All posts by mathconfidence

Fortune Cookie: How Many Steps in a Mile?

A mile walked with a friend contains only a hundred steps

The experience of walking a mile with a friend can be so engaging that it may feel like only a hundred steps.
But mathematically speaking, those would be mighty BIG steps.
With 5280 feet per mile, 100 steps would make each step 52.8 feet: almost twice as long as the long jump record set in 1991 by Mike Powell.  Dividing 5280 feet by 29.375 feet/step is about 180 consecutive long jumps which would likely make anyone forget they were taking a walk with a friend (not to mention, we did not count the long runup to the long jump).

Surely this fortune from the Chinese restaurant: “A mile walked with a friend contains only a hundred steps” is using a metaphor.  Usually for most people, there are about 2000 steps in a mile.

So grab a friend and take a walk and feel only 5% of your steps!!

Increasing the Math Willingness of Students

Embedded image permalink

Boosting Math Confidence is most of what I do in the classroom and one-on-one.  I named my website Math Confidence as it is the opposite of Math Anxiety.   Grouping students may increase classroom discussion although sometimes the sharper students will just tell the reluctant students.

Here are some things I do to encourage participation:
Note: this may not lead to everyone being part of the whole class discussion but at
least it makes the more reluctant students do Math 😉 and it gives the teacher a lot of material from which to lead the discussion.

Independent Work

5 or so mins of independent work (the room is slient) so I can walk around and work with s’s one on one.  This could include comparison type questions, matching, or other low-intensity tasks.

Surveying without Student Names

low tech: index cards or Post Its
high tech: Nearpod, Poll Everywhere or Kahoot (disclaimer: I have not used Kahoot yet but plan to next year)

blind voting:  everyone puts their head on their desk and votes (I can see but fellow
students cannot!)

Increase Self-Awareness

A lot of Math mistakes are “fuzzy errors” rather than conceptual errors.  A lot of the questions I ask are self-reflective, metacognitive questions such as “Is it bigger or less than 1/2? Why?”, “Easy, Medium or Hard?” and “Is that your final answer?”.  And for reluctant students, building confidence often comes from being ok with making mistakes and correcting them.

Allowing/Requiring Open Book/ Open Note Exams
Math is not about memorization and I have the great fortune of being able to allow students to use their notes/textbooks during quizzes and tests.  This boosts confidence for many students that they do not have to memorize but instead figure it out!!
I also share that iif they write nothing then their score will be nothing and talk to students about reading over the entire exam before they get started and figuring out their “Easy, Medium or Hard?”.

Launching into a Lesson (vs a Do Now)

stomprocketThe best time to teach something new is usually when the period has just started and students are freshest.  A Launch is a question or a pattern or something to think on to introduce a new concept.

In contrast,  a Do Now is usually ties to something they already know.  A Do Now can be great for starting the class with a routine so students settle into class. although sometimes the Do Now can take quite a while and “Now” can become “Later”.  If you must have a Do Now, keep it short and sweet and try the Launch right afterwards.

Do you want your students to know what you are going to do before you do it?  In some schools, the culture is to have routines in the classroom and I can understand that perspective.  But too often the Do Now is followed by going over Homework and the opportunity to learn new material is put off until there is not much time left in the period.

Here is an example of a Launch for Exponential Functions   from the most recent College Algebra lesson.

Enjoy these definitions of launch and feel f any launc(

launch 1

(lônch, länch)

v. launched, launch·ing, launch·es


a. To throw or propel with force; hurl: launch a spear.
b. To set or thrust (a self-propelled craft or projectile) in motion: launch a rocket; launch a torpedo.
2. Nautical To put (a boat) into the water in readiness for use.
3. To set going; initiate: launch a career; launch a business venture. See Synonyms at begin.
4. To introduce to the public or to a market: launched the new perfume with prime-time commercials on the major networks.
5. To give (someone) a start, as in a career or vocation.


1. To begin a new venture or phase; embark: launch forth on a dangerous mission; launched out on her own after college.
2. To enter enthusiastically into something; plunge: launched into a description of the movie.

Practice for Your Regents (Finals)!!!: Class Grade not predictor of Final Exam Grade

Warning: Class average is NOT a predictor of final exam grade.

In New York State, having a passing grade in a class does not mean you will pass the Regents.

There is a need for many students to take Mock Regents at home in a proctored fashion.  Some teachers are not finishing curricula and many students need more practice than what they are getting in school.

As report card grades are composed of many different things like classwork, participation, projects etc. students and families are not informed as to the likelihood of the student passing the exam.  And many students and their families are surprised when their Regents results are less than expected.

This past Tuesday June 2 were the ELA and Common Core Geometry Regents.

Study before the Regents week!  Regents begin again on Tuesday June 16th!

Which exam is when:

June 2015 Regents Schedule

Practice, Practice, Practice:

All Old Regents for Free Practice

Previous Math Regents Exams for Practice

HMX Earth Science Exams and Resources

Subscribe to Problem-Attic

Barron’s Books for Regents\

Pass the Regents Classes in and around NYC

Mr. Klaff Global History Review

May 2015 Brain Teaser Solution

Q: Here is the Math/logic brain teaser that took the Internet by storm in mid-April 2015:

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates: May 15 May 16 May 19 June 17 June 18 July 14 July 16 August 14 August 15 August 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively. Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.

Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.

Albert: Then I also know when Cheryl’s birthday is.

So when is Cheryl’s birthday?

A: July 16th.
Can’t be a unique day. Therefore it cannot be May or June.

July 14 July 16
August 14 August 15 August 17

Has to be unique

July 16
August 15 August 17

If Bernard know and Albert now knows that it has to be July 16th. If it was August then Albert would not know.

(Thanks to Adam Schwartz for this solution!)