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Instructional Guide 2012-2013

Mathematics Fourth Grade Second Nine Weeks

Topic Lesson WEEKS 1-3

The first constructed response assessment will be administered during this window. Estimating Products

Arrays and an Expanded Algorithm EnVision Math Transitioning to Common Core, Lesson 7-4A,

“Arrays and An Expanded Algorithms” Multiplying 2-Digit by 2-Digit Numbers

7-2 7-3

7-4A 7-5

Two Question Problems Estimating Quotients

EnVision Math Transitioning to Common Core, Lesson 8-3A “Estimating Quotients for Greater Dividends”

Dividing with Remainders

7-7 8-2

8-3A 8-3

Dividing 2-Digit by 1-Digit Numbers Dividing 3-Digit by 1-Digit Numbers Deciding Where to Start Dividing

8-5 8-6 8-7

WEEKS 4-6

Factors Prime and Composite Numbers

Multiple-Step Problems

8-8 8-9 8-10

Points, Lines, and Planes Line Segments, Rays, and Angles

Measuring Angles EnVision Math Transitioning to Common Core

Lesson 9-3A, “Understanding Angles and Unit Angles” Lesson 9-4A, “Measuring with Unit Angles”

9-1 9-2 9-3

9-3A 9-4A

Polygons Triangles

Quadrilaterals

9-4 9-5 9-6

WEEKS 6-9 Fractions and Division

Estimating Fractional Amounts 10-2 10-3

Equivalent Fractions EnVision Math Transitioning to Common Core

Lesson 10-5A, “Number Lines and Equivalent Fractions” Fractions in Simplest Form

Improper Fractions and Mixed Numbers

10-4 10-5A 10-5 10-6

Comparing Fractions Ordering Fractions Writing to Explain

10-7 10-8 10-9

Expectations:

This map is intended to guide the instruction and encourages flexibility and differentiation within classrooms.

All content is to be taught within the respective nine week periods.

Students are to engage in mathematics learning centers (small group intervention, on-level or advanced center

activities) weekly.

In preparation for future implementation of the Common Core State Standards (CCSS), each grading period

teachers are to administer one free-response test, which is comparable to the how students will be assessed

according to the CCSS. Free-response Test Masters are included in Teacher’s Teaching Tool Masters envelope.

Please visit www.elementarymathmcs.weebly.com for additional instructional ideas, resources, and strategies.

AT A GLANCE PACING SCHEDULE All content is to be taught in the specified order and within the respective nine week periods. The pacing allows for teachers to be able to cover the material

in-depth and ensure student understanding.

The first constructed response assessment will be administered in the window from October 15, 2012 to October 26, 2012.

The new Constructed Response Assessment (CRA) will be a key part of the transition to the Common Core State Standards in Mathematics and will

replace the CRA that was previously given in grade 3. The new CRA will be a performance-based assessment designed to elicit student responses that

reflect higher levels of thinking and reasoning.

http://www.elementarymathmcs.weebly.com/

Instructional Map- Common Core Connections Subject Mathematics Grade: Four Grading Period: 2nd

Please note that all information is continually being revised and updated. Revised September 21, 2012

This map is intended to guide the instruction and encourages flexibility and differentiation within classrooms. Memphis City Schools

All content is to be taught within the respective nine week periods. of 16

Common Core Standards Connections are in GREEN The purpose of the map is to provide awareness to the Common Core Standards and the correlation to the TN State Standards. Students will be assessed based on the TN Diploma Standards until 2014-2015.

Extend understanding of fraction equivalence and ordering.

4.NF.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.

4.NF.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.

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

4.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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.

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.

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.

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

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).

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.)

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?

Required Fluencies for Fourth Grade: • Add/subtract within 1,000,000 (4.NBT.4)

The Fourth Grade TNCore Focus Standards for the 2012-2013 school year are: Extend understanding of fraction equivalence and ordering Build fractions from unit fractions by applying and extending previous understanding of operations on whole numbers






Quarter Two - Common Core State Standards Crosswalk Correlations:

To view the alignments between the K-8 Common Core State Standards and the current Tennessee Mathematics Standards please click on the link below and go to Mathematics: Grades K-8. TN Common Core Math Crosswalk

CC.4.OA.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.

CC.4.NBT.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.

CC.4.NBT.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.

CC.4.NF.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.

CC.4.NF.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.

CC.4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

CC.4.G.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.

CC.4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

o CC.4.MD.5a 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.

o CC.4.MD.5b An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

http://www.corestandards.org/Math/Content/4/NF/A/1

http://www.corestandards.org/Math/Content/4/NF/A/2

http://www.corestandards.org/Math/Content/4/G/A/2

http://www.corestandards.org/Math/Content/4/MD/C/5

http://www.corestandards.org/Math/Content/4/MD/C/5/a

http://www.corestandards.org/Math/Content/4/MD/C/5/a

http://www.corestandards.org/Math/Content/4/MD/C/5/b

http://www.corestandards.org/Math/Content/4/MD/C/5/b






Mathematical Practices 1. Make sense of problems and persevere in solving them. Mathematically proficient students in fourth grade know that doing mathematics involves solving problems and discussing how they solved

them. Students explain to themselves the meaning of a problem and look for ways to solve it. Fourth graders may use concrete objects or pictures to help them conceptualize and solve problems. They may

check their thinking by asking themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another method to check their answers.

