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.

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

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I'm a math teacher, researcher, writer, and facilitator of professional development for teachers. Email me at mathforteaching@gmail.com.