Math Activity - Mr. L's Math

KenKen and Number Sense

Math Activity, Mr. L's Videos, Puzzle Comments Off

Mar 072012

KenKen 6x6 Number Sense

KenKen is a self-motivating puzzle that builds number sense. As an added bonus, using this teaching and learning tool builds creative logical thinking and patterns of self-reliance. It also develops strong focus for an extended period of time, a necessary skill in mathematical problem solving. This article spotlights some of the prime factorization, number trees, and number combinations found in KenKen.

KenKen and Sudoku share two of the same rules, which makes an easy transition for teachers and students: numbers in each row and column must not repeat. The third rule sets KenKen apart as being more mathematical than Sudoku. In KenKen there are Cages, which are heavily outlined areas with specific numerical properties.

The most commonly used puzzles for classroom use are 4×4, 5×5, and 6×6. As with Sudoku, KenKen comes in several levels of difficulty. This allows the instructor to introduce the puzzle at the elementary level, and then gradually ramp up the challenge level as students are ready.

Here is a 6×6 KenKen from the 3-7-12 issue of the NY Times at the Medium difficulty level:

What I suggest solvers do is write the possible numbers at the top or bottom as on a number line. This gives a sense of number magnitude and provides a great help when solving.

A. Look at the 9+ cage: How many different sets of three numbers add up to nine? Hint: there is more than one way.

B. Check out the 4+ cage: How many different sets of three numbers multiply to 4? Again, there is more than one way.

C. Now let your eyes rest on a similar region, the 24+ cage, with even more possibilities. Hint: what is the prime factorization of 24, and how many ways can you make a factor tree for 24?

By looking at numerical possibilities, along with other clues from rows and columns, it’s possible to solve this KenKen by logic and reasoning alone, with no guesswork. This is the hallmark of great mathematical thinking!

Every teacher that has talked/emailed me after using KenKen with students is enthusiastic in support of this methodology. Students always look forward to doing KenKens, and it’s always a great addition to a Friday workday, or useful as extra credit. Give it a try, and you will be a hero with your students!

KenKen puzzles can be found for free on several websites. Here are my two favorites, which publish six new puzzles daily: www.nytimes.com/ref/crosswords/kenken and www.kenken.com

The second site also has allows participants to receive regularly via email a nine page PDF file with KenKen puzzles in sizes from 3×3 through 6×6, including answers – something for everybody!

Math Made Fun – a Video Series for Math Mavens and Future Math Mavens

Math Activity, Mr. L's Videos 1 Response »

Apr 132011

Baravelle Spiral Cord Heath 217x300 Math Made Fun a Video Series for Math Mavens and Future Math Mavens

Baravelle's Spiral - Cord Heath

On my mathvideouniversity site on youtube, I’ve begun a series of videos intended to bring FUN into the math classroom while still teaching sound mathematics. My coauthor, Brad Fulton, and I have created literally thousands of pages of activities on Microsoft Word and PowerPoint that are currently residing on our hard drives. Prior to making these videos, the only people who were able to take advantage of these resources were our students and the folks who attended our workshops/conferences or bought our books and DVDs.

We want to make this exciting mathematics more available to a wider audience, and have decided that creating online videos will do the trick! Our goal is to create videos of 5 – 10 minute duration that are tightly focused around one topic that show some fascinating aspects of mathematics. Here are some ways/reasons these videos can be used:

It’s possible to do things on a video that are not able to be done in a classroom
Students can watch these videos any time – pause/rewind any part of video
Parents/tutors can watch with students to give help as needed
They allow parents to keep in contact with what’s going on in the classroom
A new model: Instruction can happen outside the classroom & tutoring can happen inside the classroom
Students need to see that education/training is available to suit their schedules
Allows educators to view video to improve instructional strategies
Can be used for teacher inservice training at workshops/faculty meetings
Can be used for individual teacher enrichment/education
Can showcase teachers at their best – without having to deal with daily issues
And lastly, a substitute can show the video so that instruction can take place in a teacher’s absence

KenKen Player – Now Embedded on mrlsmath

Math Activity, Website Resource No Responses »

Apr 012011

KenKen embedded on mrlsmath dot com 150x150 KenKen Player – Now Embedded on mrlsmath

Embedded KenKen Player

KenKen Player – Now you can play KenKen on the mrlsmath.com website.

Click the following link for the newly released (Beta version) of the online KenKen Player, from the makers of the game that’s catching on in math classes across the U.S.A. Enjoy the experience; it’s a great way to share the game in a classroom of inquiring minds. Please keep in mind that this is a Beta version of the software that’s embedded in my blog; there may be glitches, and if so, please let me know so I can report back to the folks at kenken.com.

Games and Puzzles that Reach the Kids and Teach the Standards

Math Activity, Puzzle 3 Responses »

Nov 272009

The title of this post is from a conference session at the California Math Council conference at Asilomar in December, 2009. You may download the handout, with instructions for some activities, through the following link:

Games and Puzzles that Reach the Kids and Teach the Standards – download file

Puzzles and Games are a great way to build enthusiasm, excitement, and skills in a math classroom. When these are used properly, there is always an underlying mathematical theme that is being explored or reinforced. Students learn the value of logical thinking, proper planning, and long-term focus.

Mathematical games can develop a lot of creativity and number sense in students. Many times a game or puzzle at first looks overwhelming, but becomes manageable after focusing on the key concept. Motivation is almost always inherent in a game or puzzle; this creates conceptual emotion which is a key to successful learning.

