It's possibly one of the most mysterious and misunderstood manipulative. After all they're just a lot of colored blocks of different sizes, right? WRONG! Actually, each block carries with it an undisclosed but very real value! Within this mysterious truth, there are varied numeration activities you can use to develop your students understanding.
- Missing facts
- Strip Diagram (models) for addition and subtraction
- Exponential growth/patterns
Today, I want to share my thoughts with you concerning the following 4th grade TEK (which is also echoed in 5th grade):
"Solve problems related to perimeter [and area] of rectangles where dimensions are whole numbers" 4.5D
"Represent and solve problems related to perimeter [and/or area and related to volume]."
5.4H
If you've taught 4th for any amount of years, you know perimeter has come a long way (in reference to how its tested). Back in the day, students were simply responsible for being able to calculate the distance around a regular shape (rectangle or square).
So how do we assist students in utilizing the basic concept of "adding up all the sides" of a figure to find perimeter to apply it to a composite figure like the one above?
Well obviously there's the "sit & get" method. Teacher places a sample problem under the document camera (or projects it on the SmartBoard) and students watch the teacher demonstrate how to solve it!
But I'd like to submit that we not bore our students and more importantly that we present to them a more concrete approach to understanding and even figuring out a solution on their own. Will they struggle? Absolutely. But concrete understanding is more long term than memorizing.
So first, play with this model yourself until you're comfortable enough to present it to your students.
1. Pull those Cuisenaire rods from off your shelf (and dust them off) LOL!!
2. Give each group or pair of students their own bag. Allow them to explore with the values by facilitating the following question:
"If a white square unit has a value of 1, can you determine the values of the other colored blocks?"
(Give them a few minutes to engage in math discourse with their partner(s) and develop their own methods for determining the values of the remaining blocks). *You may find that some students critically think by placing two colors together to determine the value of another. Others may line up various square units to find the value of a block...while some still may simply line them up by height*
Allow them an opportunity to share their groups' method.
3. After establishing the value of each, build your own composite figure. *Hint: Make sure you've determined ahead of time which blocks you will use in your example.
As you can see I have a total width of 10 (orange block) and a total length of 8 (brown block).
4. Here's where the critical thinking and thus the development of the concept will erupt!
Have students determine "which 2 (color) blocks might equal the length of the (10) orange block." *Hint: If need be, help them by suggesting they only look at the horizontal blocks first.
They should uncover that a blue block (6) is part of the length of the orange block (10) and a length of 4 (the purple block) is needed.
This concept will help them see part of their solution for solving a missing side is to add up the smaller sides that compose the longer side that runs the same direction. Facilitate this discussion with probing questions:
- "What relationship did we see with the long block and the 2 shorter blocks?"
- "What did all three blocks have in common?"
If the brown block has a value of 8, which two blocks do we need to consider to find the compatible sides? (yellow and green)
You might ask:
- "What are the values of the yellow and green block combined?"
- "If the yellow block has a value of 5, what might be the value of the green block?"
Perimeter = 10 + 5 + 6 + 3 + 4 + 8 = 36 (units)
The following website has a great interactive lesson and activity to reiterate this strategy.
(click below)
I'd admonish teachers to work with students to develop a colorful anchor chart that visually stimulates students and gives them a point to refer back to.
A few final things:
1. This would make for an excellent hands-on mini-lesson prior to getting into a guided math or station rotation.
2. This may also suffice as the instruction you complete with your small group at your horseshoe (small group) table during Guided Math or station time.
3. Be sure that after handling the concrete models, you expose students to opportunities to demonstrate (represent) and solve this concept on paper. *As modeled in the anchor chart, I would even encourage use of colors in their drawings for your visual learners!
Let me know how it worked for you and your students! I welcome feedback!
Websites:
www.sohcahtoa.org.uk
www.pixshark.com
