GRADE 6 MATH CURRICULUM

Course Title:Grade 6 Mathematics

Description:

As the first course in the 6-12 Mathematics Program, the Grade 6 Mathematics curriculum is designed to provide a transition between the elementary and secondary programs. As they were in the elementary program, the mathematical processes (problem solving, communication, reasoning, connections and representation) continue to be essential in the learning of mathematics. Added to these are the CCSS Practices of adaptive reasoning, strategic competence, conceptual understanding, procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently, and appropriately) and productive disposition (See Appendix A).

In addition to the identification and development of all content prescribed by national and State Standards, this Grade 6 curriculum underscores the importance of developing mathematical thinking as foundational for future success. As a result, daily mathematical instruction requires students to: consider a model, situation, or task; make mathematical decisions and execute them; and explain, justify, and evaluate their strategies.

Sixth grade mathematical content is focused on big ideas, such as equivalence, number sense, properties, operational reasoning, variables and statistical thinking. Content primarily focuses on: number systems (rational numbers and integers); proportional reasoning (ratio and rates); computation; equivalent forms of and solutions to expressions and equations; and data distributions and variability. Appropriate for the developmental level of sixth graders, concepts and skills are initially presented through models, and real and familiar situations, followed by activities that enable students to conjecture and test, and to determine, develop and articulate generalizations and distinctions.

This course is designed to provide students with an appropriate balance between the development of key concepts and the mastery of skills. With that in mind, this curriculum guide defines the learning objectives and content outline that drives the choice of instructional activity and assessment.

Evaluation:

Student performance will be measured using a variety of tools, including (but not limited to) quizzes and tests, class work and homework. All sixth graders will also take common departmental assessments, including common tests on designated objectives, as well as Midterm and Final Exams. Based on curriculum and instructional modifications(See Appendix C), these assessments vary for each level. Similar to high stakes State assessments, district assessments will reflect a balance between concepts, skills, and applications.

New Jersey Core Curriculum Content Standards:

The delineation of objectives and content outline reflects not only complete coverage of the NJ CCSS for 6th grade (coded under objectives and detailed in Appendix B), this framework for instruction also draws from all the current empirical research and professional literature available at the time of its development.

Textbook and Instructional Resources:

The adopted textbooks include Everyday Mathematics, Middle School Math (Scott Foresman), and Math in Context. To address number sense and operational sense, and to insure broad and tailored coverage of all objectives, additional teacher resources(e.g., the Groundworks series, SATs, Skill Power-6, Road to Reasoning, Computational Competencies, Math Connections, and various released items from national and international tests.

