Pre-Algebra 1

I am very happy to be teaching Pre-Algebra I again this year.  The syllabus will soon be posted below.  Please see my Homework and Handouts page for assignments. What a wonderful group of middle school students are in my class!

Syllabus: Pre-Algebra 1

 

Teacher: Ron BosLun

Website: http://compass-school.org/ron

Email: ron@compass-school.org

Text: JUMP Math Grade 7, workbooks 1 and 2

Time Frame: Full year

Course Overview:

This semester, we will continue to solidify students’ arithmetic mastery and work on their problem-solving skills as well as exploring topics in geometry and probability. We will spend the first half of the semester reviewing fractions and decimals and solving increasingly challenging problems that apply these skills to real-world contexts. The second half of the semester will focus on perimeter and area (touching on the related topics of unit conversion, algebraic formulas, ratios, pi, and irrational numbers), angles and triangles, and probability. The year will conclude with another inquiry project and a comprehensive final exam.

 

New Routines This Semester:

-          Students will have specific Khan Academy goals during each unit, only being allowed to pick the exercises they do after they have completed those goals.

-          Every Friday, we will spend half of class time on Khan Academy work/check-ins and half on Number Talks.

-          Students will be asked to follow a set notebook organization system and we will have notebook checks before every quiz. 

-          We will do three Problem-Solving Challenges with formal write-ups during the course of the semester.

 


Learning Outcomes:

 

Thinking and Reasoning:

  • Make sense of problems and persevere in solving them.
  • Construct viable arguments and critique the reasoning of others.
  • Apply mathematical knowledge to problems in other fields.
  • Attend to precision.
  • Maintain oversight of the big picture when solving a problem.
  • Look for and make use of patterns.
  • Transfer methods from one context to another.
  • Look for generalizations and shortcuts.
  • Ask questions, from the minute to the grand; formulate and pursue inquiries about mathematics.

 

Personal Development:

  • Effectively deal with getting stuck, e.g. by asking for help, looking for resources, or attacking the problem from a different angle.
  • Keep clear, organized notes and refer back to them.
  • Show self-direction in using class time wisely and completing assignments.

 

Communication:

  • Clearly communicate mathematical ideas, orally, visually, and in writing.
  • Present confidently and engagingly.
  • Extract information from textbooks, websites, and videos.

 

Community Involvement:

  • Collaboration in group problem-solving.
  • Respect for others’ ideas.

 

Knowledge:

Fractions and Decimals:

  • Add, subtract, multiply, and divide rational numbers.
  • Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
  • Convert a decimal to a percent and use decimals to solve percent problems.

 

Ratios and Proportional Relationships

  • Understand the concept of a ratio as a relationship between two quantities.
  • Compute ratios and relate them to fractions.

 

Expressions and Equations

  • Use formulas.

 

Measurement

  • Solve real-life and mathematical problems involving angle measure, perimeter, and area.
  • Use appropriate units.

 

Irrational Numbers

  • Understand the concept of an irrational number, including why it cannot be written as a fraction.
  • Understand what pi is and know its value to the hundredths place.
  • Understand what square roots are and calculate approximations for them to the tenths place.

 

Probability

Investigate chance processes and develop, use, and evaluate probability models. 

Approx. Dates

Topic

Activities

Assessment

Extra Challenge Options

Main Learning Goals

Week 1

Decimals

- Khan Academy,

- JUMP Book 1, Unit 5

- Decimal worksheets

Quiz

Problem-solving challenges (2012 game, Znorlian, Spakk’r)

- Add, subtract, multiply, and divide rational numbers.

- Calculate fluidly and attend to precision. 

Weeks 2-6

Fractions

- JUMP Book 1, Unit 3 (individualized plan based on fraction diagnostic test)

- Khan Academy fraction exercises

- Real-world problems with fractions

- Cookie Lab

- Problem-Solving Challenge #1: Muenster Madness

Khan Academy record, workbook checks, notebook checks, word problem sheets, Cookie Lab reflection, Muenster Madness write-up, unit test

Applying fractions to order of operations problems and equations,

making up your own fraction challenges

- Add, subtract, multiply, and divide rational numbers.

- Calculate fluidly and attend to precision.

- Transfer methods from one context to another.

- Maintain oversight of the big picture when solving a problem.

- Construct viable arguments and critique the reasoning of others.

Weeks 7-10

Perimeter and Area (classwork)

Converting between Fractions, Decimals, and Percents (homework)

- JUMP Book 1, Unit 6

- Fraction, decimal, and percent exercises in Khan Academy

- Ratio and percent number talks

- Stained Glass Challenge

- Problem-Solving Challenge #2: 36 Fences

- Problem-Solving Challenge #3: Painting a Set

Khan Academy record, workbook checks, notebook checks, class participation, write-ups of 36 Fences and Painting a Set, unit test

Bonus questions in JUMP book, brainteasers, extra challenge in Khan Academy

- Use appropriate units.

- Use formulas.

- Understand the concept of a ratio as a relationship between two quantities.

- Compute ratios and relate them to fractions.

- Understand the concept of an irrational number, including why it cannot be written as a fraction.

- Understand what pi is and know its value to the hundredths place.

- Understand what square roots are and calculate approximations for them to the tenths place.

- Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

- Convert a decimal to a percent and use decimals to solve percent problems.

- Make sense of problems and persevere in solving them.

- Construct viable arguments and critique the reasoning of others.

- Apply mathematical knowledge to problems in other fields.

Week 11

Angles and Triangles (classwork)

Converting between Fractions, Decimals, and Percents (homework)

- Parts of JUMP Book 1, Unit 4

- Fraction, decimal, and percent exercises in Khan Academy

- Ratio and percent number talks

- Triangle investigation

Khan Academy record, workbook checks, notebook checks, class participation, Triangle Investigation reflection, quiz

 

Crop Circles problem, bonus questions in JUMP book, brainteasers, extra challenge in Khan Academy

- Understand angle measure and visually compare angles.

- Use a protractor.

- Know vocabulary relating to angles, triangles, and polygons.

- Investigate angle relationships in triangles.

- Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

- Convert a decimal to a percent and use decimals to solve percent problems.

Week 12

Probability (classwork)

Converting between Fractions, Decimals, and Percents (homework)

- JUMP Book 2, Unit 8

- Fraction, decimal, and percent exercises in Khan Academy

- Ratio and percent number talks

Khan Academy record, workbook checks, notebook checks, class participation, quiz

 

Bonus questions in JUMP book, brainteasers

- Investigate chance processes and develop, use, and evaluate probability models.

- Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

- Convert a decimal to a percent and use decimals to solve percent problems.

Week 13

Asking and answering your own mathematical questions, review

Inquiry project, review for exam for homework, using Khan Academy as a resource

Project presentation and reflection

Go farther in your project, challenge yourself in KA

- Ask questions, from the minute to the grand; formulate and pursue inquiries about mathematics.

- Make sense of problems and persevere in solving them.

- Construct viable arguments and critique the reasoning of others.

- Apply mathematical knowledge to problems in other fields.

- Attend to precision.

- Maintain oversight of the big picture when solving a problem.

- Look for and make use of patterns.

- Transfer methods from one context to another.

- Look for generalizations and shortcuts.

Week 14

Exam

In-class review, take exam

Final exam

Bonus questions on exam

All the knowledge goals from the year!

 

From September:

Course Overview:

This course has two main goals: solidifying students’ arithmetic skills to get them ready for algebra and introducing students to the art of thinking like a mathematician. To this end, the course consists of three strands: 1) classwork from the JUMP Math workbooks, 2) homework from Khan Academy, a website that allows students to complete exercises at their own pace, and 3) problem-solving activities, both from the JUMP Math books and supplementary, culminating in an inquiry project. The routine for most class days will be as follows:

 

Routine:

- 10 minute warm-up, usually one of the following:

-          Math videos

-          Khan Academy

-          Number Talks*

-          Math games (Fraction War, Set, etc.) 

- Classwork: JUMP Math

- Homework: Khan Academy (http://khanacademy.org)

 

*Number Talks consist of short mental-math exercises, followed by a chance for students to share their solution methods.  These not only build skill in doing mental arithmetic, but also develop students’ flexibility in thinking about math, which translates to better fluidity in other areas of math as well.

 

 


Learning Outcomes:

 

Thinking and Reasoning:

  • Make sense of problems and persevere in solving them.
  • Construct viable arguments and critique the reasoning of others.
  • Apply mathematical knowledge to problems in other fields.
  • Attend to precision.
  • Maintain oversight of the big picture when solving a problem.
  • Look for and make use of patterns.
  • Transfer methods from one context to another.
  • Look for generalizations and shortcuts.
  • Ask questions, from the minute to the grand; formulate and pursue inquiries about mathematics.

 

Personal Development:

  • Effectively deal with getting stuck, e.g. by asking for help, looking for resources, or attacking the problem from a different angle.
  • Keep clear, organized notes and refer back to them.
  • Show self-direction in using class time wisely and completing assignments.

 

Communication:

  • Clearly communicate mathematical ideas, orally, visually, and in writing.
  • Present confidently and engagingly.
  • Extract information from textbooks, websites, and videos.

 

Community Involvement:

  • Collaboration in group problem-solving.
  • Respect for others’ ideas.

