GEEM - Teaching and Learning

C2.4 Solve inequalities that include an operation and natural numbers up to 50, and verify and present solutions using models and graphical representations.

Activity 1: Broad inequality situation

Present the following scenario to the students.

Nicolas has permission from his parents to play video games for a maximum of 30 minutes a day. This morning, he played for 17 minutes. When he arrives from school, Nicolas plays his video games again, while respecting his parents' instructions.

Ask the students to indicate on a number line the number of minutes Nicolas could have played his video games when he came home from school.

Represent the situation using an inequality

This morning, Nicolas played his video games for 17 minutes. We want to know how many minutes Nicolas could have played his video games after school, so 17 + m. He can play up to a maximum of 30 minutes per day.

To find the number of minutes Nicholas could have played his video games after school, we need to solve the following inequality:

17 + m ≤ 30

m	17 + m	≤ 30
0	17	yes
1	18	yes
2	19	yes
3	20	yes
4	21	yes
5	22	yes
6	23	yes
7	24	yes
8	25	yes
9	26	yes
10	27	yes
11	28	yes
12	29	yes
13	30	yes
14	31	no
15	32	no
16	33	no

m ≤ 13

Number line with numbers 0 to 30 and number 15 has a yellow circle. A left arrow is pointed from the yellow circle to value zero.

After school, Nicolas could have played his video games for 13 minutes or less. A period has been placed on the number 13 since this indicates that it is a large inequality relationship.

Ask a few groups to present their solution. Allow students to review their answers.

Activity 2: Strict inequality situation

Present the following scenario.

For safety reasons, there must be fewer than 26 people in the local municipal pool. Knowing that there are already two families of four in the pool, what are the possible numbers of additional people who can join them?

Represent the situation using an inequality

Since the number of people currently in the pool is 8 and there must be fewer than 26 people, we can represent the situation using the following inequality:

8 + n < 26

where n is the number of people

n	8 + n	< 26
0	8	yes
1	9	yes
2	10	yes
3	11	yes
4	12	yes
5	13	yes
6	14	yes
7	15	yes
8	16	yes
9	17	yes
10	18	yes
11	19	yes
12	20	yes
13	21	yes
14	22	yes
15	23	yes
16	24	yes
17	25	yes
18	26	no
19	27	no
20	28	no
21	29	no
22	30	no

n < 18

Number line with numbers 0 to 30 and number 18 circle. A left arrow is pointed from value 18 until value zero.

According to the table above, fewer than 18 people can join the other two families in the pool. A blank dot has been placed over the number 18 since this indicates that it is a strict inequality relationship.

Ask a few groups to present their solution. Allow students to review their answers.

m	17 + m	≤ 30
0	17	yes
1	18	yes
2	19	yes
3	20	yes
4	21	yes
5	22	yes
6	23	yes
7	24	yes
8	25	yes
9	26	yes
10	27	yes
11	28	yes
12	29	yes
13	30	yes
14	31	no
15	32	no
16	33	no

n	8 + n	< 26
0	8	yes
1	9	yes
2	10	yes
3	11	yes
4	12	yes
5	13	yes
6	14	yes
7	15	yes
8	16	yes
9	17	yes
10	18	yes
11	19	yes
12	20	yes
13	21	yes
14	22	yes
15	23	yes
16	24	yes
17	25	yes
18	26	no
19	27	no
20	28	no
21	29	no
22	30	no

m	17 + m	≤ 30
0	17	yes
1	18	yes
2	19	yes
3	20	yes
4	21	yes
5	22	yes
6	23	yes
7	24	yes
8	25	yes
9	26	yes
10	27	yes
11	28	yes
12	29	yes
13	30	yes
14	31	no
15	32	no
16	33	no

n	8 + n	< 26
0	8	yes
1	9	yes
2	10	yes
3	11	yes
4	12	yes
5	13	yes
6	14	yes
7	15	yes
8	16	yes
9	17	yes
10	18	yes
11	19	yes
12	20	yes
13	21	yes
14	22	yes
15	23	yes
16	24	yes
17	25	yes
18	26	no
19	27	no
20	28	no
21	29	no
22	30	no

m	17 + m	≤ 30
0	17	yes
1	18	yes
2	19	yes
3	20	yes
4	21	yes
5	22	yes
6	23	yes
7	24	yes
8	25	yes
9	26	yes
10	27	yes
11	28	yes
12	29	yes
13	30	yes
14	31	no
15	32	no
16	33	no

n	8 + n	< 26
0	8	yes
1	9	yes
2	10	yes
3	11	yes
4	12	yes
5	13	yes
6	14	yes
7	15	yes
8	16	yes
9	17	yes
10	18	yes
11	19	yes
12	20	yes
13	21	yes
14	22	yes
15	23	yes
16	24	yes
17	25	yes
18	26	no
19	27	no
20	28	no
21	29	no
22	30	no