity to share their success in learning difficult or new concepts as well as recognize what was challenging for them. (Three key ideas I will remember; Two things I am still struggling with; One thing that will help me tomorrow)





Traffic Light Cards

Traffic Light Cards are a monitoring strategy that can be used at any time during instruction to help gauge student understanding. The colors indicate whether students have full, partial, or minimal understanding. Students are given three different-colored cards, asked to self-assess their understanding about the concept or skill they are learning, and hold up the card that best matches their understanding.

Traffic Light Cups

Traffic Light Cups are used during group work and student investigations to signal to the teacher when groups need help or feedback. Red, yellow, and green stackable party cups placed in the center of a group’s table or workstation represent whether the group is able to proceed without the need for teacher intervention or whether they need assistance.

Variations of Traffic Light Formatives

Traffic Light Dots

Traffic Light Dots provide a way for students to self-assess areas of their work. Small peel-off dots serve as traffic signal icons. Students place the dots in the margins of their work to indicate areas where they feel they were successful (green), areas where they aren’t sure about their work and would like feedback (yellow), and areas where they feel they didn’t understand or perform well on the task and need help (red).

Variations of Traffic Light Formatives

Two-Minute Paper

Two-Minute Paper is a quick and simple way to collect feedback from students about their learning at the end of an activity, field trip, lecture, video, or other type of learning experience. Write two questions on the board or on a chart that you want students to respond to. Give students two minutes to write and then collect their papers. After their responses have been analyzed, share the results with students the next day, letting them know how you are going to use the feedback they shared with you.

• What was the most important thing you learned today?

• What did you learn today that you didn’t know before class?

• What important question remains unanswered for you?

• What would help you learn better tomorrow?





Two Stars and a Wish

Two Stars and a Wish is used in “comments-only marking.” It is a way to balance positive comments with the need for improvement when providing students with feedback on their work. The first sentence describes two good features of the section of work that is commented on. The second sentence encourages revision or further improvement.

Two-Thirds Testing

Two-Thirds Testing provides an opportunity for students to take an ungraded “practice test” two thirds of the way through a unit. It helps to identify areas of difficulty or misunderstanding through an instructional unit so that interventions and support can be provided to help them learn and be prepared for a final summative assessment. Working on the test through discussions with a partner or in a small group further develops and solidifies conceptual understanding.

What Are You Doing and Why?

What Are You Doing and Why? is a short, simple monitoring strategy to determine if students understand the purpose of the activity or how it will help them learn. At any point in an activity the teacher gets the students attention and asks a “What are you doing and why are you doing it?” question. Responses can be shared with the class, discussed between partners, or recorded in writing as a One-Minute Paper to be passed in to the teacher. The data are analyzed by the teacher to determine if the class understands the purpose of the activity they are involved in.

Whiteboarding

Whiteboarding is used in small groups to encourage students to pool their individual thinking and come to a group consensus on an idea that is shared with the teacher and the whole class. Students work collaboratively around the whiteboard during class discussion to communicate their ideas to their peers and the teacher.

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Intervention/Remediation Guide

Resource Location Description Intervention Lessons (Student and Teacher pages)

Math Diagnosis and Intervention System

Use for pre-requisite skills or remediation. For grades K-2, the lessons consist of a teacher-directed activity followed by problems. In grades 3-5, the student will first answer a series of questions that guide him or her to the correct answer of a given problem, followed by additional, but similar problems.

Meeting Individual Needs Planning section of each Topic in the enVision Math Teacher’s Edition

Provides topic-specific considerations and activities for differentiated instruction of ELL, ESE, Below-Level and Advanced students.

Differentiated Instruction Close/Assess and Differentiate step of each Lesson in the enVision Math Teacher’s Edition

Provides lesson-specific activities for differentiated instruction for Intervention, On-Level and Advanced levels.

Error Intervention Guided Practice step of each Lesson in the enVision Math Teacher’s Edition

Provides on-the-spot suggestions for corrective instruction.

ELL Companion Lesson Florida Interactive Lesson Support for English Language Learners

Includes short hands-on lessons designed to provide support for teachers and their ELL students, useful for struggling students as well

FINAL Grade 4 Mathematics Curriculum Map December...

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Transcript of FINAL Grade 4 Mathematics Curriculum Map December...