Appendix C: Example Chinese G4 Lesson Plan about Formal Teaching of the CP and AP of Multiplication
Commutative and Associative Properties of Multiplication
G4 Textbook p.60, Worked Examples #3 and #4; Exercise 10: #1-3 Teaching Objectives
- 1 Create real-life situations, let students experience the process of exploring the commutative and associative properties (CP & AP) of multiplication, promote understanding and mastery of these properties and the ability to use letters to represent them.
- 2 Teach students to use the CP and AP of multiplication to calculate in effective ways, and let them see the value of applying the properties. Cultivate students’ sense of exploration and problem-solving ability, and enhance their awareness of applying math in the real world.
- 3 Cultivate students’ ability to observe, compare, and summarize, and help them experience a sense of success in math activities.
Important Points of Teaching
Promote an understanding of the CP and AP of multiplication, guide students to generalize/summarize the properties by themselves, and then apply the properties to calculate in effective ways.
Difficult Points of Teaching
Let students experience the process of exploring the properties, and grasp the features of the CP and AP of multiplication.
I Introduction with Conversation
- 1 Show the questions on the PPT
- 1 How do we use letters to represent the properties of addition? CP of addition: a + b = b + a
AP of addition: (a + b) + c = a + (b + c)
- 2 Calculate the following in effective ways
- 67+ 87+ 13 6+ (59+54)
- 2 Reveal the topic
In addition, there are CP and CP. Do these properties exist in other operations? What properties does multiplication have? (Write the topie on the board)
II Communication and Sharing
- 1 Explore the CP of multiplication
- 1 Show textbook p.60 Example #3 on the PowerPoint. Ask the students to look at the picture, and talk about the known conditions and the question.
- 2 Students will solve the problem individually, and then share with the elass.
Solutions: 5x3 = 15 (people) or 3 x 5 = 15 (people)
- 3 Establish the equation.
- • Ask students to write these two number sentences into one equation:
- 3 x 5 = 5 x 3
- • Follow-up: How many more equations like this can you write?
- 4 Observe and discover: Observe these equations, and tell me what you have found.
- • Guide the students to find out: When we multiply two numbers, we switch their position, the product remains unchanged.
- • Point out that this is the CP of multiplication.
- 5 Use letters to represent the CP of multiplication.
- • If we use letters a and b to represent the two faetors, the property above can be written as:
a x b = b x a (write on the board)
- 2 Explore the AP of multiplication
- 1 Show textbook p.61, Example #4 on PPT.2
Ask the students to solve the problem individually, and then share the solutions with the class. Students may have the following solutions:
- • Method #1: First find out the number of participating people in one grade.
- (23 x 5)x 6
- • Method #2: First find out the total number of classes in this school.
- 23 x (5 x 6)
- 2 Ask students: Observing the numbers and results in these two number sentences, what have you found?
® The three faetors in each number sentence are the same.
© Whether you multiply the first two numbers together, or the last two numbers together, the product remains unchanged.
3 Now let’s do some calculation and comparison. Show the PPT: Does the property exist in the following pairs of number sentences?
©18x5x2 18 x (5 x 2)
© 13 x 25 x 4 13 x (25 x 4)
©24 x (125 x 8) 24 x 125 x8
Based on comparisons, students will obtain a clear understanding: When multiplying three numbers together, whether we first multiply the first two numbers or first multiply the last two numbers, the product remains unchanged. The teacher will point out that this is the AP of multiplication.
4 Use letters to represent the AP of multiplication.
If we use the letters a, b, and c to represent all three faetors, the properties above can be written as: (on board)
(a x b) x c = a x (b x c)
III Feedback and Improvement
2 Complete “Let’s Practice” on textbook p.61
Ask students to first fill in the answers in the textbook, and then explain what properties they used.
3 Complete #1 of Exercise 10 on textbook p.65
Ask students to read the problem first, and then ask them to explain how to use the CP of multiplication to check the answer. Finally, ask students to compute the problem and check the answer individually.
4 Complete #3 of Exercise 10 on textbook p.65
Ask students to report the products of three numbers on each group of balloons, and then share the calculation methods.