schoolwires.henry.k12.ga.us · web viewrevised october 23, 2012. page 19 of 20. revised october...

HENRY COUNTY SCHOOLS

STANDARDS-BASED REPORT CARDTEACHER SUPPORT MATERIALS

MATHEMATICS

GRADE 4GRADE 4

Curriculum MapMATHEMATICS

Henry County Schools(adapted from Georgia Department of Education)

UPDATED JULY 2013Common Core Georgia Performance Standards

SEMESTER 1 SEMESTER 2Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 85 weeks 4 weeks 3 weeks 6 weeks 5 weeks 5 ½ weeks 5 ½ weeks 2 weeks

Whole Numbers, Place

Value and Rounding in

Computation

Multiplication and Division of

Whole Numbers

Fraction Equivalents

Operations with Fractions

Fractions and Decimals

Geometry Measurement Show What We Know

MCC4.NBT.1 MCC4.NBT.2MCC4.NBT.3 MCC4.NBT.4MCC4.OA.3

MCC4.OA.1MCC4.OA.2MCC4.OA.3 MCC4.OA.4MCC4.OA.5MCC4.NBT.5MCC4.NBT.6

MCC4.NF.1MCC4.NF.2

MCC4.NF.3MCC4.NF.4

MCC4.NF.5MCC4.NF.6MCC4.NF.7

MCC4.G.1MCC4.G.2MCC4.G.3

MCC4.MD.1MCC4.MD.2MCC4.MD.3MCC4.MD.4MCC4.MD.5 MCC4.MD.6 MCC4.MD.7

ALL

These units were written to build upon concepts from prior units, so later units contain tasks that depend upon the concepts addressed in earlier units.All units will include the Mathematical Practices and indicate skills to maintain.

NOTE: Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics.

Grades 3-5 Key: G= Geometry, MD=Measurement and Data, NBT= Number and Operations in Base Ten, NF = Number and Operations, Fractions, OA = Operations and Algebraic Thinking.

Fourth Grade Yearlong Mathematics Rubric 1st Nine Weeks

The following standards are addressed for the first time in the FIRST NINE WEEKS

Standard and Element(s)

Critical Need (0)The student is not making progress toward achieving

the standard

Emerging (1)The student

demonstrates limited or minimum progress

or is unable to:

Progressing (2) The student is progressing

toward achievement but inconsistently:

Meets (3)The student consistently

and independently:

Exceeds (4)The student, with

evidence of exceeding, consistently and independently:

Evidence/Notes

Uses strategies involving the four operations with whole numbers to solve problems

MCC4.OA.1 MCC4.OA.2 MCC4.OA.3

The student is not making progress toward achieving the standard

Demonstrate fluency and the ability to solve problems involving the operations of whole numbers


Applies and reasons through multiple strategies, which demonstrates fluency and flexibility, and the ability to solve multi-step problems involving the operations of whole numbers

Represents verbal statements of multiplicative comparisons as multiplication equations

Demonstrates

understanding of the relationship between dividend, divisor, and quotient and understands and interprets any remainder in context

Satisfies all requirements of “meeting the standard” for a score of 3 AND Consistently applies and reasons through multiple strategies which demonstrates fluency and flexibility with whole numbers AND decimals numbers

Students should know which operations are needed to solve the problem. Drawing pictures or using models will help students understand what the problem is asking. They should check the reasonableness of their answer using mental computation and estimation strategies.





the standard



or is unable to:




and independently:



Evidence/Notes

Recognizes, understands and uses factors and multiples

MCC4.OA.4


Recognize, understand and use factors and multiples

Understand and recognize prime and composite numbers

Recognizes, understands and uses factors and multiples in the range 1 to 100

Understands and recognize prime and composite numbers

Recognizes, understands, and uses factors and multiples within 1 to 100, appropriatelyDemonstrates an understanding of prime and composite numbers and is able to fluently recall them and use them in appropriate mathematical situations

Understands and uses divisibility for common factors

Uses knowledge of factors, multiples, and divisibility beyond 100 and sees the patterns in numbers to make generalizations about given numbers that extend beyond the context of the problem

This standard requires students to demonstrate understanding of factors and multiples, divisibility, and characteristics (including odd/even and prime/composite) of whole numbers.Important Fact: Prime numbers have exactly two factors, the number one and their own number





the standard



or is unable to:




and independently:



Evidence/Notes

Generates and analyzes patterns

MCC4.OA.5


Generate numerical or geometric patterns that follow a given ruleIs unable to identify relationships in the patterns and is unable to describe and make generalizations from those patterns

Generates numerical or geometric patterns that follow a given ruleInconsistently identifies relationships in the patterns

Inconsistently describes or makes generalizations from patterns

Generates numerical and/or geometric patterns that follow a given rule

Consistently identifies relationships in the patterns and/or describe and make generalizations based on apparent features of the pattern that were not explicit in the rule itself

Consistently and independently justifies reasoning for why the rule works for all numbers in the pattern

Analyzes and compares the relationships between two numerical patterns using 2 given rules with more complex numbers and describe generalizations using more complex numerical patterns

As students generate numeric patterns for rules, they should be able to “undo” the pattern to determine if the rule works with all of the numbers generated. In analyzing the pattern, students need to determine how to get from one term to the next term.





the standard



or is unable to:




and independently:



Evidence/Notes

Identifies and applies understanding of place value for multi-digit whole numbers

MCC4.NBT.1 MCC4.NBT.2 MCC4.NBT.3


Demonstrate an understanding of place value through number recognition, comparison, or rounding

Demonstrates an understanding of place value through number recognition, comparison, and rounding

Demonstrates an understanding of place value through number recognition, comparison, and rounding. The student is also able to create numbers that meet specific criteria. The student appropriately uses >, =, and < symbols to record results of comparisons

The student is able to round multi-digit whole numbers to any place up to 1,000,000

Is able to extend understanding of place value for multi-digit whole numbers to decimals and apply reasoning with multi- digit whole numbers to decimals to the hundredths

Students also need to create numbers that meet specific criteria. Example: rounding to digits other than the leading digit (round 23,960 to the nearest hundred). Students should also begin to develop some rules for rounding, building off the basic strategy of; “Is 48 closer to 40 or 50?” Students need to generalize the rule for much larger numbers and rounding to values that are not the leading digit





the standard



or is unable to:




and independently:



Evidence/Notes

Uses place value understanding and properties of operations to perform multi-digit arithmetic



Generalize an understanding of place value to 1,000,000 within the context of arithmetic

Apply an understanding of models to develop, discuss, and use efficient, accurate, and generalizable methods of multi-digit arithmetic

Generalizes an understanding of place value to 1,000,000 within the context of arithmetic

Apply an understanding of models to develop, discuss, or use efficient, accurate, or generalizable methods of multi-digit arithmetic


Demonstrates and applies an understanding of models to develop, discuss, and use efficient, accurate, and generalizable methods of multi-digit arithmetic. The student is able to consistently illustrate and explain calculations using a variety of models and representations

Is able to extend understanding of properties to perform multi-digit arithmetic and apply the same understanding and reasoning for decimal numbers to the hundredths

Students develop strategies that they understand, can explain, and can think about, rather than merely follow a sequence of directions that they don't understand.Number Talks help students learn from each other and acquire efficient strategies for number computation.Each teacher is encouraged to include a scheduled Number Talk in the schedule for each day (10 – 15 minutes of the day).

Revised October 23, 2012 of 20

Fourth Grade Yearlong Mathematics Rubric 2nd Nine Weeks

The following standards are addressed for the first time in the SECOND NINE WEEKS



the standard



or is unable to:



Meets (3)The student

consistently and independently:



Evidence/Notes

Uses strategies involving the four operations with whole numbers to solve problems

MCC4.OA.1 MCC4.OA.2 MCC4.OA.3



Demonstrates fluency and the ability to solve problems involving the operations of whole numbers

Applies and reasons through multiple strategies, which demonstrates fluency and flexibility, and the ability to solve multi- step problems involving the operations of whole numbers

Represents verbal statements of multiplicative comparisons as multiplication equations

Demonstrates understanding of the relationship between dividend, divisor, and quotient and understands and interprets any remainder in context

Satisfies all requirements of “meeting the standard” for a score of 3 AND Consistently applies and reasons through multiple strategies which demonstrates fluency and flexibility with whole numbers AND decimals numbers

Students should know which operations are needed to solve the problem. Drawing pictures or using models will help students understand what the problem is asking. They should check the reasonableness of their answer using mental computation and estimation strategies.






the standard



or is unable to:







Evidence/Notes

Recognizes, understands and uses factors and multiples

MCC4.OA.4


Recognize, understand and use factors and multiples

Understand and recognize prime and composite numbers

Recognizes, understands and uses factors and multiples in the range 1 to 100

Understands and recognize prime and composite numbers

Recognizes, understands, and uses factors and multiples within 1 to 100, appropriately

Demonstrates an understanding of prime and composite numbers and is able to fluently recall them and use them in appropriate mathematical situations

Understands and uses divisibility for common factors

Uses knowledge of factors, multiples, and divisibility beyond 100 and sees the patterns in numbers to make generalizations about given numbers that extend beyond the context of the problem

This standard requires students to demonstrate understanding of factors and multiples, divisibility, and characteristics (including odd/even and prime/composite) of whole numbers.Important Fact: Prime numbers have exactly two factors, the number one and their own number.






the standard



or is unable to:







Evidence/Notes

Generates and analyzes patterns

MCC4.OA.5


Generate numerical or geometric patterns that follow a given rule

Identify relationships in the patterns

Describe and make generalizations from those patterns

Generates numerical or geometric patterns that follow a given rule

Identifies relationships in the patterns

Describes or makes generalizations from patterns

Generates numerical and/or geometric patterns that follow a given rule

Identifies relationships in the patterns and/or describe and make generalizations based on apparent features of the pattern that were not explicit in the rule itself

Justifies reasoning for why the rule works for all numbers in the pattern

Analyzes and compares the relationships between two numerical patterns using 2 given rules with more complex numbers and describe generalizations using more complex numerical patterns

As students generate numeric patterns for rules, they should be able to “undo” the pattern to determine if the rule works with all of the numbers generated. In analyzing the pattern, students need to determine how to get from one term to the next term

Identifies and applies understanding of place value for multi-digit whole numbers


Demonstrate an understanding of place value through number recognition, comparison, or

Demonstrates an understanding of place value through number recognition, comparison, and

Demonstrates an understanding of place value through number recognition,

Is able to extend understanding of place value for multi-digit whole numbers to decimals

Students also need to create numbers that meet specific criteria. Example:






the standard



or is unable to:







Evidence/Notes

Uses place value understanding and properties of operations to perform multi-digit arithmetic



Generalize an understanding of place value to 1,000,000 within the context of arithmetic

Apply an understanding of models to develop, discuss, and use efficient, accurate, and generalizable methods of multi- digit arithmetic


Applies an understanding of models to develop, discuss, or use efficient, accurate, or generalizable methods of multi- digit arithmetic


Demonstrates and applies an understanding of models to develop, discuss, and use efficient, accurate, and generalizable methods of multi-digit arithmetic. The student is able to consistently illustrate and explain calculations using a variety of models and representations

Extends understanding of properties to perform multi-digit arithmetic and applies the same understanding and reasoning for decimal numbers to the hundredths

Students develop strategies that they understand, can explain, and can think about, rather than merely follow a sequence of directions that they don't understand.Number Talks help students learn from each other and acquire efficient strategies for number computation. Each teacher is encouraged to include a scheduled Number Talk in the schedule for each day (10 – 15 minutes of the day)






the standard



or is unable to:







Evidence/Notes

Explain and use fraction equivalence and ordering in problem solving contexts

MCC4.NF.1 MCC4.NF.2


Use models to compare two fractions with different denominators in a problem solving context

Creates and/or uses models to compare two fractions with different denominators in a problem solving context

Independently and consistently creates and/or uses models to compare two fractions with different denominators in a problem solving context

Consistently and independently uses benchmark fractions and number sense of fractions to estimate mentally and assess reasonableness when solving problems in context

Independently and consistently explains and uses fraction equivalence and ordering of fractions involving mixed numbers and improper fractions in problem solving contexts

Student is able to demonstrate an understanding of fraction equivalence and operations with fractions through modeling. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions.The student should be able to use benchmark fractions as an estimation strategy.






the standard



or is unable to:







Evidence/Notes

Apply basic whole number operations to build fractions from unit fractions

MCC4.NF.3 MCC4.NF.4


Is unable to model and build fractions from unit fractions.

Is unable to solve problems using visual models and write equations to represent the problems.

Is unable to add or subtract fractions (including mixed numbers) using strategies and fractional number sense

Is unable to solve word problems involving the multiplication of a fraction by a whole number using a variety of strategies

Inconsistently models and builds fractions from unit fractions.

Inconsistently solves problems using visualInconsistently writes equations to represent problems.

Inconsistently uses strategies for adding or subtracting fractions using fractional number sense

Inconsistently solves word problems involving the multiplication of a fraction by a whole number using a variety of strategies

Independently and consistently creates models and applies whole number fractions from unit fractions.

Independently and consistently solves problems using visual models and writes equations to represent problems.

Consistently and independently uses strategies for adding or subtracting fractions using fractional number sense

Consistently and independently solves word problems involving the multiplication of a fraction by a whole number using a variety of strategies

Demonstrates mastery as described in the “meets” column AND Applies basic whole number operations to other fractional operations (including multiplication of fractions by fractions and division of fractions)

Solves contextual problems involving operations of fractions with unlike denominators using numerous visual models and writes equations to represent the problems

Students are expected to solve contextual problems using visual models and write equations to represent the problems.Students should be able to solve the problems using visual models and write equations to represent the problems in order to demonstrate understanding.

Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators, in general. But, addition and subtraction with unlike denominators in general is not a requirement at this grade


Fourth Grade Yearlong Mathematics Rubric 3rd Nine Weeks

The following standards are addressed for the first time in the THIRD NINE WEEKS



the standard



or is unable to:




and independently:


evidence of exceeding,

consistently and

Evidence/Notes

Understand decimal notation for fractions, and compare decimal fractions

MCC4.NF.5 MCC4.NF.6 MCC4.NF.7


Is unable to compare and connect fractions to decimals (up to the hundredths)

Is unable to demonstrate flexibility with converting fractions to decimals and decimals to fractions

Inconsistently compares and connects fractions to decimals (up to the hundredths)

Demonstrates flexibility with converting fractions to decimals and/or decimals to fractions using fractional and decimal number sense

Independently and consistently compares and connects fractions to decimals (up to the hundredths) using >, =, and < symbols

Demonstrates flexibility with converting fractions to decimals and decimals to fractions using fractional number sense (uses fractions and decimals interchangeably).

Extends understanding of decimal fractions and apply understanding to all four operations through visual models and equations

Extends understanding of decimal fractions to non-decimal fractions

Applies understanding to all four operations through visual models and equations

Uses fractions and decimals interchangeably based on the context given in a problem

Students should be able to model fractions of tenths and hundredths and express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.When comparing two decimal fractions they need to demonstrate understanding as it relates to the same whole.Students should acquire fractional number sense of decimal fractions (without needing to use the long division procedure).


Fourth Grade Yearlong Mathematics Rubric 3rd Nine Weeks

The following standards are addressed for the first time in the THIRD NINE WEEKS



the standard



or is unable to:




and independently:



consistently and

Evidence/Notes

Draw and identify lines and angles, and classify shapes by properties of their lines and angles (including line of symmetry).

MCC4.G.1 MCC4.G.2 MCC4.G.3


Does not draw and/or identify points, lines, line segments, rays and angles in 2D shapes and/or use these characteristics to classify shapes

Cannot identify characteristics of right triangles

Is unable to identify line‐

symmetric figures or draw lines of symmetry.

Inconsistentlydraws and identifies points, lines, line segments, rays and angles in 2D shapes and/or inconsistently uses these characteristics to classify shapesIdentifies characteristics of right triangles

Identifies line‐symmetric figures or draw lines of symmetry.

Consistently and independently draws and identifies points, lines, line segments, rays and angles in 2D shapes and/or inconsistently uses these characteristics to classify shapes

Identifies right triangles

Identifies line‐symmetric figures and is able to consistently draw lines of symmetry.

Extends understanding of the properties of 2-D figures by applying this knowledge to 3-D figures (using points, lines, line segments, rays and angles, as well as the presence of parallel and perpendicular lines and lines of symmetry)

Students must be able to identify and classify right triangles in order to meet this standard.

Students must be able to use properties of parallel and perpendicular lines to classify 2-D figures.


Fourth Grade Yearlong Mathematics Rubric 4th Nine Weeks

The following standards are addressed for the first time in the FOURTH NINE WEEKS



the standard



or is unable to:




and independently:



consistently and

Evidence/Notes

Solve problems involving conversion of measurements from a larger unit to a smaller unit within the same systemMCC4.MD.1 MCC4.MD.2


Unable to solve multi- step problems involving conversion of measurements within the same system

Inconsistently solves multi-step problems involving conversion of measurements within the same system

Independently and consistently solves multi-step problems involving conversion of measurements within the same system

N/A Students should be able to create conversion tables and express smaller units in terms of larger units (Example: 1 foot is 12 times as long as 1 inch.)






the standard



or is unable to:




and independently:



consistently and

Evidence/Notes

Solve problems involving measurement including area and perimeter for rectangles.

MCC4.MD.3 MCC4.MD.2


Is unable to solve real- world, contextual problems involving measurement including area and perimeter of a rectangle

Inconsistently solves real-world, contextual problems involving measurement including area and perimeter of rectangles using visual models and/or formulas

Independently and consistently solves real-world, contextual problems involving measurement including area and perimeter of rectangles using visual models and formulas

Extends and applies understanding of area and perimeter to other 2-D shapes using visual models and formulas by solving contextual problems involving figures other than rectangles

Students should be able to derive formulas for calculating area and perimeter using the conceptual understanding generated from studying visual models. While students are expected to use formulas to calculate area and perimeter of rectangles, they need to understand and be able to communicate their understanding of why the formulas work and justify their reasoning. This standard calls for students to generalize their understanding of area and perimeter by connecting the concepts to mathematical formulas. These formulas should be derived through experience with visual models not memorization






the standard



or is unable to:




and independently:



consistently and

Evidence/Notes

Represent and interpret data

MCC4.MD.4


Create line plots of measurements expressed in unit fractions and/or is unable to solve addition and subtraction problems involving the data in the line plot

Creates line plots of measurements expressed in unit fractions and/or inconsistently solves addition and subtraction problems involving the data in the line plot

Creates line plots of measurements expressed in fractions of a unit and solves addition and subtraction problems involving the data presented in the line plot

Explores the variability of data presented in line plots and makes inferences based on statistical reasoning

Fractions used on the line plots should be to the nearest ½, ¼ or 1/8 of a unit

Understand concepts of angles and measuring angles

MCC4.MD.5 MCC4.MD.6 MCC4.MD.7


Use knowledge of angle measurement to sketch angles of a specified measure OR

Find the measure of a specified angle by adding its decomposed parts, OR

Solve addition and subtraction problems to find unknown angles ona diagram in real-world situations

Uses knowledge of angle measurement to sketch angles of a specified measure, find the measure of a specified angle by adding its decomposed parts, and/or solve addition and subtraction problems to find unknown angles on a diagram in real-world situations

Uses knowledge of angle measurement to sketch angles of a specified measure, find the measure of a specified angle by adding its decomposed parts, and solve addition and subtraction problems to find unknown angles on a diagram in real-world situations(by solving problemswith adjacent angles)

N/A Students should be able to use the protractor to measure angles in whole number degrees. Students should understand that an angle that turns through 1/360 of a circle is called a“one‐degree angle,” and that an angle that turns through n one-degree angles is said to have an angle measure of ndegrees

Standards for Mathematical Practice**These should be scored using the Academic Performance Level Behaviors scores**

Standards for Mathematical Practice Rarely (1) Sometimes (2) Usually (3) Consistently (4) Evidence/Notes

The SMPs are addressed on an ongoing basis through grading periods 1 – 4Makes sense of problems and perseveres in solving them

MCC4.SMP.1

Student is rarely able to explain to himself/herself the meaning of a problem and is unable to independently determine an appropriate strategy/tool to use to solve the problem

Student inconsistently explains to himself/herself the meaning of a problem and/or is inconsistently able to independently determine an appropriate strategy/ tool to use to solve problems. Student needs prompting by the teacher on a regular basis

Student usually explains to himself/herself the meaning of a problem and determines an appropriate strategy/ tool to use to solve the problem

Student independently and consistently explains to himself/herself the meaning of a problem and determines an appropriate strategy/ tool to use to solve the problem

In fourth grade, students should know that doing mathematics involves solving problems and should discuss how they solved them. Students should 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. This should be assessed ongoing throughout the school year

Reasons abstractly and quantitatively

MCC4.SMP.2

Student is rarely able to connect a quantity to a written symbol and rarely demonstrates a clear understanding of the meaning of a quantity as represented in a problem solved

Student is inconsistently able or may require teacher prompting to connect a quantity to a written symbol and sometimes demonstrates a clear understanding of the meaning of a quantity as represented in a problem solved

Student usually connects a quantity to a written symbol and demonstrates a clear understanding of the meaning of a quantity as represented in a problem solved most of the time using objects, pictures, drawings.However, the student may have difficulty with more complex problem solving.

