Education Unboxed has posted some playful addition games for young learners. If your browser has as much trouble displaying Vimeo content as mine does, I’ve included the direct links:
Photo by Luis Argerich via flickr. In this Homeschooling Math with Profound Understanding (PUFM) Series, we are studying Elementary Mathematics for Teachers and applying its lessons to home education.
The basic idea of addition is that we are combining similar things. Once again, we meet the counting models from lesson 1.1: sets, measurement, and the numberline. As homeschooling parents, we need to keep our eyes open for a chance to use all of these models — to point them out in the “real world” or to weave them into oral story problems — so our children gain a well-rounded understanding of math.
Addition arises in the set model when we combine two sets, and in the measurement model when we combine objects and measure their total length, weight, etc.
One can also model addition as “steps on the number line”. In this number line model the two summands play different roles: the first specifies our starting point and the second specifies how many steps to take.
— Thomas H. Parker & Scott J. Baldridge
Elementary Mathematics for Teachers
Kitten and I covered triangular numbers a couple months ago in our Competition Math for Middle School book, but I think it’s time to revisit the topic. I like the method James Tanton gives in this new video:
[Photo by stevendepolo.]
Math concepts: addition, subtraction, multiplication, division, powers and roots, factorial, mental math, multi-step thinking
Number of players: any number
Equipment: deck of math cards, pencils and scratch paper, timer (optional)
[Photo by woodleywonderworks.]
The question came from a homeschool forum, though I’ve reworded it to avoid plagiarism:
My student is just starting first grade, but I’ve been looking ahead and wondering: How will we do big addition problems without using pencil and paper? I think it must have something to do with number bonds. For instance, how would you solve a problem like 27 + 35 mentally?
The purpose of number bonds is that students will be comfortable taking numbers apart and putting them back together in their heads. As they learn to work with numbers this way, students grow in understanding — some call it “number sense” — and develop a confidence about math that I often find lacking in children who simply follow the steps of an algorithm.
[“Algorithm” means a set of instructions for doing something, like a recipe. In this case, it means the standard, pencil and paper method for adding numbers: Write one number above the other, then start by adding the ones column and work towards the higher place values, carrying or “renaming” as needed.]
For the calculation you mention, I can think of three ways to take the numbers apart and put them back together. You can choose whichever method you like, or perhaps you might come up with another one yourself…
[Photo by angela7dreams.]
A forum friend posted about her daughter’s adventure in learning the math facts:
She loves stories and drawing, so I came up with the “Math Friends” book. She made a little book, and we talked about different numbers that are buddies.
[Photo by Photo Mojo.]
Yahtzee and other board games provide a modicum of math fact practice. But for intensive, thought-provoking math drill, I can’t think of any game that would beat Contig.
Math concepts: addition, subtraction, multiplication, division, order of operations, mental math
Number of players: 2 – 4
Equipment: Contig game board, three 6-sided dice, pencil and scratch paper for keeping score, and bingo chips or wide-tip markers to mark game squares