6th- 8th Grade Curriculum Day

Jeanine LynchFebruary 19, 2014

Catawba County Schools

Norms for our day:“ Be Attitudes”

BE present - silence your phones and put away your lap top until needed

BE positive and respectful

BE engaged and contribute equally

Introductions

Take a few minutes tointroduce yourself to your

table group.

CCS RESOURCES

Website – Curriculum Secondary Education

› Grade Levels› NCSCOS› Symbaloo – Web Resources

Learning Goals for Today

PWBAT- Recognize and identify the mathematical practices being used during math activities presented.

PWBAT – Include the mathematical practices in the thoughtful planning of lessons.

PWBAT – Identify the mathematical practices that were used in content activities

PWBAT – Locate and record resources on various websites shown for use by teachers in your grade level.

8 Standards for Mathematical

Practice

Mathematically Proficient

Students…….

8 Standards for Mathematical

Practice1. 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.

8 Standards for Mathematical

Practice5. 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.

8 Standards for Mathematical

Practice

Let’s Jigsaw……...

TIMER

8 Standards for Mathematical

Practice

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

8 Standards for Mathematical

Practice2. Reason abstractly and quantitatively.

8 Standards for Mathematical

Practice

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

8 Standards for Mathematical

Practice

4. Model with mathematics.

8 Standards for Mathematical

Practice

5. Use appropriate tools strategically.

8 Standards for Mathematical

Practice

6. Attend to precision.

8 Standards for Mathematical

Practice

7. Look for and make use of structure.

8 Standards for Mathematical

Practice

8. Look for and express regularity in repeated reasoning.

Critical Areas of 6th GradeSixth Grade

Domain DomainThe Number System Apply and extend previous

understandings of multiplication and division to divide fractions

Compute fluently with multi-digit numbers and find common factors and multiples

Apply and extend previous understandings of numbers to the system of rational numbers.

 

Expressions and Equations Apply and extend previous

understandings of arithmetic to algebraic expressions.

Reason about and solve one-variable equations and inequalities.

Represent and analyze quantitative relationships between dependent and independent variables.

 

Ratio and Proportional Relationships Understand ratio concepts

and use ratio reasoning to solve problems

Geometry Solve real-world and

mathematical problems involving area, surface area, and volume.

Statistics and Probability Develop understanding of

statistical variability. Summarize and describe

distribution. 

 

27-32%

30%

27-

32%

30%

12-17%14%

12-17%

16%

7-12%10%

The Number System(30%)

Expressions and Equations(30%)

60% of the 6th grade EOG

Critical Areas of 7th Grade

Seventh GradeDomain Domain

 Ratio and Proportional Relationships Analyze proportional

relationships and use them to solve real-world mathematical problems

Expressions and Equations Use properties of

operations to generate equivalent expressions

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

 

Geometry Draw, construct, and

describe geometrical figures and describe the relationships between them.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Statistics and Probability Use random sampling to

draw inferences about a population.

Investigate chance processes and develop, use and evaluate probability models

The Number System Apply and extend previous

understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

 

 

22-27%

26%

22-

27%

26%

22-27%24%

12-17%

14%

7-12%10%

Ratios and Proportional Relationships(26%)

Expressions and Equations(26%)

52% of the 7th grade EOG

(Geometry -24%)

Critical Areas of 8th GradeEighth Grade

Domain Domain 

Expressions and Equations Work with radicals and

integer exponents Understand the connections

between proportional relationships, lines and linear equations.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Functions Use functions to model

relationships between quantities

Define, evaluate, and compare functions

 

.

Geometry Understand congruence and

similarity using physical models, transparencies, or geometry software.

Statistics and Probability Investigate patterns of

association in bivariate data.

 

The Number System Know that there are

numbers that are not rational, and approximate them by rational numbers.

 

27-32%

32%

22-

27%

24%

20-25%22%

15-20%

16%

2-7%6%

Functions(24%)

Expressions and Equations(32%)

56% of the 8th grade EOG

Released Test Items

Released EOG Test Forms

CCSS 8.EE.2

Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Big Idea: Explore with manipulatives why some numbers are perfect squares and others are not then how this translates into square roots!

SWBAT understand what it means to square a number, understand a number is not a perfect square, and how to estimate square roots.

As we work through these standards today, use conceptual strategies as you solve problems. The standards call for us to teach conceptually and to use models and drawings.

Once we show kids the “tricks or procedure, the conceptual piece gets lost.

Perfect Squares Tiles Activity

Learning Target: I will understand what it means to be a square number, be a perfect square, and take the square root of a number.

Work in groups to complete the questions #1-8. 10 minutes

Be prepared to present the question #asked.

Mini wrap-up

Perfect Squares Tiles Activity 1. Using the square tiles, make the smallest perfect square you

can. › a. How many tiles did you use? › b. What are the dimensions of your square (length and width)?

