Multiplication and Addition
If students see that addition and altercation is similar because In multiplication you simply repeat the Dalton problem several times then they will have an easier time learning to multiply numbers. A way in which students can relate Dalton and multiplication Is by teaching them and having them work on grouping. By grouping the students will need to draw circles for the first number that Is being multiplied and starts Inside the circles for the second number that Is being multiplied.
For example In the student will need to draw 3 circles and then the student will need to draw 5 stars inside each circle. This way the student will be able to see that they are simply adding 5 three times. The commutative property states that the order in which you add or multiply two numbers does not affect the result. (ABA=baa) For example 3*5=5*3=15. A way that this property is connected to thinking strategies is by grouping. The teacher may have the students first draw 3 bubbles and 5 stars inside each bubble and then have them count the stars for the total of 15 stars.
Then the teacher can have the students draw 5 bubbles and put 3 stars inside each bubble ND once they have done this the teacher can once again make the students count the stars and they will realize that it once again equaled 15 stars, signifying that the two ways came out with the same answer, teaching them the commutative property. The associative law states that when you add or multiply numbers, the grouping of the numbers does not affect the result ((ABA)c=a(BC). For example (2*6)3=2(6*3)=36. The associative property can be worked out by drawing it out and grouping together.
For example for the (2*6)3=2(6*3) problem the students can draw 3 bubbles and raw 12 stars inside each bubble or draw out 2 bubbles and draw 18 stars inside each bubble, if the students count both of the different group of stars there will be 36 stars in each picture, therefore showing the students that the order In which the numbers are multiplied does not affect the outcome. The distributive law states that multiplying a number by a group of numbers added together Is the same as doing each multiplication separately. When the distributive property Is used you distribute a number to get the same answer. (b + c) = ABA + AC and (b + c)a = baa + ca) For example 2(3+4)= With the deliberate property the students can connect It to a thinking strategy Is by skip counting. For example In the problem 2(3+4) the students can either break the problem apart and do It separately or do It together, they can skip count by as 3 times and then by as 4 times and add the numbers or skip count by as 7 times, both will equal 14. One conceptual error that may be associated with addition and multiplication Is that students may rush themselves ND not look at the sign if it is addition or multiplication.
One way to help the worksheet using highlighters. Once the worksheet is handed out to the students the teacher can ask the students to take out their highlighters and when they are working out each problem they must first highlight the sign, whether it is addition or multiplication, this way they will take their time and look at the sign to correctly answer the problem. A second misconception associated with multiplication is that the students may not correctly work out the distributive law.
In a problem such as (2+4) they may forget that they must distribute the 3 to each number and instead do 3*2+4. A way to help the students not commit this error is to first hand them out a worksheet that they only need to write the next step they will take, such as 3(2+4)=3*2+3*4. A second way to help the students not commit this error is to have them draw an error from the number three to the number to and a second arrow from the number three to the number 4 for each problem, this way the students will remember that they must multiply the first number to each number inside the parenthesis first.