6th maths assignment answer key

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6th Grade Math Worksheets

Count on our printable 6th grade math worksheets with answer keys for a thorough practice. With strands drawn from vital math topics like ratio, multiplication, division, fractions, common factors and multiples, rational numbers, algebraic expressions, integers, one-step equations, ordered pairs in the four quadrants, and geometry skills like determining area, surface area, and volume, organizing numerical data as dot plots, histograms and box plots, finding mean, median, and quartiles of datasets, these pdfs become your often go-to place. Grab your ticket to a great start with our free math worksheets for grade 6 students!

Select Grade 6 Math Worksheets by Topic

Explore 4,600+ Sixth Grade Math Worksheets

Division | 4-Digit by 2-Digit and 3-Digit

Divide a 4-digit number by a 2-digit or 3-digit number, starting from the largest place value and dividing your way down to the last digit to find the quotient and remainder (if any).

• Download the set

Drawing Shapes to Represent the Ratio

Jazz up your ratio skills with our 6th grade math worksheet pdfs. Direct students to visually represent the terms of each ratio by sketching the specified number of shapes.

Multiplying Two Fractions by Cross Cancelling

Breaking down the numerator and denominator into prime factors, cross-cancelling the common factors, and multiplying the uncancelled parts of the fraction are all grade 6 learners are expected to do!

Expressing Decimals in Words | Up to Millionths

Let your understanding of decimal place value soar to new heights as you dive into these printable 6th grade math worksheets and express decimals up to millionths in words and vice versa.

Finding the GCF of Two Numbers

Follow the step-by-step process of finding the GCF by listing out all the factors of each pair of 2-digit numbers, then compare the factors, figure out the common ones and the greatest among them is your answer.

Representation of Integers

Laying a strong foundation in integers becomes easy with a touch of real-world offered in these grade 6 math pdf worksheets, where each scenario should be represented with a positive or negative integer.

One-Step Equation: Addition and Subtraction | Integers

Rearrange the equation, making the variable the subject, and take the integer constant to the other side and change its sign, add or subtract to find the value of the unknown variable.

Identifying Ordered Pairs in All Quadrants

Get acquainted with the coordinate plane, the four quadrants, and the ordered pairs. Identify the point representing each ordered pair in Part A; and locate and write the x-y coordinates of each point in part B.

Determining the Area of a Square

Equip grade 6 children with these printable math worksheets, if practice in determining the area of a square is on your mind. Get students to square the fractional side lengths and compute the area.

Identifying Nets of 3D Shapes

Get 6th grade learners to imagine folding the 2D nets presented in this printable math worksheet along the edges and visualize the 3D shapes that can be constructed from them.

• Grab the Worksheet

Surface Area using Nets | Counting Squares

Whether it is refining or testing skills in counting the unit squares to determine the surface area of rectangular prisms, cubes or triangular prisms from their nets, these pdfs serve the purpose.

Five-Number Summary

Descriptively analyze each dataset, by rearranging the values in ascending order and figuring out the maximum and minimum values, and the lower or 1st, median or 2nd, and upper or 3rd quartiles.

Division of 5-Digit Numbers by 1-Digit and 2-Digit Divisors

Push boundaries and brush up your division skills with adequate practice provided by these exercises in dividing 5-digit numbers with single and double-digit divisors.

Ratio Word Problems | Part-to-Part

Put your analytical skills to test with our 6th grade math worksheet pdfs. Study the data given in the pictogram and answer the set of questions detecting the part-to-part ratio in each scenario.

Multiplying Mixed Numbers and Fractions

Effortlessly multiply mixed numbers and fractions by converting the mixed numbers to improper fractions, cross cancelling the common factors and then multiplying what's left over.

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HMH Into Math Grade 6 Answer Key PDF | HMH Into Math 6th Grade Answers

Houghton Mifflin Harcourt Into Math Grade 6 Answers helps the students to gain knowledge in math concepts. Parents, students, and even teachers can check unit wise, module wise HMH Into Math Grade 6 Answer Key PDF for a better understanding of the concepts.