2. Reason abstractly and quantitatively. Mathematically proficient fourth graders should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a

logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions

and decimals. Students write simple expressions, record calculations with numbers, and represent or round numbers using place value concepts.

3. Construct viable arguments and critique the reasoning of others. In fourth grade, mathematically proficient students may construct arguments using concrete referents, such as objects, pictures, and

drawings. They explain their thinking and make connections between models and equations. They refine their mathematical communication skills as they participate in mathematical discussions involving

questions like “How did you get that” and “Why is that true?” They explain their thinking to others and respond to others’ thinking.

4. Model with mathematics. Mathematically proficient fourth grade students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing

pictures, using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all

of these representations as needed. Fourth graders should evaluate their results in the context of the situation and reflect on whether the results make sense.

5. Use appropriate tools strategically. Mathematically proficient fourth graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might

be helpful. For instance, they may use graph paper or a number line to represent and compare decimals and protractors to measure angles. They use other measurement tools to understand the relative size

of units within a system and express measurements given in larger units in terms of smaller units

6. Attend to precision. As fourth graders develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are

careful about specifying units of measure and state the meaning of the symbols they choose. For instance, they use appropriate labels when creating a line plot.

7. Look for and make use of structure. (Deductive Reasoning) In fourth grade, students look closely to discover a pattern or structure. For instance, students use properties of operations to explain

calculations (partial products model). They relate representations of counting problems such as tree diagrams and arrays to the multiplication principal of counting. They generate number or shape patterns

that follow a given rule.

8. Look for and express regularity in repeated reasoning. (Inductive Reasoning) Students in fourth grade should notice repetitive actions in computation to make generalizations Students use models to

explain calculations and understand how algorithms work. They also use models to examine patterns and generate their own algorithms. For example, students use visual fraction models to write equivalent

fractions.






To promote focus and give educators the opportunity to begin to explore the new standards (and the critically important accompanying Constructed Response Assessment), the State Department of Education decided to narrow the focus of the TCAP for the next two school years (2012-13 and 2013-14), by removing 15-25% of the SPIs in each grade in mathematics, grades 3-8.In selecting which SPIs to remove, the following was considered:

Which SPIs focused on content that will not be covered in the CCSSM? Which SPIs focused on content that will be covered in a meaningfully different way in the CCSSM?

Which SPIs shifted up grade levels in the Common Core? State Performance Indicators (SPIs) dropped from the 2012-2013 Mathematics Grades 3-8 TCAP SPI Code PI Language SPI Language

SPI 0406.1.2 Compare decimals using concrete and pictorial representations. SPI 0406.1.3 Determine the correct change from a transaction. SPI 0406.3.2 Make generalizations about geometric and numeric patterns. SPI 0406.4.3 Construct geometric figures with vertices at points on a coordinate grid. SPI 0406.4.5 Identify attributes of simple and compound figures composed of 2- and 3- dimensional shapes. SPI 0406.4.6 Determine situations in which a highly accurate measurement is important.

SPI 0406.4.10 Identify images resulting from reflections, translations, or rotations. SPI 0406.5.3 Given a set of data or a graph, describe the distribution of the data using median, range, or mode. SPI 0406.5.4 List all possible outcomes of a given situation or event.

The TCAP will remain similarly slimmed and narrowed in the 2013-2014 school year. In 2014-2015, PARCC assessments will replace all TCAP exams. In order to emphasize the importance of the Focus Standards and provide students and teachers feedback on readiness for the CCSSM, as well as prepare students for the types of extended, innovative item types they will likely see on PARCC exams, we will be expanding the Constructed Response Assessment (CRA) to all grades 3-8. The new CRA will only assess the TNCore Focus Standards in math. Students will take three CRA’s: the first assessment will be administered in a window from October 15, 2012 to October 26, 2012. (Source: www.TNCore.org)






The Common Core State Standards in Mathematics (CCSSM) present an opportunity to engage students more deeply in the types of problem solving and mathematical thinking that build the fundamental and adaptive math skills necessary for life after high school. Please find below information about the key instructional shifts called for by the CCSSM:

Instructional Shifts

1. Focus strongly where the Standards focus Focus: The Standards call for a greater focus in mathematics. Rather than racing to cover topics in today's mile-wide, inch-deep curriculum, teachers use the power of the eraser and significantly narrow and deepen the way time and energy is spent in the math classroom. They focus deeply on the major work * of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom.

