Do relationships matter? How do relationships define us and construct meaning?

Is this the core concept we want our students to discover about rational numbers? I’m late to the game in terms of developing good essential questions so I would appreciate your feedback. In the past I didn’t have any EQ for rational numbers. As a result, I’ve been doing a lousy job of constructing a purpose for learning. In fact, my daily learning targets are playing cards pulled from the Trivial Pursuit Rational Number edition. For example:

Students will be able to:

- place whole numbers, decimals, fractions, and integers on a number line
- convert a decimal to a rational number
- calculate rational numbers in an expression
- identify whether the square root of a number is a rational or irrational number

Do you see what I mean about teaching trivia? I am so caught up in the minutiae students don’t see the relevance or the big picture.

I also have the Trivial Pursuit expansion pack for Number Properties.

Students will be able to:

- Identify and apply the commutative property
- Identify and apply the distributive property
- Identify and apply the associative property

If I make a conscious effort to link the essential question back to the learning target will students construct a deeper meaning of rational numbers and the number system? If I ask students to ponder the essential question in their math journals or with exit slips I can monitor their depth of understanding.

It’s not too late for me to go back and fix my blunder. We just kicked off number properties and have yet to start rational numbers.

How do we get students to see the big picture?

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Mary … just a couple of thoughts … we learn properties to provide “proof” for the way we manipulate numbers; to simplify computation; to enhance mental operations. Properties remind me of the laws governing driving. I can turn right on red; I can make U-turns at certain kinds of intersections; etc. Properties of numbers allow me to group and regroup numbers to simplify calculations.

Rational numbers are needed depending on the accuracy needed in problem solving. I don’t need decimals if when I shop all of the prices are rounded to the nearest dollar. But I’m going to need rational numbers if prices are rounded to the nearest penny. In sciences where accuracy matters (space science comes to mind) it matters when I multiply by the square root of 2 or its decimal approximation.

I’m not good with essential questions … I’m wondering what question, then, would help students get at the significance of rational numbers.

Hey Beth!

I’m not disagreeing with you at all. I’m basing my essential question on the definition of rational numbers within the 7th grade NS standards. You’re essential question might be, “When does accuracy matter?” which may describe the need for rational numbers. Can accuracy, estimation, approximation, etc. also be characterized as a type of relationship?

My smidgen of understanding of essential questions is that they can be topical or global. I prefer the global because I can connect to a broader idea such as: the relationship between the good and evil, the part to whole relationship between a child and family, how who we are may be altered based on certain situations, how relationships can work in tandem to make life easier (number properties).

What I struggle with is my focus on the daily targets. They have become myopic. I lose sight of the big picture and thus the students see this stuff as trivia. Does that make sense?

Mary – that makes perfect sense. I love global statements for the same reason … just find them difficult with some topics in math 🙂

One resource I have used for more global thinking is a list of universal themes and generalizations. Here is one such list that comes out of some gifted education materials: https://docs.google.com/document/d/1k6WJiByqqBabKig2nNSP_vPauFkMIff4BGFV7Y_gjv8/edit?usp=sharing

I’m in awe of your effort! I am doing well to focus on big ideas within the discipline! Love how our blogging community stretches us!

That is a fabulous list of themes. They are timeless, universal, and are probably not limited to gifted education! I’m going to share it with our curriculum committee when we meet next month.

I come from a literature background so it may be a bit easier for me to make those connections. Though I still have a tough time writing good essential questions.

Thanks for sharing the link, Beth. I’m going to use it. In fact it should be included in Julie’s list of resources for next week’s blog topic. It may have a limited audience, but it is incredibly worthwhile.

I like the EQ you wrote, but a big consideration for me is “can I make a lesson around my EQ question?” I always try and start a unit with a lesson that leads them to a big EQ type question . So if you have a lesson that helps kids talk about the importance of relationships, then you can use the open ended EQ question as a response to their class work.

If I can’t find a way to talk about the EQ in a lesson, then I scrap the question and rewrite it. Usually any question involving “why” can spin your trivial pursuit question into an EQ. So if your original EQ doesn’t work, you can try creating a new one from the trivial pursuit questions.

“So if your original EQ doesn’t work, you can try creating a new one from the trivial pursuit questions.” Excellent idea. I’m going to have another go with a different class on Wednesday. Today was not a good day but for different reasons!