Students can get the exact step by step solution for every question of HMH Into Math 6th Grade Textbook which is useful to complete the homework and assignments easily. Download and access free HMH Into Math Answer Key PDF to make your preparation efficient.

HMH Into Math Grade 6 Answers | HMH Into Math 6th Grade Answer Key PDF

Free easy access to Houghton Mifflin Harcourt Into Math Grade 6 Answer Key Chapterwise is given below in PDF format. So, students who wants to improve their mathematics knowledge, and problem-solving skills can download HMH Into Math Grade 6 Solutions PDF. Start your preparation to score the best marks in the exams.

HMH Into Math Grade 6 Answer Key Pdf Unit 1 Number Systems and Operations

• Module 1 Integer Concepts
• Lesson 1 Identify and Interpret Integers
• Lesson 2 Compare and Order Integers on a Number Line
• Lesson 3 Find and Apply Absolute Value
• Into Math Grade 6 Module 1 Review Answer Key
• Module 2 Rational Number Concepts
• Lesson 1 Interpret Rational Numbers
• Lesson 2 Compare Rational Numbers on a Number Line
• Lesson 3 Find and Apply LCM and GCF
• Lesson 4 Order Rational Numbers
• Into Math Grade 6 Module 2 Review Answer Key
• Module 3 Fraction Division
• Lesson 1 Understand Fraction Division
• Lesson 2 Explore Division of Fractions with Unlike Denominators
• Lesson 3 Explore Division of Mixed Numbers
• Lesson 4 Practice and Apply Division of Fractions and Mixed Numbers
• Lesson 5 Practice Fraction Operations
• Into Math Grade 6 Module 3 Review Answer Key
• Module 4 Fluency with Multi-Digit Decimal Operations
• Lesson 1 Add and Subtract Multi-Digit Decimals
• Lesson 2 Multiply Multi-Digit Decimals
• Lesson 3 Divide Multi-Digit Whole Numbers
• Lesson 4 Divide Multi-Digit Decimals
• Lesson 5 Apply Operations with Multi-Digit Decimals
• Into Math Grade 6 Module 4 Review Answer Key

HMH Into Math Grade 6 Answer Key Unit 2 Ratio and Rate Reasoning

• Module 5 Ratios and Rates
• Lesson 1 Understand the Concept and Language of Ratios
• Lesson 2 Represent Ratios and Rates with Tables and Graphs
• Lesson 3 Compare Ratios and Rates
• Lesson 4 Find and Apply Unit Rates
• Lesson 5 Solve Ratio and Rate Problems Using Proportional Reasoning
• Into Math Grade 6 Module 5 Review Answer Key
• Module 6 Apply Ratios and Rates to Measurement
• Lesson 1 Use Ratio Reasoning with Circle Graphs
• Lesson 2 Use Rate Reasoning to Convert Within Measurement Systems
• Lesson 3 Use Rate Reasoning to Convert Between Measurement Systems
• Into Math Grade 6 Module 6 Review Answer Key
• Module 7 Understand and Apply Percent
• Lesson 1 Understand, Express, and Compare Percent Ratios
• Lesson 2 Use Strategies to Find a Percent of a Quantity
• Lesson 3 Solve a Variety of Percent Problems
• Into Math Grade 6 Module 7 Review Answer Key

