I have a 5-year old who seems to have a knack for math. She can borrow/carry in the hundreds, she can do multiplication through 5's, etc. Her teacher is not differentiating her work, so I do feel like I need to meet her where she's at when at home. However she is only 5, and I want her to enjoy math and not burn out. Any ideas on how to challenge her in a fun, enjoyable way?

Math is a difficult subject to differentiate. If you choose to teach at home, you may put her in a situation where you're forced to accelerate. Multiplication tables are 3rd/4th grade material. 5th grade is longer calculations and fractions. 6th grade introduces ration and proportion, 7th and 8th grade are pre algebra and pre-geometry. Math can force you into an uncomfortable situation!

At 5 years old, my son was doing math about the same level as your daughter. He begged to "do workbook" and I obliged. In 2nd grade I moved him to a public virtual charter school that does continuous progress acceleration for all students. Now he's 4th grade, homeschooled, and doing Algebra 2. Now what?! I can't put him back into public school until 6th grade (when middle school does subject acceleration), unless I grade skip him (no thanks). I can't teach him pre-calc or stats - I haven't taken them. I'm looking at not teaching him math, which is technically in violation of state homeschool requirements, or sending him to the community college for math class (which costs less than a semester of tutoring).

Math K - 4 is mainly memorizing facts. A child can get WILDLY accelerated by teaching elementary math at home. Please consider the possible consequences. If she is otherwise happy in school, I recommend taking a close look at if doing math at home is a good idea.

Logic puzzles are another fun way of feeding a math-talented child's need for stimulation. Childhood favorites of mine include Raymond Smullyan's "What is the Name of this Book?", and others, Martin Gardner's many math and logic puzzle books, and the Dover Recreational Math series. I also like Greg Tang's math picture books. I believe there are other recommendations in the Recommended Resource forum.

While I agree that afterschooling can result in insurmountable distance between instructional level and available instruction in a conventional schooling situation, one should also consider the possible damage to math enthusiasm when one is constantly forced to do math far below one's level, without any outside relief. Some children become convinced that they are bad at math, because they are bad at maintaining interest or attention in unchallenging drills day after day (which can also generate errors that, ironically, keep them out of the top math group in a class).

At that age my son loved the Penrose books, bedtime math books, and Beast Academy guidebooks as far as stuff to read and think about goes. We focused more on logic than math in our homeschool because he was a few years ahead just learning through play (and he loves math, so much much of his play revolved around math). Some of the logic stuff DS enjoyed included: Laser Maze, mazes in general, board games/card games/chess, and Sudoku. One of his favorite games at that age was Prime Climb. He went through a phase where he loved to graph equations and we did that for a while for math. I also had him do word problems at the level he was able to do calculations at, so about 3rd/4th grade level. This was challenging for him without further advancing his formal math instruction and a very useful skill for school and life.

A current favorite is a puzzle book called Pinwheel Paintdoku and his favorite game right now is Mancala (which I've only managed to beat him at once) and his favorite electronic toy is his lights out cube. Since DS is in school again we just have fun and play board games at home and I really think that teaches a lot of skills/math/logic.

Another book that is fun is You Can Count on Monsters, which is "about" prime factorization, but is a picture book of 100 monsters, each of which has elements based on its prime factors. Lots of fun little details to pore over while getting familiar with numbers. Games are also a great choice. Prime Climb is fun, and Incan Gold is a great one for subtly teaching division and remainders (and is fun for all involved).

The Number Devil is pretty cool.

We gave our DD the SG Maths books to do at home - she devoured them. The stuff is very well presented and simple to follow she she taught herself from these books at an insane rate - not even realizing it was 'homework' LOL

Also try the SG challenge questions.

Beast Academy wasn't out when she was younger so we went right into AOPS pre algebra when she was in 4th grade but I have heard good things about it.

Another great source of challenge that may keep you a little closer to grade level for a while is math contest questions. Math Kangaroo seems to be particularly "non-curriculum-y", with more problem solving, logic and visual puzzles. Different kids love different kinds of math, so you can experiment with the many fantastic books above to see what appeals. Numberphile videos on Youtube are also wonderful to view and discuss together.

SaturnFan - if your son still has any lingering love for graphing equations, mine loses himself for days on the Desmos graphing calculator (https://www.desmos.com). In addition to endless making your own to see what they look like, there's also a whole library of funky graphs and pictures people have made. DS loves to try and deconstruct them and understand why the equations used produce the results seen.

And if you have a Mac, the native graphing app is quite fun as well.

For a 5 year old, **helping** mum with baking (cakes/bread) is really good across many areas - maths, physics, chemistry, comp sci. Lot of hands-on activity, learning to follow an algorithm (the recipe) and doing things in order, lot of measuring of different types of things - fluids, powders, oven temperatures, concept of time. And the good thing is that at the end, something good comes out of it - you can sit down together and eat something nice.

Kids get how to measure a line, they start to struggle with area and doing stuff with volumes can be really confusing so the more practical experience they have in the 3D world the better.

Later - building a castle with boxes, cellotape and scissors (maybe with friends); lego and other building toys.

My kids really enjoy looking at math posters on the wall, working through math games online, and fun math reading like Bedtime Math. Board games are brilliant for strategic thinking, and there are lots of games that require logic/spacial skills, like Rush Hour.

At my kids' school, real math differentiation didn't start until age 6; at age 5, there was so much playtime my oldest didn't mind spending a few minutes doing simple math. Keep an ear on what she thinks about math at school and keep doing fun things at home. My oldest says that math is his favorite part of schoolwork (play/recess/PE being his favorite part of school), which is why we haven't needed to address in school work (yet).