### Algebra Survival e-Workbook arrives TODAY!!

**The “Algebra Survival” Program goes totally electronic!**

Singing Turtle Press is delighted to announce that the companion **Workbook** for the Algebra Survival Guide is **now available in eBook format.
**

**The “Algebra Survival” Program goes totally electronic!**

Singing Turtle Press is delighted to announce that the companion **Workbook** for the Algebra Survival Guide is **now available in eBook format.
**

35.686975
-105.937799

This is Part 6 in my series for helping students make fewer mistakes in algebra.

In this post I show how — by using the double-slash notation — students can avoid mistakes when factoring by grouping.

35.686975
-105.937799

**Category:**

Algebra, Double-Slash, Double-Slash, Factoring, Math Instruction Techniques, Tutoring, Uncategorized

This is the fifth in a series of posts on how to help students make fewer mistakes in algebra.

So far I have introduced a form of notation I have developed, the double-slash, which looks like this:

//

and I have described some of the ways that students can use it.

I’ll continue the conversation by showing how this notation can help students combine like terms with greater care.

35.686975
-105.937799

**Category:**

"Scaffolding" in Math, Algebra, Double-Slash, Double-Slash, LIke Terms, Math Instruction Techniques, Order of Operations, Practice Problems, Pre-Algebra, Simplifying Expressions, Solving Equations, Uncategorized

**Tagged with:**

- Algebraic Expressions
- combine like terms
- combining like terms
- descending order
- Double-Slash
- how to combine like terms
- how to simplify algebraic expressions
- like terms
- Order of Operations
- practice problems
- simplifying algebraic expressions
- simplifying expressions
- Use double-slash to separate like terms
- Using the Double-Slash

Combining integers … does any early algebraic skill cause more problems?

If so, I can’t think of one.

Fortunately, though, using the double-slash notation that I’ve been talking about this week helps students make sense of this tricky topic.

Even a problem as simple as the following can be made easier with the double-slash:

– 2 + 5 – 3 + 7 – 9

35.686975
-105.937799

When we left off, we were talking about the double-slash, a form of notation I’ve developed that helps students attain greater focus when simplifying algebraic expressions.

With greater focus, students make fewer mistakes. With the double-slash at their disposal, students avoid the mistake of combining terms that should not be combined. In the following example, students use the double-slash twice to simplify an algebraic expression:

+ 8 – 2(3x – 7)

= + 8 // – 2(3x – 7)

= + 8 // – 6x + 14

= – 6x // + 8 + 14

= – 6x + 22

By cordoning off the section with the distributive property: – 2(3x – 7), the double-slash allows students to see it distraction-free. With this heightened level of focus, students are more likely to work out the distributive property correctly, then continue on, simplifying the whole expression with no mistakes.

35.686975
-105.937799

When I left off yesterday, I pointed out a certain kind of algebra expression that tends to lead students to make mistakes. It was an expression like this:

8 – 2(3x – 7)

I pointed out that students often mistakenly combine the 8 and the 2, to get this:

= 6(3x – 7)

= 18x – 42

The theme of these posts is: how to help students avoid mistakes in algebra.

35.686975
-105.937799

Anyone who has worked with students learning algebra knows the truth to the maxim: MISTAKES HAPPEN.

This is the first in a series of posts offering PRACTICAL SUGGESTIONS for decreasing the number of algebraic mistakes students make.

First, it’s useful to recognize a key fact: we can’t help students with mistakes if we don’t know what causes those mistakes.

Years of tutoring have taught me a lot about why students make mistakes. And one major cause of mistakes in algebra is that students combine terms that should not be combined. Not all their fault, though. Students are often confused about what they may and may not combine. And it is tricky!

Take a problem like this: 8 – 2(3x – 7)

Certainly some kids can simplify this expression with no trouble. But in my experience, many struggle with a problem like this (when first learning it), and quite a few stay befuddled for quite some time.

The biggest mistake is that students think they can and should combine the 8 and the 2 through subtraction, proceeding like this:

8 – 2(3x – 7)

= 6(3x – 7)

= 18x – 42

**Q: How can we help students avoid this mistake?**

**A: Use a mark that show students what gets combined and what stays separate.**

I will start to elaborate on how I do this in tomorrow’s post.

**Extra, extra! ** I thought it would be interesting for you readers to send in comments on the kinds of algebraic mistakes that “drive you up the wall” the most. When I get a number of comments in, I will conduct a poll to see which mistakes people find most vexing. Should be “fun.”

35.686975
-105.937799

At Singing Turtle Press, we believe everyone should succeed at math, no matter how math phobic, no matter how right-brained, no matter what. Our products help students K-12 and beyond, including English language learners, and adults returning to college.
Visit Josh's new blog at http://www.algebrawizard.com/blog/

- Algebra Survival Guide
- Algebra Survival Guide Workbook
- Dr. Nicki's Guided Math Blog
- Education Bug
- Eureka Moments in Math and Science
- Great College Counselor
- Hands On Math
- Homeschool Math Blog
- Josh Rappaport TUTORS students ONLINE!
- LCM with 3+ Numbers
- Let's Play Math
- Math Education News
- Math Goodies
- Read&WritExchange
- SingingTurtle.com
- The Old Schoolhouse
- Wild About Math
- William's MathTuition Blog

- 982,690 hits

S | M | T | W | T | F | S |
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 |

