Parent Options for Summer Math Enrichment at Home
Marsha Landau, Ph. D.
Mathematics Education Specialist
Update: This post was used in preparation for two parent seminars on April 18, 2015, intended for
parents of gifted children enrolled in the Saturday Enrichment Program at the Center for Talent Development, Northwestern University. I shared some of my favorite picks among free apps, including those for iPad, that purport to be about mathematics for young students.
Aside from specific recommendations, we discussed what characterizes a good app or website for your children in contrast to much of the useless proliferation of options available. We talked about effective use of "screen time" with your children, and your own role in the activities.
Of course, because of questions and discussion, we didn't get to everything I had hoped, so this collection of links will stay here for future exploration.
ONLINE
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:
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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.
MOBILE DEVICES
for learning fun:
DragonBox Algebra 5+ on the App Store on iTunes - Apple (iPad)
DragonBox Algebra 5+ - Android Apps on Google Play (Android)
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.
Coding:
Learn | Code.org is a website where your child can learn to code. There are several options for getting started. One of the available apps is
Lightbot, available online and for both iOS and Android. I chose
Lightbot - One Hour Coding '14 on the App Store on iTunes. The objective is to light up the blue squares. You can direct your little robot =to move forward, turn, or light the square it is standing on. You can also build routines for the robot to execute. In the picture below, the routine P1 consists of the moves forward, forward, forward, light, turn 90° in the clockwise direction:
The next step is to use the routine in a loop. And so on.
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
Combinations Created to play like SET, with 3 levels of difficulty. Free version has innocuous ads along the very bottom of the screen.
Tangram iPad Apps I tried and LIKED:
Big Block Tangram Puzzle -- Free provides a few shapes to cover with the tangram pieces. You can move and rotate the pieces. There are no solutions.
Note: Many other tangram apps are available!
Big Block Tangram Puzzle-Free on the App Store on iTunes
TanZen Lite is a good one. Full rotations are possible, not just multiples of 90°.
TanZen Free - Relaxing tangram puzzles on the App Store on iTunes
Another good one called
Tangram Free by Jiuzhang Tech Ltd offers clockwise turns of 45° (incrementally) and flips. Many free puzzles.
Tangram Free on the App Store on iTunes
The advantage of
EZ Tangram HD is that you can choose "free mode" where you can create your own shapes instead of just trying to build an outline given to you by the game. This one is also available for android.
EZ Tangram HD (七巧板) on the App Store on iTunes
Kookie Tangram is multilingual! Colorful, and lets you know when you are correct. Three levels of difficulty.
kookie - Tangram on the App Store on iTunes
***Best tangram app: 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.
http://bit.ly/letstansclassic 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.
school learning-related apps:
Mystery 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.
6 Numbers As described in this review,
6 Numbers (iOS) review | SocialTimes, it "is somewhat akin to the “numbers round” in the long-running French game show Des Chiffres et de Lettres, better known to English-speakers in its British incarnation as Countdown. Players are given a target number to attain, and must reach it by using only the six numbers provided up to once each, and the four basic arithmetical operators as many times as they desire. Calculations can be completed in multiple steps by feeding the answer to a previous equation into the next one, so in this way the player can work with a much wider range of possible numbers than the selection of six initially appears to offer." I find it much more interesting than a worksheet!
6 Numbers by Brainbow on the App Store on iTunes (free)
Here's a shot of the play (please ignore the reflections!!):
The free version includes addition and multiplication. A multiplication example is shown:
Grade 3 Math is decent (one of a series by Logtera). What I don't like about it:
•The voice over reads 5 x 9 as "5 multiplied by 9" instead of "5 times 9." I think 5x9 is 9 multiplied by 5. And it matters.
•It is sectioned off by operation, so even though there are some good word problems, if you are doing the "subtraction" section, all the problems will involve subtraction. This cuts down drastically on the need for thinking.
3rd Grade Math : Common Core worksheets game for kids. on the App Store on iTunes
Mathmateer is strictly drill and practice, but the reviews suggest that children will do it, so it beats a worksheet by a mile and saves paper. Topics drilled include even numbers, telling time, counting money, 3D shapes, and basic arithmetic operations.
Counting and Skip Counting by IKIDSPAD doesn't do much but succeeds at what it is designed to accomplish. Free version has ads at the top of the screen.
Hey Math! a Singapore Math product, is not very impressive. I watched a video (for grade 3) about adding fractions. Students are TOLD the mathematical procedures without delving into WHY. There was an appropriate setting (Lee is planting vegetable and flower gardens) and the diagrams were fine, but this was no better than a typical textbook lesson. The voice over was a woman with an accent (no surprise from Singapore Math!).
Splash Math provides school-type exercises for practice. Modules are available for grade K-5, and there is
one version that goes across the elementary grades.
Digital Manipulatives:
Here's a screenshot from the multiplication game:
(If we have time I'll demonstrate why during the workshop.) My issues persisted when I watched the instructional
videos. I found myself asking "Why? Why? Why?" throughout.
Dare to Share Fairly provides base 10 "blocks" that can be used to model the sharing meaning of division. I'd use the blocks to act out a division problem, get the answer, and then repeat, connecting each step of the actions on the blocks to the steps in the written long division algorithm.
