Complements of 10

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SWBAT fluently solve combinations of ten. SWBAT represent combinations with a standard equation notation. SWBAT use their knowledge of 10 to solve a story problem.

Big Idea

Quicker than the Flash. Today your students will work on their complement of 10 fluency. They will then solve a story problem that will allow them to connect their knowledge of ten in a real world situation.

Warm Up

5 minutes

I start by posting my 101-200 classroom number grid.  Today, I want to focus on counting backwards and forwards between numbers on this grid.  I have a card with a green dot and a red dot on it. These cards easily slide into the pockets of the number grid and act as a visual for where we will start and stop our count.  

"Who can tell me a number between 160 and 180?  Great, Timmy said 168.  Who can come put the green dot card on the number 168?  Who can give me another number between 160 and 180? Great, 180 is in our range.  Who could put the red card in the 180 slot?  Now, I want to start at 168 and stop at 180.  I would like you to say the numbers as I point to each one."

I then repeat this process with a few more numbers.  Finally I end it with the numbers 101 (start at) and 120 (stop at).  I want to focus on the transition form 109-110.  This is often still a stumbling block for first graders. Often kids will say 109 and then say 200. This discussion will allow me to address the error in thinking.  This has the students practicing counting to 120, which is a CCSS first grade expectation (CCSS.Math.Content.1.NBT.A.1).

Introducing Complements of 10 With 10 Frame Cards

15 minutes

I ask the kids to sit in a circle on the carpet.  I want to introduce them to a new game with the 10 Grid Cards.  If you don't have any of these cards, you can use playing cards (using the ace as a 1 and going through 9).

There is a video in the section resource Making Complements of 10) that highlights how I introduced this activity.

"We are going to learn how to play a new game today.  The goal of the game is to make as many combinations of 10 as you can.  To play the game you will need a deck of ten frame cards (or paling cards).  You will take out the tens and just use the 1-9 cards and you will play with a partner (I did make one team of 3 because I had an odd number). To start, you make 4 rows of 5 cards with the numbers facing up.  You put the extra cards on the side, face down.  The first person scans the cards to find two numbers that make ten, and then picks them up as they say the two numbers. Your partner needs to agree that the cards do make ten.  You can check by counting the dots.  If you need to do this, I want you to count on from the highest number.  After you take two cards, you replace them with two new ones from the "extra" pile that you made at the start.

Once you can no longer make any more combinations, you will use the recording sheet (see section resource) to write an equation for each combination.  Let's play a few rounds together to make sure everyone understands." 

The students are recording their equations on a recording sheet and using standard notation in coin so.  They are modeling their answer with mathematics, which allows them to engage in MP4 (CCSS.Math.Practice.MP4), which states that mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation.

It is expected that "1st grade students can add and subtract within 20, demonstrating fluency for addition and subtraction within 10" (CCSS.Math.Content.1.OA.C.6).  This activity's repetitiveness allows for this fluency to build.

Differentiation:  I have for students who are secure with their complements of ten and this activity would not be rigorous enough for them.  So, I have also added a complements of 20 game.  I introduced this to them after I got the rest of the class going on the 10's game.

To play this game you will need the Combinations of 20 recording sheet and a 20 sided die numbered 1-20.  This game is also played in groups of two but can easily be played in a team of three or 1, based on your need.

"I am going to have this group work on a game that is a little different.  However, you will still need to use your knowledge of 10 to solve for 20.  You will  use this die and this recording sheet. The first person rolls and states the number rolled.  The second person has to state the number that goes with the rolled number to make 20.  You each write the combination (on your recording sheet) and then prove to me how you know.  Show me how you made ten and then ten more."  

Students are adding two numbers to make a ten and then the third number to make 20 (16+4=20). The 6 & 4 can be added to make a ten and then the other ten added to make a 20 (CCSS.Math.Content.1.OA.B.3). The students are also showing how they know their answer is correct and modeling how they added the numbers to get 20, encouraging students to attend to precision and try to communicate precisely to others (CCSS.Math.Practice.MP6). 

There is a video in this section's resources that demonstrate this activity being played.  There are examples of who students did this in the Station Time resource section. 

Station Time

30 minutes

Students have a choice of two activities during station time.  They can start with either one but they need to play both before the station time is finished.

Complements of 10:  This game was just explained in the previous section.  There are examples of completed recording sheets in the section resource.

Complements of 20:  This game was just explained in the previous section.  There are example of completed recording sheets  in the section resource.

Three Stacks:  This activity was introduced and played in a previous lesson.  You should review the lesson and print off the materials needed.  This game is also focusing on combinations of 10.

Story Problems

15 minutes

I finish today's lesson by giving the students a story problem that will allow them the opportunity to use their knowledge of complements of 10 in a real life situation.  There are two problems in the section resource.  One is a challenge problem for those kids who are already secure with their complements of 10.  You will need to make copies of each one.

I read the first problem out loud and ask the students to create a picture, of what is going on, in their mind.  I then ask a few students to repeat the 'action" to the class.  I then send them off to solve the problem.

I read the 2nd problem, to the those who I have chosen for the challenge task, and then send them off to solve their problem.

I have included a few examples of student work.  The challenge problem example demonstrates how a student used two know facts to quickly get the answer.

The "Intervention With Explanation" problem is an example of a student who gets the math but has a hard time using words to explain what he did.  You can see how I went back and walked him through it and modeled a more efficient way of representing his thinking.

The other two examples are of someone who met the expectation by using a know fact to solve the problem and of someone who is still trying to count all and made a mistake inner computation.   

"Students are using addition and subtraction within 20 to solve word problems.  They are using objects, drawings, and equations with a symbol for the unknown number to represent the problem (CCSS.Math.Content.1.OA.A.1)."