Looking at the heart shaped tangram type puzzles, floating around this time of year, I spotted an easy opportunity to practice multi-step problem solving skills with my younger children (ages 8-11).
One of the first hurtles students hit in high school geometry is the switch over from simple equations to multi-step problem solving. This transition can be made easier by introducing younger children (long before they reach high school geometry) to the concept in simple ways through puzzles, or games, using the math they already know, or can easily grasp.
So, back to the tangram - if you ask a child to find the area of a heart shape, like the one below, they will most likely be stumped.
It is not one of the usual shapes found in math books. There is no simple formula for the area of heart.
So, we come to the first step of multi-step problem solving, determining what we already know. Depending on the age of the children, they will probably know the formal for finding the area of a square.
|length x width = area|
They might also know how to find the area of a triangle.
|1/2 base x height = area|
And, most will be able to put the two together to find the area of a right trapezoid (even if they don't know what it's called, or realize they have just taken a baby step into the kind of problem solving we're talking about).
|height x base = area|
Some children will even already know the formula for the area of a circle. If they don't, they can learn it pretty easily, even if they don't fully understand its meaning. It might be a good time to pull out Cindy Neuschwander's Sir Cumference books.
|πr² = area|
So, that's what we know. Be what we need to know is the area of a heart.
|? = area|
How can we use what we know, to find out what we need to know? That's where the tangram comes into play. By matching the colors of the shapes within the tangram to the shapes the children already know how to solve for area, the problem becomes simple.
And hopefully, at this point, children will be able to see on their own, that for this particular heart, the problem can be solved with fewer steps, as well.
We will do each of the steps above, with paper cut-out of the shapes, too. Just to add an element of familiar, hands on learning to the process.