Geoboard offers all the fun of the physical geoboard without shooting rubberbands to contend with. The "about" button on the app provides a link to web resources and a web version. I love geoboards because there are so many math concepts you can explore using them.
Tools:
Quick Graph is a graphic calculator with a genuinely helpful User Guide. I think it would be fun for your child to do a lot of free exploration
before turning to the guide, in order to get a feel for some of the app's capabilities. 2D and 3D graphing, works with all coordinate systems, solves, equations, etc. I need to spend more time with this one myself--I might spring for the paid version, just to support the development of such an excellent free app. The free version has relatively unobtrusive ads in the bottom left corner of the screen.
Quick Graph: Your Scientific Graphing Calculator on the App Store ...
GeoGebra is, in my opinion, the best of the free dynamic geometry apps currently available. It plays like Geometer's Sketchpad, an expensive bit of software, and there is a wealth of resource material available online (tutorials, youtube videos, blogs, chats) to help you use it effectively.
Or just be filled with wonder. Take a look at this hexagonally-based tessellation:
http://tube.geogebra.org/student/m28861.
iPad Apps I tried and deleted:
Aliens and Numbers -- what is available FREE is an opportunity to trace numerals 1 through 9. You can also try other elements which are for sale that are essentially worthless compared with other, better apps and free websites.
doodlenumbers
Absolutist Pocket Tangrams makes a competitive game out of tangrams--you are battling an unseen opponent and the clock. Placement of the piecesinto the outline provided does not require any flips or turns, at least on the levels I explored. The sound is extremely annoying. Turn it off even for a trial.
Tangram Mania
Tangram HD Lite because I couldn't find out how to flip the parallelogram.
Crazy Tangram
Arithmetic Invaders (very little is available in the free download)
Math Olympiad lets you solve only 6 challenging problems before you have to pay to continue. Otherwise I liked it--the problems were interesting and the answers were explained well.
Math. by
Your Teacher contains a set of problems for each topic you choose, and it is very comprehensive. However, digging deeper into the material on "Multiplying Fractions," I watched a video where the teacher was advocating "cross-cancellation" (which is NOT a real math thing!). The video on "Dividing Fractions" presents the rote rule (invert and multiply) but offers absolutely no rationale. What a wasted opportunity!
Algebalance - It took too long to get going, then the grammatical errors in the text drove me crazy.
Neither here nor there:
Gobblet! plays like the physical game, but if you aren't playing a real friend in real time you might make a move then wait hours, or longer, for your opponent to engage. And I can't tell how much privacy you have to sacrifice to play. To play against a facebook friend, for example, the game receives your public profile and friend list.
downloaded but not yet evaluated:
Minds of Modern Mathematics is a timeline with internal and external links to people and events in the history of math.
Websites with More Ideas for Apps
BOOKS
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.
Your child might be interested in doing some challenging problem solving over the summer to maintain and enhance her/his concepts and processes. My own enrichment students LOVE to work on contest problems. Here are some books you might consider purchasing:
Math Olympiad Contest Problems for Elementary and Middle Schools, Vol. 1 I own and use this one extensively.
The Original Collection of Math Contest Problems: Elementary and Middle School Math Contest problems
MOEMS Contest Problems, Volume 3 (Division E & M) I don't own this book (yet), but I have the contests over the years. The problems are excellent. You can check out their website for free:
Sample Contest
Competition Math for Middle School
Math Olympiad Contest Problems, Volume 2 (REVISED) I own this and use it with my enrichment students.
For middle school and beyond, please visit the excellent
Bookstore - Art of Problem Solving. I used the competition preparation 2-volume set with my best student several years ago (he has since graduated from Yale) and I was pleased to see how much (pre-calculus) mathematics I learned as we worked through the problems.
Available online:
It is not necessary to spend money to work on contest-level problems. For example, MATHCOUNTS has a user-friendly website with links to
Past Competitions | MATHCOUNTS. Another wonderful resource is
American Mathematics Competitions | Mathematical Association of America.
I use
Creative Math Problems with my own students--there are links to MANY excellent problem sets. See also
More than 20,000 mathematics contest problems and solutions.
CRAFTS
For a "homelier" activity, try quilt design (which may or may not continue with quilt-making). My granddaughter created her own interpretation of a task, Nine-Patch Patterns, that I found in the book
Math By All Means, Geometry Grades 1-2. Using 1-inch squares and the triangles that result from cutting some of them in half, she created this pattern:
As you can see, she chose to use 2x2 rather than 3x3 squares as the basis for her symmetric design, but it was a "free play" activity, so I just asked her a lot of math-y questions while she worked. She found that the triangles were all isosceles right triangles, that two of them could be joined to make a square, a larger triangle, or a parallelogram, and that the blue "tilted" squares down the center of her pattern had an area equal to two of the smaller squares. Productive enough for me! You can find (almost) countless examples of nine-patch quilts online, for example,
on Pinterest. Personally, I like the rotational symmetry in this design:
For more on quilting, see my
previous blog post about enriching math at home. For an iPad app, try
Quilt Studio.
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