Informational Math NightGrades 6-9

Reading Public Schools

December, 2013

� Shift in Standards

�New Math Sequences

�Options for Sequence Changes

�Placement for Grade 7

�Curriculum Resources & Information

• The new Massachusetts Curriculum Frameworks emphasize

coherence at each grade level – making connections across content

and between content and mathematical practices in order to

promote deeper learning.

• The standards focus on key topics at each grade level to allow

educators and students to go deeper into the content.

• The standards also emphasize progressions across grades, with the

end of progression calling for fluency – or the ability to perform

calculations or solving problems quickly and accurate.

• The Standards for Mathematical Practice describe mathematical

“habits of mind” or mathematical applications and aim to foster

reasoning, problem solving, modeling, decision making, and

engagement among students.

• Finally, the standards require students to demonstrate deep

conceptual understanding by applying them to new situations.

Key Instructional Shifts in Mathematics

“These standards are

not intended to be new

names for old ways of

doing business. They

are a call to take the

next step.”

Massachusetts Curriculum

Framework for Mathematics

� Students should be actively

engaged in doing meaningful

mathematics, discussing

mathematical ideas, and applying

mathematics in interesting,

thought-provoking situations.

� Student understanding is further

developed through ongoing

reflection about cognitively

demanding and worthwhile tasks.

� Tasks should be designed to

challenge students in multiple ways.

� Activities should build upon

curiosity and prior knowledge, and

enable students to solve

progressively deeper, broader, and

more sophisticated problems.

The new standards state that “educators

will need to pursue, with equal intensity,

three aspects of rigor in the major work of

each grade:

� conceptual understanding,

� procedural skill and fluency

� applications.”

It's not that I'm so smart, it's just that I stay with problems longer.

Albert Einstein

Standards for Mathematical Practice

“The Standards for Mathematical

Practice describe ways in which

developing student practitioners of

the discipline of mathematics

increasingly ought to engage with the

subject matter as they grow in

mathematical maturity and expertise

throughout the elementary, middle,

and high school years. Designers of

curricula, assessments, and

professional development should all

attend to the need to connect the

mathematical practices to

mathematical content in mathematics

instruction.”

(From the Massachusetts Curriculum Framework for Mathematics)

• “A large majority of middle school math teachers say the common core is more

rigorous than their state's prior mathematics standards. The teachers surveyed

seemed especially upbeat about the math practice standards. In all, 71 percent of

teachers agreed or strongly agreed that the focus on math practices is the ‘biggest

innovation’ of the standards, with 95 percent saying that participating in those

practices is essential for students to learn math.”

Ed Week / July 29, 2013 / “Math Teachers Find Common Core More Rigorous Than Prior Standards”

• "The practice standards are exquisite. . . .” Philip Uri Treisman, professor of math and public affairs at the University of Texas

• "The common-core standards and assessments put us in a different game. . . Of

course, the content counts. I'm a mathematician. You've got to get it right, and get

it right in the right ways. But the real action is in the mathematical practices . . .”Alan Schoenfeld, NCTM member and professor of mathematics, University of California, Berkeley

• "It's going to be more challenging . . . more rigorous . . . And I'm here to tell you

that's a good thing, because we've been lying to ourselves and everybody else . . .

We've inflated our levels of proficiency."Matthew Larson, math specialist in Lincoln, Nebraska and a board member for NCTM

Ed Week / April 24, 2013 / “What Do Math Educators Think About the Common Core?”

Math Educator Perspectives on the

New Practice Standards

“To acquire the mathematical background you need, . . . you should

study mathematics every year in secondary school. But simply taking

mathematics is not enough. You should acquire the habit of puzzling

over mathematical relationships. When you are given a formula, ask

yourself why it is true and if you know how to use it. When you learn

a definition, ask yourself why the definition was made that way. It is

the habit of questioning that will lead you to understand mathematics

rather than merely to remember it, and it is this understanding that

your college courses require. In particular, you should select

mathematics courses that ask you to solve hard problems and that

contain applications (‘word problems’). The ability to wrestle with

difficult problems is far more important than the knowledge of many

formulae or relationships.”

