Limerick is currently in love with numbers.
He counts everything he can, comparing amounts and sizes: he counted all the straps on the plastic pool chairs at the public pool Saturday afternoon, at least ten times in a row; he makes long chains of flakes and counts them over and over again as he builds to find out how long they are and which color is the longest; he counts the number of bites or slices on his plate and recounts each time he eats one. Essentially, he is spending time with the numbers and quantities, becoming friends with them, getting to know how they interact with each other and discovering their unique qualities.
He will break numbers down into their component groups: if he builds a tower with fourteen wooden blocks, he will tell me proudly that it is two groups of seven. When he expanded his tower to eighteen blocks, I asked if it could split into two equal groups and he lined them up into two equal lines and counted each one to make sure that they both contained nine blocks. When I then asked if it could split into three groups, he made many little groups of three blocks and found out there were six of them – so, six groups of three and three groups of six. Since he’s been doing this on his own anyway, I introduced the vocabulary of “even” and “odd” to him.
“See this group of seven? I can’t break it into two groups of the same size – one of them is always bigger than the other. Numbers like that are called odd.”
Limerick pondered, then declared, “But eight is two groups of four!”
“Exactly! Numbers that can be split into two groups of the same size are called even!”
“Nine would be five and four,” Limerick told me with a slight frown, “but ten would be five and five!”
“So nine is odd, and ten is even!”
We’ll see if he remembers – he tends to hold a new word to himself for a week or so after he learns it, before he brings it out for everyday use.
Emboldened by all the math talk going on, I pulled out one of my favorite math tools from my own childhood (one that I believe my mom created, and that she now uses in her job as a remedial math professor at the community college):
It’s a physical representation of place value – the numbers on the cards in front show what the number would look like written down, while the buckets hold the appropriate number of craft sticks. In this picture, there are three single craft sticks in the box on the right, six bundles of ten craft sticks each in the middle box (the tens place), and nothing in the box on the left (the hundreds place).
We pulled out some huge foam dice and decided to take turns rolling and adding the number we rolled to the number already in the buckets:
Sometimes the boys knew right away what the answer would be; other times they would line up all the sticks to count them to make sure, and to bundle up the new ten-pack if needed.
Before this we hadn’t done much with written numbers – the boys know all the digits, but they didn’t understand double digit numbers. So it was a bit confusing at first for them, but by the time we stopped I think they were beginning to understand what the numbers meant and looked like, which is really cool!
Math tools and games like this aren’t necessary for learning math – Limerick has certainly been picking up on concepts ranging from quantitative comparison to division (with even a touch of fractions) just from everyday conversations about the numbers around us – but they are definitely helpful for illustrating a specific concept, challenging the mind to use a concept in a new way, or just having fun together with numbers! And since all you need for this particular tool are buckets, sticks, and paper, it doesn’t get much easier 🙂