There are four children in Marie's family.

She is less than 11 years old and is the oldest.

There's a two year age difference to twins, Grace and Lily, who come next.

Tom, who is older than 5 is two years younger than the twins.

How old are each of the children?

In solving this problem students use the equality and inequality symbols : =, <, > to express family age relationships. As they do so, they become increasingly familiar with the meaning of each symbol: "is equal to", "is less than" and "is greater than" respectively. Students also use the comparative language of "older" and "younger".

Copymaster of the problem (English)

Cards with the symbols =, >, <

### Problem

There are four children in Marie's family. She is less than 11 years old and is the oldest. There's a two year age difference to twins, Grace and Lily, who come next. Tom, who is older than 5 is two years younger than the twins. How old are each of the children?

### Teaching Sequence

- Have students talk with each other about the ages of their brothers and sisters, using words older, younger.
- Using the >, < symbols record some comparative age statements for the siblings of one student.
- Ask what symbol would be used to show the age of twins (=), and why this is so.
- Read the problem to the class, emphasising that students should be able to show their solution.
- As the students work on the problem, ask them to explain their thinking using the <, > symbols.
- Share the solutions.

#### Extension

Write a problem using <, > or = age clues for the people in your family. Ask a classmate to see if they can solve your problem.

### Solution

Marie is less than 11 and Tom is more than 5. The ages of the children are therefore 6, 7, 8, 9 or 10. The problem requires students to use common sense and logic to recognise that twins are the same age and the age range is from 6 to 10.

As there is a difference of 2 years between each year of birth, the ages must be 6, 8 and 10.

Marie’s age = 10 (check 10 < 11); and Tom’s age = 6 (check 6 > 4); and Grace’s age = 8 (check 10 – 2 = 8 and/or 6 + 2 = 8); and Lily's age = 8 (check 8 = 8).