Multiplication, Part 1
Understanding Multiplication
Summary: Multiplication involves more than memorizing facts. A full explanation of the whole process of learning multiplication step-by-step.
Multiplication is a skill that is learned. If done sequentially, the child will do better with memorizing his/her multiplication facts. More important than the surface memorization of facts, like 6x 5 = 30, is the underlying concept. Concept development is key. First, the child needs to understand patterns and skip counting, for example: 2, 4, 6, 8 ... and 3, 6, 9, 12 ..., and 5, 10, 15 ..., okay. Use the hundreds chart. Does the child use the skip counting of 5s on the clock? Great!
Second, the child needs to be able to do repeated addition, for example: 3+3+3+3 = 12. Use 6 inch pieces of yarn and make groups together if groups of objects. And example would be, take 12 buttons. Have the child lay out the strings of yarn in three circles. Have her/him put four buttons in each. Ask, what do you have? Three circles/groups of four buttons. How many are there all together? 12 Then, do the same, but have her/him lay out four circles of three buttons in each, and so on.
Third, the child needs to know and be able to do "fact families," for example: 3+3+3+3= 12 4 +4+4=12 3x4=12 4x3=12.
Fourth, the child needs to understand and do arrays. Before memorizing multiplication facts, the child needs to understand, visualize and use square and rectangular arrays. Arrays are objects (dots or stars in rows and columns, for example, a three by five array of dots; or another example, a five by five array of stars. The child should recognize objects in an array, name the array of dots on paper (for example, it is a 3 by 5 array with 15 total dots), manipulate arrays to see patterns, and start seeing the connection to multiplication facts (So, 3x5=15). The child memorizes facts through 5x5. The goal is to gain enduring understanding. In this case, the enduring understanding is that multiplication is a short cut for addition. At this stage, there are many sub-skills: Shows multiplcation with single digits on a number line, Shows multiplication with single digits repeated addition, Writes/solves multiplication equations with single digits, Solves problems using multipliation with single digits repeated addition. Writes/solves multipication equations with single digits. Then, comes facts 6x6 through 10x10 and 11x11.
Fifth, the child needs to understand rate of change. These problems look like word problems. If I have 6 desks with 4 legs per desk, how many legs are there in all? The child should be able to write this as an equation, 6 x 4 = 24, so, 24 legs.
In fourth grade, teachers start by assessing how many students are proficient with their multiplication facts. Meaning, asessing whether they have them memorized, in order to pass a timed test. In the next article, Multiplication, Part 2, I explain how to make memorizing multiplication facts easy.
Fifth, the child needs to understand rate of change. These problems look like word problems. If I have 6 desks with 4 legs per desk, how many legs are there in all? The child should be able to write this as an equation, 6 x 4 = 24, so, 24 legs.
In fourth grade, teachers start by assessing how many students are proficient with their multiplication facts. Meaning, asessing whether they have them memorized, in order to pass a timed test. In the next article, Multiplication, Part 2, I explain how to make memorizing multiplication facts easy.
No comments:
Post a Comment