Appendix B: Example Chinese G1 Lesson Plan about “Making a Ten to Add” (Informal Teaching of the AP)

Plus Something

Teaching Objectives

• 1 Students will explore methods to compute “9 plus something” (Jiu- Jia-Ji) in real-world situations. Through discussions of different computational methods, students will begin to understand how to apply the strategy “making a ten to add” for mental math.
• 2 Students will explore different computational methods and gain experience from mathematical activities. Students will begin to develop the abilities to observe, manipulate, analyze, and compare, and learn how to think and express ideas logically.
• 3 Through participation in the math activities, students will develop the habit of thinking independently, gain experience from their success, and increase their interest in mathematics.

Important Points of Teaching

Master the computational method of 9 plus something.

Difficult Points of Teaching

Understand and master the strategy of “making a ten to add.”

Teaching Material

Two bundles of little sticks

Teaching Process

I Create a Scenario, and Introduce the Lesson with Review

T: (Show PPT) Hi kids, look! who is it? (Mr. Monkey). He will be learning math with us today!

Let’s do some mental math first. (Students take turns) (Read the questions and results)

10 + 4= 10 + 7= 10 + 5= 10 + 2= 10+1= 10 + 6= 10 + 3 =

Т: How can you figure them out so fast?

T: Yes! This is what we have learned before, ten plus something equals to ten-something¹!

II Teach the Worked Example 1 Students compute 9 + 4 independently

Transition: Mr. Monkey thinks that we did a great job with mental math.

So he treats us with apples from his fruit store!

T: Look at the picture carefully, how many apples are inside the box, and how many are outside?

T: Can you pose a question that can be solved with addition?

S: How many apples are there in total? (T: Good question!)

T: Who can combine the information and the question, and state this math problem completely?

T: There are 9 apples inside the box, and 4 apples outside the box. How many apples are there in all?

T: To find the total amount of apples, what can we do?

S: To find the total amount of apples, we need to combine the 9 apples inside the box and the 4 apples outside the box together. We use addition to compute.

T: What’s the number sentence? (On board: 9 + 4 = )

T: 13, do we all agree?

T: How did you compute it? Take out your little sticks and work on them. Share with your deskmates about the process.

Student report: Can you share your method by pointing to the picture here?

Possible methods:

© Count it: count 4 numbers beginning from 9.

© Take 1 apple, and put it inside the box, 10 + 3 = 13.

T: Why do we take 1 apple from the 4 first, and put it into the box?

S: So we can fill the box, which has 10 apples in total.

T: If we take 1 apple from the ones outside of the box, how many apples are left outside?

T: Which means we separate the 4 apples into what and what?

S: 4 is separated into 1 and 3 T: We first compute 9 plus what?

S: First compute 9 plus 1, which equals 10 (Record on board: )

T: And then compute what? (Give hint by hand gesture)

S: And then compute 10 plus 3, which equals to 13 T: Oh, so we can actually compute 9 plus 4 in this way (Think aloud): We separate 4 into 1 and 3, 9 plus 1 equals 10, 10 plus 3 equals 13 T: Can you state this process by yourself?

196 Appendix В

T: Who can state the process completely for us? (Invite 2 students)

T: Are you able to say this process? Tell your deskmates about it.

T: I have a question now, why do we separate 4 into 1 and 3?

S: Because 1 plus 9 gives us 10

T: Yes, today we are going to learn 9 plus something, so we take 1 from 4 to make a 10.

® View 9 as 10, compute 10 + 4 = 14, and then 14-1 = 13.

@10 + 4= 14,9 + 4= 13

Teacher will listen to students’ answers and record them on the board. Teacher will summarize: We have thought of different methods to compute 9 + 4, the first method is..., and the second method is...

2 Teach how to use “make a ten to add” to compute 9 + 7

T: Mr. Monkey thinks that you have learned so well! So, he decided to invite us to visit his garden!

T: Which two parts have the flowers in the picture been separated into? How many flowers are there in total? How can we write a number sentence to solve it? (On board: 9 + 7)

T: Can you first circle 10 flowers and then do the computation? Circle them on your textbook, and fill in your thinking process in the numerical expression on the right side of the picture. (Ask the students to open their textbook to p.88, and find “Give a Try”)

Report: Can you point to the numerical expression that you wrote, and tell your class how you computed it?

3 Students work with the sticks independently, and compute 9 plus something

T: Mr. Monkey saw that we are all doing a good job, so he would like to try one! (Shows the picture) Which number sentence does Mr. Monkey want to try?

T: Take a guess, how will Mr. Monkey compute it? Fill in your answer. Conclusion: How did Mr. Monkey compute 9 plus 6? (Take one stick and put it together with the 9 sticks to make a ten.)

Why did he take 1 stick and put it together with the 9 sticks?

4 Students practice independently

T: Mr. Monkey took a lot of sticks, and placed them like this pattern (Show “Think then practice” #2). It asked us to first circle 10 sticks and then compute. So, let us first circle and then compute. (Complete #2)

Talk to your deskmates about how you computed it.

Project student work on the board and ask them to share.

5 Students pose problems about “9 plus something” to test the others

Ask: Who can come up with a problem about 9 plus something to test us?

Students will come up with 2~3 questions. (Ask the “little teachers” to make comments on the questions.)

III Find the Pattern and Enhance Thinking

T: During this lesson, we have learned some addition problems. Let’s read these number sentences together. While we are reading, please think about what you have found.

S may say: The first number is always 9.

Teacher then reveals the lesson topic: Today, we have learned 9 plus something (write the lesson title on the board).

T: Have you found anything else new? (Point to the number sentences and read them again, hint with emphasis.)

T: What did you find? (The “something” in “ten-something” is always 1 less than the number that is added to 9².)

T: Why is the “something” in “ten-something” always 1 less than the number that is added to 9?

Show: 9 + □ = 1П, can you fill it?

T: If I write 5 on the first box, what about the second box? If I write 7 on the first box, what about the second box? Now, if we are going to compute 9 plus something, can we finish it both quickly and accurately?

T: Who wants to be the little teacher? Please post a problem to test us!

IV Summary

Conclusion: What have we learned today? How can we compute 9 plus something effectively?

Notes

• 1 As noted in Section 4.4, the names of teen-numbers in Chinese indicate the place value. For instance, 11 is called ten-one; 12 is read as ten-two. Thus, 10 + something = 10-something.
• 2 For instance, in the ease of 9 + 4 =13, Chinese students will read it as “9 plus 4 equals ten-three.” The digit “3” on the ones place of the sum is “1” less than the number “4” that is added to 9.