with Kim Rodgers
Things are shaping up...
For the last two weeks we have been using an image of a scale to talk about balancing equations. We’ve had different combinations of weights, represented by shapes, on each end of the scale. Our goal is to make each set of the weights equal to the other side of the scale. This week, for example, we had a square and triangle on one side, with a circle on the other. The constraints were as follows:
They talked with their partner about what they knew from the information given. Often kids jump right into solving the problem without stopping to see what they already know. A few kids skipped this step and found out that they could have saved themselves some work if they had taken a moment to acknowledge the constraints on each shape first. They then discussed what they needed to do to balance the scale, which was to find possible values for the square and triangle so that s + t = 17.
Another scale had four triangles (t) on one side with one hexagon (h) on the other. They came up with at least five possible weight values to make the scale balance. Some included fractions, even a challenge of a five digit decimal that one student completed! After sharing their favorite combinations, we came up with a rule to explain all possibilities: 4t = h.
We finished with a scale that had a rectangle and two squares on one side, with a trapezoid on the other. The only constraint given was that the rectangle = 3 lbs. Before finding values for the shapes, the students came up with algebraic expressions to represent this scale, such as:
Next week, we’ll follow up with possible values and what we can know about this equation from the information given.
In the coming weeks, we will be using base ten blocks to help us visualize the distributive property over addition and subtraction, represented as:
a(b+c) = (ab) + (ac), and
a(b-c) = (ab) - (ac)
Each pair of students will need 35 ones (or units), 15 tens, and 1 hundred. If you have a set you could donate to the class, please put these pieces in a ziplock bag with your child’s name on it. Please e-mail me at firstname.lastname@example.org to let me know. I will be making sets from card stock to fill in if we don’t have 5-6 sets for the class.
Also, I’m including a photo of our Algebra Tool Kit up to this point. Please make sure your child has his/her kit up to date. Some students were absent when we began creating it, and some students can’t seem to find theirs. We will be adding to the kit throughout the rest of the class so that it can be something they look back on to find strategies to use when attacking math problems.