‘Tis the season for nasty storms. An icy blast has turned our road into a sheet of glass for the second night in a row, and the wind chill is trying for a record low. Break out the hot chocolate, and settle in, ’cause Baby it’s cold outside! If you’re snowed (or iced) in with bored kids, here’s a holiday gift from me to you. I created these coloring pages for my homeschool co-op math kids this semester, but now I’ve collected them into a 24-page PDF booklet for your family to enjoy. Geometric Coloring Designs Happy Christmas! P.S.: I originally posted this on the General Education board. Thanks to the discussion there, I've updated the file to include my favorite "how to play with graph paper" links. If you think of anything else I ought to add, I'd love to hear your suggestions! And if you have any trouble with the link, the book is also available at my publishing blog's free downloads page.

The coloring book file is now updated (and new link edited into the original post) to include most of the above how-to-use-this links.

And here's another idea for using graph paper: rotational symmetry designs. Or for younger children, draw a line down the middle, and then try to make the two sides of your design into mirror-images of each other.

Maybe something like this? There's so-o-o-o-o much to love in this article! Doodling with Froebel

Hunter, I've just updated the file link above (Geometric Coloring Designs) to include four additional pages of square graph paper, for playing with grid designs. And here are a few more ideas for graph paper doodling: Creative Graph Paper Designs

I've updated the coloring book file to release it as Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0). Feel free to share the file with your friends or pass it around online, but please keep the front and back matter (attribution and info about my books) intact. But mostly, I hope you enjoy it!

I don't know what you've seen. But in addition to regular coloring designs, you could use them to create visual-algebra patterns: Visual PatternsOr play Gomoku -- like Tic-Tac-Toe, but going for five in a row. I've played that on square grids. I don't know how it would work on the triangles or hex pages. Experiment :) Or play Boxes on the dot pages, but you may want to tear the paper into quarters for a less tedious game. Graph Paper Drawing – Where Art and Maths Combine The Graph-It Game

‘Tis the season for nasty storms. An icy blast has turned our road into a sheet of glass for the second night in a row, and the wind chill is trying for a record low. Break out the hot chocolate, and settle in, ’cause Baby it’s cold outside! If you’re snowed (or iced) in with bored kids, here’s a holiday gift from me to you. I created these coloring pages for my homeschool co-op math kids this semester, but now I’ve collected them into a 24-page PDF booklet for your family to enjoy. Geometric Coloring Designs Happy Christmas!

I'm cheap, or the budget was always tight. Almost all the math games we played used normal cards or dice, or occasionally dominoes. I've shared many of them on my blog: Math Games Archive

Bar diagrams work very well for showing simple equivalent ratios. To go from 5/6 to 10/12 is to cut each unit in half. 15/18 cuts each original unit into thirds. Beyond that, the diagram isn't helpful -- but once the idea has been mastered with smaller numbers, students should be able to come up with impressive equivalent ratios like 55/66 or 300/360, just playing around. Not that they will probably ever use monster ratios like that in solving a math problem. But proportional thinking like this is very important. Playing with ratios helps solidify the foundation for linear equations in algebra. Bar diagrams in general are a pictorial form of algebra, and the type of thinking involved in solving them will carry through to manipulations with letters later on. Especially in the ability to translate a word problem or real-life situation into math equations. Very helpful!

In my opinion, this problem is pushing the limit beyond which bar model diagrams are not useful, and just-plain algebra works better. I suspect that is why the book gives the diagram, rather than expecting the student to produce it. It is useful for kids to understand that ratios can be split to make equivalent ratios -- that 5/6 or 10/12 or 15/18 all name the same relationship. Then the student can use her knowledge of equivalent fractions to identify other similar ratios, and maybe make up a couple similar-ratio problems of her own. Making up problems is a great way to wrap one's brain around a challenging topic.

Social Sciences here, too. I did my first three kids' transcripts by "school year," but that required a lot of virtual time-machinery. For the last two, I gave up on the fiction and arranged courses by subject.

I remember when we started homeschooling, how easy it was to fall into the trap of trying to do "school at home." And how often that turned me into the textbook police, trying to enforce a sit-at-your-desk-and-fill-in-the-page compliance. With experience, though, I realized that one of the best things about homeschooling is the freedom to not be schooly. Now some of my favorite memories are the times I spent on the couch with my daughter, doing her math lessons Buddy-style, all the way into high school. Don't be in a hurry to push your little ones (and 8yo is still quite young) into independent work.

