Lou Maynus,Lead Coordinator

Mathematics and Middle Level EducationOffice of Instruction, WVDE

The Next Generation Grade 8 standards are of significantly higher rigor than the former Grade 8 standards.

linear relationships and equations functions irrational numbers geometry standards that relate graphing to

algebra statistics presented is more sophisticated bivariate data.

The Next Generation Grade 8 standards are

of significantly higher rigor than the former Grade 8 standards.

linear relationships and equations functions irrational numbers geometry standards that relate graphing to

algebra statistics presented is more sophisticated bivariate data.

M.8.NS.1   M.8.NS.2                           M.8.EE.1  M.8.EE.2                            M.8.EE.3   M.8.EE.4                           M.8.EE.5 M.8.EE.6 M.8.EE.7   M.8.EE.8 M.8.F.1 M.8.F.2 M.8.F.3 M.8.F.4

M.8.F.5 M.8.G.1 M.8.G.2                                M.8.G.3 M.8.G.4                               M.8.G.5 M.8.G.6 M.8.G.7 M.8.G.8 M.8.G.9 M.8.SP.1 M.8.SP.2 M.8.SP.3 M.8.SP.4

M.8.NS.1   M.8.NS.2                           M.8.EE.1  M.8.EE.2                            M.8.EE.3   M.8.EE.4                           M.8.EE.5 M.8.EE.6 M.8.EE.7   M.8.EE.8 M.8.F.1 M.8.F.2 M.8.F.3 M.8.F.4

M.8.F.5 M.8.G.1 M.8.G.2                                M.8.G.3 M.8.G.4                               M.8.G.5 M.8.G.6 M.8.G.7 M.8.G.8 M.8.G.9 M.8.SP.1 M.8.SP.2 M.8.SP.3 M.8.SP.4

Mathematics Progression

http://www.youtube.com/watch?v=a-P9KQdhE0U

7

Algebra, MjAdvanced Mj

Mathematics, Mjand Real Life Mj

Proportional MjReasoning Mj

Fractions MjMultiplicative MjReasoning Mj

Additive MjReasoning Mj

The Important Connection Mj

8

Algebra, MjAdvanced Mj

Mathematics, Mjand Real Life Mj

Proportional MjReasoning Mj

Fractions MjMultiplicative MjReasoning Mj

Additive MjReasoning Mj

The Important Connection Mj

9

Use Basic Dimensions

of Mathematica

l Competency

Model

Abstract to Models

Revise and Improve Models

Apply Models

Represent

Understand and Use Numbers

and Operations

Create Representational Devices

Revise Representational Devices

Interpret Representational Devices

TranslateRepresentational Devices

Integrate Representational Devices

Recognize the Effect of Assumptions

Recognize Improbable

Results

Communicate

Use Metacognitio

n

Discover/Create New

ResultsConnect Generalize

Provide Supporting Examples

ProvideCounter-examples

PoseConjectures

Evaluate Arguments

Develop Informal

Proof

Recognize Need for

Formal Proof

Use Inference

Understand and Use

Measurements

Understand and Use

Geometry

Understand and Use Algebra

Use Representation

s Fluently

Use Procedures

Fluently

Use Conceptual Knowledge

Understand and Use Data Analysis and Probability

Use Percentage With

Understanding

Generate an Equation

Solve Equations and Inequalities

and Simplify Expressions

Use, Graph, and Reason About Linear Functions and Some

Non-linear Functions (Quadratic Functions)

Use and Understand Algebraic Notation

Work in 2- and 3-Dimensional Space

Using Distance and Angle

Understand Properties and Similar Figures

Understand Transformations

Estimate and Approximate

Use Formulas to Determine Perimeter

and Area of 2-Dimensional Shapes

Use Formulas to Determine Surface

Area and Volume of 3-Dimensional Shapes

Calculate the Probability of

an Event

Use and Interpret

Descriptive Statistics

Use and Interpret Data

Displays

Apply Conceptual Knowledge

Broadly

Apply Conceptual Knowledge

Deeply

Understand and Use Content-Specific

Procedures and

Language

Use Cross-Cutting

Mathematical Processes

Mathematical

Competency

Use Qualitative Reasoning

Justify

Argue

Understand and Operate With Real Numbers

Use Proportionality

With Understanding

Reason About Quantities

Use Ratio With Understanding

Use Rate With Understanding

CBAL Middle School Mathematics Competency Model

10

Use Basic Dimensions

of Mathematica

l Competency

Model

Abstract to Models

Revise and Improve Models

Apply Models

Represent

Understand and Use Numbers

and Operations

Create Representational Devices

Revise Representational Devices

Interpret Representational Devices

TranslateRepresentational Devices

Integrate Representational Devices

Recognize the Effect of Assumptions

Recognize Improbable

Results

Communicate

Use Metacognitio

n

Discover/Create New

ResultsConnect Generalize

Provide Supporting Examples

ProvideCounter-examples

PoseConjectures

Evaluate Arguments

Develop Informal

Proof

Recognize Need for

Formal Proof

Use Inference

Understand and Use

Measurements

Understand and Use

Geometry

Understand and Use Algebra

Use Representation

s Fluently

Use Procedures

Fluently

Use Conceptual Knowledge

Understand and Use Data Analysis and Probability

Use Percentage With

Understanding

Generate an Equation

Solve Equations and Inequalities

and Simplify Expressions

Use, Graph, and Reason About Linear Functions and Some

Non-linear Functions (Quadratic Functions)

