Lesson Study Research Lesson: Teaching subtraction of integers

This year, we introduced Lesson Study to the mathematics teachers of Sta Lucia High School, a public school in Pasig City, Philippines. I am working with a group of 5 teachers, all teaching Mathematics I (Year 7 maths). We implemented the lessons last month and with their permission I am sharing the latest version of the lesson. Note that while the objective of the lesson is for students to understand subtraction of integers, the lesson was also so designed to develop students mathematical thinking skills and thinking habits.

1. Representing integers with chips.

Representing integers using + and - chips

2. From ‘chips representations’ to number sentences.

'Chips representations' to number sentences

3. Taking away integers using chips.

In #3, the student should have added 5 negative chips and 5 positive chips to 8 positive chips. From there she can now take away -5.

Subtracting integers using chips

4. Making conjectures/generalizations: The students used chips to find the integer equal to the given expressions. They were asked to classify the equations according to the sign of the difference and answer the question When does subtraction operation give a negative result? a zero? a positive result?

Negative, Zero, and Positive Difference

The students observed that: If you take away a bigger number from a smaller number, the result is negative. If you takeaway a smaller number from a bigger number, the result is positive. If you take away a number from itself, the result is zero.

5. Making observations and inferences from patterns in the table of subtraction of integers.

Students initially filled-up the subtraction tables using chips until they discovered the pattern. They were then asked to write at least three observations about the values in the table and explain why the patterns will hold.

Patterns in the table of integers

6. And ah, yes, we have a rule to derive. We asked students to write equations from the subtraction table and compare them to equations from the addition table that give the same result. They observed that taking away a number is the same as adding its opposite.

Linking subtraction and addition

Of course, how we wish we have an electronic whiteboard or at least a decent whiteboard and a set of chips for the 5o students.

The lesson study group re-viewing the video of their lesson implementations:

Dianne, Mrs. Jose (head of dept), Lorraine, and Rina. Not in the photo: Nida and Ronald



2 Responses to Lesson Study Research Lesson: Teaching subtraction of integers

  1. fatguy says:

    addition of integers is easier

  2. Mary Ann D. Barlis says:

    Subtraction of integers is one of the least learned lessons in mathematics. Though it was already introduced in GRade VI, still my fourth year students cannot master it well… thanks for trying presenting a lesson study research that will develop mathematical thinking of the students.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: