Let Me Count The Ways to Get An Answer

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SWBAT demonstrate their thinking in problems that require addition and subtraction of one and two digit numbers

Big Idea

One Common Core goal for second grade is the ability to use place value in the addition and subtraction of numbers to 100. This lesson is a foundation for this skill.

Warm Up

10 minutes

Students are now aware of place value as it applies to digits in numbers. Today we begin to explore how place value can help us in the addition and subtraction of numbers. An important Common Core shift that I'm addressing in this lesson is the development of understanding and the use of models that represent that understanding. My focus today is on exposing students to strategies based on place value.

I begin by putting a problem on the board:

There are 18 students on the playground. 9 more students join them. 3 of the students play on the swings. How many students are on the playground?

Students solve the problem independently in their journals while I circulate around noting who has a strategy to solve the problem, and who does not. I use this time to scaffold students from where they currently are demonstrating understanding, to the next step in developing fluency with addition and subtraction. This may be different for each child. I look at a child who may have added 18 + 3 and forgotten the 9. I ask them if they could draw a picture to show what is happening in the problem. We read the problem together and see if we can visualize what we are reading. (This ties in to learning visualization in reading comprehension.)

When most students identify that they are ready (by a thumbs up), I ask for a student volunteer to share how they solved the problem. Students just want to give an answer, but I ask them to tell me how they found that answer. I ask other students to decide if the answer makes sense. (Mathematical Practice 3: "Construct viable arguments and critique the reasoning of others" is being built up here).

When students do not solve a problem correctly, we think about what steps they took that are correct, and what might have been confusing. I ask for other volunteers to also share how they solved the problem. I allow children to write their solutions on the board and try to leave as many of them visible as possible.

Now I ask students if everyone solved the problem in the same way? (Hopefully not). I then ask if there is any one right way to solve the problem? I encourage students to realize that different strategies are possible.

I tell students that today we will create some problems of our own and try to solve each other’s problems when we are done.

Teaching The Lesson

30 minutes

I ask students if they know what information needs to be in a math problem if others are going to be able to solve it?  (They often mention numbers, signs, etc.) I show them a problem with no question and ask if they can solve it?

“There are 8 ducks on the fence. There are 9 ducks in the pond.”

Many children immediately want to respond that the answer is 17. I tell them that the answer I am thinking of is 1 and ask them why I was able to get 1 while they got 17? We realize that the question makes a difference to the solution. We talk about the importance of a question in a word problem. I could have said:

  • How many ducks in all?
  • How many more ducks in the pond?


These questions lead to different answers.

I tell them that today they will write word problems that must ask a question at the end. I give them a word problem form that has a space for a picture, for the words of the problem, for the question, and for the answer. The layout helps students to remember the parts.

I tell them that today the numbers they use can only have 2 digits and that the digit in the tens place can not be greater than 5 and the digit in the ones place can not be bigger than 5. I ask them what number that is?

This discussion reviews the terms and place value concepts from the last unit. Research has taught us that children must hear things many times before they use them automatically so I use all opportunities to repeat the terms and concepts previously taught.

I give students 15 minutes to finish writing a word problem and putting a picture that matches the problem on their papers. 

Students who finish early have the option of playing a math game independently on the iPad, or completing a challenge page that I have laid out. 


10 minutes

In this section of the lesson, I want to encourage students to really meet the objective of this lesson and demonstrate their thinking. Just giving an answer is not enough. Because students are using 2 digit numbers in today's problems, I want to encourage students to use tens and ones to solve a problem. If students are just counting everything out by ones, they are not using place value to solve problems. I encourage the students to think about how using tens and ones might help them to solve the problem. I do not expect students to suddenly use tens and ones, but I can scaffold them through solving a problem by using concrete models such as base 10 blocks, or counting blocks,  to show the numbers, and the asking which digit is in the ones place and for each number, and then asking if we could add just the ones? Could we add the tens? Could we put these together? I want to move students forward in their thinking by not just doing the problem for them, but instead asking questions, using base ten blocks as a visual, and walking through the problem together. 

I give students a chance to share an example of the word problems they created. The student reads the problem aloud and then asks for volunteers to tell how they solved the problem. As we did earlier in the lesson, we discussed whether the solution was logical.  Students come up to the board and show their solutions. We talk about other options for solving the problem that other students may have used. 

If a student says they just "knew it." I ask them to talk more about what they "just knew," (ie did they count up or down, did they recognize a partner of ten, etc.) I also encourage the use of the math tools such as number lines and number grids that are on their desks. 

We save the other problems for tomorrow.