X Represents Groups Of

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Students will be able to write word problems to describe a context in which a total number of objects can be expressed, as well as write an expression for a given situation.

Big Idea

Children will work to write math stories that could be used to describe situations for a given multiplication expression, using the correct multiplier and group size.

Mini Lesson

10 minutes

My students are able to write an expression for a multiplication story that reaches the correct product.  However, many of them are writing the factors in the wrong order, telling me they are still unable to understand the concept of equal groups of objects being added.  I decided to change some vocabulary around for this lesson and deliver an explicit lesson on "groups of". 

Mathematicians, please join me at the community center for our mini-lesson. I have noticed that you are doing a fantastic job at solving word problems that involve multiplication.  That is not an easy task and you are thinking very hard.  Today I want to show you a way that will help you even further understand what the equation is actually telling us.  

Please look at this equation on the board.  Normally we would say "4 times 5 equals 20".  If you remember back, the second factor is what we have called our group size.  So, for today and the next couple of days, we will read our equations like this, "4 groups of 5 equals 20".  When I read it that way, it is easier for me to imagine a story to go with it.  Let's see, it is almost Halloween, so I will use candy as my unit.  I could think about it like this: "I got 4 bags of candy. Each bag had 5 pieces of candy.  I have 20 pieces of candy in all."

Will you try with your partner to think of another story that would work for this expression?

Story Writing

15 minutes

Following the mini-lesson and group practice, I give the children an equation on the board and have them write it in their math reflection journal. They are asked to write a word problem that could describe the equation.  As they work, I expect several to be confused on which factor is the group size. I will continue to help them "restate" the equation using the phrase "groups of". 

Boys and girls, I would like you to try to write a story now, in your reflection journals, for the expression 3 x 7 = 21.  Would someone please read this equation for us, using our phrase "groups of"?

When you begin your work, don't forget to keep reading your equation. Think of things that might come in groups, like candy, fields of pumpkins, bushels of apples, trees with changing colored leaves...

Sharing Journals

10 minutes

I always like to have the students share on the board, or just from their seats, the work they have done in their reflection journals.  Although many like to keep their work private, but share their thinking aloud, the more we share, the more risks they all end up taking.  It is also a perfect time to guide them in discussing each other's thinking and strategies.  At this age, just working on metacognition is huge and this format allows us to do it with meaning. 

Writing Equations to Match Stories

20 minutes

My school utilizes a curriculum resource that supplies workbooks for the students. This is one lesson where I am able to use the pages and feel comfortable with the purpose. I have my students turn to a page of the book with several multiplication word problems and work to write the proper equation for the story.  I am looking here for more than the correct product.  I am more interested in the expression that tells the story.

Ok mathematicians, let's change it up a bit.  You have been thinking a lot today about group sizes of objects and writing stories.  Now I would like for us to practice reading the stories and writing the expressions.  When we read the stories, we will need to decide what the group size is and what we are going to do with the groups.  Remember our chart of the steps we need to follow when we work on word problems.  It is here on the board for you to refer to. 

Let's do the first one together.

This video shows a group of students working to understand the "equal group size" and on their way realize a bit about division! 

Wrap Up

5 minutes

Boys and girls, would someone tell me what they thought was a really important part of our lesson today when we worked with word problems?  What was helpful for you today so your brain could work smarter?

During this conversation, I allow all responses, but if I don't hear it, I will remind the children that understanding the multiplication symbol tells us about the how many groups and about the group size.