We would hope that students would master their basic multiplication facts, from 0x0 to 9x9, by the end of the third grade.
That said, we hear a lot of talk about how our students have little to no fluency in their times tables. Fourth grade teachers often have to reteach these facts.
Frustrating? Yup.
But it's also a place where I have some choices to make. I am of the belief that I need to teach to the top of my class and bring others along for the ride, rather than teach to the middle. That's easier said than done, but I'm constantly trying to do it.
In this case, while I know I need to reteach the times tables, I also need to make it interesting for the students have already mastered their third grade skills (and not forgotten them over the summer). Ergo, I introduce exponents and square roots early in the fourth grade. In this way, we can cover the same skills, but add a new way to look at them.
The first problems we work on are the squares (or doubles as some refer to them): 3x3, 4x4, 5x5, ..., 8x8, 9x9. If parents want to help with this, they can reinforce the classroom by encouraging their fourth graders to constantly recite the square products: 9, 16, 25, 36, 49, 64, 81 (forwards and backwards). For more, have you read Stepping Up to Multiplication?
Now, in addition to the standard multiplication sentence, students learn the proper way to write six to the second power, or six squared (which is 36, of course). Then, to turn it around, these guys are ready for, What is the square root of 36? The answer to that one is six. Knowing these things forward and backward - and overlearning them - even with the "new" way of denoting these ideas.
Hopefully, while one student is internalizing squares and square roots, four others are mastering the products to basic multiplication problems.
Finally, I am introducing the measurement of area. This week, we learned the formula for finding the area of a rectangle - Length times Width. With this, we have an instant application for our multiplication skills. I've been proud of the way this year's class has reacted so far, and I've seen some faces light up with understanding. Some students just need to feel like they are worth the efforts that I put in to help them learn difficult things and make them seem simple.
That said, we hear a lot of talk about how our students have little to no fluency in their times tables. Fourth grade teachers often have to reteach these facts.
Frustrating? Yup.
But it's also a place where I have some choices to make. I am of the belief that I need to teach to the top of my class and bring others along for the ride, rather than teach to the middle. That's easier said than done, but I'm constantly trying to do it.
In this case, while I know I need to reteach the times tables, I also need to make it interesting for the students have already mastered their third grade skills (and not forgotten them over the summer). Ergo, I introduce exponents and square roots early in the fourth grade. In this way, we can cover the same skills, but add a new way to look at them.
The first problems we work on are the squares (or doubles as some refer to them): 3x3, 4x4, 5x5, ..., 8x8, 9x9. If parents want to help with this, they can reinforce the classroom by encouraging their fourth graders to constantly recite the square products: 9, 16, 25, 36, 49, 64, 81 (forwards and backwards). For more, have you read Stepping Up to Multiplication?
Now, in addition to the standard multiplication sentence, students learn the proper way to write six to the second power, or six squared (which is 36, of course). Then, to turn it around, these guys are ready for, What is the square root of 36? The answer to that one is six. Knowing these things forward and backward - and overlearning them - even with the "new" way of denoting these ideas.
Hopefully, while one student is internalizing squares and square roots, four others are mastering the products to basic multiplication problems.
Finally, I am introducing the measurement of area. This week, we learned the formula for finding the area of a rectangle - Length times Width. With this, we have an instant application for our multiplication skills. I've been proud of the way this year's class has reacted so far, and I've seen some faces light up with understanding. Some students just need to feel like they are worth the efforts that I put in to help them learn difficult things and make them seem simple.
