Hairy Money!
As I near my 20th year in Education, I’ve learned a great many tricks designed to “help” students on their paths to successfully understanding math. Some of these “tricks” are simply that...a trick that happens to work.
A trick that often causes students to stray away from truly grasping math in the long run; or causing students to eventually hate math because every year they learn a new “trick”.
A trick that eventually expires and has no mathematical foundation.
For more examples that include concepts from grades 2 through Algebra 1, download this free ebook - Nix the Tricks.
But when I ran across “hairy money”, at first I wondered if this cute approach to skip counting values was actually a trick or what we might call a Tiered strategy.
A tiered strategy is one that takes an approach to learning by encompassing some layer of instructional support [ie: number sense in this case]. A tiered strategy is often used during explicit and systematic instruction. In math (intervention) it’s coupled with manipulatives and graphic organizers.
So for example, if I were teaching a 3rd grader to add 3-digit numbers with regrouping, I might show them how to line up their place value, then add beginning with their ones place. Next I might model how we regroup to the tens place and so on through the hundreds place.
But if this 3rd grader struggles with this abstract algorithm, the most appropriate thing to do is intervene by scaffolding back to a more concrete approach to instruction within this concept. Explicit and systematic instruction would include pulling out place value charts (graphic organizer) and base ten blocks (ones units, ten rods and hundred flats,...even a thousand cube). I would then create 3 (no more than 4) steps walking the student through adding with regrouping beginning at the ones place. Teaching the child to rename ones larger than 9 as tens and ones (regrouping) using the models.
Then I would wean the student away from the concrete and have them still use the place value chart (a smaller one/maybe drawn) along with a model drawing of base ten blocks to represent their work. Finally, I would build the student’s efficacy back towards abstract. All of the steps listed above are tiered strategies.
They are the foundations that should have been essentially introduced to the student in the previous grade levels to build their ability to fluently do the algorithm in their current grade.
So what tiered strategies did I list in this example?
Base ten blocks
Place value charts
Model drawings
Regrouping with models
Steps based on place value understanding
All of these tiered strategies point back to number sense development.
So let’s talk about “hairy money”. The process of students placing hair on top of each coin (in increments of 5) atop the nickel, dime and quarter. So a nickel would receive one hair (so students count once by 5); a dime would receive two hairs (so students skip count twice by 5) and five hairs atop the quarter (to skip count five times by 5).
When all the coins are lined up (in order from least to greatest value...which coincidentally would be a step), students then place the appropriate hairs above each respective coin. Their final step would be to skip count by fives until all quarters, dimes and nickels are added up, and then count on by ones for every remaining penny.
The way Texas standards (TEKS) indicate to count money values, as a number sense strategy, is to have students skip count. Instruction includes tiered number sense-based strategies that include pulling out a hundreds chart (graphic organizer) and play money/coins. Then laying coins on the hundreds chart to help students connect number patterns to skip counting!
So the question is, “Is hairy money” a number sense (tiered) strategy? Or is it a trick?
My thoughts are, it’s a scaffolded strategy. It does encompass number sense (therefore making it a strategy) but it restricts the students from fully developing the ability to skip count by twos, fives and tens which is a more efficient way to find a value. This skip counting ability transcends other concepts beyond 1st and 2nd grade! So I might reserve it for a back-up rather than introduce it as a Tier 1 approach! Ideally, as early as 1st grade, students should learn to count a set of items/objects efficiently. Grouping items and then skip counting those groups. Their mastery is evident when they can flex between skip counting (ie: skip count by 10s, then by 2s; or by 10s then 5s and 2s or 1s).
From there, students are expected to efficiently count base ten blocks where again, they skip count between 100s, 10s and 1s (or by 2s). So I would contend that students CAN be taught to skip count by 25s, then by 10s, 5s, and 1s to demonstrate mastery of efficient counting and understanding of number patterns. But those are my thoughts.
Let me know what you think!
Free Virtual Resources for Counting Money:
Math Learning Center - Money App
Toy Theater - Money Strips
Toy Theater - Coin Bank
Illuminations - Coin Box
*Math Playground (Money Activity) - Puzzle Pic Money
Math Playground - Interactive 100s Chart
Toy Theater - 100s Chart
ABCya - 100s Chart
*PS: If you pay for Brainingcamp, they have a hundreds chart component and you can change the settings from “basic” to “money”. With this resource you can place coins on the hundreds chart to show the culminating value! It’s incredible!
