Pre-Algebra
EMS 8th Grade Math Department / Unit 2: Exponents and Scientific Notation
Unit 3: Rational and Irrational Numbers / Dates: September 18th – October 22nd
Math Florida Standard(s)
Benchmarks, Descriptions
and DOK levels / MAFS.8.EE.1.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. MAFS.8.EE.1.3: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. MAFS.8.EE.1.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. MAFS.8.BS.1.1 (DOK 1): Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. MAFS.8.NS.1.2 (DOK 2): Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions. MAFS.8.EE.1.2 (DOK 1): 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.
Learning Goal / Students will know, apply, and evaluate the properties of integer exponents and be able to generate equivalent numerical expressions, including scientific notations. Students will know and distinguish between rational and irrational numbers, and be able to use rational approximations of irrational numbers for value estimation.
Essential Question(s) / How do you apply the concepts of numbers and their relationships to solve various problems you are faced with in daily life? What does a square root tell us? What is the difference between a rational and irrational number? How do we estimate irrational numbers?
Assessments / Pre-Assessments / KWL on Exponents, Skills Practice Pg. 642
Formative Assessments / Cornell Notes Practice, Summary and Comprehension Ratings, Homework Assignments
Summative Assessments / Mid Chapter 7 Quiz, Test on Real Numbers
Progress Monitoring/ Feedback Loop / Homework: Practice K Worksheets for Lessons 7-1, 7-2, 7-3, 7-4, 7-5, 1-3, 10-2.
Mid-Chapter 7 Quiz
Higher Order Question(s) / How are exponents related to the four arithmetic operations? Why do you apply the properties of integer exponents to produce equivalent expressions? Why did you choose ______unit of measure? How is scientific notation used? When and why would you use scientific notation? Why does a decimal expansion eventually repeat? How can you use rational approximations of irrational numbers to compare the size of irrational numbers? Why should you estimate the value of expression involving irrational numbers using rational approximations?
Key Vocabulary / Exponential Form, Exponent, Base, Power, Negative Exponent, Scientific Notation, Real Numbers, Rational Numbers, Density Property, Irrational Numbers, Square Roots, Cube Roots, Rational Approximations
Monday, October 19th, 2015 / Intro to Squares and Roots / Rigor Level: 2
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will explore the concepts of squares and square roots through hands-on manipulatives and completion of charts and tables.

BELL RINGER
( 5 minutes) /
  • ELL Vocabulary Support Page

I DO: /
  • Go over expectations for exploration activities.
  • Go over expectations for entering the room and bellwork.

WE DO: /
  • Practice learning Squares and cubes
  • Where do we find these used in the real world
  • Algebra 1 book Page 24

YOU DO: /
  • Monitor yourself on the leaning goal chart

Homework /
  • Create and illustrate a real world problem using a square or a cube. Answer it.

EXIT TICKET:
(5 minutes) /
  • #10 Why are 10 and –10 both square roots of 100?

Tuesday, October 20th, 2015 / Square Roots / Rigor Level: DOK 2
6th Period Fills Out PSAT Answer Blank Form
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will find the positive and negative square roots of numbers through guided notes and practice problems.

BELL RINGER
( 5 minutes) /
  • Practice squares and cubes/

I DO: /
  • Monitor and encourage

WE DO: /
  • Share out homework
  • Cornell notes on negative and positive squares and cubes.

YOU DO: /
  • Summarize It!

Homework /
  • Worksheet

EXIT TICKET:
(5 minutes) /
  • Explain what you know about square roots and cube roots

Wednesday, October 21th, 2015 / Square Roots / Rigor Level: DOK 2
6th Period Takes PSAT in the Afternoon
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will estimate square roots to the nearest whole number.

BELL RINGER
( 5 minutes) /
  • Practice squares and cubes/

I DO: /
  • Go over Vocabulary
  • Re-Teach Estimate Square Roots to Nearest Whole Number Pg. 29

WE DO: /
  • Practice Problems Pg. 29

YOU DO: /
  • Practice Form G Pg. 23 all

Homework /
  • None

EXIT TICKET:
(5 minutes) /
  • Error Analysis Problem

Thursday, October 22th, 2015 / Estimate Square Roots / Rigor Level: DOK 2
Pre-Algebra Daily Agenda
Daily Objective /
  • Students will show mastery on their knowledge of squares and cubes and how they are used in the real world today using a quiz

BELL RINGER
( 5 minutes) /
  • Practice squares and cubes

I DO: /
  • Monitor and assess

WE DO: /
  • Discuss questions on squares and cubes

YOU DO: /
  • Quiz on squares and cubes.

Homework /
  • None.

EXIT TICKET:
(5 minutes) /
  • Rate Yourself on Learning Goal Scale what did you learn this week. 3-5 sentences.

Friday, October 23th, 2015 / Rigor Level: DOK 3
Pre- Algebra Daily Agenda
Daily Objective /
  • No school

BELL RINGER
( 5 minutes)
I DO:
WE DO:
YOUDO:
Homework
EXIT TICKET:
(5 minutes)

Note: Learning Scales, Accommodations, and Math Practice Standards are below.