Into Math Grade 6 Answer Key Unit 3 Expressions, Equations, and Inequalities

• Module 8 Numerical and Algebraic Expression
• Lesson 1 Understand and Apply Exponents
• Lesson 2 Write and Evaluate Numerical Expressions for Situations
• Lesson 3 Write Algebraic Expressions to Model Situations
• Lesson 4 Interpret and Evaluate Algebraic Expressions
• Lesson 5 Identify and Generate Equivalent Algebraic Expressions
• Into Math Grade 6 Module 8 Review Answer Key
• Module 9 Solve Problems Using Equations and Inequalities
• Lesson 1 Write Equations to Represent Situations
• Lesson 2 Use Addition and Subtraction Equations to Solve Problems
• Lesson 3 Use Multiplication and Division Equations to Solve Problems
• Lesson 4 Use One-Step Equations to Solve a Variety of Problems
• Lesson 5 Write and Graph Inequalities
• Into Math Grade 6 Module 9 Review Answer Key
• Module 10 Real-World Relationships Between Variables
• Lesson 1 Represent Equations in Tables and Graphs
• Lesson 2 Write Equations from Verbal Descriptions
• Lesson 3 Write Equations from Tables and Graphs
• Into Math Grade 6 Module 10 Review Answer Key

HMH Into Math Answers Grade 6 Unit 4 Relationships in Geometry

• Module 11 Polygons on the Coordinate Plane
• Lesson 1 Graph Rational Numbers on the Coordinate Plane
• Lesson 2 Graph Polygons on the Coordinate Plane
• Lesson 3 Find Distance on the Coordinate Plane
• Lesson 4 Find Perimeter and Area on the Coordinate Plane
• Into Math Grade 6 Module 11 Review Answer Key
• Module 12 Area of Triangles and Special Quadrilaterals
• Lesson 1 Develop and Use the Formula for Area of Parallelograms
• Lesson 2 Develop and Use the Formula for Area of Triangles
• Lesson 3 Develop and Use the Formula for Area of Trapezoids
• Lesson 4 Find Area of Composite Figures
• Into Math Grade 6 Module 12 Review Answer Key
• Module 13 Surface Area and Volume
• Lesson 1 Explore Nets and Surface Area
• Lesson 2 Find Volume of Rectangular Prisms
• Lesson 3 Solve Volume Problems
• Into Math Grade 6 Module 13 Review Answer Key

Into Math Book Answers Grade 6 Unit 5 Data Collection and Analysis

• Module 14 Data Collection and Displays
• Lesson 1 Explore Statistical Data Collection
• Lesson 2 Display Data in Dot Plots
• Lesson 3 Make Histograms and Frequency Tables
• Into Math Grade 6 Module 14 Review Answer Key
• Module 15 Measures of Center
• Lesson 1 Explore Mean as Fair Share
• Lesson 2 Find Measures of Center
• Lesson 3 Choose a Measure of Center
• Into Math Grade 6 Module 15 Review Answer Key
• Module 16 Variability and Data Distribution
• Lesson 1 Explore Patterns of Data
• Lesson 2 Display Data in Box Plots
• Lesson 3 Find Mean Absolute Deviation
• Lesson 4 Explore Measures of Variability
• Lesson 5 Describe Distributions
• Into Math Grade 6 Module 16 Review Answer Key

Benefits of Solving HMH Into Math 6th Grade Answers

Students can get the benefits of HMH Into Math Grade 6 Answer Key PDF from this section. The following mentioned benefits will let you know the importance of the solution key HMH Into Math. So, have a look at them once:

• Detailed explained answer for all math problems of 6th grade is available in HMH Into Math 6th Grade Solution Key PDF.
• This answer key offers solutions for practice tests, unit tests, and chapter test questions.
• HMH Into Math 6th Grade Textbook Answer Key is a quick reference guide for homework help & better practice sessions.
• Overall it clears all your doubts regarding the subject and enhances subject knowledge.

We are hoping that the details covered here about Houghton Mifflin Harcourt Into Math 6th Grade Solutions PDF are true as per my knowledge. Download HMH Into Math Grade 6 Answer Key PDF to begin effective preparation. Stay in touch with our site to get other grades answer keys for free of cost.

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Free Math Printable Worksheets with Answer Keys and Activities

Other free resources.

Feel free to download and enjoy these free worksheets on functions and relations. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

• Long Division with Remainders
• Long Division with Remainders #2 (Zeros in the Quotient)
• Long Division with 2 Digit Divisors
• Whole Number by Unit Fraction
• Equation of Circle
• Simplify Imaginary Numbers
• Adding and Subtracting Complex Numbers
• Multiplying Complex Numbers
• Dividing Complex Numbers
• Dividing Complex Number (Advanced)
• End of Unit, Review Sheet
• Distance Formula
• Simplify Rational Exponents (Algebra 2)
• Solve Equations with Rational Exponents (Algebra 2)
• Solve Equations with variables in Exponents (Algebra 2)
• Exponential Growth (no answer key on this one, sorry)
• Compound Interest Worksheet #1 (No logs)
• Compound Interest Worksheet (Logarithms required)
• Factor Trinomials Worksheet
• Factor by Grouping
• Domain and Range (Algebra 1)
• Functions vs Relations (Distinguish function from relation, state domain etc..) (Algebra 2)
• Evaluating Functions (Algebra 2)
• 1 to 1 Functions (Algebra 2)
• Composition of Functions (Algebra 2)
• Inverse Functions Worksheet (Algebra 2)
• Operations with Functions (Algebra 2)
• Functions Review Worksheet (Algebra 2)
• Logarithmic Equations
• Properties of Logarithms Worksheet
• Product Rule of Logarithms
• Power Rule of Logarithms
• Quotient Rule of Logarithms
• Solve Quadratic Equations by Factoring
• Quadratic Formula Worksheets (3 different sheets)
• Quadratic Formula Worksheet (Real solutions)
• Quadratic Formula (Complex solutions)
• Quadratic Formula (Both real and complex solutions)
• Discriminant and Nature of the Roots
• Solve Quadratic Equations by Completing the Square
• Sum and Product of Roots
• Radical Equations
• Mixed Problems on Writing Equations of Lines
• Slope Intercept Form Worksheet
• Standard Form Worksheet
• Point Slope Worksheet
• Write Equation of Line from the Slope and 1 Point
• Write Equation of Line From Two Points
• Equation of Line Parallel to Another Line and Through a Point
• Equation of Line Perpendicular to Another Line and Through a Point
• Slope of a Line
• Perpendicular Bisector of Segment
• Write Equation of Line Mixed Review
• Word Problems
• Multiplying Monomials Worksheet
• Multiplying and Dividing Monomials Sheet
• Adding and Subtracting Polynomials worksheet
• Multiplying Monomials with Polynomials Worksheet
• Multiplying Binomials Worksheet
• Multiplying Polynomials
• Simplifying Polynomials
• Factoring Trinomials
• Operations with Polynomials Worksheet
• Dividing Radicals
• Simplify Radicals Worksheet
• Adding Radicals
• Multiplying Radicals Worksheet
• Radicals Review (Mixed review worksheet on radicals and square roots)
• Rationalizing the Denominator (Algebra 2)
• Radical Equations (Algebra 2)
• Solve Systems of Equations Graphically
• Solve Systems of Equations by Elimination
• Solve by Substitution
• Solve Systems of Equations (Mixed Review)
• Activity on Systems of Equations (Create an advertisement for your favorite method to Solve Systems of Equations )
• Real World Connections (Compare cell phone plans)
• Identifying Fractions

Trigonomnetry

• Law of Sines and Cosines Worksheet (This sheet is a summative worksheet that focuses on deciding when to use the law of sines or cosines as well as on using both formulas to solve for a single triangle's side or angle)
• Law of Sines
• Ambiguous Case of the Law of Sines
• Law of Cosines
• Vector Worksheet
• Sine, Cosine, Tangent, to Find Side Length
• Sine, Cosine, Tangent Chart
• Inverse Trig Functions
• Real World Applications of SOHCATOA
• Mixed Review
• Unit Circle Worksheet
• Graphing Sine and Cosine Worksheet
• Sine Cosine Graphs with Vertical Translations
• Sine, Cosine, Tangent Graphs with Phase Shifts
• Sine, Cosine, Tangent Graphs with Change in Period, Amplitude and Phase Shifts (All Translations)
• Tangent Equation, Graph Worksheet
• Graphing Sine, Cosine, Tangent with Change in Period
• Cumulative, Summative Worksheet on Periodic Trig Functions - period, amplitude, phase shift, radians, degrees,unit circle
• Ratio and Proportion
• Similar Polygons
• Area of Triangle
• Interior Angles of Polygons
• Exterior Angles of Polygons

• Identifying Fractions Worksheet
• Associated Powerpoint
• Simplify Fractions Worksheet (Regular Difficulty)
• Associated PowerPoint
• Simplify Fractions Worksheet (Challenging Difficulty level for advanced learners)
• System of Linear Equations Worksheet
• System of Linear Equations - Real World Application
• Compositions of Reflections. Reflections Over Intersecting Lines as Rotations

All of these worksheets and activities are available for free so long as they are used solely for educational, noncommercial purposes and are not distributed outside of a specific teacher's classroom.

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FREE 6th Grade Math Test And Answer Key: Prepare Students For State Assessments

Christi Kulesza

This 6th grade math test is perfect for assessing your students’ math knowledge. The test includes multiple-choice questions, short answer response questions and an extended response question all focused on topics from the 6th grade math standards.

What content is covered in 6th grade math? 

What to expect from this 6th grade math test, aligned to the common core standards, how to use this 6th grade math test, methodology behind this 6th grade math test, 6th grade math test: practice ccss state test, multiple choice questions, extended response questions.

Curriculum and standards vary by state, but most state’s math standards cover similar topics. 

This math test assesses students’ knowledge and understanding of sixth grade topics such as: 

• Ratios and percentages
• Rational numbers
• Operations with decimals
• Division of fractions
• One and two-step word problems
• One-variable equations and inequalities
• Algebraic expressions and exponents
• Graphing on the coordinate plane
• Area, volume and surface area of shapes (parallelograms and quadrilaterals)
• Measuring side lengths

6th Grade Common Core Practice Test

Download this free 6th grade math test for state assessment preparation. Includes answer key and rationale with answers organized by standard.

This 6th grade mathematics will help to prepare students for their state’s assessment at the end of the year. 

The math practice test includes: 

• 40 multiple-choice questions
• 2 extended response question 
• Answer key 
• Answers sorted by domain

Created by experienced elementary math teachers, this test is designed for use in a 6th grade math classroom. Test questions are aligned to the sixth grade Common Core State Standards and cover content from the following CCSS domains: 

• Ratios and Proportional Relationships
• The Number System
• Expressions and Exponents 
• Statistics and Probability

6th grade math questions 

There are 42 questions of increasing difficulty and three question types:

• Multiple choice
• Short answer response
• Extended response

A detailed answer key is provided for the multiple choice section. This includes 

• The correct answer for each question 
• The standard(s) the question covers 
• The depth of knowledge (DOK) level of the question. 

Short answer and extended response questions include a scoring guide with a detailed rationale for each possible score students can receive. 

As well as helping with scoring each test, the answer key and rationale inform teachers of the areas each student may need help with. 

Standards are mixed throughout the test and questions are in no particular order to reflect state assessments. To help teachers better track student understanding, a second answer key, organized by domain, is also provided.

Use this 6th grade math test in class as a mock state assessment. It will help to familiarize 6th grade students with the length of the test and the types of questions they’ll see. 