Preparing for College Mathematics

Harvard’s Thoughts on Mathematics

Math 7 and Math 7 Enhanced• Students develop an understanding of and applying

proportional relationships; develop an understanding of operations with rational numbers and working with expressions and linear equations; work with two- and three- dimensional shapes to solve problems involving area, surface area, and volume; and draw inferences about populations based on samples

Math 7/8• Students develop a deep unified understanding of rational

numbers; study algebraic functions focusing on problem solving with linear functions and systems of equations, statistics topics including comparing data sets, random sampling and bivariate data; and problem solve involving two and three dimensional geometry concepts

Grade 7 Courses

Grade 8 Courses

Math 8 and Math 8 Enhanced

• In-depth study of linear relationships and equations, with the

addition of functions, the exploration of irrational numbers,

geometric graphing to algebra, statistics and the connection

linear relations with the representation of bivariate data. Many

more algebra standards are evidenced in these courses than in

the previous Framework.

Algebra I

• The Algebra 1 course of the new Framework progresses from the

Grade 8 algebra topics, expanding the study of functions to

exponential and quadratic relationships, as well as other topics

previously taught in Algebra II and high school courses.

� Unit assessments from

6th grade curriculum

� Spring cumulative

assessment in May (will

include open-response

and novel application

questions)

� IOWA Algebra readiness

assessment (for 7/8

acceleration option) or

Skills assessment (for

Enhanced option)

Grade 6 Criteria for placement in Grade 7

“One of the questions I am frequently asked by teachers, parents, and

reporters is, ‘When should students take algebra?’ Let’s assume that we’re

talking about a college preparatory Algebra 1 course. The content and

instruction must be designed to develop both conceptual and procedural

understanding. For students to be considered successful in first-year algebra,

the expectation must be that reasoning and making sense will be priorities of

both teaching and learning.”

“Requirements for taking algebra in the middle grades should be clear and

must not be compromised. Successful completion of a rigorous algebra

course requires students to have prerequisite mathematical understandings

and skills as well as a work ethic that includes the tenacity to stick with a

problem or concept until it makes sense and the willingness to spend more

time on assignments and class work.”

Algebra: Not 'If' but 'When'By NCTM President Linda M. Gojak

December 3, 2013

“Furthermore, a key characteristic of students who are successful in algebra,

no matter when they take it, is a level of maturity that includes a readiness to

understand abstract mathematical definitions, to work with abstract models

and representations, and to understand and make connections among

mathematical structures—and this readiness should extend to making

abstract generalizations.”

“My experience, both as a student and as a teacher, leads me to believe that

we do more harm than good by placing students in a formal algebra course

before they are ready . . . .”

http://www.nctm.org/about/content.aspx?id=40258

Algebra: Not 'If' but 'When'By NCTM President Linda M. Gojak

(excerpts continued) . . .

Grade Levels & Shift in Standards

� Compute fluently with integers, decimals, fractions, and percents

� Identify and use the properties of integer exponents

� Identify and use the Order of Operations

� Identify and use the associative, commutative, distributive, identity, and inverse

properties

� Understand and use appropriate vocabulary (for example variable, terms, factors,

coefficients.)

� Write one variable expressions

� Perform arithmetic operations on polynomials.

� Create and solve linear, absolute value equations and inequalities in one variable.

� Solve quadratic equations by inspection, taking the square root, factoring, and the

quadratic formula.

� Solve a system of linear equations in two variables.

� Understand that the graph of an equation in two variables represents all solutions.

� Understand that a function from one set (called the domain) to another set (called

the range) assigns to each element of the domain exactly one element of the

range.

� Define a linear or quadratic function and represent with a table, rule, or graph

(and translate among the three.)

� Write a function that describes a relationship between two quantities.

� Understand and calculate the measures of central tendency

� Represent data with plots on the number line (dot plots, histograms, and box

plots.)

� Represent data with bar graphs, circle graphs, and stem-and-leaf plots

� Represent data on a scatterplot, and fit a linear function for a scatterplot.

Grade

11

Algebra

Grade 8

Grade 7

Some Algebra standards, and . . .

Former Algebra I (2000) content now in earlier grades

Grade Levels & Shift in Standards

� Compute fluently with integers, decimals, fractions, and percents� Identify and use the properties of integer exponents

� Identify and use the Order of Operations

� Identify and use the associative, commutative, distributive, identity,

and inverse properties� Understand and use appropriate vocabulary (for example variable, terms, factors,

coefficients.)

� Write one variable expressions� Perform arithmetic operations on polynomials.

� Create and solve linear, absolute value equations and inequalities in one variable.

� Solve quadratic equations by inspection, taking the square root, factoring, and the

quadratic formula.

� Solve a system of linear equations in two variables.

� Understand that the graph of an equation in two variables represents all solutions.

� Understand that a function from one set (called the domain) to another set (called

the range) assigns to each element of the domain exactly one element of the

range.

� Define a linear or quadratic function and represent with a table, rule, or graph

(and translate among the three.)

� Write a function that describes a relationship between two quantities.

� Understand and calculate the measures of central tendency� Represent data with plots on the number line (dot plots, histograms, and box

plots.)

� Represent data with bar graphs, circle graphs, stem-and-leaf plots� Represent data on a scatterplot, and fit a linear function for a scatterplot.

Grade

11

Algebra

Grade 8

Grade 7

Some Algebra standards, and . . .

Former Algebra I (2000) content now in earlier grades

Grade Levels & Shift in Standards

� Extend the properties of exponents to rational exponents.

� Reason quantitatively and use units to solve problems.

� Use and explain the properties of rational and irrational numbers (why the sum or product

of two rationals is rational, etc.)

� Interpret the structure of expressions – complete the square to reveal maximums or

minimums; use the properties of exponents to transform exponential functions.

� Understand that polynomials are closed under addition, subtraction, and multiplication.

� Create and solve quadratic and exponential inequalities in one variable

� Solve quadratic equations by completing the square.

� Derive the quadratic formula by completing the square.

� Solve a system consisting of linear and quadratic equations in two variables.

� Graph the solutions to a linear inequality in two variables as a half-plane and the system

of linear inequalities as the intersection of half-planes.

� Use function notation and interpret statements that use function notation.

� Recognize that sequences are functions.

� Interpret key features of graphs and tables in terms of the quantities.

� Define a linear, quadratic or exponential function and represent with a table, rule, or

graph.

� Graph an exponential function and a piece-wise function including absolute value showing

intercepts and end-behavior.

� Write arithmetic and geometric sequences both recursively and with an explicit formula.

� Identify the effects of translations of f(x).

� Find inverse functions.

� Compare linear, quadratic, and exponential models.

� Use statistics appropriate to the shape of the data distribution.

� Use the mean and standard deviation of data to fit it to a normal distribution.

� Compute (using technology) and interpret the correlation coefficient of a linear fit.

Grade

11

Algebra

Grade 8

Grade 7

More Algebra I standards, and . . . Content now in Algebra I, previously in Algebra II or Precalculus

Grade Levels & Shift in Standards

� Extend the properties of exponents to rational exponents.

� Reason quantitatively and use units to solve problems.

� Use and explain the properties of rational and irrational numbers (why the sum or product

of two rationals is rational, etc.)

� Interpret the structure of expressions – complete the square to reveal maximums or

minimums; use the properties of exponents to transform exponential functions.

� Understand that polynomials are closed under addition, subtraction, and multiplication.

� Create and solve quadratic and exponential inequalities in one variable

� Solve quadratic equations by completing the square.

� Derive the quadratic formula by completing the square.

� Solve a system consisting of linear and quadratic equations in two variables.

� Graph the solutions to a linear inequality in two variables as a half-plane and the

system of linear inequalities as the intersection of half-planes.

� Use function notation and interpret statements that use function notation.

� Recognize that sequences are functions.

� Interpret key features of graphs and tables in terms of the quantities.

� Define a linear, quadratic or exponential function and represent with a table, rule, or

graph.

� Graph an exponential function and a piece-wise function including absolute value

showing intercepts and end-behavior.

� Write arithmetic and geometric sequences both recursively and with an explicit

formula.

� Identify the effects of translations of f(x).

� Find inverse functions.

� Compare linear, quadratic, and exponential models.

� Use statistics appropriate to the shape of the data distribution.

� Use the mean and standard deviation of data to fit it to a normal distribution.

� Compute (using technology) and interpret the correlation coefficient of a linear fit.

Grade

11

Algebra

Grade 8

Grade 7

More Algebra I standards, and . . . Content now in Algebra I, previously in Algebra II or Precalculus

� 5-weeks, 8:00 a.m. – 11:30 a.m.,

Monday – Thursday, (70 hours)

� June 30th – July 17th, and then

resuming August 4th – August 14th

� No classes during weeks of July 21 or

August 18

� Course open only to students who will

be entering 10th grade in the fall, have

completed Algebra 1 successfully, and

for advancing/accelerating purposes

� 2 credits earned upon successful

completion / is not included in GPA

Summer Geometry Class

Curriculum Resources & Information

� Web-based curriculum management tool

� Year 1 – Math Courses Grades 6-8

� Year 2 – Expansion to Grades 3-12

� Teacher Resource

� Parent Resource

Public Site View

Public Site View

Questions