Learning Objective
The student will ... / Content Outline / Instructional Materials / Assessments
1. Expand the understanding of the number system and the sense of magnitudes of number to include integers, and negative rational numbers.
6NS 5, 6 / Concepts
  1. Represent integers with two-colored counters and number lines to understand that positive and negative numbers are used together to describe quantities having opposite directions or values.
  2. Use positive and negative numbers to represent quantities in real world contexts; explain the meaning of zero in each.
a. Recognize that the opposite of the opposite of a number is the number itself.
Relations
  1. Represent equivalent forms of integers and negative rational numbers.
  2. Order and sequence integers and negative rational numbers.
  1. Write, interpret, and explain statementsof order for rational numbers in real world contexts.
/ Everyday Math Unit 1
SF Middle School Math: Course 1
Ch 9-1 pp.468-471
supplementary instructional:
Skill Power-6
Math Connections
District constructed tasks / NJ ASK-6
District Common Assessment
Writing tasks
Lesson warm-ups
Closure tasks
Group work checklist
Homework
2. Represent, order, and interpret in real situations involving the absolute value of rational numbers.
6NS 7 /
  1. Represent the absolute value of rational numbers on a number line.
  2. Interpret or determine absolute value as magnitude for a positive or negative quantity in a real-world situation.
  3. Recognize and create equivalent values in an absolute value expression.
/ Everyday Math Unit __
SF Middle School Math: Course 1Ch __ pp.__
supplementary instructional:
Math Connections (ms)
District constructed tasks / NJ ASK-6
District Common Assessment
Writing tasks
Lesson warm-ups
Closure tasks
Group work checklist
Homework
3. Solve real world and mathematical problems by graphing points on a Cartesian plane.
6NS 8, 6G3 /
  1. Represent points in the plane with integers and negative rational number coordinates.
  2. Find and position integers and other rational numbers on the coordinate plane.
  3. Recognize and express that signs of numbers in ordered pairs indicate locations in quadrants.
  4. Solve real world and mathematical problems by graphing
  5. Use coordinates to find distance between points with the same first coordinate or the same second coordinate.
  6. Recognize that when 2 ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
/ Everyday Math Unit 2
SF Middle School Math:
Ch. 9 les. 5-6 pp.488-497
Les Enhance.Transp.45-6
Math in Context Operations,
Patterns and Symbols ,
Figuring All the Angles
District constructed tasks
Supplements:
Math Connections p38 / NJ ASK-6
District Common Assessment
Writing tasks
Lesson warm-ups
Closure tasks
Group work checklist
Homework
4. Apply number theory concepts to real-world and mathematical problem situations.
6NS 4 /
  1. Generate patterns of divisibility on a chart (Sieve of Eratosthenes)
  2. Sorting tasks to generate divisibility rules
  3. Prime factorization (w/ tree diagrams; exponential notations)
  4. Identify the GCF and LCM using a Venn diagram
  5. Find the GCF of 2 numbers less 100 and the LCM of 2 numbers 12.
  6. Use the distributive property to express a sum of 2 whole numbers 1-100 with a common factor.
/ Everyday Math Unit __
SF Middle School Math: Course 1Chapter 5
supplementary:
Groundworks:
Reasoning w/Number
Math Connections (ms)
District constructed tasks / NJ ASK-6
District Common Assessment
Writing tasks
Lesson warm-ups
Closure tasks
Group work checklist
Homework
5. Extend the understanding of the number system by constructing meanings for fractions. / Concepts
  1. part/whole meaning/representations
  1. linear: Cuisenaire rods & points or lengths on a number line
  2. area: Pattern blocks or geoboards or drawings
  3. discrete: 2-colored counters
  1. for all models: unit - nonunit fractions - mixed numbers
  2. density and magnitude
  3. negative number coordinates
Relations
  1. equivalence
  2. order and sequence
  3. relation to half
/ Everyday Math Unit 4
SF Middle School Math: Course 1
Chapter 5 les. 4-6,8 pp.288-301,308
supplementary: SkillPower
Groundworks:
Reasoning w/Number
Math Connections (ms)
District constructed tasks / NJ ASK-6
District Common Assessment
Writing tasks
Lesson warm-ups
Closure tasks
Group work checklist
Homework
6. Extend the understanding and use of arithmetic operations to fractions; develop, apply and explain procedures for computation and estimation with fractions.
6NS 1 / Addition & subtraction -
  1. Estimation
  2. review w/ like denom.
  3. reinforce unlike denom.
  4. regroup w/ mixed no.
  5. Expressions and equations with fractions
Multiplication & division -
  1. Estimation
  2. Extend contexts and meaning across number systems
  3. Interpret and compute quotients for division of fraction problems
  1. mult/div by whole no.
  2. mult./div by fractions
  1. Represent/interpret stories and visual models, and compute quotients of fractions, and solve word problems involving division of fractions by fractions
Mixed operations
  1. Investigate properties in operations on fractions with and without variables.
/ Everyday Math Lesson 4.8
SF Middle School Math: Course 1
Chapter 6 lessons 1-6 pp.324-356