Teachers may choose to use this test in a few different ways: 

• Set as a mock state assessment
• During small group practice; students may collaborate and talk through the questions
• Set as homework
• Break questions down in math intervention groups
• Assess student knowledge of a particular topic; teachers may use questions individually as exit tickets or quizzes
• Identify areas of support for students
• Identify students who require a math intervention

At Third Space Learning we know that no one knows your students like a teacher does so schools decide which standards each student needs additional practice with each week.  Each one-on-one math tutoring lesson is designed to close learning gaps and address misconceptions and high-quality math tutors personalize the pitch and pace to fit each student. After each session, teachers receive a detailed report for each student, showing topics covered, skills practiced and progress made.

Before creating this test, our expert math teachers reviewed state assessments from multiple states and compared the distribution of domains throughout the tests and standards within each domain. Based on this data, questions are expertly written to best show students’ understanding of each standard. 

The distribution of domains within this test is as follows:

• Ratios and Proportional Relationships – 14%
• The Number System – 26%
• Expressions and Equations – 29%
• Geometry – 14%
• Statistics and Probability – 17%

Questions for our 6th grade math test follow. Don’t forget to download the free 6th grade math practice test for the answer key and answers sorted by domain to accompany these questions.

More grade level math practice tests:

• 3rd grade math practice test 
• 4th grade math practice test
• 5th grade math practice test  

READ MORE :

• 3rd Grade Math Test & Answer Key: Prepare For State Assessments
• 4th Grade Math Test & Answer Key: Prepare For State Assessments
• 5th Grade Math Test & Answer Key: Prepare For State Assessments
• 13 Effective Test Taking Strategies

The topics in Grade 6 mathematics can vary by state. Overall most states have a very similar curriculum for their sixth graders. Topics covered in Grade 6 mathematics by the majority of states are:  • Ratios and percentages • Rational numbers • Operations with decimals • Division of fractions • One and two-step word problems • One-variable equations and inequalities • Algebra exponents • Graphing on the coordinate plane • Area, volume and surface area of shapes (parallelograms and quadrilaterals) • Measuring side lengths • Time

In the sixth grade, students study algebraic expressions to help set foundations for middle school algebra. Additionally, they begin to explore negative numbers and use ratio and proportion to solve problems, use four quadrants on a coordinate grid, review long division, find quotients of a fraction, decimal arithmetic, the area of triangles and the surface area and volume of rectangular prisms.

In the first year of middle school, students should start to understand more advanced mathematics skills. They should be able to work with decimal numbers up to the hundredths place, use integers and, in algebra, understand the value of the expression. Students also need advanced skills in English, including being able to write clearly to provide detailed information, tell a story and back up their opinions on the language arts front.

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

Related articles

FREE STAAR Practice Test: Supercharge Your Assessment Preparation

FREE 3rd Grade Math Test And Answer Key: Prepare Students For State Assessments

FREE 5th Grade Math Test And Answer Key: Prepare Students For State Assessments

FREE 4th Grade Math Test And Answer Key: Prepare Students For State Assessments

3rd to 6th Grade Math Test [FREE]

Always searching for high quality, pedagogically sound, off-the-shelf questions you can trust? Help students prepare for your state’s math tests with these practice assessments carefully created by our math experts to save you time.

Includes 40 multiple choice questions with detailed answers to support test prep, covering a range of topics and aligned to state standards.

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2019-Math-Grade-6-Answer-Key

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Preview text

Grade 6 Mathematics Released Items – Answer and Alignment Document 1

Released Items Answer and Alignment Document

Mathematics – grade 6, spring 2019.

Item Number Entity ID Answer Key

Evidence Statement Key

• M22302 C 6.
• M20810P B 6.NS-
• VH083632 A, C, D 6.NS-
• M20819P B, D 6.
• M21710 D 6.G-

6. M23068 6.

• M21713 A 6.
• VH013388 A 6.
• M25394 See Rubric 6.

