Eye on Education

Decomposing the verbiage

First-grader Johnathan Herrera uses his fingers to count up a multiplication problem at Las Palmas Elementary in Patterson on March 1, 2016. Fingers are an acknowledged tool in Common Core math.
First-grader Johnathan Herrera uses his fingers to count up a multiplication problem at Las Palmas Elementary in Patterson on March 1, 2016. Fingers are an acknowledged tool in Common Core math. naustin@modbee.com

It can be disconcerting to stare at a first-grader’s homework and recognize not one thing, to be clueless in the face of simple addition.

Common Core does not much care for the fast-food version of math, the quickie recipe with the steps all laid out – just copy a page of problems and crank them out. The new standards aim to impart the mental muscles kids will need to whip through higher math when they get there.

To do that, Common Core rolled out practical tools and some seriously wonky wording. Here we offer some help deciphering the code:

Adding on: This describes adding 3 + 2 by counting to three, then counting two more. Letting your fingers do the walking down or up the number line is a key Common Core strategy.

Finding the difference: We learned subtraction as the reverse of addition, then had to grapple with negative numbers as a foreign concept years later. Common Core sees the pluses of treating minuses as the spread between two numbers. Subtraction becomes just a way of clearing away the clutter to find what’s left.

Decompose: This is the ivory tower epitome of Common Core calculating. It means to break something down into its parts, by subtraction, division, fractions ... this break it down philosophy appears in every grade so get used to it.

Tape Diagram: Two horizontal lines divided into countable boxes. ⚀⚀⚀⚀⚀ These can be subtracted by crossing off, colored in to show fractions (like three fourths) or stacked end to end to show addition. A ten frame is a 2 x 5 grid of boxes.

Commutative Property: It means 1 + 2 = 2 + 1, the order does not matter. It is an uber-simple rule we learned in algebra, but now the mystery is gone in first grade.

Centimeter cubes: Snap together little cubes form strips of 10. Ten strips form a 100-block.

String: Nothing magical here. String is the first grade equivalent of a ruler.

Fingers: No need to coyly tap under the desk. Kids are invited to use their fingers to count, or objects, or drawing circles, or using numbers. The practice has a natural shelf life as the numbers get bigger.

Number bonds: Showing a circled number with lines to its parts, like 8 with lines to a circled 5 and a circled 3.

Rekenrek: A simplified abacus with a fun-to-say brand name, these string 10 beads, five each of two colors, on metal dowels. Units usually have ten dowels.

Area model: Think of a grid of stars, 10 in each direction. Draw a line down at 3 and across at 5 – everything within that box equals 15. The Common Core-style multiplication table for third grade provides a visual understanding of area in junior high and factors in high school algebra. Progression – relating the new lesson to what is already familiar – is another cornerstone.

Arrow notation: Arrow points to the answer. The concept is it shows transition, what the first number turns into, rather than the static equals sign.

Place value chart: A box labeled hundreds, another one labeled tens and another labeled ones – you know the order. As we skip along calling out digits, it is easy to forget that 12 is not a 1 and a 2. 12 is a 10 plus 2 ones. Spelling out that construction is a cornerstone of Common Core thinking.

Expression: The early grade word for equation. Equation: A math sentence that lays out the process for solving a problem.

Arrow notation: Scratchpad scribbles get formal recognition to help first-graders show how one number becomes another number, like 26 → 36 with a +10 written above the arrow.

Algorithm: Plain ol’ problems. No wording, no explanation, just a stack of numbers ready for crunching. They still appear in Common Core, and they still have to be answered correctly. They just no longer take center stage.