2. Coherence: think across grades, and link to major topics* within grades

Thinking across grades: the Standards are designed around coherent progressions from grade to grade. Principals and teachers carefully connect the learning across grades so that students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning. Linking to major topics: Instead of allowing additional or supporting topics to detract from the focus of the grade, these topics can serve the grade level focus. For example, instead of data displays as an end in themselves, they support grade-level word problems.

3. Rigor: in major topics* pursue:

conceptual understanding,

procedural skill and fluency, and

application with equal intensity.

Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Teachers support students' ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that students have access to more complex concepts and procedures. Application: The Standards call for students to use math flexibly for application. Teachers provide opportunities for students to apply math in context. Teachers in content areas outside of math, particularly science, ensure that students are using math to make meaning of and access content.

Source: Student Achievement Partners Revised (7.2.12) and www.TNCore.org






Click here to view the Constructed Response Assessment Link: Grade 4 Mathematics.CRA.2012

The Constructed Response Assessment will focus only on math content for the 2012-2013 school year. All students in third through eighth grade will take three different assessments. All items were developed to measure the content knowledge required by the current rigorous Tennessee Curriculum Standards and the new Common Core Standards located at http://tncore.org.

The Constructed Response Assessment will be scored using a Holistic scoring method. Each individual task will be scored for consideration of the student's content knowledge and their ability to perform the math practices applicable to the assessed task. Each task will have a scoring guide unique for the task.

Each math assessment will consist of four tasks. The assessment will have a fifty-five minute time limit. Calculators may be utilized on all tasks.

Weeks 1 -3

Preparing for the Constructed Response Assessment

Sample Mathematics Assessment Tasks

Instructional tasks from TNCore.org 1. 4th Grade Task: Star Bar 2. 4th grade Task: Cookies Task

Please refer to the attached Addendum for activities to help teachers introduce and prepare students for the focus standards, all of which deal with fractions. Prepare for the Constructed Response Assessments

The Constructed Response Assessment is be to administered during week 2 or 3 of this grading period. To help students become accustomed to this type of assessment, attached are samples of instructional tasks provided by the Tennessee Department of Education. It is highly recommended that students have regular exposure to high-level tasks as it is imperative that the use of the mathematical practices become routine and embedded within students' thinking. In addition, this activity will help teachers understand the expectations of the PBA and provide guidance for planning future lessons. This quarter’s pacing has been adjusted to allow time for students to engage in the instructional tasks.

Additional Resources In order to properly prepare students for the demands of CCSSM, content and assessments, we must provide students the opportunity to think, reason, and practice engaging in problem solving and communicating mathematically. Questioning is key to facilitating student learning and the documents below include sample questions and sentence stems to help jump start students. Math Talk Starter Questions (Source: clevelandcountyschools.org). Math Talk Questions and Stems Suggested structure to help facilitate student learning and ensure students are working independently or in small groups to reach the mathematical goals of the lesson. The Structures and Routines of a Lesson (Source TNCore.org)

http://www.tn.gov/education/curriculum.shtml

http://www.tncore.org/






GLE 0406.2.1 Understand place value of numbers from hundredths to the hundred-thousands place. GLE 0406.2.2 Develop fluency with multiplication and single-digit division. GLE 0406.1.3 Develop independent reasoning t o communicate mathematical ideas and derive algorithms and/or formulas. Enduring Understandings: 1. Basic facts and place-value patterns can be used to mentally multiply a two digit number by a multiple of 10, 100, or 1,000. 2. Rounding and substituting compatible numbers are two ways to estimate products. 3. The expanded algorithm for multiplying by two digit numbers is just an extension of the expanded algorithm for multiplying one digit numbers. 4. The standard multiplication algorithm is a shortcut for the expanded algorithm. Regrouping is used rather than showing all partial products.

Knowledge and Skills

Outcomes

(Checks for Understanding)

Resources and Instructional Strategies Assessments Intervention/Enrichment Technology and Additional

Web Based Resources

SPI 0406.2.11 Solve problems using whole number multi-digit multiplication. Common Core Connection: CC.4.OA.3 CC.4.NBT.5 Learning Targets:

I can choose the correct operation to perform at each step of a multi-step word problem.

I can demonstrate multiplication of two-digit numbers using rectangular arrays, place value, and/or the area model.

Essential Questions (Topic 7): 1. What place-value patterns can be

seen when you multiply 2 digit numbers by multiples of 10 and 100?

2. What are some ways to multiply mentally?

3. How can you use rounding to estimate when you multiply?

4. How do you know if your answer is reasonable?

5. How can you use arrays to help you record multiplication?

6. How do you multiply a 2-digit number by a 2 digit number?

0506.1.3 (Prepares) Explore different methods of estimation including rounding and truncating. 0406.2.3Multiply two and three digit whole numbers. 0406.2.4 Understand and use a reliable algorithm for multiplying multi-digit numbers and diving numbers by a single-digit divisor accurately and efficiently. 0406.1.4 Use the commutative, associative, and distributive properties of numbers including oral descriptions of mathematical reasoning.

