HS Algebra

HS AlgebraFebruary 2013

“Teachers are thus free to provide students with whatever tools and knowledge their professional judgment and experience identify as most helpful for meeting the goals set out in the Standards.”~ Introduction to the CCSS

Outcomes Align the regional/district Algebra course

to the PARCC framework Create tape diagrams and double

number lines to solve application problems

Explain the information we have, need and will make do with

PARCC Resources Progressions

http://ime.math.arizona.edu/progressions/ Illustrative Mathematics

http://illustrativemathematics.org/ Common Core Tools

http://commoncoretools.wordpress.com/ Quality Review Rubrics

http://www.achieve.org/files/TriState-Mathematics-Quality-RubricFINAL-May2012.pdf

Achieve the Core http://www.achievethecore.org/

PARCC Components Key Advances from the Previous

Grade Discussion of Mathematical

Practices in Relation to Course Content

Fluency Recommendations Pathway Summary Tables Assessment Limits Tables

Imagine your perfect student…

Math Practice Meditation Imagine your best students… consider

how they showed each of these qualities… 1. Perseverance

2. Reason abstractly and quant.

3. Construct and critique

4. Model

5. Use tools strategically

6. Precision

7. Use structure

8. Find and express repeated reasoning

Look For’s in a CCLS Lesson Fluency Task (~10 mins) Modeling

Concept Building Application

Debrief Pair Sharing Exit Ticket (Daily formative assessment)

Module Sources

6-12

CCI EduTron

PK-5Common Core Inc

ConstructScope and Sequence PK-8

Grade Level Map

Modules

Lessons

Assessment

New Module

Mid Module Assessment

End of Module Assessment

Content Gap Instruction Multiplication

Division Strategies

Algebraic Understanding

Fractions

Number Sense & Place Value

Quiz 1 What teaching materials will likely be

available?

Is State Ed is making and providing all of the math materials teachers need?

What are important documents to help build our HS curriculum?

Math Modules

PK-5Common Core

Inc

6-12CCI with

Support from EdutTron

Fluency

Application

FluencyConceptual

Required FluenciesGrade Required FluencyK Add/Subtract within 51 +/- within 102 Add/Subtract within 20

Add/Subtract within 100 (paper and pencil)3 Multiply/divide within 100

Add/Subtract within 10004 Add/Subtract within 1,000,0005 Multi-digit multiplication6 Multi-digit division

Multi-digit decimal operations7 Solve px+q=r, p(x+q)=r8 Solve simple 2x2 systems by inspection

Application

FluencyConceptual

Multiplication Facts X 1 2 3 4 5 6 7 8 9

1 1 x 1 1 x 2 1 x 3 1 x 4 1 x 5 1 x 6 1 x 7 1 x 8 1 x 9

2 2 x 1 2 x 2 2 x 3 2 x 4 2 x 5 2 x 6 2 x 7 2 x 8 2 x 9

3 3 x 1 3 x 2 3 x 3 3 x 4 3 x 5 3 x 6 3 x 7 3 x 8 3 x 9

4 4 x 1 4 x 2 4 x 3 4 x 4 4 x 5 4 x 6 4 x 7 4 x 8 4 x 9

5 5 x 1 5 x 2 5 x 3 5 x 4 5 x 5 5 x 6 5 x 7 5 x 8 5 x 9

6 6 x 1 6 x 2 6 x 3 6 x 4 6 x 5 6 x 6 6 x 7 6 x 8 6 x 9

7 7 x 1 7 x 2 7 x 3 7 x 4 7 x 5 7 x 6 7 x 7 7 x 8 7 x 9

8 8 x 1 8 x 2 8 x 3 8 x 4 8 x 5 8 x 6 8 x 7 8 x 8 8 x 9

9 9 x 1 9 x 2 9 x 3 9 x 4 9 x 5 9 x 6 9 x 7 9 x 8 9 x 9

CommutativeProperty

Identity Property

Doubles Squares(benchmark

)

Fives(benchmark)

Challenge

Gene Jordan’s work but I got the Idea from Gina King’s article:www.nctm.org teaching children mathematics • King, Fluency with Basic Addition, September 2011 p. 83

Application

FluencyConceptual

Addition Facts

Gina King’s article:www.nctm.org teaching children mathematics • King, Fluency with Basic Addition, September 2011 p. 83

Application

FluencyConceptual

Fluency Example Finger Counting 1,2,3, sit on 10 High 5

Application

FluencyConceptual

Fluency

Fast Frequent

Fun

Application

FluencyConceptual

Math Sprints

Ready, Set, Go!

Sprint A

Review

Sprint A

Math Moves

Sprint B

Review

Sprint B

Cool Down

Application

FluencyConceptual

Conceptual Modeling

Application

FluencyConceptual

Conceptual Concrete Pictorial Abstract Moving both ways

Draw a picture of 4+4+4 Show your thinking Explain, defend and critique the

reasoning of others

Application

FluencyConceptual

Concrete Model Equation

X + 3 = 5

Application

FluencyConceptual

Tape Diagram Problems Tape diagrams are best used to model ratios when the two quantities have the same units.

Tape Diagrams: Q1 1. David and Jason have marbles in

a ratio of 2:3. Together, they have a total of 35 marbles. How many marbles does each boy have?

Tape Diagrams : Q2 2. The ratio of boys to girls in the

class is 5:7. There are 36 children in the class. How many more girls than boys are there in the class?

