Missing Numbers in Japanese

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Objective

Students will be able to complete math sentences where the missing number can be found in any position.

Big Idea

Students build a stronger understanding of number and tie it in to Japanese counting and to provides a great review.

Warm Up

5 minutes

I begin today by counting to 20 in Japanese. I write the Japanese number words on the board as we count to give students a visual for the second part of the lesson. 

I write ichi - 1, ni - 2, san - 3, she - 4, go - 5, rocku - 6, nana - 7, hatch - 8 , qu =9, ju = 10

We count by 1's, 2's forward and backward in Japanese once the numbers are written on the board.

Next I call out a number and the students hold up that number of fingers. 

I ask students if it is hard or easy to count to 10 in Japanese? Would they like to learn to count even higher in Japanese? We will be working with the numbers above ten. I tell them that the Japanese count using place value so instead of 11, they say ten-one or ju-ichi. I tell them that we will work with these larger numbers today, remembering that we say how many tens (ten, 2 tens, 3 tens, 4 tens and how many ones when we say the numbers in Japanese, so if they can count to 10, they can count to 99 or qu -ju- qu (9 ten 9).

Now students are ready to use the Japanese names for numbers in missing number equations.

Missing Number Equation Practice

15 minutes

I begin today by reviewing the idea of how we can figure out a missing number in any position in an equation.  I begin by explaining that the Japanese count using place value strategies. When they want to say 11, they say 10  1  or ju ichi. If they want to say twenty they say 2 tens or ni - ju. 

I put   9 + ________ = 23   How do we say 9 in Japanese? (qu). How do we say 23? (ni ju san - 2 ten three). Now we need to find the missing number.    I ask students how we might figure out the missing number. (count up on the number grid from 9 to 23, count back from 23 to 9, subtract 23 - 9). I remind students that we had used a magnifying glass to represent the missing number. I tell students they can draw in the magnifying glass to help them remember that they want to figure out the missing number.

I also suggest that we can find the missing number by visiting Mt. Fuji (Japan's tallest mountain). I draw the outline of a mountain on the board and put 23 at the top. At the bottom I put 9 on one side and the magnifying glass on the other to signify the number I don't know.  When we find the answer we all try to say it in Japanese (ju she - 14).

Together we do several of the missing addend problems. _____ + 12 = 25,    30 - _______ = 14, 26 - ___________ = 18. I ask a volunteer to draw Mt. Fuji for us each time and then add in the missing number when we solve the problem. I am hoping students will begin to use the structure of the problem to solve missing number problems (MP 7).When I am sure students understand what they need to do, I tell students that they will be working in partners to create a problem, and ask the problem in Japanese and have a partner solve the problem.

I hand out a practice page for students to work on. I circulate around to listen to student thinking as they try to solve missing addend problems. 

Working with Missing Addends

20 minutes

I partner students up. I choose one student to be my demonstration partner. I create the problem 8 + _____ = 21. I read it "hatch plus __________ = ni ju ichi". I ask my partner if they can figure out what number is missing and say it in Japanese. I suggest they write the numbers they recognize first, so if they recognize hatchi as  8, they would write the 8 + ____ and then try to decipher the ni ju ichi to get 21. Once they have deciphered the two numbers and translated them from Japanese they are ready to subtract, count or use another strategy that makes sense to them to find the answer.  My partner now subtracts 21 - 8 to get 13 and then says ju san . 

I tell students that they will write down 3 problems with all numbers less than 29, figure out how numbers are read in Japanese, and then partners will take turns sharing the numbers and solving each other's equations.

I remind them of the numbers 11 - 29. We say them out loud and I write them on the board for reference. ju-ichi, ju- ni, ju-san, ju-she, ju-go, ju-rocku, ju-nana, ju-hatchi, ju-qu, ni-ju

ni-ju-ichi, ni-ju-ni, ni-ju-san, ni-ju-she, ni-ju-go, ni-ju-rocku, ni-ju-hatchi, ni-ju-qu.

Closing

15 minutes

I bring the class together on the rug. I ask them whether it was harder for students to solve the math or figure out the Japanese? Most of the students will say that the Japanese was more difficult. 

I praise students for trying this hard activity. I ask if they would like to try to count to 50 in Japanese? I remind them that the Japanese count ten-one, ten - two, ten-three, just as if we were taking the numbers apart by tens and ones. When we get to 20 it is 2 tens, twenty one is 2 tens -one, twenty two is 2 tens two, etc. 

We count slowly to 50. I want students to feel a sense of accomplishment when they realize how they can use the Japanese counting system because of their own understanding of tens and ones.