Grade 5 arithmetical science lesson plan for APEC Tsukuba International conference 2016
Takao Seiyama

Research theme: Research on active learning prevention of current arithmetic lessons through amodel lesson for introduction of ratio, which aims to conduct active learning
1. Lesson title: Active learning through comparing long leg robot drama posters (Learning unit: ratio)
2. Research subject and materials(1) Research subject
The Central Council for Education of Japan advised that active learning should be independent-cooperative
learning to find out and solve the learning assignment in November 2014 (regarding curriculum standard ofprimary and secondary education). We can pick up key words such as independent (positive learning),
cooperative, active and exploration. Active learning should be imagined as arithmetical activities in arithmetic
lessons because the activities are assorted independent-objective aware-pupil centred activities related toarithmetical assignments. The types of the activities are operational-experiential, research based, exploratory,
application of pupils’ thinking, expansive-applicable activities and so forth.
In 1998 and 2008, the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) revised
the Guidelines for the Course of Study and kept on emphasizing that such arithmetical activities should beconducted in primary schools. Why has MEXT modified the name of the learning approach to “Active learning”
and started recommending teachers to conduct? As the reason of this MEXT advice, we might assume that
active learning is not common in Japanese primary schools. Through this research, we would like to discuss
why arithmetic lessons are not active and what are preventing the lessons from being dynamic.
(2) Lesson materials
When we compare two different values in our daily lives, we generally use the difference. Comparison by times
are commonly used when the difference between two values are expressed like two times bigger (longer), threetimes bigger (longer) and a half times bigger (longer). Comparison using times is not common in our everyday
lives. Teachers are demanded to teach that a ratio is a relationship between two numbers indicating how manytimes the first number contains the second. We can intentionally show extremely wrong comparison samples
to let the pupils find out the concept of the ratio.
Let us assume that a primary school class intends to play a drama. A long leg robot appears in the drama. Inorder to advertise the drama, three groups of the class drew the drama posters. Each of them has the robot
image on it. Let us check which poster can show the robot leg length correctly.
We can give above assignment to this research model lesson class and let the pupils think how to compare thebody length and the leg length of the robot.
The long leg robot
Body length
Leg length

40 cm
24 cm

40 cm

24 cm

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Images of the robot on the actual posters
Group 1
Body length
50 cm
Leg length
24 cm

Group 2
50 cm
30 cm

Group 350 cm
34 cm

Robot image

This question gives pupils an opportunity to find out same ratios. Group 2 drew the robot image with the leg
length to the body length ratio 0.6 to 1. The group 2’s ratio is same to the original ratio of the leg length to thebody length. Group 3 robot image has the 16 cm length difference between the body length and the leg
length. After pupils realise each group’s drawing plan, let the pupils discuss which poster can show the robotleg length correctly.
The research model lesson teacher can intentionally introduce debate like “The difference between the bodylength and the leg length is 16 cm. If the difference must be always constant, a 100 cm long body robot
has 84 cm long legs.” We should expect the learners can find out a new comparison style beyond thedifference.
We can also introduce how to use proportional estimation.
Group 2 robot body length: 50 cm, Original robot body length: 40 cm
50 ÷ 40 = 1.25 (The group 2 robot image has 1.25 times longer body length than the original robot.)
The length of the legs must be 1.25 times longer.
24 x 1.25 = 30 (cm)Then we move on to next step.
If we multiply the original body length by 2, the body length is 80 cm and the leg length is 48 cm.
If we multiply the original body length by 3, the body length is 120 cm and the leg length is 72 cm.
After each calculation we have to confirm the followings.
Original robot,
Leg length ÷ Body length: 24 ÷ 40 = 0.6
Group B robot,
Leg length ÷ Body length: 30 ÷ 50 = 0.6
80 cm long body robot,Leg length ÷ Body length: 48 ÷ 80 = 0.6
120 cm long body robot, Leg length ÷ Body length: 72 ÷ 120 = 0.6
Each robot’s leg length to body length radio is 0.6 to 1. These robots’ leg lengths are 0.6 times longer
than the body lengths. To find out the same value is important to understand the concept of theratio.
3. Objective and teaching plan of the unit (11 lesson hours)(1) Objective
 Pupils will be able to understand the meaning and usage of ratio and percentage. They will be able to apply
the ratio concept to solve the questions.
(2) Teaching plan
1) 2 hours, Meaning and usage of the ratio (This lesson plan is the first lesson)2) 3 hours, Percentage
3) 4 hours, How to apply percentage to our daily life4) 2 hours, Review and exercises
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4. Teaching of this lesson(1) Objective
 Pupils will be able to use ratio (times) to compare objects instead of using difference.
(2) Lesson development
Major Learning activity
1. Let us check which poster can show the robot leg
length correctly.

Remarks A primary class is going to play a dram. In order toadvertise the drama, three groups of the class drew
posters, on which the main character “Long LegRobot” is drawn.

Teacher (T): (Show the actual long leg robot to theclass.) The body length of the robot is 40 cm and theleg length is 24 cm.
(Show actual posters to the class.) Which poster canshow the robot length correctly?
Child or Children (C): The group 1 robot’s leg lengths
are less than a half of the body length. They are too
short and not correct.
C: I think group 3’s poster is correct because the length
difference between the body and the leg is 16 cm.
The original robot has the same difference.
C: I think group 2 drew the robot correctly.
30 ÷ 50 = 0.6 The leg length is 0.6 times of the bodylength. This is same to the original robot.

 Keep on talking with the children; show the class theimages of the posters and lengths of the robot bodyand legs drawn on the posters.
Group 1
Group 2
Group 3
Body length
50 cm
50 cm
50 cm
Leg length
24 cm
30 cm
34 cm

2. Discussion on comparisons using the difference andthe ratio
T: We have two styles to compare objects. One isusing the difference and another is using times.
C: If we can use the length difference to draw therobot correctly, a 100 cm body length robot must have
86 cm long legs. It does not show the correct imageof the original robot.
C: If a robot body is 20 cm long, a leg must be only 4cm long.
C: If we apply the idea “The leg length is 0.6 times ofthe body length”, the 100 cm long body robot has 60
cm long legs and the 20 cm long body robot has 12 cm
long legs.

 Prepare a piece of paper to draw a 100 cm bodylength robot on it. Let children think about thelength of the legs of the robot. Use Group 2 style andGroup 3 style to determine the legs length.

3. Review the usage of the comparison
C: Using the original robot’s design, we divided the leg
length by the body length and the answer was 0.6.
We found a correct image using this value.
T: The value 0.6 is called the leg length to the bodylength ratio.

 Teach children that a ratio is a relationship between
two numbers indicating how many times the firstnumber contains the second.
Let the class confirm that we used the concept of theratio to find out the correct robot drawing.

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