Nrich puts out a math Advent calendar for students, with links to one math game or activity each day from December 1-25. Or you can find lots of goodies on my Math Adventures for All Ages or other Internet Resource Pages at my blog.

There are several ideas for exploring tessellations in this blog post -- and links to coloring pages, too. Coloring a tessellation may make it easier (compared to when he just looks at one) for your son to follow how the pattern rotates and interlinks. I don't know what age your son is, but one of the best ways to start with tessellations is by playing with pattern blocks: How can you cover the table without gaps? (Printable pattern blocks available here. Print on card stock, or laminate the paper, because stiff ones are easier to manipulate than plain paper.) Then ask the same question about other polygons: triangles, squares, pentagons, hexagons, etc. Which ones can cover the table (or graph paper) without gaps? Which can't, and why? And with pentominoes and similar shapes, like the Don Steward page above. Have your son design his own shapes on graph paper, using simple straight grid lines. Can he make a shape that won't tessellate? How does he know it won't? Can he make a shape that will tessellate? Draw the tessellation on graph paper. Then, if he wants to try one of the more creative tessellation patterns, he should have enough background to make it easier to follow the instructions.

Maybe try focusing on problem-solving strategies for awhile, perhaps with one of the Ed Zaccaro books?

If he is doing well in the class, then he almost certainly understands the basics he will need later. I wouldn't worry. The problem with giving solutions in high school math is that there is *always* more than one way to work any math problem. [in my Let's Play Math book, I explain *four* ways to think through "6+8=?"!] There is no way a solution guide can cover all the options, so they have to choose just one way and explain that. It's helpful if a student has no idea how to approach the problem, but it's only one possibility out of many that are all equally valid.

Is this something she has to turn in, or is the teacher just wanting her to have some experience with math outside the classroom? If the latter, you might try using other open-question resources like Estimation 180 or "Would You Rather?" Estimation 180 Would You Rather? (Math) More online resources

We never used to, but they might have changed the system. Registering lets them store the levels you pass, I think, so it would definitely help with vocabulary words, and probably with the basic math, so you don't start out at the beginning each time.

Practice math while doing a good deed: Free Rice Multiplication or Basic Math (prealgebra)

There is an encouraging series of posts on the Angelicscalliwags blog. Scroll down to read the series in order, bottom to top: Helping a Struggling Math Student

If you'd like to enrich your child's (or your own) experience of math, check out the Math Teachers at Play math education blog carnival. It's like an online magazine of sorts -- a table of contents to recent bits of online mathy fun. This month's carnival features prime numbers, multiplication, arithmetic puzzles, magic, word problems, picture puzzles, games, mathematical conversations, and much more. Math Teachers at Play #101

I'm not sure if this is what you had in mind, but I posted a series of blog articles about the original "Better Late Than Early" math educator, L. P. Benezet. It contains a summary of the math his students did each year of school. The transition seemed to consist primarily of measurement (all types) and mental-math word problems. Delayed Arithmetic series

Or you could try Patty Paper Geometry.

Caveat: I'm as old as the dinosaurs, as homeschoolers go. We used the original Singapore Primary Math (durians and all) before the days of the HIG and other books. That said... Flash cards: Not necessary at all. From what I've heard, this is one place where I would disagree strongly with the HIG author (and many other homeschoolers). The kind of thinking used in solving flash cards is not the kind of thinking you need in math. Games are MUCH better practice because they promote flexibility and strategic reasoning. I've shared a lot of math practice games on my blog, for free. Please don't use flash cards unless your kids really enjoy them. Lessons: See mental math, below... Mental math: Vital. But you don't necessarily need the HIG extra practice pages. Do the textbook lesson as daily mental math, with a white board as backup when needed. Talk about the various ways you might think through a problem. Try to find more than one way to do calculations. Build mental agility and flexible thinking. Allow the workbook problems to be done mentally, and even take dictation from your student (writing notes and answers for him/her) if that helps. Intensive practice or other supplements: Optional. Try not to overload your students. Some kids (not mine!) enjoy math and will cheerfully do more than others. Some people use the IP book in place of the regular workbook. Some people prefer other supplements, such as living math read-alouds or math circle playgroups.