Academic Vocabulary rounding estimate array algorithm

EnVision Teacher’s Edition Topic 7, pp. 144a - 153b Lesson 7-2 Estimating Products (4.OA.3) Lesson 7-3 Arrays and an Expanded Algorithm (4.NBT.5) EnVision Math Transitioning to Common Core, Student Lesson Lesson 7-4A, pp.12-13, Arrays and An Expanded Algorithms

Lesson 7-5 Multiplying 2-Digit by 2-Digit Numbers (4.NBT.5)

EnVision Student’s Edition pp. 144 - 153

Interdisciplinary Connections

WorldScapes Readers, “First in Space” p.6-7

Math Project p.141 Teacher–selected Pearson ancillary resources

Daily Spiral Review

Problem of the Day

Interactive Learning Recording Sheet

Visual Learning Animation

Practice/Reteach Workbook

Enrichment

Quick Check

Center Activities

Home-School Connection

Vocabulary Cards

Etools electronic manipulatives

The Language of Math Topic 7

Vocabulary Cards

Vocabulary Activities

Reading Comprehension and Problem Solving

Written and Oral Language in Math


Houghton Mifflin Everyday Counts Calendar Math Calendar, Counting Tape, Daily Depositor, Coin Counter,Clock

Formative

Teacher Observations

Daily Spiral Review Master

7-2, 7-3, 7-5

Quick Check 7-2, 7-3, 7-5

Close and Assess 7-2, 7-3, 7-5

TCAP Reteaching, pp 160-161, Sets B-E

Common Core Connection:

High-level tasks (Please visit www.TNCORE.org)

Teacher Generated Assessing/Advancing Questions

Please visit

www.elementarymathmcs.weebly.com for additional CCSSM instructional

resources and strategies.

Intervention Stanford Math ELL Visual Learning ELL Assessment Strategies Differentiated Centers RTI - Diagnostic and Intervention Systems Reteach Master 7-2, 7-3, 7-5

Enrichment Stanford Math Differentiated Centers Enrichment Master 7-2, 7-3, 7-5

Stanford Math http://stanfordmathproxy.mcsk12.net/

www.pearsonsuccessnet.com

www.eduplace.com/math/mw

www.education.ti.com

www.tnelc.org/math

stemresources.com

illuminations.nctm.org/indes.aspx

elementary.nettrekker.com/subject/?ctgry_id=E102494

streaming.discoveryeducation.com/

www.internet4classrooms.com

www.sheppardsoftware.com

www.henryanker.com

www.woodlands-junior.kent.sch.uk/ Examples of High Rich Task

www.exemplars.com

www.TNCORE.org enVision Math Technology Pouch: (all material on CD’s are included on-line except for Quiz Show)

Visual Learning Animations

Exam View

Electronic Teachers Edition

Electronic Student Edition

Electronic Manipulatives enVision Student e-tools

www.pearsonsuccessnet.com – Under My Teacher Resources click Student Edition; click to open, click “e” to open e-tools

enVision Teacher e-tools

www.pearsonsuccessnet.com – Under My Teacher Resources click Teacher’s Edition; click to open, click “e” to open e-tools

Teachers should emphasize the use of calculators which students are permitted to use on the TCAP Assessment. Texas Instrument (TI) 15 is recommended.

Weeks 1-3



http://stanfordmathproxy.mcsk12.net/

http://www.pearsonsuccessnet.com/

http://www.internet4classrooms.com/

http://www.sheppardsoftware.com/

http://www.henryanker.com/

http://www.woodlands-junior.kent.sch.uk/

http://www.exemplars.com/









GLE 0406.2.2 Develop fluency with multiplication and single-digit division. GLE 0406.2.6 Solve problems involving whole numbers, fractions, and/or decimals using all four arithmetic operations. Enduring Understandings: There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients. The remainder when dividing must be less than the divisor. The nature of the question asked determines how to interpret and use the remainder.

Knowledge and Skills Outcomes

(Checks for Understanding) Resources and Instructional Strategies Assessments Intervention/Enrichment

Technology and Additional

Web Based Resources

SPI 0406.2.11 Solve problems using whole number multi-digit multiplication. SPI 0406.2.12 Solve problems using whole number division with one-or-two digit divisors Common Core Connection: CC.4.OA.3 CC.NBT.6

Learning Targets:

I can choose the correct operation to perform at each step of a multi-step word problem.

I can interpret remainders in word problems.

I can use mental math or estimation strategies to check if my answer is reasonable.

I can solve division of multi-digit number by one-digit number using the properties of operation and equations.

I can explain my chosen strategy.

0406.2.13 Solve multi-step problems of various types using whole numbers, fractions, and decimals. 0506.1.3 (Prepares) Explore different methods of estimation including rounding and truncating. 0406.2.14 Understand the role of the remainder in division.

Essential Questions: 1. How can you use place

value and patterns to help you divide mentally?

2. When and how do you estimate quotients to solve problems?

3. What does it mean when you divide and some are left over?

Academic Vocabulary Remainder Estimate

EnVision Teacher’s Edition. Topic 7. pp. 140a – 151b Lessons 7-7 Two Question Problems

Topic 8. pp. 169a – 169b: Lesson 8-2 Estimating Quotients (4.OA.3)

EnVision Math Transitioning to Common Core, Student Lesson 8-3A, pg.14 - 15 “Estimating Quotients for Greater Dividends”

Lesson 8-3 Dividing with Remainders (4.NBT.6, 4.OA.3)

enVision Math Student’s Edition pp. 156-157, pp. 166-169


WorldScapes Readers, “First in Space” p.6-7 ( Topic 7)

Math Project p.141 ( Topic 7)

WorldScapes Readers, “All Tied Up” p.8-9 ( Topic 8)

Math Project p.163 ( Topic 8) Teacher–selected Pearson ancillary resources

Daily Spiral Review

Problem of the Day




Enrichment

Quick Check

Center Activities


Vocabulary Cards


The Language of Math Topic 7 & 8

Vocabulary Cards





WorldScapes Readers, “All Tied Up” p.8-9

Houghton Mifflin Everyday Counts Calendar Math Calendar, Counting Tape, Daily Depositor, Coin Counter,Clock

Formative



7-7, 8-2, 8-3



TCAP Test Prep (Topic 7)

TCAP Reteaching , pg 161, Set F (Topic 7)

TCAP Reteaching , pg 192, Set B & C (Topic 8)

Summative Topic 7 Multiple Choice Test Master

Alternate Assessments:

For Topic 7

Free- Response Test Master

Performance Assessment Master




Please visit

www.elementarymathmcs.weebly.com

for additional CCSSM instructional


Intervention Stanford Math ELL Visual Learning ELL Assessment Strategies Differentiated Centers RTI - Diagnostic and Intervention Systems Reteach Master 7-7, 8-2,

8-3

Enrichment Stanford Math Differentiated Centers Enrichment Master 7-7, 8-

2, 8-3





www.tnelc.org/math

stemresources.com






www.henryanker.com


www.exemplars.com



Exam View








Weeks 1-3


















GLE 0406.2.2 Develop fluency with multiplication and single-digit division Enduring Understandings: Basic facts and place value patterns can be used to divide multiples of 10 and 100 by 1-digit numbers. The relationship between multiplication and division and estimation can be used to determine the place value of the largest digit in a quotient. Every counting number is divisible by 1 and itself, and some counting numbers are also divisible by other numbers. Some problems can be solved by first finding and solving a sub-problem(s) and then using that answer.

Knowledge and Skills and Mathematical Practices

Outcomes



Web Based Resources

SPI 0406.2.12 Solve problems using whole number division with one-or-two digit divisors. Common Core Connection: CC.4.NBT.6 Learning Targets:



0406.2.4 Understand and use a reliable algorithm for multiplying multi-digit numbers and dividing numbers b a single-digit divisor accurately and efficiently. 0406.2.6 Divide three-digit whole numbers by one-digit divisors fluently with pencil and paper.

Essential Questions (Topic 8) 1. How does a digit’s position

affect its value? 2. How can you use place

value and patterns to help you divide mentally?

3. When and how do you estimate quotients to solve problems?

4. What does it mean when you divide and some are left over?

5. What do you do when there are not enough hundreds to divide?

6. How can you use multiplication to find all the factors of a number?

7. How can you sort numbers by their factors?

8. What hidden questions lie within a multiple-step problem?

EnVision Teacher’s Edition. Topic 8. pp. 174a – 181b:

Lessons 8-5 Dividing 2-Digit by 1-Digit Numbers( 4.NBT.6)

Lessons 8-6 Dividing 3-Digit by 1-Digit Numbers (4.NBT.6)

Lessons 8-7 Deciding Where to Start Dividing (4.NBT.6)

enVision Math Student’s Edition pp. 174-181 Interdisciplinary Connections


Math Project p.163

Teacher–selected Pearson ancillary resources

Daily Spiral Review

Problem of the Day




Enrichment

Quick Check

Center Activities


Vocabulary Cards


The Language of Math Topic

Vocabulary Cards





Houghton Mifflin Everyday Counts Calendar Math Calendar, Counting Tape, Daily Depositor, Coin Counter, Clock, Graph

Formative



8-5, 8-6, 8-7



TCAP Reteaching, Set E-Set G, pp 192-193

Tennessee Handbook Lesson TN-1 The TN Handbook Lessons and Practice offer practice, reinforcement, and review of TB SPIs and CFUs. You may choose to teach this lesson now but it recommended that these lessons be taught during TCAP Blitz.




