Judo competition
This is a level 5 number activity from the Figure It Out series. It is focused on adding, subtracting and multiplying integers. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Adding, subtracting and multiplying integers.
Judo competition
Achievement objectives
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
Required materials
- Figure It Out, Level 4+, Number, Book Six, "Judo competition", pages 14–15
- a classmate
See Materials that come with this resource to download:
- Judo competition activity (.pdf)
Activity
Activities 1 and 2
For students who are not familiar with how negative numbers work, at least for addition and subtraction, a number line could be a good means of helping to develop their understanding.
Integers are also known as “signed” numbers, but notice the convention regarding the use of signs: a negative sign denotes a negative number, but the accepted assumption is that a number without a sign is a positive number.
The number line can help the students to see that:
- i. addition usually means go to the right along the number line, for example, 2 + 5 = 7 (begin at 2, add 5, and you end up at 7). The same happens if you start on a negative number, for example, -6 + 9 = 3 (begin at -6, add 9, and you end up at 3).
- ii. subtraction usually means to go left along the number line, for example, 7 – 3 = 4 (begin at 7, subtract 3, and you end up at 4). Another example would be 2 – 5 = -3 (begin at 2, subtract 5, and you end up at -3). A third example is -2 – 4 = -6 (begin at -2, subtract 4, and end up at -6).
Dealing with a negative means moving in the opposite direction. For example:
3 |
+ |
5 |
= |
8 |
|
3 |
+ |
-5 |
= |
-2 |
Start at 3 |
|
move 5 right |
|
end at 8. |
|
Start at 3 |
|
move 5 left |
|
end at -2 |
-2 |
- |
4 |
= |
-6 |
|
-2 |
- |
-4 |
= |
2 |
Start at -2 |
|
move 4 left |
|
end at -6. |
|
Start at -2 |
|
move -4 right |
|
end at 2. |
You need to emphasise the “0” point on a number line and the fact that a number and its opposite will always add up to 0. For example, 3 + -3 = 0, so 3 + -5 is 3 + -3 + -2, which is 0 + -2 or -2.
The students may be able to summarise all this along the following lines as a basis for tackling the judo competition tasks:
Operation |
Direction |
Example |
|---|---|---|
Add a positive |
Go right |
-2 + 4 = 2 |
Subtract a positive |
Go left |
2 - 4 = -2 |
Add a negative |
Go left |
-2 + -4 = -6 |
Subtract a negative |
Go right |
2 - -4 = 6 |
The other understanding required of students for these activities is what happens when integers are multiplied by other integers. This can be summarised as:
Integer x integer |
Example |
|---|---|
+ x + = + |
3 x 4 = 12 |
- x - = + |
-3 x -4 = 12 |
+ x - = - |
3 x -4 = -12 |
- X + = - |
-3 x 4 = -12 |
Note that only + x + and + x - are involved in this activity.
Activity 1
1.
a. Jason 7, Emily -3, Ruth 8, Ben -6, Kate 7, Tom 11.
b. Strategies will vary. One strategy could be:
- I added all the positives together, then added all the negatives together, and found the distance.
2.
a. Jason's, Emily's, and Kate's scores.
b. 17 points. (Tom has 11, and Ben is on -6).
3.
-9
4.
24
Activity 2
1.
a. Jason 12, Emily -34, Ruth 24, Ben 6, Kate 14, Tom 40.
b. 74
2.
a. 62
b. 86
Activity 3
1-3.
Responses will vary. Teacher to check. A possible score sheet could be:
- Jason: ippon, chui (24)
- Ruth: yuko, koka (9)
- Ben: waza-ari, shido (12)
- Kate: chui, koka (-3)
- Tom: ippon, koka (33)
Score for the round: 75
Total score: 86 + 75 = 161
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