Chapter 7 lessons 1-6 pp.365-396
supplementary materials:
Math Connections (ms)
Jacob’s Algebra
SAT & NAEP released items
District constructed tasks / NJ ASK-6
District Common Assessment
Writing tasks
Lesson warm-ups
Closure tasks
Group work checklist
Homework
7. Develop the number sense necessary for computation.
Compute fluently with multi-digit numbers, including decimals.
6NS 2, 3 /
  1. If possible, divide out common factors in dividend and divisor before dividing
  2. Informally model select division situations w/ Base 10 to reinforce fair sharing and transition to the standard algorithm. (Levels 2 and 3)
  3. Fluently divide multi-digit numbers using the standard algorithm
  4. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
  5. Apply properties: identity commutative associative distributive
/ Everyday Math Unit 5
SF Middle School Math:
Chapter 3 lessons 5-12
supplements: Skill Power-6
Groundworks:
Reason w/Numbers
Computation.Competencies
Math Connections (ms)
District constructed tasks / NJ ASK-6
District Common Assessment
Writing tasks
Lesson warm-ups
Closure tasks
Group work checklist
Homework
8. Develop meaning for ratios and proportions.
9. Develop meaning for percents.
Develop, apply, and explain methods for solving problems involving proportions and percents in a variety of situations.
Use proportional reasoning to solve real world and other math problems.
RP 1, 2, 3 /
  1. Ratios
  1. Model and explain the concept of ratio and use of ratio language to describe a ratio relationship between two quantities.
  2. Distinguish part to part and part to whole
  3. Identify the differences between ratios vs. fractions
  4. Model and explain the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use ratio language in the context of a ratio relationship.
  5. Determine equal ratios and rates
  1. Proportions (with the focus on proportional reasoning)
  1. Develop conceptual meaning
  2. Make representations
  3. Reason through qualitative comparisons
  4. Use proportional language in describing, explaining, justifying or evaluating examples and situations
  1. Applications:
  1. Make tables with equivalent ratios relating quantities with whole number measurements; use the tables to compare ratios.
  2. Use proportional reasoning to convert measurement units, emphasizing the multiplicative nature of this activity.
  3. Plot pairs of values on the coordinate plane; compare to find equal ratios.
  4. Solve unit rate problems, including those involving unit pricing and constant speed.
  5. Solve problems involving scale drawings
  6. Solve problems involving similar figures
  1. Percents
  1. Conceptual meaning using percent bars
  2. Representations- area and discrete models
  3. Find the percent of a quantity as a rate per 100.
  4. Estimate the percent of a given whole.
  5. Solve problems involving finding the whole, given the part and percent.
  6. Applications
  1. Converting fractions, decimals, and percents
/ SF Middle School Math: Course 1
Chapter 10 les.1-4,6-11 pp.513-572
supplementary instructional:
Per Sense (MiC)
Grasping Sizes (MiC)
Ratios and Rates (MiC) / NJ ASK-6
District Common Assessment
Writing tasks
Lesson warm-ups
Closure tasks
Group work checklist
Homework
10a. Develop, apply and explain a variety of strategies for determining perimeter, circumference, area, surface area.
Solve real world problems involving area and surface area.
6G 1, 3, 4
10b. Develop, explain, and apply a variety of strategies for determining volume.
6G 2 /
  1. Find the area of right triangles, other triangles, special quadrilaterals, and other polygons by composing into rectangles or decomposing into triangles and other shapes.
  2. Develop formulas for solving problems related to measurement.
  3. Apply all of the above in the context of solving real world/math problems.
  4. Represent 3D figures using nets made up of rectangles and triangles; use the nets to find surface area of the figures. apply in real/math contexts.
  5. Demonstrate and explain the impact of the change of an object’s linear dimensions on its perimeter, area, or surface area. (Level 4)
/ SF Middle School Math: Course 1
Ch.4 les.1,4-9 pp.210-214, 228-261
Ch. 11 les. 1-7 pp. 580-613
supplementary instructional:
Reallotment (MiC)
Made to Measure (MiC) District constructed tasks / NJ ASK-6
District Common Assessment
Writing tasks
Lesson warm-ups
Closure tasks
Group work checklist
Homework
Measurement concepts:
  1. Apply understanding of measurement to construct shapes
  2. Develop formulas for solving problems related to volume.
  3. Solve real world and other math problems by finding the volume of a rectangular prism with fractional edge lengths
  4. Demonstrate and explain the impact of the change of an object’s linear dimensions on its volume. (Level 4)
/ SF Middle School Math: Course 1
Ch.4 les.1,4-9 pp.210-214, 228-261
Ch. 11 les. 1-7 pp. 580-613
supplementary instructional:
Reallotment (MiC)
Made to Measure (MiC) / NJ ASK-6
District Common Assessment
Writing tasks
Lesson warm-ups
Closure tasks
Group work checklist
Homework
11. Understand and use variables to evaluate and simplify expressions.
6 EE 1, 2, 3, 4 / Variables
  1. Represent and solve problems generated from concrete, pictorial, and symbolic representations
