This is only my second year teaching 5th grade. I just finished introducing geometry to my second group of students and I have reached the same tough question for the second year in a row. Upon assessment and reflection, I find that my students are having similar struggle this year as they did last year. They can identify the shapes, but they can't explain the rules of that shape.

For example, they know what a square is, but they can't explain why a square is also a rectangle. Or why a rectangle is a parallelogram, even though they know what a rectangle looks like and what a parallelogram will look like on the test. I taught the rules, but I focused on the vocabulary and the nomination of the shapes.

Should I reteach the rules of the shapes even though they are not tested?

Why I should - it is important that they know why a square is a rectangle but a rectangle is not a square in terms of creating a solid foundation in geometry. I am not only preparing my students for the upcoming test, I am preparing them for middle school. I know that most students really struggle with the abstract parts of math (algebra or trigonometry or calculus) because they often learned the how but not the why.

Why I shouldn't - maybe that part of the shapes is not tested because it's not necessary at this developmental point in the students' learning. I ask this question with almost every lesson I plan. Teachers often teach shortcuts that are often, in my opinion, not healthy. Some teach lattice for multiplication. Some teach that an estimation is a guess. Some teach the trick to finding common denominators without ever teaching why it works. Sometimes it is good to not go too deep, sometimes it is important to spend time laying the strong foundation.

How do I decide when to teach them just enough to get the question right on the test and when to spend time on things that may not be necessary for the test this year but will provide a good foundation?

My vote is to teach the reason behind the answer. But, wait till the math assessment is over. There is all kinds of ripe learning time available during the 4th quarter.

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