Please visit




8-7


6, 8-7





www.tnelc.org/math

stemresources.com






www.henryanker.com


www.exemplars.com

www.TNCORE.org

enVision Math Technology Pouch: (all material on CD’s are included on-line except for Quiz Show)


Exam View



Electronic Manipulatives

enVision Student e-tools





Weeks 1-3


















GLE 0406.2.2 Develop fluency with multiplication and single-digit division. GLE 0406.2.3 Identify prime and composite numbers. GLE 0406.2.6 Solve problems involving whole numbers, fractions, and/or decimals using all four arithmetic operations. Enduring Understandings: Some counting numbers have exactly two factors; others have more than two. Some problems can be solved by first finding and solving a sub-problem(s) and then using that answer.


Outcomes



Web Based Resources

SPI 0406.2.12 Solve problems using whole number division with one-or-two digit divisors. SPI 0406.2.4 Find factors, common factors, multiples, and common multiples of two numbers. Common Core Connection: CC.4.NBT.6 Learning Targets:



Essential Question: 1. How does a digit’s position affect

its value?

0406.2.4 Understand and use a reliable algorithm for multiplying multi-digit numbers and dividing numbers by a single-digit divisor accurately and efficiently. 0406.2.6 Divide three-digit whole numbers by one-digit fluently with pencil and paper. 0406.2.13 Solve multi-step problems of various types using whole numbers, fractions, and decimals. 0406.1.9 Develop a story problem that illustrates a given multiplication or division number sentence

Academic Vocabulary Prime number Composite number Factors

EnVision Teacher’s Edition. Topic 8, pp. 182a – 187b: Lesson 8-8 Factors (4.NBT.6) Lesson 8-9 Prime and Composite Numbers (4.NBT.6) Lesson 8-10 Multiple-Step Problems (Problem Solving) (4.NBT.6)

EnVision Student’s Edition pp. 182-187

Teacher–selected Pearson ancillary resources

Daily Spiral Review

Problem of the Day




Enrichment

Quick Check

Center Activities


Vocabulary Cards


The Language of Math Topic 8

Vocabulary Cards



Written and Oral Language in Math \

Houghton Mifflin Everyday Counts Calendar Math Calendar, Counting Tape, Daily Depositor, Coin Counter, Clock , Graph

Formative



8-8, 8-9, 8-10

Quick Check 8-8, 8-9, 8-10


TCAP Test Prep, pp 188-189

TCAP Reteaching, Set H-Set K, pp 192-193

Tennessee Handbook Lesson TN-2 The TN Handbook Lessons and Practice offer practice, reinforcement, and review of TN SPIs and CFUs. You may choose to teach this lesson now but it recommended that these lessons be taught during TCAP Blitz. Summative

Multiple Choice Test Master Topic 8

Cumulative Test Topics 1-8, pp 95 – 98

Benchmark Test Topics 5-8, pp 99-109 Alternate Assessments:

Free Response Test Master





Please visit www.elementarymathmcs.weebly.com for

additional CCSSM instructional resources

and strategies.


8-10


9, 8-10





www.tnelc.org/math

stemresources.com






www.henryanker.com


www.exemplars.com



Exam View








Weeks 4-6


















GLE 0406.2.6 Solve problems involving whole numbers, fractions, and/or decimals using all four arithmetic operations. GLE 0406.1.3 Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas. GLE 0406.2.4 Identify prime and composite numbers. GLE 0406.2.6 Solve problems involving whole numbers, fractions, and/or decimals using all four arithmetic operations.


Outcomes



Web Based Resources

SPI 0406.4.1 Classify lines and line segments as parallel, perpendicular, or intersecting.. Common Core Connection: CC.4.G.1 CC.4.MD.5 Learning Targets:

I can draw an example of a point, line, line segment, ray, right angle, acute angle, obtuse angle, perpendicular lines, and parallel lines.

I can look for and identify the following in a given two-dimensional figure: Point Lines, Parallel lines, Perpendicular lines, Line segments, Ray, Angle, Right angle, Acute angle, and Obtuse angle.

I can identify parts of an angle.

Essential Question:

1. How does geometry better describe objects?

0406.4.3 Classify angles and triangles as obtuse, acute, or right. 0406.4.4 Measure and draw angles. Academic Vocabulary Point Lines Parallel lines Plane Intersecting lines Perpendicular lines Line segments Ray Angle Right angle Acute angle Obtuse angle Straight angle Degree Protractor

EnVision Teacher’s Edition Topic 9. pp. 196a – 201b Lesson 9-1 Points, Lines, and Planes (4.G.1) Lesson 9-2 Line Segments, Rays, and Angles (4.G.1, 4.MD.5) Lesson 9-3 Measuring Angles (4.MD.5a, 4.MD.5b) EnVision Math Transitioning to Common Core Lesson 9-3A, pg.22–23, “Understanding Angles and Unit Angles” Lesson 9-4A, g.24-25, “Measuring with Unit Angles” EnVision Student’s Edition pp. 196-201


