Ways to Make 7- A Lesson on Decomposing

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Students will be able to decompose the number 7.

Big Idea

After decomposing the numbers 1 to 6, this lesson brings in a new twist with a story that shows a fun way to look at the number 7!

Problem of the Day

5 minutes

I start each math lesson with a Problem of the Day.  I use the procedures outlined here on Problem of the Day Procedures.

Today's Problem of the Day:

Ben has four cars.  Show two ways that he can group his cars.

I set this problem up with some structures to help the students organize their thinking.  I give two boxes split into two sections each to help the students see that they need to create groups.  I also add blank number sentence frames to remind the students to also write their answers as an equation.  On the Notebook file, the four cars are set to Infinite Cloner.  This way the students can use them to create two different groupings.  If you do not have a SMART Board, you can use the PDF and toy cars, car pictures, or students' drawings.  This problem is difficult for some students because it asks for two ways of representing the joining.  This is necessary because standard K.OA.3 says that students need to be able to decompose numbers less than or equal to ten in more than one way. The idea that numbers can be put together or broken apart to make other numbers is a critical understanding in the development of computational fluency. 

Since we do this whole group, I have two students come up and work on this problem.  I have one student create the first grouping and another student create a different grouping.  I remind students to check their work when they are finished and have the class tell if they agree or disagree by showing a thumbs up or thumbs down.  

Presentation of Lesson

25 minutes

I start this lesson by hanging a piece of chart paper on the front board.  I attach a large number 7 to the top of the chart.

We have been decomposing numbers.  Yesterday we worked on the number 6 and today we will work with the number 7.  Can anyone think of a way that we can represent the number 7?  We will get to our number sentences in a few minutes.  Let's start with some other ways.

I call on students to tell ideas for how to represent 7.  I add the ideas to our chart.  I have a variety of pictures available, but I also draw any additional ideas that students come up with.  Some ideas include dots in a ten frame, dots on a domino, bears, tally marks, and cubes.  I repeat this same activity for each number.  Rather than getting bored with the same activity, students actually get more confident each day and come up with more ways to represent the numbers. Why is it important to collect this information in a number of ways? Because this is how a young child develops understanding of quantities. I want my students to recognize that the symbol "7" is a quantity, and I want them to know that they can use a variety of models to represent that quantity. Creating these charts also gives you a nice visual to display in the classroom for the students to reference later.

We have been using counters to come up with the equations for each number.  Today we are going to read a story and use some ducks to help us come up with the equations for 7.  This book is called Quack and Count by Keith Baker. 

I leave the 7 chart hanging on the board and show the Quack and Count Notebook File with the seven ducks on the SMART Board.  As I read the book, I stop throughout to have student manipulate the ducks on the board and for me to add the equations to our chart.  When we are finished, I tell students that they are going to be practicing decomposing the number 7 on a Ways to Make 7 worksheet.

You are going to be doing this paper on your own, but we are going to go over the directions together.  When you get to your seat, do not touch your cup of counters.  You need to get out a pencil and put your name on your paper.  When your name is on your paper hold your pencil in the air, that will let me know that you are ready to start.

I use the procedures outlined here on the Paper Procedures.  Prior to this lesson, I placed a plastic cup at each students' place containing seven two-color counters.  I use the two-color counters so that the students can use the same 7 counters to create different groupings by just flipping some over.

Count the ducks.  Write the numbers to complete each equation.

The first thing the directions tell you to do is count the ducks and write the number to complete each equation.  You may use your counters if needed.  You will notice that the last two questions do not have pictures for you to count.  For these two questions, you will need to use the counters to come up with your own ways to make 7.  Raise your hand if you need help.

I walk around and make sure that students are correctly counting the ducks and/or counters and writing their equations.  When students are finished with their paper, they can put it in the basket and get their center.


20 minutes

The centers for this week are:


I quickly circulate to make sure students are engaged and do not have any questions about how to complete the centers.   I pull two or three groups during centers and work with them depending on the time they need (5 - 10 minutes).

Today I am focusing on addition with all of the groups.  While my students are doing well on our addition lessons and centers, as we near the end of unit assessment, I would like to observe them more closely as their work through word problems.  I verbally give the group a word problem.  I have them solve it using manipulatives and write the equation.  With students who are able to do this easily, I also have them try with drawing pictures instead of manipulatives.  Some examples I use:

Sara has 4 banana.  Lisa has 4 apples.  How many pieces of fruit do they have?
Eyan has 2 apples.  James has 4 oranges.  How many pieces of fruit do they have?
Matthew has 5 strawberries.  Thomas has 2 bananas.  How many pieces of fruit do they have?

Prior to clean up, I check in with each table to see how the centers are going.  My students have been struggling with getting cleaned up quickly and quietly after centers.  Lately I have been using counting down from 20 slowly instead of a clean up song.  Counting backwards is as critical as counting up. Students need to be able to know the number that comes before, as well as after, any given number (w/i 10, w/i 20, etc.). Counting back is a critical strategy for subtraction.

The students like to count backwards with me as they clean up and I can lengthen or reduce the clean up time based on how students are doing and how much time we have.


5 minutes

To close, I put a student's paper on the document camera a project it on the SMART Board and have that student explain their work.  I have the student use the color counters to show how he or she came up with the equations in numbers 5 and 6.  I mention positive things noticed during centers as well as something that needs to be better next time. 

I review what we did during our whole group lesson.  "Today we learned about different ways to make 7.  Tomorrow we will be working on different ways to make 8."