Expressions
  1. Develop an intuitive/logical meaning, with reference to time and position.
  2. Apply and extend prior knowledge of arithmetic to algebraic expressions
  1. Write and evaluate numerical expressions involving whole number exponents.
  2. Write and evaluate expressions in which a variable is a placeholder.
  1. Translate between expressions written in words and symbols
  2. Identify parts of an expression using mathematical terms
  3. Evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real-world problems.
  4. Perform arithmetic operations, including those involving whole number exponents, in the conventional order with and without parentheses.
  1. Apply the properties of operations to generate equivalent expressions.
  2. Identify when 2 expressions are equivalent, regardless of which value is substituted into the variable.
/ Everyday Math Unit 6
SF Middle School Math: Course 1
Chapter 2 lessons10-11 pp.110-117
supplements: Algebridge
Expressions and Formulas Comparing Quantities (MiC)
District constructed tasks / NJ ASK-6
District Common Assessment
Writing tasks
Lesson warm-ups
Closure tasks
Group work checklist
Homework
12. Represent and solve simple equations using concrete and informal models, as well as appropriate paper-and-pencil techniques.
Reason about and solve one-variable inequalities.
6EE 5, 6, 7, 8 / Equation
  1. Build structure and logic through balance representations w/ problems
  1. Focus on and emphasize equivalence as key across varied tasks.
  2. Recognize substitution as a logical approach to finding solutions.
  1. Solve real world and other math problems by writing and solving equations in the form of x + p = q, and px = q for cases in which p, q, and x are all non-negative rational numbers.
Inequalities
  1. Approach solving an inequality as a process of answering the question: which values from a specific set, if any, make an inequality true?
  2. Represent solutions of inequalities on number line diagrams.
  3. Substitute to determine if a given number in a set makes an inequality true.
  4. Recognize that the inequalities ( x>c or x<c) have infinitely many solutions.
  5. Write an inequality of the form x>c or x<c to represent a constraint or condition in a real world or ther math problem.
/ Everyday Math Unit 3
SF Middle School Math: Course 1
Chapter 2 lessons12-13 pp.118-126
supplements: Algebridge
Algebra Puzzles and Problems #6
District constructed tasks / NJ ASK-6
District Common Assessment
Writing tasks
Lesson warm-ups
Closure tasks
Group work checklist
Homework
13. Represent and analyze quantitative relationships between dependent and independent variables.
6EE 9 /
  1. Use variables to represent two quantities in a real world problem that change in relationship to one another; write an equation to express one quantity (dependent variable), in terms of the other quantity (independent variable).
  2. Analyze the relationship between the dependent independent variables using
  1. Tables and graphs
  2. Relating these to one another
/ Everyday Math Unit 10
SF Middle School Math:
Chapter 9 lesson 7
supplements: MIC Expressions&Formulas
District constructed tasks / NJ ASK-6
District Common Assessment
Lesson warm-ups
Closure tasks
Group work checklist
Homework
14. Select and use appropriate graphical representations and measures of central tendency for sets of data. 6SP 3 / 1. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
2. Distinguish measures of center
Mean mode median
3. Examine range, spread, gaps, and (effect of) outliers
4.Graphic representations / Everyday Math Unit 3
SF Middle School Math:
Chapter 1 lessons 7 - 9
supplements:
Exploring Data
District constructed tasks / NJ ASK-6
District Common Assessment
Lesson warm-ups
Closure tasks
Group work checklist
Homework
15. Develop understanding of statistical variability.
Make inferences and formulate and evaluate arguments based on data analysis and data displays.
6SP 1, 2, 4, 5 / Summarize and describe distributions
  1. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
  2. Summarize numerical data sets in relation to their contexts; e.g. :
  1. Reporting the number of observations
  2. Describing the nature of the attribute under investigation, including how it was measured and its unit of measurement
  3. Given quantitiative measures of center (median and/or mean) and variability (interquartile range and /or mean absolute deviation), as well as describing an overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
  4. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
Variability
  1. Recognize that a measure of variation describes how its values vary with a single number.
  2. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answer.
  3. Understand that a set of data collected to answer a statistical question has a distribution that can be described by its center, spread and overall shape.
/ Everyday Math Unit 6
SF Middle School Math:
Chapter 1 all lessons
supplementary
Exploring Data
Data About Us (CM)
Picturing Numbers (MiC)
Tracking Graphs (MiC)
Dealing with Data (MiC)
District constructed tasks / NJ ASK-6
District Common Assessment
Lesson warm-ups
Closure tasks
Group work checklist
Homework

Adoption date: July 2012Page 1