WorldScapes Readers, “Dazzling Designs” p.12-13


Daily Spiral Review

Problem of the Day




Enrichment

Quick Check

Center Activities


Vocabulary Cards


The Language of Math

Vocabulary Cards





Formative Teacher Observations


9-1, 9-2, 9-3



TCAP Reteaching, pp.212, Sets A-C

Summative

Team/ Teacher -created assessment from Lessons 9-1, 9-2, 9-3




Please visit





9-3


2, 9-3





www.tnelc.org/math

stemresources.com






www.henryanker.com


www.exemplars.com



Exam View








Weeks 4-6


















GLE 0406.4.1 Understand and use the properties of lines, segments, angles, polygons, and circles. GLE 0406.1.1 Use mathematical language symbols and definitions while developing mathematical reasoning. GLE 0406.1.2 Apply and adapt a variety of appropriate strategies to problem solving including estimation and reasonableness.


Outcomes



Web Based Resources

SPI 0406.4.4 Identify acute, obtuse, and right angles in 2-dimensional shapes. SPI 0406.1.4 Compare objects with respect to a given geometric or physical attribute and select appropriate measurement instrument.

Common Core Connection: CC.4.G.2

Learning Targets:

I can classify two-dimensional shapes into categories based on the angles.

I can identify a right triangle.

Essential Question (Topic 9): 1. How does geometry better

describe objects? 2. What are some geometric

names for lines? 3. What geometric terms describe

types of angles? 4. How can you draw an angle? 5. How do you identify polygons? 6. How can you classify triangles? 7. How can you classify

quadrilaterals?

8. How can you make and test generalizations about right triangles?

0406.4.5 Determine if a figure is a polygon. Academic Vocabulary Polygon Sides Vertex Triangle Quadrilateral Pentagon Hexagon Octagon Rhombus Trapezoid Rectangle Square Isosceles triangle Scalene triangle Right triangle Obtuse triangle Acute triangle

EnVision Teacher’s Edition Topic 9. pp. 202a – 207b Lesson 9-4 Polygons (4.G.2) Lesson 9-5 Triangles (4.G.2) Lesson 9-6 Quadrilaterals (4.G.2) EnVision Student’s Edition pp. 202-207


WorldScapes Readers, “Dazzling Designs” p.12-13


Daily Spiral Review

Problem of the Day




Enrichment

Quick Check

Center Activities


Vocabulary Cards



Vocabulary Cards







9-4, 9-5, 9-6




TCAP Reteaching, pp.213, Sets D-F

Tennessee Handbook TN-3 & TN-4 The TN Handbook Lessons and Practice offer practice, reinforcement, and review of TN SPIs and CFUs. You may choose to teach this lesson now but it recommended that these lessons be taught during TCAP Blitz.

Summative

Multiple Choice Test Master Topic 9







Please visit





9-6


5, 9-6





www.tnelc.org/math

stemresources.com






www.henryanker.com


www.exemplars.com



Exam View








Weeks 4-6



















Outcomes



Web Based Resources

SPI 0406.2.5 Generate equivalent forms of common fractions and decimals and use them to compare size. Common Core Connection: CC.4.NF.1

Learning Targets:

I can explain why fractions are equivalent using models.

I can generate equivalent fractions by multiplying and dividing the numerator and denominator by the same number.

Essential Questions: Why express quantities, measurements, and number relationships in different ways?

0306.2.11 (Reviews) Identify fractions as parts of whole units, as parts of sets, as locations on number lines, and as division of two whole numbers. 0406.1.2 Identify the range of appropriate estimates, including over-estimate and under-estimate.

Academic Vocabulary Fraction Denominator Numerator Benchmark fraction

EnVision Teacher’s Edition. Topic 10. pp. 216a – 223b

Lesson 10-1 Regions and Sets (4.NF.1)

Lesson 10-2 Fractions and Division (4.NF.1)

Lesson 10-3 Estimating Fractional Amounts (4.NF.1)

EnVision Student’s Edition pp. 216 - 223


WorldScapes Readers, “All Roads Lead to Rome” p.4-5


Daily Spiral Review

Problem of the Day




Enrichment

Quick Check

Center Activities


Vocabulary Cards



Vocabulary Cards






Daily Spiral Review Master 10-1,10-2, 10-3

Quick Check 10-1, 10-2, 10-3


TCAP Reteaching, pp.224 Sets A-C

Summative Team-created assessment from Lessons 10-1, 10-2, 10-3




Please visit

www.elementarymathmcs.weebly.com for additional CCSSM instructional resources

and strategies.

Intervention Stanford Math ELL Visual Learning ELL Assessment Strategies Differentiated Centers RTI - Diagnostic and Intervention Systems Reteach Master 10-1, 10-

2, 10-3

Enrichment Stanford Math Differentiated Centers Enrichment Master 10-1,

10-2, 10-3





www.tnelc.org/math

stemresources.com






www.henryanker.com


www.exemplars.com

www.TNCORE.org



Exam View







www.pearsonsuccessnet.com – Under My Teacher Resources click Teacher’s Edition; click to open, click “e” to open e-tools Teachers should emphasize the use of calculators which students are permitted to use on the TCAP Assessment. Texas Instrument (TI) 15 is recommended.

