The Relation between Multiplication and Division - Elementary Math
This is a complete lesson with teaching and exercises about the relationship between multiplication and division, meant for third grade. They are opposite. In this educational resource page you will find lesson plans and teaching tips about resources to explore the relationship between multiplication and division . Multiplication and division are closely related, given that division is the inverse operation of multiplication. When we divide, we look to separate.
Well, think about it. We could make 1 jump. We could do 1 jump. My computer is doing something strange. We could do 1 jump, 2 jumps, 3 jumps, and 4 jumps. Now, does this make sense in this world right over here?
So we swap the numerator and the denominator. And then what do we get?
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In the numerator, once again, we get 8 times 3, which is And in the denominator, we get 3 times 2, which is 6. So now we get 24 divided by 6 is equal to 4. Now, does it make sense that we got half the answer? If you think about the difference between what we did here and what we did here, these are almost the same, except here we really just didn't divide. Or you could say you divided by 1, while here you divided by 2.
Well, does that make sense? Because here you jumped twice as far.
The Connection Between Division and Multiplication
So you had to take half the number of steps. And so in the first example, you saw why it makes sense to multiply by 3. When you divide by a fraction, for every whole, you're making 3 jumps.
So that's why when you divide by this fraction, or whatever is in the denominator, you multiply by it. And now when the numerator is greater than 1, every jump you're going twice as far as you did in this first one right over here.
And so you would have to do half as many jumps. Hopefully that makes sense. Ask students to split the pops in half and have a student count the total number of halves. Ask students if they notice anything about the size of the ten pieces compared to the original 5 freezer pops. Student should note that they are smaller. Elicit that they are half the size of the original freezer pops.
Ask a volunteer to write a number sentence to represent the 5 freezer pops divided in half and the answer on the board.
Understanding division of fractions (video) | Khan Academy
Then, remind the class that when we ask how many of something is in something else, that is a division situation e. Students will enjoy eating freezer pops before moving on to next examples. Move from demonstration to lesson, see Attachment TeachingPhase.
What activities or exercises will the students complete with teacher guidance? Place students in pairs and pose another situation.
Model this situation and write a number sentence. Monitor partners working on the task and ask the same type of guiding questions when students appear to be struggling with how to represent the situation.
Ask for a volunteer to provide the number sentence. Students will do another problem: I have two thirds of a rectangle and I want to divide it by one half. How many pieces will I have? Once again students should be multiplying second denominator by first numerator, then dividing by product of first denominator and second numerator. What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Students will do the following exercises independently and teacher will circulate to assist. Students will draw a model first, then write the mathematical sentence and finally solve the sentence using the algorithm discovered. How many strips will she get from the 3 yards of ribbon? How many batches of cookies can Winton make? How will the teacher assist students in organizing the knowledge gained in the lesson?
Now that we understand what to do when dividing fractions, I will give you my little keys to help you remember. Anchor the first fraction. You are on a boat. Flip-flop use the reciprocal of the second fraction. You need the flip-flops on your boat. Multiply Have a good time x on your boat. Go back over examples from the Teaching Phase and use the steps from above to help students see how they can help them remember the rule for dividing fractions.
Summative Assessment Students will answer questions using rectangular models. Write this statement on the board, "I know how to multiply fractions, I understand their meaning, and I could teach my neighbor how to multiply fractions. Once students have chosen the corner that best represents their response to the statement, have students discuss for 1 minute why they chose that corner. Give students 2 minutes to discuss and list as many concepts and procedures associated with multiplying fractions as they can.
Give students from each group an opportunity to tell all they know about multiplying fractions.
Students should be able to explain how to change a mixed number to an improper fraction and vice versa, put a whole number over one, use cross cancellations, and write a fraction in simplest form. Students should recognize the word of as an indication to multiply.