Tape Diagrams Q3: Comparing 3 itemsLisa, Megan and Mary were paid

$120 for babysitting in a ratio of 2: 3: 5. How much less did Lisa make than Mary?

Tape Diagrams Q4: Different RatiosThe ratio of Patrick’s M & M’s to Evan’s is 2: 1 and the ratio of Evan’s M & M’s to Michael’s is 4: 5. Find the ratio of Patrick’s M & M’s to Michael’s.

Tape Diagrams Q5: Changing RatiosThe ratio of Abby’s money to Daniel’s is 2: 9. Daniel has $45. If Daniel gives Abby $15, what will be the new ratio of Abby’s money to Daniel’s?

Double Number Line Double number line diagrams are best used when the quantities have different units. Double number line diagrams can help make visible that there are many, even infinitely many, pairs of numbers in the same ratio—including those with rational number entries. As in tables, unit rates (R) appear in the pair (R, 1).

Double Number Line: Finding average rate It took Megan 2 hours to complete 3

pages of math homework. Assuming she works at a constant rate, if she works for 8 hours, how many pages of math homework will she complete? What is the average rate at which she works?

Identify properties of the RDW modeling technique for application problems Read (2x) Draw a model Write an equation or number sentence Write and answer statement

Unit Object Context

Use RDW to solve Problem

Modeling Challenge 2 boxes of salt and a box of sugar cost

$6.60. A box of salt is $1.20 less than a box of sugar. What is the cost of a box of sugar?

Salt

Salt

Sugar

$1.20

$6.603 parts = $6.60- $1.20

3 parts = $5.401 part = $5.40 ÷ 3 = $1.80$1.20+$1.80= $3.00

Challenging Problems The students in Mr. Hill’s class played games at recess.

6 boys played soccer 4 girls played soccer 2 boys jumped rope 8 girls jumped rope

1) Compare the number of boys who played soccer and jumped rope using the difference. Write your answer as a sentence as Mika did.

2) Compare the number of boys who played soccer and jumped rope using a ratio. Write your answer as a sentence as Chaska did.

3) Compare the number of girls who played soccer to the number of boys who played soccer using a ratio. Write your answer as a sentence as Chaska did.

Mika Said: “Four more girls jumped rope than played soccer.”

Chaska Said: “For every girl that played soccer, two girls jumped rope.”Mr Hill Said: “Mika compared girls by looking at the difference and

Chaska compared the girls using a ratio”

Challenging Problems Compare these fractions:

Which one is bigger than the other? Why?

and

ApplicationApplication

FluencyConceptual

Application The beginning of the year is

characterized by establishing routines that encourage hard, intelligent work through guided practice rather than exploration.

Slower and deeper Use the Read-Draw-Write (RDW) steps

Application

FluencyConceptual

Application

Wrap upThanks for coming!

Links www.btboces2.org/mathpd http://

www.parcconline.org/samples/mathematics/grade-6-slider-ruler

http://www.parcconline.org/samples/mathematics/grade-7-mathematics

www.Engageny.org

High School FunctionsA--‐REI.4. Solve quadratic equations in one variable.

High School Illustrative Sample Item

Seeing Structure in a Quadratic Equation

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A-- REI.4. Solve quadratic equations in one variable.‐

High School Illustrative Sample Item

Seeing Structure in a Quadratic Equation

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A-- SSE, Seeing Structure in Expressions‐

Aligns to the Standards and Reflects Good Practice

High School Sample Illustrative Item: Seeing Structure in a Quadratic Equation

Task Type I: Tasks assessing concepts, skills and procedures Alignment: Most Relevant Content Standard(s)A-REI.4. Solve quadratic equations in one variable.

a) Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from

this form.b) Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the

square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a bi for real

numbers a and b.Alignment: Most Relevant Mathematical Practice(s)

Students taking a brute-force approach to this task will need considerable symbolic fluency to obtain the solutions. In this sense, the task rewards looking for and making use of structure (MP.7).

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Aligns to the Standards and Reflects Good Practice

High School Illustrative Item Key Features and Assessment AdvancesThe given equation is quadratic equation with two solutions. The task does not clue the student that the equation is quadratic or that it has two solutions; students must recognize the nature of the equation from its structure. Notice that the terms 6x – 4 and 3x – 2 differ only by an overall factor of two. So the given equation has the structure

where Q is 3x – 2. The equation Q2 - 2Q is easily solved by factoring as Q(Q-2) = 0, hence Q = 0 or Q = 2. Remembering that Q is 3x – 2, we have

.These two equations yield the solutions and .

Unlike traditional multiple-choice tests, the technology in this task prevents guessing and working backwards. The format somewhat resembles the Japanese University Entrance Examinations format (see innovations in ITN Appendix F). A further enhancement is that the item format does not immediately indicate the number of solutions.

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Gr. 7 Ratios and Proportions:Equivalent Ratios and Fractions

Gr. 7 Ratios and Proportions:Equivalent Ratios and Fractions

Gr. 7 Ratios and Proportions:Equivalent Ratios and Fractions

Gr. 7 Ratios and Proportions:Equivalent Ratios and Fractions

Math SprintsFluency in a minute

“Teachers are thus free to provide students with whatever tools and knowledge their professional judgment and experience identify as most helpful for meeting the goals set out in the Standards.”~ Introduction to the CCSS