In the end, we are hoping for two things: understanding and fluency. Understanding is demonstrated by being able to show many ways of finding an answer. For instance, a student could be looking at the problem 4x3. He or she could show an array made with objects, a written equation, equal groups of dots drawn inside of circles, and skip counting on a number line. He or she should also be able to verbally explain why each of these represents the idea that three groups of four (or four groups of three) equals twelve. After this, they must know how to interpret a multiplication problem as a word problem.
We are looking for a student to be able to say, "Well, if there are seven rows of chairs, and I put eight chairs in each row, there will be fifty-six chairs altogether." This, along with drawing a picture or using manipulatives, would demonstrate understanding. This poster helps to illustrate what third graders must understand:
|Click on either picture to download both (FREE) from Teachers Pay Teachers.|
Of course, students need a way to show their understanding, so I have made a page so that they can "Give Me 5." After they are used to this template, they can easily do the same thing in their math journals or on a blank piece of paper.
**UPDATE: I have added a second set to the free download that replaces the word problem with repeated addition!**
True understanding of these concepts does not happen after one or two lessons... it may take weeks for some students. Some will find a favorite method and may not want to use others. I encourage them to keep trying all of them (Here's where a gesture and a smile can accomplish so much! Just hold up your hand with your fingers spread apart and they'll know you mean "Give Me 5"), and I ask LOTS of questions while they are working:
- "How does that work?"
- "Could you do that a different way?"
- "Why did you choose that method?"
- "What else could you use to show the equation?"
- "Why is every one of your word problems about aliens?" (true story!)
After the understanding has been established, it is time to develop fluency. The Common Core State Standards call for students to:
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. (3.OA.7)
Next time, we'll talk about fluency and memorization. (You can find that post HERE.) I hope that you find my "Give Me 5" pages helpful in your classroom. Please leave a comment and let me know!