Part B: 275 Part C: 180 Part D: 840

Part A: See Rubric Part B: See Rubric

• M20051P A 6.RP
• VF643078 See Rubric 6.C-

Grade 6 Mathematics Released Items – Answer and Alignment Document 2

Notes: - Other valid equations are acceptable. - Correct solutions based on incorrect equations are acceptable.

Part A: A Part B: B

#9 M25394 Rubric

Score Description

Student response includes the following 3 elements. - Modeling component = 1 point o Valid equation that can be used to estimate the average monthly lunch cost

Modeling component = 1 point o Valid work or explanation for provided estimate

Computation component = 1 point o Correct estimated lunch cost for 26 employees based on equation given

Sample Student Response: First I need to estimate the monthly cost. Although there is an increase over the three months, I will use an average since it is only 3 data points. So I added the three amounts and divided by 3. Since I am estimating, I dropped the cents.

So, I estimate it costs about $155 per month for 18 employees.

Since , I used $9 as my estimate for the amount per employee.

Grade 6 Mathematics Released Items – Answer and Alignment Document 4

1 Student response includes 1 of the 2 elements. 0 Student response is incorrect or irrelevant.

#11 1103-M20660 Rubric Part B

Student response includes the following 2 elements. - Computation component = 1 point o Correct inequality comparing the opposite of 2 and the opposite of n

• Reasoning component = 1 point o Valid explanation of provided inequality using the number line as a reference

Sample Student Response:

Since n is more than 2, it is above 2 and farther away from 0 than 2. When you take the opposite of 2, you get -2. When you take the opposite of n, you get – n. The opposite of n will be farther away from 0 than -2. So that means

#13 VF643078 Rubric

Student response includes the following 3 elements. - Computation component = 1 point o The student indicates that both expressions are equivalent to the expression 10x + 15y

Reasoning component = 1 point o Correct reasoning using the distributive property

Reasoning component = 1 point o Correct reasoning using the associative property, the commutative

Grade 6 Mathematics Released Items – Answer and Alignment Document 5

property, or by “combining like terms”

Sample Student Response: 5(2x + 3y) = 10x + 15y by distribution 3 x + 6y + x + 3(2x + 3y) = 3x + 6y + x +6x + 9y, by distribution = 3x + x +6x + 6y + 9y, by the associative property = 10x + 15y, by combining like terms Therefore, yes, they are both equivalent to each other because they both are equal to 10x + 15y. Notes: - The student may receive both reasoning points if they reason by applying the substitution property and evaluate for stated values of x and y. - The student may receive a combined total of 2 points if the reasoning processes are correct but the student makes one or more computational errors resulting in incorrect answers. - The student cannot receive more than 1 point for showing the equivalent expression 10x + 15y for both expression 1 and expression 2 if he/she shows no work or insufficient work to indicate a correct reasoning process.

2 Student response includes 2 of the 3 elements. 1 Student response includes 1 of the 3 elements.

0 Student response is incorrect or irrelevant.

#15 1298-M21432 Rubric Part A

Student response includes the following 3 elements. - Computation component = 1 point o Correct dimensions of the fish tank, 22 inches by 28 inches by 28 inches

• Computation component = 1 point o Correct volume, in cubic inches, of the fish tank, 17,

Grade 6 Mathematics Released Items – Answer and Alignment Document 7

17,248 by 231 and get 74. (or number of gallons based on volume calculated in Part A).

The maximum number of gold fish that Darren can put in this fish tank is 7 goldfish (or number of goldfish based on number of gallons calculated above).

If each gold fish needs 10 gallons of water, then 74  10 = 7 so 7 goldfish (accept 6 if student mentions leaving air space at the top of the tank and shows work adjusting the number of gallons of water needed).

Or other valid response.

2 Student response includes 2 of the 3 elements.

1 Student response includes 1 of the 3 elements.

• Multiple Choice

Course : Mathematics

University : bicol university.

• Discover more from: Mathematics Bicol University 841   Documents Go to course
• More from: Mathematics Bicol University 841   Documents Go to course