MATH 6

LENGTH OF TIME: one year

GRADE LEVEL: 6

DESCRIPTION OF COURSE:

In Grade 6, instructional time will focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.

COURSE STANDARDS:

Students will:

1.  Build on their prior work in measurement and in multiplication and division as they study the concepts and language of ratios and unit rates.

2.  Build on their prior work in measurement and in multiplication and division as they study the concepts and language of ratios and unit rates.

3.  Solve ratio and rate using tape diagrams, tables of equivalent ratios, double number line diagrams, and equations.

4.  Plot pairs of values generated from a ratio or rate on the first quadrant of the coordinate plane.

5.  apply and extend their understanding of multiplication and division to divide fractions by fractions.

6.  Apply and extend their understanding of multiplication and division to divide fractions by fractions.

7.  Build fluency with adding, subtracting, multiplying, and dividing multi-digit decimal numbers using standard algorithms

8.  Extend the concepts of factors and multiples to include Greatest Common Factor and Least Common Multiple.

9.  Understand rational numbers as points on the number line and to extend previous understandings of numbers to the system of rational numbers, which now include negative numbers

10.  Represent points in the plane with negative number coordinates and, as part of doing so, see that negative numbers can represent quantities in real-world contexts.

11.  Order numbers and understand the absolute value of a number.

12.  Solve real-world and mathematical problems by graphing points in all four quadrants, a concept that continues throughout to be used into high school and beyond.

13.  Relate algebraic expressions back to arithmetic and the properties of arithmetic (commutative, associative, distributive).

14.  Write, interpret, and use expressions and equations as they reason about, and solve, one variable equations and inequalities.

15.  Analyze quantitative relationships between two variables.

16.  Find the area of triangles and other two-dimensional figures.

17.  Use formulas to find the volumes of right rectangular prisms with fractional edge lengths.

18.  Use negative numbers in coordinates as they draw lines and polygons in the coordinate plane.

19.  Find the lengths of sides of figures, joining points with the same first coordinate or the same second coordinate and apply these techniques to solve real-world and mathematical problems.

20.  Develop an understanding of statistical variability and apply that understanding as they summarize, describe, and display distributions.In particular, careful attention is given to measures of center (e.g., mean, median, mode) and variability (e.g., range, interquartile range, and/or mean absolute deviation).

RELATED PA ACADEMIC STANDARDS FOR MATHEMATICS

CC.2.3.6.A.1 Apply appropriate tools to solve real-world and mathematical problems involving area, surface area, and volume.

CC.2.2.6.B.1 Apply and extend previous understandings of arithmetic to algebraic expressions.

CC.2.4.6.B.1 Demonstrate an understanding of statistical variability by displaying, analyzing, and summarizing distributions.

CC.2.2.6.B.2 Understand the process of solving a one-variable equation or inequality and apply it to real-world and mathematical problems.

CC.2.2.6.B.3 Represent and analyze quantitative relationships between dependent and independent variables.

CC.2.1.6.D.1 Understand ratio concepts and use ratio reasoning to solve problems.

CC.2.1.6.E.1 Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

CC.2.1.6.E.2 Identify and choose appropriate processes to compute fluently with multi-digit numbers.

CC.2.1.6.E.3 Develop and/or apply number theory concepts to find common factors and multiples.

CC.2.1.6.E.4 Apply and extend previous understandings of numbers to the system of rational numbers.

PERFORMANCE ASSESSMENTS:

Students will demonstrate achievement of the standards by:

1.  Performance on the Grade 6 PSSA.

2.  End of Module Exams.

3.  Performance on online/computer based instructional and assessment programs

4.  Completion of application projects

5.  Monthly baseline testing growth

6.  MAP growth over the course of the school year.

TITLES OF UNITS:

1.  Module 1: Ratios and Unit Rates 7 Weeks

2.  Module 2: Arithmetic Operations 5 Weeks

3.  Module 3: Rational Numbers 5 Weeks

4.  Module 4: Expressions and Equations 9 Weeks

5.  Module 5: Area, Surface Area and Volume 5 Weeks

6.  Module 6: Statistics 5 Weeks

SAMPLE INSTRUCTIONAL STRATEGIES:

1.  Make sense of problems and persevere in solving them.

2.  Reason abstractly and quantitatively.

3.  Construct viable arguments and critique the reasoning of others.

4.  Model with mathematics.

5.  Use appropriate tools strategically.

6.  Attend to precision.

7.  Look for and make use of structure.

8.  Look for and express regularity in repeated reasoning.

MATERIALS:

1.  Teacher generated/researched materials

2.  Calculators

3.  Computers/Tablets

4.  Interactive Projection Systems

5.  CPS systems

6.  Manipulatives

METHODS OF ASSISTANCE AND ENRICHMENT:

1.  Math program/website generated lessons based on assessment results and skill progress for both assistance and enrichment

2.  Resource/Math Facts assistance based on MAP results, classroom formative and summative assessments and student self-assessment.

METHODS OF EVALUATION:

1.  Assessment performance

2.  Skill and concept based computer/website performance

3.  Homework

4.  Growth as measured against Curriculum-Based Assessments and standardized MAP tests.

INTEGRATED ACTIVITIES:

1. Concepts

- ratios

- rational numbers

- common factors

- multiples

- algebraic expressions

- equations

- inequalities

- dependent and independent variables

- area and volume

- statistical variability

- data distributions

2. Communication

-listen and understand

-respond orally and in writing

-exchange information orally

-read and use a variety of methods to understand texts/other written material

-interpret information

-produce, perform, or exhibit work

3. Thinking/Problem Solving

-compute, measure, estimate

-construct (geometry)

-to interpret answers in correct context

-recognize patterns

-to apply the various problem solving strategies to different situations

-make predictions (proportion probability)

4. Application of Knowledge

-demonstrate connections, relationships to real world situations

-evaluate work using various criteria

5. Interpersonal Skills

-team work

-demonstrate skills

-work cooperatively

-communicate effectively

Math 6

Revised February 2015