Scale / Learning Goals Scale: Exponents, Scientific Notation, Rational & Irrational Numbers
4.0 / Apply knowledge of exponents, scientific notation, rational and irrational numbers to real-world situations.
3.5 / In addition to 3.0 skills, I can do some of the 4.0 skills.
3.0
(GOAL)
With no help, I can do all these skills. / Use rational approximations to compare the size of irrational numbers and estimate the value of expressions.
Evaluate square and cube roots of small perfect squares and cubes.
Compare large or small quantities expressed as a single digit times an integer power of 10.
Perform operations with numbers expressed in scientific notation.
2.5 / In addition to all 2.0 skills, I can do some of the 3.0 skills.
2.0
With no help, I can do all these skills. / Locate irrational numbers on a number line using rational approximations.
Apply properties of integer exponents to generate equivalent numerical expressions.
Use square root and cube root symbols to represent solutions to equations in the form x2=p and x3=p.
Convert very large and very small quantities into scientific notation.
Distinguish between rational and irrational numbers.
1.5 / On my own, I can do some of the 2.0 and 3.0 skills.
1.0 / With help, I can do some of the 2.0 and 3.0 skills.
0.5 / With help, I can do some of the 2.0 skills.
0.0 / Even with help, I have no success.
WICR Strategies used during each unit.
Writing
Writing activities that help
students understand the
content / Inquiry
Questioning strategies
that help students
understand the content / Collaboration
Working together with a
partner or in a group of
students to understand, to
problem solve, or to
complete a task/project / Reading
Any strategies in reading
that help students
understand
Writing-to-Learn
• summaries
Process Writing
• using a rubric as evaluation
On-Demand/Timed-Writing
• writing that is completed in class within a set amount of time
• grade is evaluated using a rubric
Cornell Notes
• taking notes on the most important information
• summarizing
• using the notes to study
Reflective Writing
• students write about what they have learned and what they still need / Higher-Level Questioningin Classes
• Costa’s Level 1: Studentsfind the answers right therein the text.
• Costa’s Level 2: Studentsmust figure out the answerfrom information in thetext.
• Costa’s Level 3: Studentsapply what they havelearned or use what theyhave learned to evaluate orcreate. / Think Pair Share
Sharing Ideas With a Partner or in a Group
Carousel or Gallery Walk
Problem Solving in Groups
Projects in Groups / Before Reading Activities
• vocabulary activities
• accessing prior knowledge
• making predictions
During Reading Activities
• marking the text
• Cornell notes
• graphic organizers
After Reading Strategies
• summarizing
• group projects
Accommodations used daily on an individual basis in accordance with IEP and 504 plans and ELL Students
  • Read directions for the student
  • Check for understanding
  • Allow to leave class for assistance
  • Extra time for exams
  • Daily agenda
/
  • Allow student time to step out to de-escalate
  • Testing in small groups
  • Use of a planner/binder for organization
  • English Language Dictionary
/
  • Extended time on assignments =1 day
  • Preferential seating
  • Written direction given
  • Break directions into chunks
/
  • Read Aloud to Students
  • Visual manipulatives
  • Cooperative Learning,
  • Vocabulary, Description, Introduction,
.
Student Friendly Mathematical Practice Statements
MAFS.K12.MP.1.1 Make Sense of Problems and Persevere in Solving Them
• Make a plan! • Try different approaches when your problem is hard. • Solve your problem in more than one way. • Check whether your solution makes sense.
MAFS.K12.MP.2.1 Reason Abstractly and Quantitatively
• Explain the meanings of the numbers, words, pictures, symbols, and objects you and others use.
MAFS.K12.MP.3.1 Construct Viable Arguments and Critique the Reasoning of Others.
• Explain both what to do and why it works. • Work to make sense of others’ mathematical thinking.
MAFS.K12.MP.4.1 Model with Mathematics
• Apply math to real-world situations. • Use models such as graphs, drawings, tables, symbols, numbers, and diagrams to solve problems.
MAFS.K12.MP.5.1 Use appropriate Tools Strategically
• Choose appropriate tools for your problem. • Use mathematical tools correctly and efficiently. • Estimate and use what you know to check the answers you find using tools.
MAFS.K12.MP.6.1 Attend to Precision
• Communicate your mathematical thinking clearly and precisely. • Use the level of precision you need for your problem. • Be accurate when you count, measure, and calculate.
MAFS.K12.MP.7.1 Look for and Make Use of Structure
• Find, extend, analyze, and create patterns. • Use patterns and structures to solve problems.
MAFS.K23.MP.8.1 Look for and Express Regularity in Repeated Reasoning
• Use patterns and structures to create and explain rules and shortcuts. • Use properties, rules, and shortcuts to solve problems. • Reflect on your thinking before, during, and after you solve a problem.