Saturday, December 24, 2016

Create an Amazing Math Library -- Free!

Here are links to a collection of free downloads of excellent books and resources for math teachers and others who enjoy math:

100 Great Problems of Elementary Mathematics (Dover) - Heinrich Dörrie.pdf - Google Drive

Teaching Problem-solving in Undergraduate Mathematics

Schoenfeld: Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics.

Symmetries of the Plane

Creative Thinking in Mathematics with Tangrams and The Geometer’s Sketchpad

Larson's "Problem Solving through Problems"

Math Magic Archive

Recreations in the Theory of Numbers


Math from Three to Seven The Story of a Mathematical Circle for Preschoolers

Can you solve Martin Gardner’s best mathematical puzzles? | Science | The Guardian

Aha! Solutions - Martin Erickson.pdf - Google Drive

Saturday, December 17, 2016

PSM Workshop for Teachers -- Writing Math Quarter Exams


Describe your typical process for writing each math quarter exam.

Sample answers:

Find and copy last year’s exam

Use the unit tests from the publisher for the units covered

Complete the following:  A good quarter exam in math …

~tests what was taught

~does not test what was not taught 

~emphasizes important topics (e.g., if 3 weeks of instruction were devoted to a particular topic, then about 1/3 of the points on the test should be assigned to that topic) 

~assesses every CCSS identified in the quarter outline 

~assesses not just recall of facts, definitions, and memorized procedures but also higher order thinking

~challenges the strongest students in the class 

~uses a variety of item types: multiple choice, short answer, extended response 

~puts students under at least a slight pressure for time 

~does not use any items identical to those the students have seen before

What materials should be at hand?

~textbook and relevant ancillary materials

~grade level pages from the CCSS

~quarter outline

~outside assessment resources

NEVER: anything from


Find resources where items are keyed to CCSS. Has links to CCSS tasks by grade level, starting with grade K.

North Carolina:  (end-of-grade released forms; math and ELA/Reading, grades 3-8)

New York:

Grades K-2 materials must be pulled out of the individual modules:



PARCC (for grades 3-8) (answer key link provides CCSS for each sample item)

Achieve the Core (for grades 2-8)

Additional notes for PSM teachers:  Check the Google Drive using the path PSMMathMarshaDVD--Workshops:Presentations--PSM 2016 teacher workshop preparing quarter exams to find materials related to this workshop and additional resources such as math clip art and images. Also on PSMMathMarshaDVD are grade-specific files containing a folder of assessment resources (mostly not keyed to the CCSS but possibly useful).

Collect items!

Then check the match between items on the test and the CCSS—in both directions.

Then arrange the items in a sensible order and assign points to the items.

Do the points for each larger topic correspond to the amount of instructional time devoted to the topic? Make adjustments to the points or add items if needed.

Check for the variety of item types: multiple choice, short answer, extended response.

Check for cognitive levels—are there enough basic level items so that a student who has been paying attention in class, taking notes, doing homework, and studying for exams can earn at least a grade of C? Do the other items have the potential to spread the grades in a way that shows what they know? Are there one or two items that will really challenge your best students?

Is the test long enough to keep everyone profitably busy for the entire time devoted to the exam?
After all this fine tuning, check on the layout of the problems across pages—don’t strand the directions for a problem at the bottom of one page with the item on the next page.

Take the test yourself to make sure the directions are clear and you can create an unambiguous answer key.

Finally, highlight your master copy of the CCSS for your grade level so you can see exactly which standards remain to be taught and assessed during the rest of the school year. If you are preparing your third quarter exam, make sure that what remains is doable. If not, it is better to adjust NOW and change your third quarter instructional pace instead of rushing to teach everything before your students take their standardized tests in the spring.

Thursday, September 29, 2016

Providence St. Mel Parent Workshop Saturday, October 8, 2016

Parent Resources for Encouraging and Enriching Math at Home

from Ways a Parent Can Help with Math

Websites and Readings for Parents

mathmarsha blog: CTD Parent Seminar April 18, 2015 focused on apps for mobile devices

mathmarsha blog: CTD Parent Workshop 11/3/12 addressed math and literature, projects, games, manipulatives, etc.

Helping Your Child Learn Mathematics With activities for children in preschool through grade 5

Matific Note: available as an app for iPad and Android.

Strength in Numbers | National Numeracy Challenge helps adults learn the math needed for everyday life. A good place to start if you yourself are not comfortable with math.

High School Math Review Tutorials Problems - a free resource with examples, problems, explantions and exercises.  Parents can use these free resources and problems to help your child learn math.

Maths activities for children | Family Maths Toolkit has collections of activities for age ranges 3-13. Topics include: around the house, math and money, games, out and about, books and TV. From UK.

