Three Stacks

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SWBAT fluently add combinations of 10. SWBAT use numbers and standard notation (+,-,=) to record.

Big Idea

Students use connecting cubes in a game to create a visual representation of combination to 10. The lesson ends with the students solving story problems with relational ship thinking.

Warm Up

10 minutes

Advanced Preparation:  Create a two column survey with a question at the top and the columns labeled yes or no (see picture in lesson resource).  

As students enter the classroom for math, I instruct them to read the question and then answer it with a tally mark.  Once everyone has answered I will start the conversation.

"Let's count the results for each category.  How many people said "yes?"  How many people said "no."  Now I would like you to give me one way we could represent our results using an equation.  What are some I Notice statements that you could make?  Who could write an expression using the < or > sign?"  The Core expects 1st graders to be able to represent a number of objects with a written numeral (CCSS.Math.Content.1.NBT.A.1) and also compare different quantities using symbols (CCSS.Math.Content.1.NBT.B.3).

The students are reasoning abstractly and quantitatively.  It is expected that mathematically proficient students make sense of quantities and their relationships in problem situations (CCSS.Math.Practice.MP2).

The picture in the section resource exhibits the results of the above questions.

I continue to throw in surveys throughout the year.  This allows me to spend less time in the isolated context of a unit and more time applying the concepts to real life situations.  The CCSS expect that first graders can organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another (CCSS.Math.Content.1.MD.C.4). 

Introducing Three Stacks

15 minutes

"I want to play a game that we looked at earlier in the year.  It is called Three Stacks.  The point of this game is to get three stacks of ten cubes.  We will play a demonstration game so you can see how it works.

 Let's say that Keegan (pick a kid for your class) and I are playing.  The first thing we need to do is take one recording sheet, a dot die and a number die (1-6), and we each need thirty connecting cubes.  I will choose 30 of one color and Keegan will choose 30 of another color.  It is important that we each have a different color.

 Keegan will then roll the two dice first.  I don't want to see anyone counting all on their fingers.  You must use the number die and count on or you can say the fact if you know it.  Keegan rolled a 5 and a 3.  Keegan states the answer (modeling the counting on strategy) and then builds that number with his cubes.  Now I roll and repeat the process.  I rolled a 3+2.  My total is 5.  I will connect 5 cubes and then connect it to the 8.  Let's count how many cubes this is all together.  Yes, it is 13 cubes.  However, what is the rule of the game?  There only can be 10 in a stack.  So, I need to take the extra and start the next stack.  We continue to to play until we have three stacks of 10.  

  Then we use crayons to color in the towers that we made on the recording sheet (see section resource).  

  The last step is to write an equation that shows how many cubes of each color are in each stack.  You will play in pairs and I want you to make sure you help each other and check each other's work."  The CCSS expect that first graders know that 10 can be thought of as a bundle of ten ones — called a “ten (CCSS.Math.Content.1.NBT.B.2a).”  When students are creating stacks of tens, they are engaging with this standards.  Additionally, the students are modeling with mathematics.  First grade students need to apply the mathematics they know to solve problems arising in everyday life, society, and, later, the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation (CCSS.Math.Practice.MP4). 

 *If you have an odd amount of kids, you can ask one student to play on their own.  I did this with a student who was more secure with this concept.

Playing Three Stacks

30 minutes

Students now play the game Three Stacks.  There is a video of students playing the game, coloring the sheet and an example of a finished recording sheet in the section resource.

As students are working, you should circulate amongst the groups and see:

  • How are the students finding the totaled rolled.  Are students (at minimum) using the counting on strategy?
  • How do students determine when a stack has 10?  Do they keep counting from 1?  Do they count on from the previous total? Do they use other stacks of 10 and compare?  
  • How do they record the total of each color in each stack? 

The Core expects first grade students to "add within 20, demonstrating fluency for addition within 10." Students are using strategies to create combinations of ten using two and three addends. The repetition that this activity offers, allows for students to develop the fluency that is expected (CCSS.Math.Content.1.OA.C.6).


Solving "10" Stories

15 minutes

I gather the students back on the carpet and give them each 12 connecting cubes (color doesn't matter).  

"I am going to read a story problem to you.  I don't want you to shout out the answer.  I want you to listen to the story and create a picture in your mind."

I then tell them the following story problems:

"Today at lunch we had strawberries.  Jen ate 4 strawberries.  Joe ate 6 strawberries.  How many strawberries did they eat?"

"Who can tell me what is going on in this story?  You can use your cubes or solve it any other way. Once you have an answer, I want you to put your thumb on your chin.  That will signal to me that you are finished and are ready to explain how you solved the problem."  

I then have them share how they solve the problem and write their strategies on the easel (see section resource).  Here the students are using addition within 20 to solve word problems involving situations of adding to, putting together, by using objects, drawings, and equations with a symbol for the unknown number to represent the problem (CCSS.Math.Content.1.OA.A.1).

I then tell another, related story.

"Tim and Jan were sitting at the lunch table.  Tim had 6 strawberries and Jan had 4 strawberries. How many strawberries did they have altogether?"

You should follow the same process as above but encourage them to think about the first problem and how that solution could help them solve this one.

You want to see if students start to realize that the order of numbers doesn't matter when you are adding,  If the addends are the same, the total will be the same (commutative property).

Continued Practice

5 minutes

I finish today's lesson with an activity that requires the students to combine two groups of two numbers and then determine which group has the highest total.  You will need to make enough copies of the Which Total is More Sheet (see section resource).  

I am doing this sheet to see how students are combining bigger numbers (above a total of 10) and if they can then compare two totals to see which one is larger.