There is a relationship between addition and multiplication. When you are multiplying you are simply adding the same number several times. For example 2*3 is the same as adding 2 three times, 2*3=6 which is the same as 2+2+2=6. Understanding the relationship between addition and multiplication contributes to the understanding of these concepts to the student because the student will be able to grasp the concept with more ease since they should have been experts in addition once they start learning multiplication. If students see that addition and multiplication is similar because in multiplication you simply repeat the addition problem several times then they will have an easier time learning to multiply numbers. A way in which students can relate addition 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 3*5 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. (ab=ba) 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 and 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...

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