Student consistently and independently connects a quantity to a written symbol and demonstrates a clear understanding of the meaning of a quantity as represented in a problem solved using objects, pictures, drawings

Fourth graders should recognize that a number represents a specific quantity. They should be able to 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. This should be assessed ongoing throughout the school year

Revised October 23, 2012Page 18 of 20



The SMPs are addressed on an ongoing basis through grading periods 1 – 4Constructs viable arguments and critiques the reasoning of others

MCC4.SMP.3

Student is rarely able to explain their mathematical reasoning and/or respond to others’ thinking

Student is inconsistently able or may require teacher prompting to explain their mathematical reasoning and/or respond to others’ thinking

Student usually explains their mathematical reasoning and responds to others’ thinking with some errors

Student consistently and independently constructs arguments using concrete referents, explains their mathematical reasoning and responds to others’ thinking in a mathematically appropriate way

In fourth grade, students may construct arguments using concrete referents, such as objects, pictures, and drawings. 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. This is assessed ongoing throughout the school year

Models with mathematics

MCC4.SMP.4

Student is rarely able to make connections between mathematical ideas or the student is rarely able to understand the mathematics presented in context.

Student is inconsistently able to make connections between mathematical ideas or the student is not able to understand and solve problems independently with the mathematics presented in context

Student is usually able to independently make connections between mathematical ideas. The student can demonstrate a solid understanding of mathematical ideas presented in context with a few inconsistencies at times.

Student is able to consistently and independently make connections between mathematical ideas. The student can demonstrate a solid understanding of mathematical ideas presented in context.NOTE: Fourth graders should be able to evaluate their results in the context of the situation and reflect on whether the results make sense.

Students should be able to experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, acting out, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. This is assessed ongoing throughout the school year on each assignment and assessment in conjunction with the content standard addressed




The SMPs are addressed on an ongoing basis through grading periods 1 – 4Uses appropriate tools strategically

MCC4.SMP.5

Student is rarely able to consider strategies and tools available to solve a problem or decide which tool/ strategy would be helpful

With teacher prompting, student considers available tools and strategies to solve a problem and decides which tools/strategies might be helpful

Student usually considers available tools and strategies independently when solving a problem and decides which tools/strategies might be helpful

Student consistently and independently considers available tools and strategies when solving a problem and decides which tools/strategies might be helpful

Example: Student is able to compile the possibilities into an organized list or a table, and determine whether they have all the possible rectangles

This is assessed ongoing throughout the school year through multiple tasks

Attends to precision

MCC4.SMP.6

Student begins to explain their mathematical reasoning with others but does not use clear and precise language, or student is rarely able to communicate mathematical reasoning

Student inconsistently communicates mathematical reasoning using clear and precise language

Student is usually able to communicate mathematical reasoning using clear and precise language

Student is able to consistently communicate mathematical reasoning using clear and precise language. The student uses clear and precise language in his/her discussions with others and in his/her own reasoning.

This is assessed in multiple ways throughout the school year (on each assignment and assessment).Students should be carefully specifying units of measure and state the meaning of the symbols they choose. Example: When figuring out the area of a rectangle, record answers in square units.

Looks for and makes use of structure

MCC4.SMP.7

Rarely looks closely to discover a pattern or structure in any given problem. The student can rarely generate number or shape patterns that follow a given rule

Sometimes looks closely to discover a pattern or structure in any given problem. The student can sometimes generate number or shape patterns that follow a given rule

Usually looks closely to discover a pattern or structure in any given problem. The student usually can generate number or shape patterns that follow a given rule

Consistently looks closely to discover a pattern or structure in any given problem. The student can generate number or shape patterns that follow a given rule

Example A student uses

properties of operations to explain calculations (advanced additive strategies)

A student relates representations of counting problems such as tree diagrams and arrays to the multiplication principal of counting




The SMPs are addressed on an ongoing basis through grading periods 1 – 4Looks for and expresses regularity with repeated reasoning

MCC4.SMP.8

Student is rarely able to use repeated reasoning to understand mathematical structures and generalize knowledge of such patterns to assist them in checking his/her own work

Student requires teacher prompting to generalize mathematical patterns in order to utilize this knowledge to check his/her own work by asking questions such as, “Does this make sense?”

Student usually recognizes and uses use repeated reasoning to understand mathematical structures and generalize knowledge of such patterns to assist them in checking his/her own work

Student consistently and independently generalizes mathematical patterns and utilizes this knowledge to check their own work by asking questions such as, “Does this make sense?”

Students in fourth grade should notice repetitive actions in computation and look for more efficient methods based on the number patterns. For example, students may use the distributive property as a strategy for using products they know to solve products that they don’t know. For example, if students are asked to find the product of 17 x 8, they might decompose 17 into10 and 5 and 2 and then multiply10 x 8, 5 x 8 and 2 x 8 to arrive at 80 + 40 + 16 or 136. In addition, fourth graders should continually evaluate their work by asking themselves, “Does this make sense?”

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