Ways to Make 9- A Lesson on Decomposing

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Students will be able to decompose the number 9.

Big Idea

Students will learn what it means to represent a number in different ways and will begin to explore decomposing numbers.

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:

Ellie has 6 flowers. Show two ways that she can group her flowers.

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 six flowers 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 manipulatives, picutures, 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

Prior to starting this lesson, I mixed things up by playing a short game on Starfall.  It was a really quick addition word problem game that changed things up a bit. Check it out here.


I start this lesson by hanging a piece of chart paper on the front board.  I attach a large number 9 to the top of the chart.

What number is this?  We are going to look at some other ways to represent the number 9 besides the numeral.   Can anyone think of a way that we can represent the number 9?

I call on students to tell ideas for how to represent 9.  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 will repeat this same activity for each number.  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 "9" 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.

Now we are going to look at another way that you can represent numbers.  You can use addition number sentences that are equal to the number. 

I give each student 9 connecting cubes of the same color and let them use them to come up with number sentences.  I add these to the chart.

When we are finished, I tell students that they are going to be practicing decomposing the number 9 on a Ways to Make 9 Worksheet.

You are going to work on this worksheet on your own.  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 nine two-color counters. 

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

The first thing the directions tell you to do is count the elephants 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 this question, you will need to use the counters to come up with your own ways to make 9.

I walk around and make sure that students are correctly counting 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. 

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 and project it on the SMART Board and have that student explain their work.  I have the student use the 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 9.  Tomorrow we will learn about ways to make 10."