2. Using more tiles, make the next smallest perfect square you can. › a. How many tiles did you use? › b. What are the dimensions of your square (length and width)?

3. Make the next smallest perfect square you can. › a. How many tiles did you use? › b. What are the dimensions of your square (length and width)?

4. Make the next smallest perfect square you can. › a. How many tiles did you use? › b. What are the dimensions of your square (length and width)?

5. Using all your given tiles, make the biggest perfect square you can. › a. How many tiles did you use? › b. What are the dimensions of your square (length and

width)?

6. What does it mean to square a number?

7. What does it mean for a number to be a perfect square? Can just any number be considered a perfect square, why or why not?

8. What does it mean to take the square root of a number? Think back to your tiled squares, what part of the diagram represents the square root?

A Number that is a Perfect Square

Dimensions of the Square

(length x width)

What is the Square Root of the Perfect Square Number?

Example: 1 1 x 1 1

4 2 x 2 2

9 3 x 3 3

16 4 x 4 4

25 5 x 5 5

36 6 x 6 6

49 7 x 7 7

64 8 x 8 8

81 9 x 9 9

100 10 x 10 10

9. Complete the table below by listing all the perfect squares you discovered from least to greatest.

10. What is the algebraic relationship between squaring the number and taking the square root of a number?

Solution to the expression x²

Dimensions of a tiled square

Square Root of each solution

Example: 4 2 x 2 2

3

6

12

20

34

46

57

72

11. Complete the following table without a calculator – Estimate the solutions the best you can.

Explain how you chose numbers to complete the table above.

12. Your teacher will be bringing you examples of student responses to question 9. Analyze each table and explain what the students were thinking when they completed the table and if you agree with their method. Choose a table that you feel is the most accurate.

Table A

Table B

Table C

8 Standards for Mathematical

Practice

What practices did we use?

Planning for Horizontal Alignment

Share contact information with those in your school/feeder district

Take notes on information shared and think about what your contribution could be.

What are your strengths/weaknesses? Join Dropbox Plan at least one meeting between now

& spring break

Just a bit of Housekeeping:

1. We are to teach the standards, not programs. Carnegie Learning Text is a tool. Mathia is a tool. Resources found today are tools.

2. ClassScape is a formative assessment piece. It is not intended for grades. Formative Assessment guides our instruction. ClassScape is used to inform us of where to go next.

3. How will your formative assessment guide your instruction?

4. Students should be asked to show their work.5. Be very mindful & careful of resources found online.

6. Fewer problems with written explanations work well. 7. Vocabulary development is important. It must be taught in context, interactive, not passive.8. How will you assess your students? Begin with the end in mind.9. Conceptual vs. Procedural – Remember

that once a procedure is taught it can’t be untaught.10. Teachers need to communicate to students/parents the expectation that students should ‘Comfortably Struggle’.

Benefits of Formative Assessment

Clarifying and sharing learning intentions and criteria for success

Engineering effective discussion, questions, activities, and tasks that elicit evidence of learning

Providing feedback that moves students forward

Activating students as instructional resources for one another

Activating students as owners of their own learning Marnie Thompson & Dylan Williams

Suggested Plan of Attack for Carnegie Lessons

WORK the lesson FIRST – do the Math!! PRIORITIZE – What’s the overall goal? Mark the:

› Must Do’s› Should Do’s› Might Do’s

CHUNK – Which pieces of lesson will you chunk for students?

PACE – How long will you give each student to work each chunk?

ASSESS – Which pieces will students share out and how will you know if they have mastered what you wanted?

EXIT TICKET

ON INDEX CARD COMPLETE:› ONE THING I LEARNED TODAY THAT I CAN USE

IN MY CLASSROOM IS______________________› ONE THING I WOULD LIKE TO LEARN MORE

ABOUT IS __________________________________› ONE QUESTION I STILL HAVE OR NEED HELP

WITH IS_____________________________________ Put your name on the exit ticket ONLY if

you would like me to contact you for more help!!!

As we work through these standards today, use conceptual strategies as you solve problems. The standards call for us to teach conceptually and to use models and drawings.

Once we show kids the “tricks or procedure, the conceptual piece gets lost.

8.EE.8

Analyze and solve pairs of simultaneous linear equations

Prior knowledge needed-› Solve multi-step equations› Familiarity with linear equations in two

variables

BIG IDEA – Explore representing quantities in real-world problems and finding their solutions

SWBAT › Solve systems of two linear equations with

a model› Solve systems of linear equations

algebraically› Solve real-world problems leading to two

linear equations in two variables

COOKIE CALORIE CONUNDRUM

Warm-Up Introduce Scenario – What information

do we know from information Activity

8 Standards for Mathematical

Practice

What practices did we use?

8 Standards for Mathematical

Practice

What practices did we use?