8 | 9 | 10 | 11 | 12 | 13 | 14 |

15 | 16 | 17 | 18 | 19 | 20 | 21 |

22 | 23 | 24 | 25 | 26 | 27 | 28 |

29 | 30 |

Algebra Algebra Survival Guide Coordinate Plane Divisibility Elementary Math Fractions Geometry Making Math Fun Math Facts Math in General Math Instruction Techniques Math Theories Math Tricks Mental Math Multiplication Number Sense Number Theory Order of Operations Positive & Negative Numbers Pre-Algebra Simplifying Expressions Solving Equations Tutoring Uncategorized Using STORIES

- Algebra
- Mental Math
- Order of Operations
- GCF
- math
- Math Tricks
- Multiplication
- Algebraic Expressions
- Challenge Problem
- LCM
- Algebra Survival Guide
- Divisibility
- Positive and Negative Numbers
- Word Problems
- Geometry
- Education
- LCD
- greatest common factor
- Fractions
- Finding the LCM
- Mathematics
- Problem of the Week
- divisibility tricks
- Find the GCF
- factoring
- Add new tag
- Integers
- Dividing Fractions
- Division
- Master Equations
- Help Students Understand Mistakes
- Reducing fractions
- Find the LCM
- Math Facts
- facts
- Color
- Problem of the Month
- Solving Equations
- Make Algebra Easier
- Combining Integers
- Multiplication Tricks
- Diagonals
- Mixture Problems
- Dear Aunt Sally
- Slope
- GPGCF
- How to reduce fractions
- Using stories in math
- Coordinate Plane
- Double-Slash
- Using the Double-Slash
- Common Core
- Tutoring
- dividing
- good questions
- Times Tables
- Pedagogy
- GCF and LCM
- Using Stories to Teach Math
- Math with Understanding
- Pre-Algebra
- Multiply by 25
- Elementary Math
- Math Shortcuts
- Puzzle
- Math Puzzle
- Math Problem
- Solving Proportions
- Probability
- catching fish
- Prime Numbers
- Multiplication Trick
- Multiply Quickly
- Aunt Sally
- Negative in front of parentheses
- negative before parentheses
- rate x time = distance
- Percentages
- Linear equations
- y-intercept
- Linear equation
- Cartesian coordinate system
- Reflection
- Problem of the Week-Answer
- Geometry Problem
- greatest possible greatest common factor
- Divisibility by 3
- Squaring the Circle
- Circles
- Squares
- Ratios
- Proportions
- Fun Math Problem
- eBook
- Kindle
- math in movies
- math in storylines
- calculator
- distributive property
- Least Common Multiple
- Least Common Denominator
- Lowest Common Multiple
- Lowest Common Denominator
- Positive Slope
- Negative Slope
- Difference in look of lines with positive and negative slope
- logs
- How to Find the GCF
- Combining Positive and Negative Numbers
- Using stories to explain algebra
- decimals
- percents
- Standard Form
- Slope-Intercept Form
- Find the greatest common factor
- Mistakes
- Quadratic Trinomials
- How to Factor a Trinomial
- How to Factor a Quadratic
- How to Factor a Quadratic Trinomial
- e
- curiosity
- Addition
- Teen Numbers
- help
- exponent
- instruction
- Philosphy
- Philosophy
- Espresso
- math intelligence
- sharpness
- Math problems
- Negative Signs
- Math Instruction Techniques
- Using Color
- Tug-of-War Story
- Surviving Algebra
- Teaching the Times Tables
- Teaching Methods
- Subtracting Integers
- Math Fun
- Using Color to Explain Math
- Making Math Fun
- Place Value
- Math Foundations
- Obama
- Priorities in Education
- Funding
- Schools
- Brain Twister
- Math Brain Twister
- Math Challenge
- inverse operations
- Negatives
- Multiplying by Negatives
- Tricky Algebra Problems
- Multiply
- Multiply by 11
- Multiplying by 11
- Division Tricks
- Dividing a Fraction by a Fraction
- Division of Fractions
- How to Divide Fractions
- Fraction Tricks
- Color in Geometry
- Nonagon
- Find Number of Diagonals
- Use Color in Geometry
- Answers
- discrete mathematics
- class opener
- Arithmetic
- Turtle Talk
- January 2010
- Terence Tao
- Famous Mathematicians
- Mathematicians
- Distribution
- College Algebra
- college students
- make algebra fun
- math anxiety
- algebra anxiety
- Debunking with Algebra
- Fun with Math
- Regifting Robin Debunked
- Math Trick
- "Friendly Numbers"
- Expressions
- polygons
- diagonals of polygons
- formula for number of diagonals
- Answer to Challenge Problem
- Polygon
- Formulas
- Addition and Subtraction
- Multiplication and Division
- PEMDAS
- Alternative to PEMDAS
- Basic Algebra
- Homework Help
- Teaching Resources
- How negative signs work
- Average rate of speed
- R x T = D
- rate times time equals distance
- distance
- rate
- time
- Perimeter
- Using Color in Math
- Colorizing Geometry Figures
- Brain Teasers
- Class Starters
- Teasers
- Function (mathematics)
- Graphing
- Upper and lower bounds
- domain and range
- domain
- range
- find domain and range
- find domain
- find range
- use color in math
- teaching math with color
- Skip counting
- rhythmic approach to math
- Multiplication Tables
- Learning the 3s
- Learning the Threes
- Learning times tables
- Solution
- Answer
- Games
- Problem of the Week - 9/24/2010
- Hex
- Backgammon
- Venn Diagrams
- Percentage
- Multiply by 5
- Different variables serve different purposes
- Meaning of Variables
- Variables
- Variables in Algebra
- Algebraic Variables
- slope and y-intercept
- Infinity
- Line (geometry)

%d bloggers like this: