Morning Circle and our Whole-Class Instruction today focused on the base-10 foundation of math.
Most students are comfortable with the notion of the different places — ones, tens, hundreds, thousands — and intrigued by the idea that each step to the left results in a place ten times larger.
That said, many students still scratch their heads about what number “two tens and two ones” might be (22). Similar head scratching comes when considering the answer to, “In the number 54, how many tens are then, and how many ones?”
And— we’re getting there!
We did dive a bit into money today. Students were fascinated at the the relationship between pennies, dimes and dollars, each being 10 times larger than the one preceding.
A good number of students quickly saw that:
Four dimes (tens) and three pennies (ones) = 43¢
One dollar (hundred), five dimes and three pennies = $1.53 or 153¢
Many students also met their first Rekenrek today.
Quicker than many classes, students caught onto the role of 10s in the Rekenrek’s construction:
Each rod contains 10 beads (5 white, 5 red)
The large Rekenrek has 10 rods holding a total of 100 beads
Students were excited to learn that while we only have two 100-bead Rekenreks in the class, every student has immediate access to a “Two tens” — 20-bead — Rekenrek.
The introduction of Rekenreks led directly to the high desirability of using “manipulative” in math.
We’re never quite sure where 2G students get the idea that the correct answers to math questions should magically appear in their minds after a moment of silence/stillness, but it’s been a common trait of all 2G classes!
Fingers are a handy manipulative!
Paulo, a student from my first 2G class, was a finger-calculating king, often out-performing even good memorizers through deft use of his fingers. I tell every new 2G class about Paulo and demonstrate just how fast one can calculate using your fingers.
With addition: start with the biggest number and count up using fingers
With subtraction, count down using fingers
Please encourage your student to use her/his fingers!
Young children need a tactile sense of math. In many instances, math is about things!
Rekenreks are wonderful manipulatives.
Today, not only did students quickly appreciate the ideas encapsulated within the Rekenrek’s construction, but they demonstrated they could SEE the numbers instead of counting every bead.
No need to count the bead on a road with all beads used! It’s 10!
I can count all-beads-used rods by 10s
If five of the red (or white) beads are used to show a number less than 10, I don’t need to count the red (or white) beads — there are 5 of them!
I can count by 10s, add 5 if all of the red (or white) beads are used, then just count the 1-4 beads left over!
10 - 20 - 30 - 40 - 45 - 46 - 47 - 48!
We will be doing a lot more work with Rekenreks, for the rest of the year!
Number lines are divine!
The following questions required students to mentally shift from counting by 2s to counting by 5s to counting by 10s — and to shift from skip-counting up (by 2s, 5s, 10s) up and down.
This can be quite a challenge for adults, not to mention 2G students!
Number lines are incredibly helpful with these types of problems.
Indeed, students who are lost (when hoping the answer magically materializes in their minds) immediately SEE the answers when a number line is used.
In addition to our big number line, we have a nice stash of meter (100 cm) rules that students can use as a handy-dandy number line at their work spot.
With the 10s often prominent—
— student find it easy to quickly “navigate” the number line to help answer the counting by 2s/5s/10s before and after questions.
Helping your student with math at home?
Should you end up helping your child with math challenges at home, if you can, make the problem as tactile and visual as possible.
The math-concept-comprehension progression is:
tactile (manipulative)
visual
abstract
While we adults have had many years — many decades — of manipulating abstract math ideas in our heads, much of what we take for granted is new for students.
The “problem” adults have when teaching young children is
(a) forgetting that we once could not manipulate math problems abstracting, and
(b) trying to see math problems from a young child’s pre-abstract-concept perspective
That said, “rediscovering” that perspective can be a lot of fun!
Enjoy!