 

Knowledge:

Fractions and Decimals:

  • Add, subtract, multiply, and divide rational numbers.
  • Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
  • Convert a decimal to a percent and use decimals to solve percent problems.

 

Negative Numbers:

  • Understand addition and subtraction in terms of number line diagrams and absolute value.
  • Understand the rules of multiplication and division of integers and rational numbers in terms of the properties of operations.

 

Ratios and Proportional Relationships

  • Compute unit rates, including those associated with ratios of fractions and those involving quantities measured in different units.
  • Recognize and represent proportional relationships between quantities.
  • Use proportional relationships to solve multistep ratio and percent problems.
  • Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

 

Expressions and Equations 

  • Use properties of operations to generate equivalent expressions.
  • Use formulas.
  • Write expressions or equations to represent situations and solve them.

 

Measurement

  • Solve real-life and mathematical problems involving angle measure, perimeter, area, surface area, and volume.
  • Use appropriate units.

 

Irrational Numbers

  • Understand the concept of an irrational number, including why it cannot be written as a fraction.
  • Understand what pi is and know its value to the hundredths place.
  • Understand what square roots are and calculate approximations for them to the tenths place.

 

Probability

  • Investigate chance processes and develop, use, and evaluate probability models.
    Semester 1 Outline

 

Approx. Dates

Topic

Activities

Assessment

Extra Challenge Options

Main Learning Goals

Week 1

Getting your head back into math after the summer

- Flexing your math muscles with Khan Academy

- Starting to think about math creatively and inquisitively with videos and games

Khan Academy logs

Challenge yourself in Khan Academy, try to get a question up on the Great Questions board

- Calculate fluidly and attend to precision.

- Make sense of problems and persevere in solving them.

- Ask questions, from the minute to the grand; formulate and pursue inquiries about mathematics.

Week 2

Properties of Operations, Mastering Multiplication

- JUMP Book 1,

Unit 1

- Investigating the area model of multiplication with diagrams and paper-cutting

Workbook checks, unit test, class participation

Bonus questions in JUMP book, brainteasers

- Add, subtract, multiply, and divide rational numbers.

- Understand the rules of multiplication and division of integers and rational numbers in terms of the properties of operations.

- Attend to precision.

- Look for generalizations and shortcuts.

- Transfer methods from one context to another.

Weeks 3-5

Patterns & Algebra

- JUMP Book 1,

Unit 2

- Investigating Moebius strips

- Perhaps investigating some other patterns, such as Sierpinski Bricks

Workbook checks, unit test, class participation, Moebius strip write-up

Bonus questions in JUMP book, brainteasers, extend any patterns we work with or come up with your own

- Look for and make use of patterns.

- Solve linear equations.

Write expressions or equations to represent situations.

- Use properties of operations to generate equivalent expressions.

Weeks 6-8

Factors, Multiples, and Fractions

- JUMP Book 1,

Unit 3

- Locker Lab

- Real-world problems with fractions

Workbook checks, unit test, class participation, reflection on Locker Lab

Bonus questions in JUMP book, brainteasers

- Add, subtract, multiply, and divide rational numbers.

- Calculate fluidly and attend to precision.

- Transfer methods from one context to another.

- Maintain oversight of the big picture when solving a problem.

- Construct viable arguments and critique the reasoning of others.

Week 9

Angles and Triangles

- Parts of JUMP Book 1, Unit 4

- Triangle investigation

Workbook checks, unit test, class participation, triangle write-up

 

Bonus questions in JUMP book, brainteasers

- Understand angle measure and visually compare angles.

- Use a protractor.

- Know vocabulary relating to angles, triangles, and polygons.

- Investigate angle relationships in triangles.

Week 10

Decimals

JUMP Book 1, Unit 5

Workbook checks, unit test, class participation

Bonus questions in JUMP book, brainteasers

- Add, subtract, multiply, and divide rational numbers.

- Calculate fluidly and attend to precision.

- Transfer methods from one context to another.

- Maintain oversight of the big picture when solving a problem.

 

 

Weeks 11-12 

Asking and answering your own mathematical questions

Inquiry project, Khan Academy for homework

Project write-up and presentation, Khan Academy logs

Go farther in your project, challenge yourself in Khan Academy

- Ask questions, from the minute to the grand; formulate and pursue inquiries about mathematics.

- Make sense of problems and persevere in solving them.

- Construct viable arguments and critique the reasoning of others.

- Apply mathematical knowledge to problems in other fields.

- Attend to precision.

- Maintain oversight of the big picture when solving a problem.

- Look for and make use of patterns.

- Transfer methods from one context to another.

- Look for generalizations and shortcuts.

 

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