In this Using Multiplication Facts to Find Division Facts Video, I explain the lesson for today.
We have been studying the relationship between multiplication and division. The students all know that multiplication and division have an inverse relationship. They can undo each other. Since the students are familiar with using multiplication to help them with division, for today's lesson I require the students to step outside of their comfort zones and be creative by making a study guide for future students.
I set the purpose for the lesson by saying, "We have learned that multiplication and division have an inverse relationship. Who can tell me what inverse means?" I take a volunteer to answer the question. "In past lessons, we have used multiplication to help us solve division problems with quotients of 0 or 1. In today's lesson, we use multiplication facts to help us find division facts in other division problems."
We recently learned to use multiplication facts to help with division of special quotients of 0 and 1. So, the students have been practicing using multiplication to help solve with division problems. Because this is not a new skill, the bulk of the lesson will come in the group activity section to give the students a chance to apply what they have learned. In today's lesson, I do a short interactive lesson with the students before they start their group activity.
Because I want the lesson to be in context, I have a word problem written on the board before class begins. The Direct Instruction Word Problem reads as follows: Mary has 32 books in her room. Her mom bought her a bookshelf with 4 shelves. Mary wants to put the same number of books on each shelf. How many books will Mary put on each shelf? Have the students read the word problem to themselves. Then ask, "What operation should we use to solve this problem?" I give the students a few seconds to think about it before calling on one student. "Who remembers, what operation we can use to help us solve division problems?" The students should be able to tell me that multiplication can help solve division problems. "What multiplication fact can I use to help me solve this problem?" Let's find out.
I explain to the students that because we are dividing by 4, we should find a number that multiplies by 4 and gives us a product of 32. I let them know that it is very important for them to know their multiplication facts because it will help them with their division. "Can anyone tell me what I can multiply 8 by to get 32?"
"What if you didn't know what multiplication fact could help solve this division problem, what could you do?" I take a few responses from the students. I am expecting the students to tell me that we can draw a model or an array to help us find the multiplication problem. The students should know this strategy because this is what we used with previous lessons to help with multiplication. On the board, I draw 4 circles. Then I put tally marks in each circle, one by one until I have a total of 32 tally marks. The students see from the model that 4 x 8 = 32. Therefore, the answer to the division problem of 32 divided by 4 is 8.
I share with the students that today, they are going to use this skill to compose a study guide book for future 4th graders. I use the How to Make a Study Guide power point to show them how to do this.
Because the students are familiar with this using multiplication and division as inverse operations, we can somewhat go directly into their group activity. To give the students practice and to make them think critically, I want the students to create a study guide book for future 4th graders. I want them to explain to future 4th graders how to use multiplication facts to help find division facts. If they can explain it, then they have mastered the skill.
The students make a study guide book for future 4th grade students. I print and cut out the division facts and have them in a basket at each group. I give each group 2 pieces of construction paper for the outside of the booklet, copy paper, colored pencils, and 3 pieces of yarn. I put the students in groups of 6. Each member of the group is responsible for making 4 pages of the study guide. This means that they each have 4 Division Facts. They must put their names on their 4 pages of the study guide so that I can know which student did which problems. This is a picture of a Student working on study guide. For each group, there will be a total of 24 pages in the study guide. The students are given a rubric (Rubric Using Multiplication facts to help find division facts) to follow to ensure that they have included all of the components in the study guide. The students must provide all 4 components of the rubric which are worth 25 points each: 1) a division problem, 2) multiplication problem that relates to the division problem, 3) draw a model or an array of the multiplication problem, and 4) tell how the model helps them solve the division problem. I feel that these are the most important parts that the students must be able to do in order to show they understand the relationship between multiplication and division. When all of the students have finished their pages, they must use the 3 whole punch to put holes in the paper. The group should come up with a title for their study guides. They write the title on the front of a piece of construction paper. The students put the book together with the pages between the construction paper. They use the yarn to tie the book together.
To close the lesson, I bring the class back together as a whole. I have the students place their study guides on a desk. To give the students a chance to see their classmates work and evaluate it, the students take a stroll around the classroom examining their classmates work. If the students notice anything that stands out about any of the study guides, then the students should make a note of it to share with the whole class. The students should be looking for accuracy in the guides. By doing this, it gives the students more practice with the skill because if they can find inaccuracies, then they have mastered the skill.
I ask for volunteers to share their findings with the whole class.