Parents booklet for written calculations (British) (a Word file that downloads automatically)

Written Methods of Calculation in Numeracy at Key Stage 2: A guide for parents and carers (another British one, a Word file that downloads automatically)



Here's an example of an app that's available online from NCTM. It's pitched at grades 3-8, but I wouldn't hesitate to share this with much younger children--it provides an exploration of algebraic thinking about equations using a balance scale:

Pan Balance – Shapes

Here's a screenshot:


If you remember LOGO or Turtle Geometry from the early days of home computing, you'll like Turtle Pond. This introduces children as young as pre-K to rudimentary coding.

Several good online games are available at PBS Kids Odd Squad Games. In particular, I liked "Down the Tubes." The underlying math includes number stuff (different sums to make a particular target length of tube) and geometric transformations (turns and flips). The levels build slowly, but eventually get mathematically interesting. The graphics are sufficiently eye-catching so your child will have the patience to continue to a challenging level.


NOT free:

DragonBox - Discover the game of Math 

The game claims it "secretly teaches algebra," which is true, but I think there are advantages to having a parent or teacher ask the occasional question or suggest recording what is happening in the game on paper so the algebra can be made more explicit. A good description of the game variations can be found here: DRAGONBOX ALGEBRA - The game that secretly teaches algebra.

DragonBox Elements - Geometry Proofs on the App Store (iPad  $4.99)

Get both:  DB Advanced Math Pack on the App StoreWhere to buy DragonBox for Android – Customer Feedback for DragonBoxMystery Math Museum  $3.99 on iTunes.  (It has occasionally been offered at no charge. I was lucky that way!)  My granddaughter asks to return to this one. I'll show you why I like it enough to spend $ on it.

Greater Gator on the App Store $1.99

24 Game – Math Card Puzzle on the App Store $1.99FREE

*Links to free mobile device versions of pick-a-path, equivalent fractions, and others from the National Council of Teachers of Mathematics here.

Big Seed is one of my favorites. It develops visual-spatial skills as you flip shapes to cover the presented puzzle. I find it much more challenging than my granddaughter does!

BigSeed on the App Store on iTunes

Matific - Educational Math Games For Kindergarten and Elementary School on the App Store offers hundreds of math activities, grades K-6.

Sushi Monster on the App Store

Numbers Game! - 6 Number Math Puzzle Game and Brain Training on the App Store

Geoboard, by The Math Learning Center on the App Store

Daily SET Puzzle on the App Store; alternatively, Combinations on the App Store

LetsTans Classic presents an outline to fill in, the seven tangram pieces in rich colors, and a mechanism (tapping a piece) for rotating. Many puzzles and many play options. I think this is the winner in the category. Free. iPad and iPhone.  
There are variations: Classic 2, Contours, Kids ("for the youngest solvers only"), and Silhouette (challenging! the shape you must create is NOT presented at the full size) are available as separate downloads.

Khan Academy 

GeoGebra on the App Store

Educreations Interactive Whiteboard on the App Store



Maths bingo (mobile app)

Everyday Activities

Cooking helps counting!

Act like an architect: Draw your bedroom | GreatKids

Math and Literature

mathmarsha blog: Math and Literature: Books and Suggestions/Links for How to Use Them

Math and Children's Literature -- a GREAT resource!

Math Read-aloud Books

List of recommended titles

Fruit fractions | GreatKids

Math Literature, Math Resource Book, Math, Mathematics, Elementary Math sorted by math topic--excellent resource

Home - Math Literature Connections - LibGuides at Bowling Green State University This links to pre-school list; links across the top of the page take you to lists for K-6.

Good Books for Problem-Posing Extensions

Teaching mathematics through literature shows how to use the book Jumanji by Chris Van Allsburg to explore probability, for grades 5-6.



Holidays and Seasonal

Pumpkin Math Estimates (grades 8 or 9)

Skill Practice

Problem Solving and Puzzles

Surrounding Tiles


For starters, go to my blog entry on Mathematics and Literature. You'll find suggestions for books that have mathematics in them available to your learners and ways to guide that math learning.

And, please, read the story that I have written and posted here Yes, That's My Mother! and let me know what you and your child think of it. So far I have received some useful suggestions for improvement, so I'll be posting a revision when I've had time to mull over the new ideas and create a new version.

Stuart J Murphy has written a plethora of easy readers for young children that address math topics. I'm not wildly enthusiastic about them, but they do contain pages of activities and games for parents to use to go beyond the stories. His website has free pdfs.

How to access Math Expressions online:  start here and follow the directions for you child's grade level book and resources.