Use and Understand Algebraic Notation

Work in 2- and 3-Dimensional Space

Using Distance and Angle

Understand Properties and Similar Figures

Understand Transformations

Estimate and Approximate

Use Formulas to Determine Perimeter

and Area of 2-Dimensional Shapes

Use Formulas to Determine Surface

Area and Volume of 3-Dimensional Shapes

Calculate the Probability of

an Event

Use and Interpret

Descriptive Statistics

Use and Interpret Data

Displays

Apply Conceptual Knowledge

Broadly

Apply Conceptual Knowledge

Deeply

Understand and Use Content-Specific

Procedures and

Language

Use Cross-Cutting

Mathematical Processes

Mathematical

Competency

Use Qualitative Reasoning

Justify

Argue

Understand and Operate With Real Numbers

Use Proportionality

With Understanding

Reason About Quantities

Use Ratio With Understanding

Use Rate With Understanding

CBAL Middle School Mathematics Competency Model

What happens if I skip this part?

The most common tendency in acceleration is to move students very quickly through the material at the same cognitive level of the regular track – only faster.

Select rich tasks that allow students to go much deeper with the content. Varied and interesting applications Learn other algorithms –know why they work Extend the topic to exponents Rather than flying through the same easy stuff the regular students will be doing in three weeks and then moving on to another topic.

How do I go deeper with the current content to accelerate student learning?

How do I differentiate with the same tasks without just giving more problems?

Accelerating 8th grade mathematics within the course (Functions)

Speeding Tickets

The function f(x) = 5(x – 65) + 120 is used to calculate a speeding ticket for a driver going x mph in a 65 mph speed zone.

Explain what the difference (x – 65) means in the context of this problem.

The function f(x) = 5(x – 65) + 120 is used to

calculate a speeding ticket for a driver going x mph in a 65 mph speed zone.

If the “5” in the function is changed to “4” and the “120” is changed to “180,” would speeding ticket costs increase or decrease? Show the work needed to support your answer.

The function f(x) = 5(x – 65) + 120 is used to calculate a speeding ticket for a driver going x mph in a 65 mph speed zone.  Is the set of all positive integers a reasonable domain for this function in the context of the problem? Explain why or why not and provide specific examples to support your reasoning.

 

The graph shows the relationship between the number of miles over the speed limit a person is traveling and the cost of a speeding ticket.

 Explain how the graph supports or refutes the statement

below: “As driving speeds become more reckless, the penalties

are more severe.”

In the step function above, the dependent variable is the cost of a speeding ticket. Provide a scale and labels for the axes that would make sense in the context of this problem.

Explain how the scale and labels you chose support the problem’s context.

For which level(s) of the learning progression might this section provide

evidence?

ProportionalPunch

Sweet Problem

or

Cinnamon Crunch Mighty Mint

800 1,200

Complete each statement.

The fraction of seventh graders who preferred Cinnamon Crunch is (express in lowest terms).

Suppose that in a comparison taste test of two new ice creams, 800 seventh graders preferred Cinnamon Crunch, while the remaining 1,200 seventh graders preferred Mighty Mint.

The percent of seventh graders who preferred Cinnamon Crunch is %.

Seventh graders preferred Mighty Mint to Cinnamon Crunch by a ratio of : .

Ratios Rule1 of 9 Facts

ProportionalPunch

Profit Sharing Problem

• 5 partners in Company A equally shared 2 million dollars.

• 7 partners in Company B equally shared 3 million dollars.

• 12 partners in Company C equally shared 5 million dollars.

The partners of which company received the most money per person?

Company A

Company B

Company C

Explain how you got your answer.

Ratios Rule 3 of 9 Facts

© Kirsty Pargeter/iStockphoto # 2448985

ProportionalPunch

Scale Drawing Problem

a. The length of the living room measures 2 inches on the blueprint.

What is the actual length of the living room?

feet

Explain how you got your answer:

A blueprint for a home is drawn with a scale ratio of

inch : 5 feet.

b. The width of the living room measures inch on the blueprint.

What is the actual width of the living room?

feet

Explain how you got your answer:

Ratios Rule 4 of 9 Facts

1

2

3

2

ProportionalPunch

Rate Problem

a. Complete the table below based on the graph.

The graph shows the amount of money Jake earns in terms of the time he works.

Time worked(hours)

Money earned(dollars)

Ratio

2 8

3 12

8

Money earned

Hours worked

b. Each of the ratios reduces to

c. What does that reduced ratio mean for Jake?

