Parentheses & Equal Signs

NUMBER IS IN NUMBER

When students are able to decompose and recompose numbers with fluency

they are able to make sense of the 'algorithms' adults seem to believe to be

so important in school math.

In my approach to teaching math, I put great emphasis on seeing, circling and 'counting with' small units or groupings. Instead of counting by ones to label a quantity, I put emphasis on recognizing how many sets of 2s and 3s are inside a quantity. This approach engages more students longer. This approach scaffolds students to more important thinking.

When students are focused on counting by ones, they tend to fall into a chanting stupor. They stop thinking and just repeat numbers, sometimes just mumbling sounds.

When they are challenged to see and think in small collections, at least initially, they are forced to be more present in the work. They have to think more.

Using sets of 2s and 3s moves young learners to 'big numbers' more quickly than counting by ones does. And young learners love "big" numbers.

Using sets of 2 and 3s connects to sets of multiples (counting by sequences) which allows students to push into two digit numbers.

But more important, using sets of 2s and 3s connects very quickly to seeing, thinking and counting in sets of 5. And sets of 5 become sets of 10 opening the world of base ten to students.

Base ten is about decomposing numbers into sets of tens and ones, into sets of hundreds, tens and ones, and then understanding that the groupings can be recomposed.

3 (100) = 30 (10) = 300 (1). 3 hundreds are also 30 tens are also 300 ones.

Suddenly numbers explode in size. And young learners love "big numbers'.

Counting by ones, like repeating the alphabet does ignite the same spark. More often I see counting by ones slowing down young learners, making them sluggish and listless, the chant becomes a rhythm with minimal brain engagement.

2 threes plus 2. I have 8.

Here's a critical connection all students must make:

2(2s) + 2(3) = 10

The equation above represents I know because I know 2 and 3 make 5 and 2 fives make ten.

I know because 2(2) = 4 and 2(3) = 4 and 6 is the same as 5 and 5. Two fives make 10.

I know because if I put out 4 and 6 I can rearrange to see 5 and 5. Use anything: fingers, blocks, bingo chips but focus on seeing the collections NOT COUNTING by ones.

When I spend all my time printing 2 + 2 + 3 + 3 as a young learner I can exhaust my capacity to focus because printing symbols until I have automaticity with printing, high jacks most if not all of my capacity to think. But saying and showing with materials that 2 and 2 is the same as 2(2) and 3 and 3 is the same as 2(3) builds my understanding. I do not need to print 2 + 2 + 3 + 3 to know the sum will be ten.