Opportunities for transitioning from number sense to algebra thinking abound with puzzles. Number properties show their strength in supporting algebra throughout puzzle activities. It’s always a pleasure to watch the enthusiasm and skills grow in students!

Some of these activities are from Teacher to Teacher Press books:

Simply Great Math Games

Simply Great Math Activities: Algebra Readiness

Simply Great Math Activities: Number Sense

Put these activities, puzzles, games, and ideas into regular practice, you will find increased skills and motivation in your students and more joy in your teaching.

Best wishes,

Bill Lombard (a.k.a. Mr. L)

Visual Algebra Video – Nuggets and Scales Classroom Lesson 1

Math Activity, Mr. L's Videos No Responses »

Apr 232009

This is a video introduction to the activity Nuggets and Scales from Brad & Bill’s book Simply Great Math Activities: Algebra Readiness. Teachers can use this video in the classroom as an easy way to introduce unknown quantities, set up and solve linear equations, and incorporate language in the process. This can be used to easily show students a nice transition from a visual representation to the abstract algebra.

The preceding post has a video showing teachers the pedagogical structure of the activity.

To receive all new posts – subscribe via email or RSS Web Feed.

Visual Algebra Video – Nuggets and Scales for Teachers

Math Activity, Mr. L's Videos No Responses »

Apr 232009

Here’s a video introduction to the activity Nuggets and Scales from Brad & Bill’s book Simply Great Math Activities: Algebra Readiness. It shows the teacher the pedagogical structure of the activity. This can be used to easily show students a nice transition from a visual representation to the abstract algebra, as well as incorporating language.

This video will be followed by a video for students that can be used for instruction in the classroom.

To receive all new posts – subscribe via email or RSS Web Feed.

Average Rate of Speed – a Simple Solution to a Confusing Problem

Math Activity, Mr. L's Videos No Responses »

Mar 302009

Ask people the following problem, and almost all of them will get it wrong: “If a car goes up a hill at 20 m.p.h. and comes down the same hill at 30 m.p.h., what is the average rate of speed for the whole trip?”

The “obvious” answer is 25 m.p.h., but that would be wrong. Take a quick look at a slideshow of some of the projects my students have done to see some nice explanations of confounding problems like these.

View more presentations from blombard.

Simply stated, since the car spends more time traveling at the slower speed, this has the effect of reducing the average rate of speed below the average of 20 and 30. The surprising answer to this poser is 24 m.p.h.

To receive all new posts – subscribe via email or RSS Web Feed.

Friday Afternoon Lifesavers – the Teacher’s Best Friend; Part 9, Pythagorean Tree – a Colorful Project for Geometry and Algebra Classes

Math Activity, Mr. L's Videos No Responses »

Mar 292009

Friday Afternoon Lifesavers are exactly what they sound like: at the end of the week when you and your students are running out of gas, these activities come to the rescue. They are mathematical, engaging, fun, and give the teacher a much-needed break.

Here’s a project that’s good for both algebra and geometry subjects. It has simple directions and teaches students to make accurate measurements and pay attention to symmetry and overall page layout. You can learn how to present the project to your students by viewing this screencast, or simply use an LCD projector to show your students directly in class. Pause the screencast as needed during construction steps.

Free online screen recorder

Enjoy your projects and your students will thank you when they see how nice their projects look!

To receive all new posts – subscribe via email or RSS Web Feed.

Pi-ku Poetry – a Pi Day Activity Uniting Haiku, Pi, and Graphic Art

Math Activity 1 Response »

Mar 082009

Here’s a sure-fire winner for Pi Day: have your students create Haiku poems about pi, called Pi-ku’s. Students can create one, two, or three Haiku stanzas, as well as a graphic depicting their poem. This is a great way to bring language arts, graphic arts, and mathematics together in one place! My 10th graders are doing this for Pi Day this year, and my 9th graders are creating other artistic works for mathematicians’ favorite day. You can see some of their work from prior years at Mr. L’s Student Project Work.

Pi Ku Poetry Contest

View more presentations from blombard.

- From Mr. L – You can view the embedded slideshow above or download my PowerPoint presentation to introduce Pi-ku to your students. This includes several examples so kids can get the idea.

To receive all new posts – subscribe via email or RSS Web Feed.

Friday Afternoon Lifesavers – the Teacher’s Best Friend; Part 8, Triples, Exploring Congruence and Transformations

Math Activity 4 Responses »

Mar 012009

Kids become better problem solvers by solving spatial visualization puzzles. Part 7 of Friday Afternoon Lifesavers featured Twins; it asked students to dissect a figure into two smaller, congruent figures. This activity asks for a subdivision into three congruent parts. Students are given non-standard shapes and asked to divide them into two congruent parts. Kids love this type of challenge; this activity engages all students and gives the teacher the opportunity to circulate the room and give encouragement and advice as needed without student management issues.

This activity provides the teacher the option to teach/reinforce the concepts of congruence and geometric transformations. Also available here are area, distance, angular measure, and perimeter teaching opportunities.

After students solve as many shape puzzles as they can, the teacher has the chance to take them to the next level. Hand out some blank grid paper and encourage them to create their own Triples; the only requirement is that line segments must begin and end on the intersection of two grid lines. By asking them to design these types of puzzles, students can appreciate the skill it takes to create a good puzzle by turning two congruent shapes into a larger shape and “disguising the line of separation.”

The downloadable pdf file includes the Student Puzzle Page, a Solution Page, and a blank grid page.

To receive all new posts – subscribe via email or RSS Web Feed.

Older Entries