8

2

Ratios Rule 5 of 9

.

Facts

ProportionalPunch

Golden Problem

The ratio of length to width in a golden rectangle is about .

Explain how you determined the length and width.

Leonardo da Vinci drew the face of Mona Lisa within a golden rectangle so that it would be pleasing to look at. Five hundred years later, the pleasing shape of a golden rectangle is still appreciated as a measure of physical perfection.

8

5

In addition to an 8 by 5 rectangle, a 16 by 10 rectangle is also a golden rectangle. Give the length and width of another golden rectangle.

by

Ratios Rule 7 of 9 Facts

ProportionalPunch

Rocket Problem

To lift off, a rocket’s velocity must increase quickly. That can happen only with a large mass ratio.

Mass of rocket with fuel

Mass of rocket without fuel

Apollo Saturn V explored the Moon and Mars. The mass ratio of its first-stage rocket was about 17. The mass of that rocket without fuel was about 300,000 pounds.

What was the mass of the rocket with fuel?

Show your work.

Ratios Rule 8 of 9

pounds

Mass Ratio =

Source: www.NASA.gov

Facts

ProportionalPunch

Loan Problem

Most people who buy a house have to get a loan. Banks require that the ratio of what you borrow (debt) to what you earn (income) be less than 33%.

Pat earns $4,000 a month. Would she be approved for a monthly loan of $1,500?

Explain how you got your answer.

Debt

Income< 33%

Ratios Rule 9 of 9

Income

Debt

$

$

Facts

Yes No

High School Math I course is more advanced than our previous Algebra I course.

High School Math I course starts with more advance topics and includes more in depth work

linear functions exponential functions and relationships transformations and connecting algebra and

geometry through coordinates goes beyond the previous high school

standards in statistics.

Taking High School Math I to the Middle Level

Placement DecisionsPlacement decisions should be based on a

set ofclear, consistent, transparent, and objective

criteria.

Who Is Really Ready?Which students are ready for such rigorous

mathematics at an accelerated pace?

Evidence of student’s potential in advance mathematics courses.

Creation of new pre/post assessments including

performance based tasks to be placed on Acuity. Enroll students who want the challenge – and

seek them out.

Nation

Top States

West Virginia

How many students are ready?

Teachers of High School Math I

Teachers of high school mathematics in grade 8 need the same preparation and knowledge

as other teachers of high school mathematics. The challenges of teaching this kind of “fast

track” mathematics, even to very capable students, demand a lot from teachers.

2012 -2013 Sixty high school math teachers currently teaching Math I (1905 certifications)

2013-2014 Sixty math teachers (preference given to those currently teaching Math I (1905 certifications and 5-8 1900)

2014-2015 Sixty math teachers (preference given to those with 1905 certification and 5-8 1900 who are teaching the course)

Acceleration Middle School Options

Sixth Grade

High SchoolMath II

Middle School Options for Acceleration

Sixth Grade

High SchoolMath II

15 addition

al objective

s

13 additional objectives

15 additionalobjectives 13

additional objectives

Accelerating to High School Math I in 8th grade

Day 1Integers

Day 2Integers

Day 3Transformations

Day 4Rational Numbers

Day 5Rational Numbers

•Comparing, ordering integers•Coordinate graphing•Adding integers on the number line and with tiles•Performance tasks

•Adding integers•Subtracting integers•Multiplying integers•Dividing integers•Integer rules•Performance tasks

•Transformations•Performance Tasks

•Fractions, Decimals, Percents, Conversions•Applications in estimations

Mixed, improper, with the four operations.

Accelerating to High School Math I in 8th grade

Day 1Integers

Day 2Integers

Day 3Transformations

Day 4Rational Numbers

Day 5Rational Numbers

•Comparing, ordering integers•Coordinate graphing•Adding integers on the number line and with tiles•Performance tasks

•Adding integers•Subtracting integers•Multiplying integers•Dividing integers•Integer rules•Performance tasks

•Transformations•Performance Tasks

•Fractions, Decimals, Percents, Conversions•Applications in estimations

Mixed, improper, with the four operations.

SAMPLE for fa

ce to fa

ce

or online delivery

A student is misidentified

A teacher does not have the content knowledge

9th grade 10th grade 11th grade 12th grade

HS Math I HS Math II HS Math IIISTEM(first semester block)

HS Math IV(second semester block)

AP Calculus and/orAP Prob/Stats

HS Math II HS Math III LA AP Computer ScienceOrSTEM Readiness

AP Prob/Stats

HS Math II HS Math III STEM HS Math IV AP Calculus

Avoid skipping content

Avoid permanent or over-early tracking

Avoid watered-down courses. This has detrimental effects on every high school course thereafter

Adhere to the standards for mathematical practices as well as the content

The “regular grade 8” puts you on track for college and career success.

Accelerate by going deeper.

Acceleration – however it is done- should be thoughtful.

If you move High School Math I to the Middle Level, enroll the students who can do it.