Mental Math with Place Value

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Students will be able to complete and compare addition and subtraction equations mentally, using various strategies.

Big Idea



10 minutes

To begin the lesson, I simply ask the students to come to the community area and give me a thumbs up when they have the answer to the solution to the following problems.  I explain that they need to only use their minds and be ready to explain how they arrive at their answer. 

Some of our equations include:

15 + 45 =

170 - 18 =

94 + 36 =

When students think they have an answer, I ask them to share with their shoulder partner. I then call on several students for each equation to come to the board and "list" their thinking. Below are some examples for 15 + 45.

Student 1: 10 + 40 =50, 5 + 5 = 10, 50 + 10 = 60

Student 2: 45 + 10 = 55, 55 + 5 = 60

Student 3: 45 + 5 = 50, 50 + 10 = 60

I then lead them into the active engagement in which they will also practice their journaling skills. Before sending them off to the activity, we discuss what the prompt asks them to do, and what vocabulary words they think they might use in their responses. The students discuss these terms in small groups of four. 

Then as we discuss the possible terms, I write them on the board and leave them up as reference, even though they are also displayed on the math vocabulary board.  Having them isolated is helpful for many of my students. You will see in the resources how we set the board up.

Active Engagement

25 minutes

As the students work, I pay attention to their place value understanding and listen for their ability to show their thinking in a logical order. Later in the lesson, when they were writing about their strategies, I remind them of the vocabulary terms. 

In the following clip, I was pleased with the student's strategy and communication.  I am also really impressed when she caught her own mistake, because she was walking me through her thinking.

Many students are able to use their mental strategies, but need work on writing out their train of thought.  As you watch this student, you will hear me guide him on how to share his thinking by writing.

Close and Home Practice

5 minutes

As a close, I simply remind students that we all make sense of math in our own way.  However, we have to use our knowledge of how numbers work to create our own meaning.  We also test our strategies for consistency and efficiency.

I send the journals home as home practice in order for the students to take their time in writing their thinking using our chosen vocabulary terms.  In the next lesson, they will share with a partner and compare the terms used.