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Teaching Math

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Submitted By wisegurl84
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Multiplication can be a difficult concept for students. The relationship between addition and multiplication can make it easire for students to understand the concept of multiplication. This relationship can be used to ease the learning of multiplication. In the flollowing essay I will explain the relationship between addition and multiplication as well as inclued how the Commutative, Associative, and Distributive properties apply to each and how an understanding of those principles apply to later concepts.
Students can use repeated addition, skip counting, grouping, and a number line to understand the concept of multiplication. Students can be drilled on skip counting skills to help teach multiplication skills. For example 2,4,6,8,10 is the same as 2x1,2x2,2x3,1x4,and 2x5. The concept of repeadted addition can also be used. For example 2+2+2=6. This is the same as 2x3=6. Adding 2 three times and multiplying 2x3 get the same answer of 6. Showing students 2+2+2=6 then explaining that it is faster to espress this repeated addition as 2x3=6 or how many times is 2 added(3times) to get 6.
Grouping can also be used to teach the concept of multiplication through the use of addition. The teacher can show the students this concept by drawing 3 circles on the blackboard. In each circle draw 2 dots. The multiplication process is used by saying 3 circles times 2 dots in each equals 6. The addition concept can also be used by saying 2 dots plus 2 dots plus 2 dots equals 6. Finally a number line can be used to teach the concept of multiplication. For example 0---1---(2)---3---(4)---5---(6)---7---8---9---10. Count up two, three times. Starting at zero, move up 2. Your answer is 2. Now start at 2 and move up two more times. Your answer is 4. Finally start at 4 and move up 2 times. Your answer is 6. 2x3=6.
It's also important to describe how understanding the relationship between multiplication and addition contributes to students understanding of these operations. by doing the above-mentioned concepts of multiplication, students are also reviewing and reinforcing their addition skills. by using the number line studnets are reinforcing their one to one correspondence as well as their addition skills. By using the skip counting students can review their doubles addition facts. by using groupings, students can review and practice their addition facts because they are able to quickly recognize a group of objects and represent that group with a whole number. Students are using and reviewing their addition skills by learning ways to multiply.
It's important that students recognize and understand the commutative, associative, and distributive properties. The commutative property comes from "commute or move around" (purplemath.com). For example ab=ba or 3x2=2x3. When the commutative property is used you move number around but still get the same answer. The associative property comes from "associate or group" (purplemath.com). For example a(bc)=(ab)c or 3(2x4)=(3x2)4. When the associative property is used you regroup number but stil get the same answer. The distributitive property comes from "distibuting numbers"(purplemath.com). For example a(bxc)=abxac or 2(3x4)=2(3)x2(4). When the distributitive property is used you distribute a number to get the same answer.
Each of the above-mentioned properties can be connected to thinking strategies children might use in performing computations. When using the commutative property it can be connected to grouping. The problem 2x3=3x2, students can make two circles and place 3 stars in each circle or make 3 circles and place 2 stars in each circle to discover the product. When using the associative property students are making many sets of and skip counting. For example 3(2x4)=(3x2)4 is the same as 2,4,6,8 and make three sets of 8 to produce the product of 24. When using the distributive property students can connect it to adding equal groups then making sets. For example 2(3)4 = 2(3)x2(4). They can multiply 3x4 to get 12 then make two groups of 12 to get 24.
With the relationship between multiplication and addition there are some common conceptual errors that students may develop. One misconception that students may have is adding the numbers instead of multiplying. One way to avoid this errors is to remind students they are multiplying insteadof adding and show them the difference between the signs for addition and multiplication. Show that the sign for addition is + and the sign for multiplication is x. A second misconception that studnets may have is what order to multiply numbers when a multiplication fact is in parenthesis such as in the distributitive property. Students should be taught to multiply the parenthesis first then multiply that product by the number outside the parenthesis. For example 2(3x4), multiply 3x4 to get 12 then multiply 2x12 to get 24.
There are many ways to teach multiplication to students. It is important to correct any misconceptions or errors that studnets make. By showing students the relationship between addition and multiplication they can develop a strategy to hlep them discover the correct product.

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