Weeks 7-9


















GLE 0406.4.1 Understand and use the properties of lines, segments, angles, polygons, and circles. GLE 0406.1.1 Use mathematical language symbols and definitions while developing mathematical reasoning. GLE 0406.2.4 Understand and use the connections between fractions and decimals. GLE 0406.1.2 Apply and adapt a variety of appropriate strategies to problem solving including estimation and reasonableness of the solution.


Outcomes



Web Based Resources

SPI 0406.2.5 Generate equivalent forms of common fractions and decimals and use them to compare size. SPI 0406.2. Convert improper fractions into mixed numbers and/or decimals. Common Core Connection: CC.4.NF.1

Learning Targets:

I can explain why fractions are equivalent using models.

I can generate equivalent fractions by multiplying and dividing the numerator and denominator by the same number.

0406.2.8 Generate equivalent forms of whole numbers, decimals, and common fractions

Essential Questions (Topic 10): 1. Why express quantities,

measurements, and number relationships in different ways? 1. How

can you show parts of a region?

2. How can you estimate parts?

3. How can you find 2 fractions that name the same part of a whole?

4. How do you write a fraction in simplest form?

5. How can you use benchmark fractions to compare fractions?

6. How do you write a good mathematical explanation?

Academic Vocabulary Equivalent Simplest form Whole number Improper fraction Mixed number

EnVision Teacher’s Edition. Topic 10. pp. 224a – 233b Lessons 10-4 Equivalent Fractions (4.NF.1)

EnVision Math Transitioning to Common Core Lesson 10-5A, pg.28-29, “Number Lines and Equivalent Fractions” Lessons 10-5 Fractions in Simplest Form (4.NF.1)

Lessons 10-6 Improper Fractions and Mixed Numbers

(4.NF.6)

EnVision Student’s Edition pp. 224-233




Daily Spiral Review

Problem of the Day




Enrichment

Quick Check

Center Activities


Vocabulary Cards



Vocabulary Cards






Daily Spiral Review Master 10-4,10-5, 10-6

Quick Check 10-4,10-5, 10-6

Close and Assess 10-4,10-5, 10-6

TCAP Reteaching, pp.245-246, Sets D-G

Summative Team-created assessment from Lessons 10-4,10-5, 10-6




Please visit



Intervention Stanford Math ELL Visual Learning ELL Assessment Strategies Differentiated Centers RTI - Diagnostic and Intervention Systems

Reteach Master 9-1, 9-2, 9-3

Enrichment Stanford Math Differentiated Centers

Enrichment Master 9-1, 9-2,

9-3





www.tnelc.org/math

stemresources.com






www.henryanker.com


www.exemplars.com

www.TNCORE.org



Exam View









Weeks 7-9


















GLE 0406.2.4 Understand and use the connections between fractions and decimals


Outcomes



Web Based Resources

SPI 0406.2.5 Generate equivalent forms of common fractions and decimals and use them to compare size. SPI 0406.2.6 use symbols <, >, and = to compare common fractions and decimals in both increasing and decreasing order. Common Core Connection: CC.4.NF.2

Learning Targets:

I can explain that comparing two fractions is valid only when they refer to the same whole.

I can compare two given fractions by generating equivalent fractions with common denominators.

I can record the comparison using symbols (<, >, and = ) and justify the comparison.

Essential Questions (Topic 10): 1. Why express quantities,

measurements, and number relationships in different ways? 1. How

can you show parts of a region?

2. How can you estimate parts?

3. How can you find 2 fractions that name the same part of a whole?

4. How do you write a fraction in simplest form?

5. How can you use benchmark fractions to compare fractions?

6. How do you write a good mathematical explanation?

EnVision Teacher’s Edition. Topic 10. pp. 234a – 239

Lesson 10-7 Comparing Fractions (4.NF.2) Lesson 10-8 Ordering Fractions (4.NF.2) Lesson 10-9 Writing to Explain (4.NF.2) EnVision Student’s Edition pp. 234-2369




Daily Spiral Review

Problem of the Day




Enrichment

Quick Check

Center Activities


Vocabulary Cards



Vocabulary Cards







10-7,10-8,10-9

Quick Check 10-7,10-8,10-9

Close and Assess 10-7,10-8,10-9


TCAP Reteaching, pp.244-245, Sets G-J

Summative Multiple Choice Test Master Topic 10







Please visit



Intervention Stanford Math ELL Visual Learning ELL Assessment Strategies Differentiated Centers RTI - Diagnostic and Intervention Systems Reteach Master10-7,10-

8,10-9

Enrichment Stanford Math Differentiated Centers Enrichment Master 10-7,10-

8,10-9





www.tnelc.org/math

stemresources.com






www.henryanker.com


www.exemplars.com



Exam View








Weeks 7-9













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